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A study of closure in sonata-form first movements in selected works of W. A. Mozart Batt, Robert Gordon 1988

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A STUDY OF CLOSURE IN SONATA-FORM FIRST MOVEMENTS IN SELECTED WORKS OF W. A. MOZART By ROBERT GORDON BATT B.Mus., Mc G i l l U n i v e r s i t y , 1974 L.Mus., Mc G i l l U n i v e r s i t y , 1976 M.A., M c G i l l U n i v e r s i t y , 1980 A THESIS SUBMITTED IN THE REQUIREMENTS DOCTOR OF PARTIAL FULFILLMENT OF FOR THE DEGREE OF PHILOSOPHY THE FACULTY OF (School i n GRADUATE STUDIES of Music) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1988 © Robert Gordon Batt, 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, 1 agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Music  The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date Oct. 14, 1988 Abstract This study of large-scale closure i n Mozart's sonata-form f i r s t movements focusses on the structure and function of the c l o s i n g section i n these works, the section that brings the exposition and r e c a p i t u l a t i o n sections to an end. Also taken into account are c l o s u r a l e f f e c t s of the coda (when present) and the subordinate theme area. Because sonata form i n the 18th-century involves a v a r i e t y of d i f f e r e n t l y - f u n c t i o n i n g sections such as themes and t r a n s i t i o n s , the a n a l y t i c a l approach adopted centers on matters of form—the ways i n which a l l the various channels of musical structure (primarily rhythm, melody, and harmony) i n t e r a c t to shape a p a r t i c u l a r p i e c e — a n d i n p a r t i c u l a r on the form of the c l o s i n g section. The study i s l i m i t e d to one composer's use of one section i n one formal type, thereby reaching highly s p e c i f i c conclusions about t h i s facet of sonata form at a p a r t i c u l a r stage i n music h i s t o r y . Since each section of sonata form has a d i s t i n c t , unique structure and function, the study aims at i d e n t i f y i n g these i n the c l o s i n g section, and at contrasting them with the other sections of the form. If closure i s p r i m a r i l y generated i n the c l o s -ing section, then there must be p a r t i c u l a r structures found mainly i n that sec-t i o n that are responsible for closure. The majority of Mozart's c l o s i n g sections are based on a model which can be s i m p l i f i e d to aabbcc, where each l e t t e r symbolizes one group. The second, fourth, and s i x t h entries may be e i t h e r exact repeats or variants of the f i r s t , t h i r d , and f i f t h entries r e s p e c t i v e l y . The most common lengths i n measures are (4 + 4) + (2 + 2) + ( 1 + 1 ) . An example i s the Sonata for V i o l i n and Piano i n B- f l a t Major, K. 454, mm. 50-65. Chapter 1 i s primarily a survey of previous wr i t i n g on the subject of closure. Chapter 2 presents a theory that accounts for structure at various levels of Mozart's sonata form. Chapters 3 through 6 contain discussion and analysis of different types of closing sections and movements. Chapter 7 includes a summary of the research undertaken. i v Contents Abstract. i i L i s t of Tables. v i i i L i s t of Diagrams. i x Abbreviations. x i i Preface. x i i i 1. Closure: An Introduction. 1 2. Concepts, Models, and Features. 34 Level (a): Segments. 40 Motives and Motivic Segments. 41 Grouplets. 43 Cadences. 46 Discussion of A l l Segment Types. 47 Level (b): Phrases, Groups, and Timespans. 49 Phrases. 49 Groups and Timespans. 52 Level ( c ) : Small Sections. 57 Themes. 59 Sentence. 60 Period. 62 Small Ternary. 64 Unique Themes. 66 V Transitions. 67 Retransitions. 69 Three Types of Closing Music. 70 Codettas and Codetta-Complexes. 70 Closing Sections. 74 Codas. 77 Introductions. 80 Level (d): Large Sections. 81 Expositions. 81 Deve1opment s. 90 Recapitulations. 90 Level (e): Complete Movements. 95 3. The Closing Model. 96 Symphony no. 36. 97 Symphony no. 40. 104 Symphony no. 31. 109 Symphony no. 32. I l l Symphony no. 33. 112 Symphony no. 34. 113 Eine kleine Nachtmusik. 114 Serenade K. 388. 116 Clarinet Quintet. 116 String Quintet K. 515. 117 String Quintet K. 516. - 120 String Quintet K. 593. 121 String Quartet K. 387. 124 v i S t r i n g Quartet K. 421. 125 Strin g Quartet K. 458. 126 String Quartet K. 464. 127 Strin g Quartet K. 499. 128 Strin g Quartet K. 590. 129 Strin g T r i o . 130 V i o l i n Sonatas K. 304, 377, and 454. 131 Piano Sonatas K. 284, 311, 310, 330, 457, and 533. 132 4. The Closing Codetta. 136 Symphony no. 39. 138 Flu t e Quartet K. 285. 141 String Quintet K. 614. 146 String Quartet K. 575. 151 Symphonies nos. 32 and 34; Eine k l e i n e Nachtmusik. 159 String Quartets K. 428 and 589; String T r i o K. 563. 160 Piano Sonatas K. 284, 309, 311, 333, 545, and 570. 161 5. The Closing Theme Followed by the Closing Codetta. 166 Symphony no. 41. 166 Str i n g Quartet K. 465. 172 V i o l i n Sonata K. 481. 174 Piano Sonata K. 332. 179 Piano Sonata K. 570. 181 6. Closing Sections Not Based on Models. 183 Symphony no. 35. 184 Symphony no. 38. 190 C l a r i n e t Quintet. 193 v i i Piano Quartet K. 478. 195 V i o l i n Sonata K. 306. 199 Piano Sonata K. 576. 207 7. Conclusion. 210 Notes to Chapter 2. 219 Notes to Chapter 3. 232 Notes to Chapter 4. 233 Notes to Chapter 5. 235 Notes to Chapter 6. 237 Notes to Chapter 7. 239 Glossary. 240 Bibliography. 243 Musical Examples. 1. V i o l i n Sonata K. 454. 247 2. Serenade K. 388. 255 3. Piano Sonata K. 333: Exposition. 264 4. Symphony no. 41: Trio. 266 5. String Quartet K. 464: mm. 1-22. 267 6. Piano Sonata K. 331: mm. 1-18. 267 7. String Quartet K. 465: mm. 90-113. 268 8. Piano Sonata K. 309: mm. 32-58 and 145-155. 269 9. Piano Sonata K. 570: mm. 62-85. 270 10. Piano Sonata K. 457: mm. 57-74 and 151-185. 271 v i i i Tables 1. Mozart's Works Analysed i n Chapters 3, 4, 5, and 6. 4 2. Levels, Formal Contexts, and Normative Lengths. 38 3. Summary of Thematic Structures. 66 4. Piano Sonata K. 570: Theme/Codetta Paradigm at Level (c). 182 i x Diagrams 1. One Model of Sonata Form (After Schenker). 28 2. Piano Sonata K. 333: Analysis of measures 4(4) to 10(1). 50 3. V i o l i n Sonata K. 454: Event/Timespan Relationships i n the Exposition. 55 4. Sentence Model of Thematic Structure. 61 5. Period Model of 1 Thematic Structure. 63 6. Small Ternary Model of Thematic Structure. 65 7. Serenade K. 388: Closing Section. 75 8. A Model of Exposition Structure. 82 9. Symphony no. 36: Exposition. 97 10. Symphony no. 36: Exposition Closing Section. 99 11. Symphony no. 36: Expansion i n Closing Section. 101 12. Symphony no. 36: Coda. 103 13. Symphony no. 40: Exposition Closing Section. 106 14. Symphony no. 40: P r i n c i p a l Voices i n mm. 91-95 and 279-287. 108 15. Symphony no. 32: Exposition Closing Section. 111 16. Symphony no. 33: Exposition Closing Section. 112 17. Symphony no. 34: Exposition Closing Section. 114 18. Eine k l e i n e Nachtmusik: Exposition Second-Key Area. 115 19. Eine k l e i n e Nachtmusik: Recapitulation F i n a l Section. 115 20. C l a r i n e t Quintet : Closing Section. 117 21. String Quintet K. 515: Exposition Closing Section. 118 22. String Quintet K. 515: Recapitulation Closing Section. 119 23. String Quintet K. 516: Exposition Closing Section. 120 24. String Quintet K. 593: Exposition Closing Section. 123 25. Stri n g Quartet K. 387: Exposition Closing Section. 124 26. Stri n g Quartet K. 421: Exposition Closing Section. 125 27. Stri n g Quartet K. 458: Exposition Closing Section. 126 28. String Quartet K. 464: Exposition Closing Section. 127 29. Stri n g Quartet K. 499: Exposition Closing Section. 128 30. Stri n g Quartet K. 590: Exposition Closing Section. 130 31. String T r i o K. 563: Exposition Closing Section. 131 32. Piano Sonata K. 311: Exposition Closing Section. 133 33. Symphony no. 39: Exposition and Recapitulation Closing Sections. 139 34. Flute Quartet K. 285: Exposition and Recapitulation. 142 35. Stri n g Quintet K. 614: Exposition Dominant-Key Area. 147 36. St r i n g Quintet K. 614: Coda. 149 37. String Quintet K. 614: P i t c h Reduction of Closing Section and Coda. 150 38. Strin g Quartet K. 575: P i t c h Reduction (1). 154 39. Strin g Quartet K. 575: P i t c h Reduction (2). 157 40. Symphony no. 41: Exposition Closing Section. 168 41. Symphony no. 41: Orchestration of Exposition Subordinate Theme and Closing Section. 170 42. Symphony no. 41: Closing Theme i n Exposition and Development. 171 43. Stri n g Quartet K. 465: Exposition Closing Section. 172 44. V i o l i n Sonata K. 481: Exposition Subordinate Theme. 174 45. V i o l i n Sonata K. 481: Exposition Closing Section. 175 46. V i o l i n Sonata K. 481: Recapitulation Ending. 176 x i 47. Piano Sonata K. 332: Exposition Closing Section. 180 48. Symphony no. 35: Exposition. 185 49. Symphony no. 38: Exposition Closing Section. 192 50. Piano Quartet K. 478: Exposition. 196 51. V i o l i n Sonata K. 306: Exposition. 200 52. V i o l i n Sonata K. 306: Pit c h and Timespan Reduction of Exposition Measures 26-74. 202 53. V i o l i n Sonata K. 306: Exposition Closing Section. 204 54. V i o l i n Sonata K. 306: Recapitulation Main Theme (Coda). 206 55. Piano Sonata K. 576: Exposition. 208 56. V i o l i n Concerto K. 216, Third Movement, Closing Section. 216 Abbreviations Cdta. Codetta. CS Closing section. CT Closing theme. D, Dev. Development. DC Deceptive cadence. E, Expo. Exposition. ECP Expanded cadential progression. HC Half cadence. LAC Imperfect authentic cadence. M. 1(1) Measure one, beat one. MT Main theme. PAC Perfect authentic cadence. R, Recap. Recapitulation. Retr. R e t r a n s i t i o n . ST Subordinate theme. TR T r a n s i t i o n . x i i i Preface The reader may f i n d the glossary useful not only i n that i t includes d e f i n i t i o n s of terms such as motive and phrase, but also i n that i t serves as an index f o r many of the terms I use, at least to the extent that i t refer s the reader to f u l l e r d e f i n i t i o n s of those terms. Musical examples are included only f o r chapter 2 (Concepts, Models, and Features): they are c o l l e c t e d together as a unit at the end of the d i s s e r t a t i o n . To read the four chapters dealing with analysis of complete movements—chapters 3 through 6 — t h e reader w i l l have to obtain copies of the scores of these movements (the table of contents serves as a guide f o r the scores needed f o r each chapter). For e d i t o r i a l and s t y l i s t i c matters I have been guided p r i m a r i l y by the Chicago Manual of Style (1982). I acknowledge the assistance of my supervisory committee i n preparing t h i s d i s s e r t a t i o n , e s p e c i a l l y that of my research supervisor, Dr. William E. Benjamin, whose many valuable suggestions are only r a r e l y documented i n the text. I also thank Dr. Wallace Berry, not only f o r h i s work on my d i s s e r t a t i o n , but also for permitting me to use h i s o f f i c e during the f i n a l stages of pre-paring the d i s s e r t a t i o n . I also extend my gratitude to my wife, Marie C a h i l l , f o r her assistance i n preparing t h i s f i n a l d r a f t . 1 1 Closure: An Introduction My primary goal i n t h i s d i s s e r t a t i o n i s the study of large-scale closure i n Mozart's sonata-form f i r s t movements. To t h i s end I w i l l focus my attention on the structure and function of the c l o s i n g section i n these works, the section that normally closes the exposition and r e c a p i t u l a t i o n sections of these move-ments. Aspects of global closure are often found i n the subordinate theme area and i n the coda, when the l a t t e r i s present, and these sections w i l l also be discussed. I tend not to view h i g h - l e v e l closure as the r e s u l t of processes be-gun early i n the movement, as would, f o r example, the analyst f o r whom a l l mus-i c a l coherence flows from high l e v e l , piece spanning, structures; instead, I view closure as a r e l a t i v e l y l o c a l i z e d phenomenon, heard i n the exposition i n a dissonant t o n a l i t y , then, t o n a l l y resolved, i n the r e c a p i t u l a t i o n . From time to time, however, other approaches, such as the Schenkerian one, w i l l be invoked for s p e c i f i c analyses. Summaries of and commentaries on a number of views of closure, including that of Schenker, w i l l be found l a t e r i n t h i s chapter. I see t h i s d i s s e r t a t i o n as a con t r i b u t i o n to the h i s t o r y and theory of sonata form. By "form" I mean, from one point of view, the ways i n which a l l the various channels of musical s t r u c t u r e — p r i m a r i l y rhythm, harmony, and mel-o d y — i n t e r a c t to shape a p a r t i c u l a r piece. However, i n t h i s study I am more concerned with form i n an h i s t o r i c a l sense, as the c o l l e c t i o n of norms of coor-2 dinated patterning within these channels c h a r a c t e r i s t i c of p a r t i c u l a r s t y l e s . From t h i s second point of view, studying form entails, the a p p l i c a t i o n of a series of d i s c r e t e theories, each pertaining to a more or less narrow repertory of music; f o r , the larger the repertory, the less s t y l e - s p e c i f i c i s the r e s u l -tant theory. Most textbooks and theories of form have been written neither from the f i r s t , nor from the second point of view. (Some i l l u s t r a t i o n s w i l l a r i s e i n the summaries of other approaches l a t e r i n t h i s chapter.) The standard "Forms of Tonal Music" textbook reveals l i t t l e about the unique character of s p e c i f i c pieces because i t normally presents one model f o r each type of musical form, for example, a model of sonata form a l l e g e d l y used from Haydn to Brahms. For the same reason, though, i t says l i t t l e about the conventions of p a r t i c u l a r s t y l e s . By l i m i t i n g my study to one composer's use of one section i n one formal type, I hope to be able to reach highly s p e c i f i c conclusions about t h i s facet of sonata form at a p a r t i c u l a r stage i n music h i s t o r y . Closing sections are defined as those parts of sonata forms which conclude the exposition and r e c a p i t u l a t i o n sections. An obvious f a c t about c l o s i n g sec-tions i s that they follow some statement, often thematic, i n the subordinate key area ( i n Mozart's expositions, always the dominant of a major to n i c , and the r e l -a t i v e major of a minor t o n i c ) , but one has other i n t u i t i o n s about them as w e l l . My object here i s to explain the nature and function of c l o s i n g sections. Why do c l o s i n g sections sound "closing"? Are there c h a r a c t e r i s t i c s of Mozart's c l o s i n g sections which are fundamental to the closure of most larger tonal forms? Are there archetypal c l o s i n g section patterns, and what are they? Are there aspects of e a r l i e r parts of movements which determine or condition features of these movements' c l o s i n g sections? To what extent do Mozart's c l o s i n g sections r e l y on common practices of the c l a s s i c period and to what extent are they unique 3 to h i s music? Research f o r t h i s d i s s e r t a t i o n focussed on analysis of Mozart's i n s t r u -mental works written i n the l a s t f i f t e e n years of h i s l i f e . Concertos were omitted because they use a modified type of sonata form. Minor works such as the church sonatas were also omitted. Only f i r s t movements were analysed, omitting those few f i r s t movements which are not i n sonata form. (Movements other than the f i r s t generally use other types of sonata forms and other forms altogether; i n any case, these w i l l not be considered.) This leaves about a hundred f i r s t movements, of which I analysed h a l f . Works from almost every genre were considered. The following w o r k - l i s t includes a l l of the works which were analysed. Table 1 was compiled using the same genre c l a s s i f i c a t i o n system as found i n the New Grove Dictionary. I t i s i n f a c t based on the equivalent table i n the New Grove a r t i c l e on Mozart, and on the revised version i n Sadie, The New  Grove Mozart. "K" r e f e r s to the number i n Chronologisch-thematisches Verzeichnis  sHmtlicher Tonwerke Wolfgang Amade Mozarts, ed. L. von K8chel ( L e i p z i g , 1862). "K^" r e f e r s to the number i n the s i x t h e d i t i o n of t h i s catalogue, ed. F. G i e g l i n g , A. Weinmann, and G. Sievers (1964). Items are arranged i n each category by order of K numbers. (In subsequent references to works I w i l l not use both K and numbers; the K number alone w i l l s u f f i c e . Symphonies w i l l be r e f e r r e d to by t h e i r Breitkopf e d i t i o n number, as they are best known i n t h i s way.) The dates of composition are not always c e r t a i n or agreed upon by a u t h o r i t i e s . From my study of t h i s repertory of Mozart I have formulated a theory that accounts for structure at various l e v e l s of the sonata form: t h i s theory i s the subject of chapter 2. My research indicates on the one hand that there are c e r t a i n recurring patterns and features i n many c l o s i n g sections, and on the 4 Table 1 Mozart's Works Analysed i n Chapters 3, 4, 5, and 6 Genre: t i t l e , etc. K K 6 Key Comp. c s b Symphonies (10) Breitkopf ed. no. 31, (Paris) 297 300a D 1778 1 32 318 318 G 1779 1,2 33 319 319 Bb 1779 1 34 338 338 C 1780 1,2 35, (Haffner) 385 385 D 1782 4 36, (Linz) 425 425 C 1783 1 38, (Prague) 504 504 D 1786 4 39 543 543 Eb 1788 2 40 550 550 g 1788 1 41, (Jupiter) 551 551 C 1788 3 Serenades and Divertimentos ( s t r i n g s with or without winds) (1) Eine k l e i n e Nachtmusik (strings) 525 525 G 1787 1,2 Wind Ensemble (1) Serenade (2 ob, 2 c l , 2 hn, 2 bsn) 388 384a c 1782-3 1 Chamber: Strings and Winds (2) F l u t e Quartet ( f l , vn, va, vc) 285 285 D 1777 2 C l a r i n e t Quintet ( c l , 2 vn, va, vc) 581 581 A 1789 1,4 5 Genre: t i t l e , etc. K K 6 Key Comp. cs1 515 515 C 1787 1 516 516 8 1787 1 593 593 D 1790 1 614 614 Eb 1791 2 387 387 G 1782 1 421 417b d 1783 1 428 421b Eb 1783 2 458 458 Bb 1784 1 464 464 A 1785 1 465 465 C 1785 3 499 499 D 1786 1 575 575 D 1789 2 589 589 Bb 1790 2 590 590 F 1790 1 563 563 Eb 1788 1,2 478 478 g 1785 4 Chamber: String Quintets (2 vn, 2 va, vc) (4)' Chamber: Stri n g Quartets (10) Opus 10, no. 1 ^ no. 2 no. 4 \ (Haydn no. 3 Quartets) no. 5 no. 6 J (Hofmeister) (Prussian, no. 1) (Prussian, no. 2) (Prussian, no. 3) Chamber: Stri n g Sonatas, Duos, Trio s (1) Divertimento (vn, va, vc) Chamber: Keyboard and two or more instruments (1) Quartet (pf, vn, va, vc) 6 Genre: t i t l e , etc. K K 6 Key Comp. CS b Chamber: Keyboard and V i o l i n (Sonatas) (5)' Opus 1, no. 4 304 300c e 1778 1 Opus 1, no. 6 306 3001 D 1778 4 Opus 2, no. 3 377 374e F 1781 1 Opus 7, no. 3 454 454 Bb 1784 1 481 481 Eb 1785 3 rd: Sonatas: Solo Piano (12) Opus 7, no. 2 284 205b D 1775 1,2 Opus 4, no. 1 309 284b C 1777 2 Opus 4, no. 2 311 284c D 1777 1,2 Opus 4, no. 3 310 300d a 1778 1 Opus 6, no. 1 330 300h C 1781-3 1 Opus 6, no. 3 332 300k F 1781-3 3 Opus 7, no. 1 333 315c Bb 1783-4 2 Opus 11 457 457 c 1784 1,3 533 533 F 1788 1 545 545 C 1788 2 570 570 Bb 1789 2,3 576 576 D 1789 4 Notes: Abbreviations: bsn—bassoon, c l — c l a r i n e t , f l — f l u t e , hn—horn, ob—oboe, p f — p i a n o f o r t e , v n — v i o l i n , v a — v i o l a , v c — c e l l o . The number a f t e r each genre heading ref e r s to the number of works i n that genre which are analysed here. The t o t a l number of works analysed i s 47, of which 8 are i n the minor mode. k The f i n a l c o lumn—"CS"—refers to the c l o s i n g section categories i n th i s d i s s e r t a t i o n . Type 1 i s discussed i n chapter 3, type 2 i n chapter 4, type 3 i n chapter 5, and type 4 i n chapter 6. Some works can be seen i n two ways. 7 other hand that some movements seem to be unique i n t h e i r c l o s i n g processes. Chapters 3, 4, 5, and 6 contain discussion of these types together with analyses —some i n d e p t h — o f representative examples. The general procedure that I w i l l use to study these movements involves the i d e n t i f i c a t i o n of, and the formulation of r e l a t i o n s among, the various features of the music that I have observed as c h a r a c t e r i s t i c of c l o s i n g sections, i n p a r t i c u l a r those features which are found only i n c l o s i n g sections and which presumably thereby contribute to the c l o s i n g process. The goal of my a n a l y t i c methods i s the combination of aspects of t r a d i t i o n a l thematic-motivic analysis with aspects of more recent theories of rhythm. The most important—because i t i s the most frequently used—model of c l o s i n g sections structure may be b r i e f l y discussed here (for comparison with d i f f e r e n t views of closure l a t e r i n t h i s chapter). See chapters 2 ( l e v e l [c]) and 3 for more d e t a i l e d discussion of t h i s c l o s i n g model, with examples. Some of the terms used below w i l l be given s p e c i f i c meanings i n chapter 2 (for ex-ample, codetta, codetta-complex, group, phrase, period, theme): the reader may wish to reefer to the d e f i n i t i o n s of these terms i n chapter 2 or i n the glossary. For the moment, however, the important features of the model to keep i n mind are r e p e t i t i o n , p a i r i n g , and reduction i n length of groups. The majority of Mozart's c l o s i n g sections are based on a model which can be s i m p l i f i e d to aabbcc, where each l e t t e r symbolizes one group. The second, fourth, and s i x t h entries may be e i t h e r exact repeats or variants of the f i r s t , t h i r d , and f i f t h e n tries r e s p e c t i v e l y . (That i s , one might f i n d aa^bbcc, aa^bb^cc, etc.) Normally a_ i s longer than b_, and b_ i s longer than £, the most common r a t i o being 4:2:1 between a., b_, and £, as shown i n the representation of the model below. 8 (4 + 4) + (2 + 2) + (1 + 1) a a b b c c Normally, each group ends with an authentic cadence, or at l e a s t with a tonic chord. The f i r s t eight b a r s — a a — a r e often l i k e a simple period. The l a t t e r s i x bars of the model—bbcc—balance the f i r s t eight by functioning as a codetta-l i k e subsection. These s i x bars are often characterised by fragmentation, elim-i n a t i o n , and l i q u i d a t i o n of motivic material, thereby cont r i b u t i n g to closure. A 1- or 2-bar extension of the second £ i s common. A tonic pedal, or prolonga-t i o n of tonic harmony with a s e r i e s of simple V-I progressions, i s common i n the l a t t e r s i x bars of the model. Varying the second group of a p a i r by adding ornamentation or f a s t e r note v a l u e s — e s p e c i a l l y changing eighth-notes to s i x -t e e n t h - n o t e s — i s common. The c l o s i n g model i s a type of codetta-complex; how-ever, i n those cases where the f i r s t two units (comprising the aa pair) are phrase-like, forming a simple period, the model takes on the aspect of a theme followed by a codetta. The c l o s i n g section of example 1 follows t h i s version of the c l o s i n g model f a i r l y exactly. This c l o s i n g section, i n mm. 50-65, w i l l be discussed i n some d e t a i l i n chapter 2. Discussion of a number of views of closure i s useful here i n that a l t e r -nate approaches to mine w i l l be noted, approaches that d i f f e r e i t h e r because the author has a d i f f e r e n t a n a l y t i c a l strategy and/or because the music being analysed requires a d i f f e r e n t approach. In addition, the following summaries w i l l r a i s e various issues r e l a t e d to closure and a n a l y t i c a l approach, issues that w i l l receive f u l l e r treatment i n subsequent chapters. Some h i s t o r i c a l background w i l l also be included here (e.g., LaRue). In some of these summaries 9 I w i l l comment on how the author's approach might or might not apply to Mozart's sonata-form music and/or oh how h i s approach r e l a t e s to mine; i n other cases I w i l l merely o f f e r a b r i e f summary of the author's work. Arranging the following series of summaries according to issues would be d i f f i c u l t , i f only because several writers deal with more than one issue, and would not lead to a s i g n i f i -cantly c l e a r e r presentation. Organizing i t c h r o n o l o g i c a l l y would likewise not lead to a better r e s u l t . Therefore, i f only to aid i n r e f e r r i n g to documentation of sources i n the bibliography, I have arranged the material a l p h a b e t i c a l l y . (For the remainder of t h i s chapter I w i l l forego the use of endnotes and place page references i n the text because they are so frequent. I w i l l also use short reference forms f o r documentation; a l l publications so c i t e d are r e f e r r e d to i n f u l l i n the bibliography.) In "Concepts of closure and Chopin's opus 28," Agawu takes a small reper-tory and investigates i t with respect to d i f f e r e n t kinds of c l o s u r a l processes. His study d i f f e r s from mine, however, i n that (1) Chopin's preludes are much shorter, and are i n a d i f f e r e n t form, than Mozart's sonata-form movements; (2) Agawu does f i n d a basic model that applies to many of the preludes: whereas his model applies to the whole of a prelude, mine applies only to the c l o s i n g section (the preludes are so b r i e f that closure often begins immediately, unlike sonata-form movements); and (3) he believes that understanding of the structure of nineteenth-century music i s f a c i l i t a t e d by reference to l i t e r a t u r e of the period; he s p e c i f i c a l l y uses Smith, Poetic Closure (discussed l a t e r i n t h i s chapter) i n h i s study, e s p e c i a l l y to formulate hi s d e f i n i t i o n of closure. Agawu defines closure i n three ways, aspects of which are general enough to apply to Mozart's sonata-form music: 10 1. Closure i s a function of formal p r i n c i p l e s and/or generic  signs. . . . various types of signs—some conventional, others a r b i t r a r y — a r e used to inform the l i s t e n e r of how or when a piece i s going to end. . . . 2. Closure i s not the same thing as an ending. . . . an ending r e f e r s to l o c a l elements i n a musical structure, whereas closure denotes a global mechanism. . . . 3 . Closure i s a function of both syn t a c t i c and semantic p r i n - c i p l e s . . . . [In t h i s study] references to structure [ i . e . , syntax] always denote the harmonic-structural or melodic-struc-t u r a l aspects of a piece, as d i s t i n c t from i t s ornamental aspects. "Semantic" on the other hand emb races the sense of the musical gesture, the meaning that emerges from the p a r t i c u l a r arrangement of notes. (Pp. 4 - 5 ) Agawu's f i r s t category applies to most music; i n Mozart's sonata-form music i t applies i n that a f i x e d p a t t e r n — t h e c l o s i n g m o d e l — i s used i n a f i x e d formal l o c a t i o n — t h e c l o s i n g s e c t i o n — t o generate closure. Someone who l i s t e n s perceptively to a number of these works of Mozart may recognize t h i s p a r t i c u l a r pattern's function. Agawu's second category i s again a p p l i c a b l e to most music; i n Mozart's sonata-form music the "global mechanism" would be generated by pro-cesses taking place i n the c l o s i n g section and also, to a c e r t a i n extent, i n the second theme (although i t may be possible to see c e r t a i n kinds of c l o s u r a l pro-cesses i n i t i a t e d even e a r l i e r i n the form). The " s y n t a c t i c " portion of h i s t h i r d category w i l l form the basis of my approach; h i s "semantic" portion does not apply to Mozart (although i t i s one of the most i n t e r e s t i n g and o r i g i n a l aspects of Agawu's study). There are two important issues i n the a p p l i c a t i o n of h i s " s y n t a c t i c p r i n c i p l e s " : (1) The analyst must be s e n s i t i v e to the v a r i a t i o n s i n prominence of the various dimensions or channels of structure: harmony, melody, etc., may be involved i n closure at d i f f e r e n t points i n a piece; and (2) the analyst must evaluate the s i g n i f i c a n c e of c l o s u r a l events as l o c a l , intermediate, or global (p. 6). 11 Several w r i t e r s discuss the idea of archetypal lengths f o r phrases, sections, etc. For example, i n "A theory of musical meter," Benjamin writes: The group structures of p a r t i c u l a r tonal s t y l e s , and most e s p e c i a l l y of the c l a s s i c a l s t y l e , must be understood not only to "do" things ( i n a melodic-harmonic sense), but to do them i n a s p e c i f i c number of measures. This " s p e c i f i c number" i s , to some degree, a feature of the i n d i v i d u a l piece or movement, but the idea of a normative span i n which to get things done r e l i e s on awareness of the s t y l i s t i c context as a whole. (P. 392) My c l o s i n g model i s an instance of such an archetype i n terms of both i t s t o t a l length and the i n t e r n a l grouping of phrases. Benjamin o f f e r s an i n t e r e s t i n g explanation of why many c l o s i n g sections d i f f e r i n t h e i r exposition and r e c a p i t u l a t i o n forms i n a given work: A p a r t i c u l a r problem of d i s s i p a t i n g the momentum of a context overburdened with metric l e v e l s a r i s e s with the necessity of bringing a movement to a convincing end. This i s why, i n c l a s -s i c a l sonata forms, the r e c a p i t u l a t i o n s are often expanded, i n r e l a t i o n to corresponding expositions, j u s t where they are preparing to end: These expansions o b l i t e r a t e enough l e v e l s of meter to allow a p a r t i c u l a r cadential a r r i v a l to stand out i n a way i n which the corresponding event i n the exposition did not. (Pp. 405-406) However, i t i s my observation that about as often as not Mozart's c l o s i n g sec-tions are s i m i l a r i n both exposition and r e c a p i t u l a t i o n forms i n a given work. This issue w i l l a r i s e i n subsequent chapters. Berry, i n Form i n Music, distinguishes three types of sonata-form c l o s i n g sections, based on length and constituent material. (1) "The codetta i s often a mere f l o u r i s h of cadential chords" (p. 159). He c i t e s a 2-bar example from a piano sonata by J . C. Bach (p. 159), that I would consider a c l o s i n g codetta as discussed i n my chapter 4. (2) A more sub s t a n t i a l codetta may include "some motivic material of the f i r s t group, i n casual, perfunctory references, or i t may derive from other parts of the exposition" (p. 159). He c i t e s Mozart's 12 Symphony no. 38, f i r s t movement, as an example of a c l o s i n g section based on f i r s t theme material; t h i s w i l l be discussed i n chapter 6 below. [(3)] In some examples the second tonal group leads into a d i s -t i n c t i v e new theme of r e l a t i v e l y resigned character and r e s t r i c t e d content, or into a codetta containing such a theme. A thematic e n t i t y of t h i s kind, set apart from the main, body of the second group by a t r a n s i t i o n a l passage (Mozart Sonata i n F, K. 332, m. 71), by decisive cadential punctuation, possibly including r e s t s , or appearing as part of the codetta, i s c a l l e d a c l o s i n g  theme. (P. 159) This t h i r d type corresponds to my " c l o s i n g theme followed by the c l o s i n g codetta" as discussed i n chapter 5 below. Berry's ideas of metric progression and recession as discussed i n h i s S t r u c t u r a l Functions i n Music imply that closure i s characterized by "increased s t a b i l i t y and longer units . . . recessive e f f e c t i s of d e c e l e r a t i o n , " whereas metric progression i s c h a r a c t e r i s t i c of "(a) shorter unit and (b) increased i n -s t a b i l i t y , often s i g n i f i c a n t i n a process of mounting i n t e n s i t y ; progressive e f f e c t i s of a c c e l e r a t i o n " (p. 378). Berry's approach i s i n c o n f l i c t with my research to the extent that my c l o s i n g model i s characterized by shorter and shorter units (which to Berry would s i g n i f y i n s t a b i l i t y ) . However, Berry's approach does explain the end of the subordinate theme area, which often features increasing unit s i z e (see Caplin, below, f o r discussion of t h i s ) . And i n a more recent a r t i c l e Berry appears to r e s t r i c t h i s notion of a c c e l e r a t i o n to develop-ment sections of sonata forms and such a r e s t r i c t i o n would a l l e v i a t e the c o n f l i c t between Berry's approach and mine. (See "Rhythmic accelerations i n Beethoven," Journal of Music Theory, 22 [1978], 177-178.) 13 Caplin's "The 'expanded cadential progression': a category f o r the analysis of c l a s s i c a l form" (hereafter r e f e r r e d to as Caplin, ECP), i s p a r t i c -u l a r l y relevant to my topic because (1) i t deals with a repertory that overlaps with mine, (2) i t deals with closure of the sonata-form subordinate theme area, the area d i r e c t l y preceding the c l o s i n g section, (3) i t provides a way of d i s -t inguishing subordinate theme closure from c l o s i n g section closure, and (4) i t uses a n a l y t i c a l techniques s i m i l a r to some of those i n my t h e s i s . Although the a r t i c l e was published only l a s t year, I have had the benefit of studying an e a r l i e r d r a f t of i t , and have incorporated i n my own work the ECP concept as an a n a l y t i c a l t o o l . As many readers may not have read Caplin's a r t i c l e , i t may be useful to explain here the e s s e n t i a l features of the ECP i n a d d i t i o n to a few other r e l a t e d aspects of Caplin's approach to t h i s music. Following Ratz and Schoenberg, both of whose approaches are discussed l a t e r i n t h i s chapter, Caplin considers (as do I) that a theme i s to be seen "not merely as a melody or c o l l e c t i o n of motives within a given tonal region, but rather as a complete musical complex that includes a soprano and bass count-erpoint, a d e f i n i t e harmonic plan, a phrase-structural design, and cadential closure" (p. 216). The types of themes encountered i n the c l a s s i c a l s t y l e w i l l be discussed i n chapter 2; f o r now i t may be noted that the subordinate theme i s d i f f e r e n t i a t e d i n part from the main theme by a looser structure that i s generated i n one respect by an "expansion of the cadential harmonies at the close of the theme" (p. 216). Caplin's goal i s to formulate "how such an expan-sion i s achieved and how i t functions within the context of a complete subor-dinate theme" (p. 217). In discussing the types of cadential a c t i v i t y i n the second key area, he notes that 14 a fundamental d i s t i n c t i o n must be drawn between the cadential progression that t r u l y closes the subordinate theme and those harmonies that follow the actual cadence and serve to r e i n f o r c e i t s f i n a l t o n i c . These "nonfunctional" cadence formulas provide the harmonic basis f o r the codettas that constitute the c l o s i n g  section of the exposition. . . . The cadence formulas of the codettas are often compressed i n r e l a t i o n to the expanded cad-e n t i a l harmonies that are an i n t e g r a l part of the subordinate theme proper.and that e f f e c t i t s closure. (P. 217) Indeed, the varying degree of cadential expansion and compression within an exposition often proves to be a useful guide for d i s -tinguishing between the subordinate area proper and the c l o s i n g section. (P. 227) In Caplin's view, then, the expanded cadential progression closes the subordin-ate theme, with the c l o s i n g section functioning "as a s e r i e s of codettas that prolong the cadential t o n i c " (p. 253). (See chapter 2, note 28, f o r further discussion of the ECP.) An issue that w i l l be discussed l a t e r here i s the ex-tent to which the ECP, i n c l o s i n g the subordinate theme, also closes the e n t i r e exposition (and r e c a p i t u l a t i o n ) , and that to which, as I would often claim, the c l o s i n g section plays a d i s t i n c t , e s s e n t i a l r o l e i n providing closure f o r these large sections. I f i n d that i n Mozart's works the c l o s i n g section may not a l -ways be merely a "series of codettas," at l e a s t not i n the r e s t r i c t e d sense that Caplin appears to use the term. (I define "codetta" i n chapter 2; examples of Caplin's codettas include Beethoven, Piano Sonata i n F Minor, op. 2, no. 1, f i r s t movement, mm. 41[3]-48, Caplin's example l [ c ] ; and Mozart, Piano Sonata i n D Major, K. 576, f i r s t movement, mm. 53-58, Caplin's example 2[c], discussed i n my chapter 6.) The few examples of c l o s i n g sections that Caplin c i t e s are a l l very short and c l e a r l y do not p a r t i c i p a t e i n large scale closure to any s i g -n i f i c a n t extent. In a personal communication (July 5, 1988), he writes that he i s i n c l i n e d toward the view that the c l o s i n g section "does function to create closure f o r the exposition, at the same [time] as i t functions p o s t - c a d e n t i a l l y f o r the subordinate theme." 15 In discussing the c l o s i n g section i n Beethoven's Piano Sonata op. 2, no. 1, f i r s t movement, made up of three s i m i l a r 2-bar codettas, he notes that i t does not have a true cadential r o l e ; i t does not a r t i c u l a t e thematic closure. That purpose has already been f u l f i l l e d by the genuine cadential phrase [the ECP]. Rather, the codettas function here to d i s s i p a t e the energy b u i l t up by the cadential expansion at the close of the theme. They are c l e a r l y necessary f o r dynamic and rhythmic reasons, but they could have been elim-inated without a f f e c t i n g the fundamental thematic and tonal structure of the exposition. (P. 222) Many of Mozart's c l o s i n g sections are s i m i l a r i n length, structure, and function to t h i s one of Beethoven (they are of a type I c a l l the c l o s i n g codetta; see chapter 4 f o r examples). Caplin subsequently discusses K. 576, which has a c l o s i n g section s i m i l a r to t h i s one. Longer c l o s i n g sections, ones normally based on the c l o s i n g model, have a more s i g n i f i c a n t function than merely d i s s i p a t i n g subordinate theme energy, and could l i k e l y not be eliminated without a f f e c t i n g the exposition structure. Davis, "Harmonic rhythm i n Mozart's sonata form," a study s i m i l a r to mine i n i t s choice of repertory, demonstrates that "Mozart appears to d i s t i n g u i s h var-ious areas as c l e a r l y by harmonic-rhythmic s t r u c t u r i n g as by other compositional procedures such as melodic d i f f e r e n t i a t i o n and changes of instrumentation or t e s s i t u r a " (p. 27). A portion of h i s conclusions regarding exposition c l o s i n g sections may be quoted: The K section i s the most s t r o n g l y - a r t i c u l a t e d subdivision of the exposition, and to help the cadential d r i v e , i t usually provides one or more marked accelerations preceding a terminal punctuation of slower harmonic rhythm. The r e s u l t i n g j u x t a p o s i t i o n of f a s t and slow produces a c h a r a c t e r i s t i c harmonic-rhythmic contrast. . . . o s c i l l a t i n g harmonies appear more frequently i n the K sec-t i o n than i n any.of the preceding sections. They are used p r i -marily for a r t i c u l a t i o n , occurring at the beginning and less often at or near the close of a theme or section. To end a K section, Mozart favours sustained harmonies over o s c i l l a t i o n progressions. 16 . . . Through the juxtaposing of a c t i v e and stable areas, most K sections emphasize harmonic-rhythmic contrast over other f e a -tures of design. (P. 33) Davis gives many i l l u s t r a t i o n s of these points, f o r example, the f i r s t movement of the Piano Sonata i n F Major, K. 533, mm. 89-102. Regarding r e c a p i t u l a t i o n c l o s i n g sections, he writes, i n part: When greater s t a b i l i t y i s required to consummate an e n t i r e move-ment, r e c a p i t u l a t i o n s conclude with further s t a b i l i z i n g additions. Internal changes that occur usually heighten contrast. Thus, as K sections tend to lengthen i n r e c a p i t u l a t i o n s , the elements of a r t i c u l a t i o n tend to increase. (P. 41) He uses the f i r s t movements of the Symphonies nos. 40 and 41 as i l l u s t r a t i o n s . Hatmaker's "A theory of timbre i n the l a t e C l a s s i c a l symphony" confirms my observation that many of Mozart's symphonic f i r s t movements end with t u t t i s , t h i s being an aspect of closure: The " a r r i v a l " function of t u t t i and the phenomenon of timbre dominance gives r i s e to a timbral structure i n the C l a s s i c a l symphony,.the "timbre progression." The timbre progression, which may be defined as a succession of timbre events beginning with a p a r t i a l ensemble and ending with t u t t i , t y p i c a l l y shows a gradual "growth" (successive events increasing i n likeness to t u t t i ) i n the C l a s s i c a l symphony. This tendency of growth toward t u t t i , combined with t u t t i ' s function as a sign of closure, allows me to i n f e r a paradigm of timbre progression . . . that of the p a r t i a l ensemble progressing to t u t t i . (Pp. 3-4) In general, a f a s t rate of timbre change i s associated with t r a n s i t i o n a l , modulating music and a slower rate with s t a b i l i t y . . . . The ends of many symphonies exemplify the l a t t e r . (P. 31) Hopkins, i n "Secondary parameters and closure i n the symphonies of Gustav Mahler," understands closure to be operative at various l e v e l s and i n various parameters, as does Meyer (see below). (Melody and harmony are Hopkins's primary parameters, the others secondary. Rhythm i s not a parameter.) Most of h i s chapter 1, "Closure," i s relevant to my t o p i c , as he here summarizes closure i n l a t e eighteenth- and early nineteenth-century music. For example, he discusses 17 how d i f f e r e n t parameters can create closure. In the following quotation, from t h i s chapter, he considers an aspect of closure i n eighteenth-century music re l a t e d to my c l o s i n g model: The degree of closure i s also p a r t l y a consequence of i t s length. In general, closure i s stronger when i t i s prolonged. For i n -stance, composers of the c l a s s i c a l period commonly strengthened primary parametric closure at the ends of large sections and movements by extending the chord of r e s o l u t i o n . The extension might be produced by repeating scalar or t r i a d i c p i t c h patterns based on the tonic, r e i t e r a t i n g the tonic harmony one or more times, or simply sustaining the tonic chord. (Pp. 14-15) Kramer, i n "Beginnings and endings i n Western a r t music," discusses closure of music i n the common p r a c t i c e period, focussing on t o n a l i t y : "Only once t o n a l i t y became f u l l y developed was i t possible f o r an e n t i r e composition to be a r e a l i z a t i o n of a s i n g l e tonal process" (p. 1). Although Kramer does not discuss d e t a i l s of such processes, he i s l i k e l y r e f e r r i n g to, f o r example, the o v e r a l l view of a movement provided by a Schenkerian Ursatz. However, he also discusses a somewhat d i f f e r e n t approach to closure, an approach based not on an o v e r a l l process but on a h i e r a r c h i c a l arrangement of cadences: A strong cadence ends not. only i t s phrase but also several pre-ceding phrases. A phrase group i s created i n t h i s manner. The f i n a l cadence of the piece i s of course the strongest, since i t must bring to a close the e n t i r e work. Thus closure, l i k e ton-a l i t y i t s e l f , i s h i e r a r c h i c a l . (P. 2) Again, Kramer does not elaborate on the hierarchy of closure. The comparison of cadential hierarchy with tonal hierarchy does not always apply to Mozart's works. Although a section such as a theuie may be closed by v i r t u e of i t s f i n a l cadence being the strongest, i n Mozart's sonata-form movements the strongest cadence occurs at the end of the subordinate theme ( i . e . , the ECP), with the 18 c l o s i n g section prolonging the f i n a l harmony, perhaps with weaker cadences or cadence-like progressions. Only i n those movements i n which the ECP i s p a r t i c -u l a r l y lengthy could one say that i t dominated a l l other cadences i n the whole movement. Another way Kramer explains endings i s by reference to convention: Anything i s possible at the beginning but by the end the nature of the piece dic t a t e s the nature of i t s ending procedures. I t i s these strategies of ending more than the conventionalized last-thing-heard that are suggested by the piece's i n t e r n a l pro-cesses, and thus there are many routes to closure. . . . the prolongation of the f i n a l tonic, on the other hand, i s harmonic-a l l y rather standard . . . ; the actual c l o s i n g gesture i s often a stock convention, loosely linked or a c t u a l l y unrelated to the processes or materials of the composition. (P. 3) Kramer's discussion here i s not s t y l e - s p e c i f i c and i s thus rather general. If anything, i t applies more to romantic period music, i n which, f o r example, almost anything can happen at the beginning of a work, unlike i n c l a s s i c music. Kramer's "many routes to closure" would not apply to Mozart's sonata-form music, as most of t h i s repertory i s conventionalized at le a s t with respect to o v e r a l l harmonic motion and form. However, the c l o s i n g section i s perhaps more often made of "stock conventions" than i s the preceding subordinate theme area, with the exception of the ECP. Furthermore, the c l o s i n g section i s i n fac t often comprised of material "loosely linked or a c t u a l l y unrelated" to e a r l i e r sections. F i n a l l y , Kramer also contrasts two explanations of endings, context and formula: (1) "An ending can be defined as the place at the close of the piece where a l l of i t s tensions have been resolved" (p. 6). In terms of my repertory, the c l o s i n g section i s i n th i s view the lo c a t i o n of tonic s t a b i l i t y , and melodic and rhythmic l i q u i d a t i o n . (2) "An ending can also be defined by the actual shape or p r o f i l e of the f i n a l sounds—a thing (or product) rather than a pro-cess" (p. 6). In Mozart, the c l o s i n g section, from t h i s standpoint, i s a con-19 ventionalized form, usually an instance of the c l o s i n g model, and i t follows the conventionalized ECP. LaRue's study of the eighteenth-century symphony (New Grove Dictionary, "Symphony: I " ) , includes discussion of the development of s p e c i f i c s t y l i s t i c features that apply to most of c l a s s i c period music. "To understand Classicism there i s no better exercise than to follow the long evolution of the 18th-century symphony" (p. 438). No mere c o l l e c t i o n of t r a i t s . . . can generate the f u l l character of Classicism, which r e s u l t s not from i n d i v i d u a l processes but rather from a higher c o n t r o l , or c o n c i n n i c i t y , a s k i l f u l and elegant arrangement and adjustment of the various elements. Once t h i s c e n t r a l technique became current, composers could perfect various other c h a r a c t e r i s t i c s that d i s t i n g u i s h a C l a s s i c a l sym-phony, notably a hierarchy of punctuation necessary to c l a r i f y more complicated phrase, sentence and paragraph structures; and a d i f f e r e n t i a t i o n and l a t e r s p e c i a l i z a t i o n of sections (primary, t r a n s i t i o n a l , secondary and c l o s i n g ) . . . . The C l a s s i c a l s t y l e signals the contrast between primary and secondary groups not merely from changes i n melody but also from changes i n dynamics, texture, rhythm (both chord and surface) and phrase u n i t . (P. 440) The "hierarchy of punctuation," the " d i f f e r e n t i a t i o n and s p e c i a l i z a t i o n of sec-t i o n s , " and the "changes i n phrase u n i t " are a l l c e n t r a l features of the develop-ment of sonata form (about which LaRue i s e s s e n t i a l l y w r i t i n g ) , and are also cen-t r a l to my study of closure i n that closure i s centered i n a s p e c i a l i z e d section having i t s own types of punctuation and phrase u n i t s . In LaRue's summaries of the s t y l e s of i n d i v i d u a l composers there are a number of references to c l o s i n g processes. The Viennese J . B. Vanhal (1739-1813) has "a kinship to Mozart i n the use of gentle, retrospective c l o s i n g themes that i n t e r p o l a t e a moment of quiet before the f i n a l trumpets" (p. 444). J . W. A. Stamitz (1717-1757) developed "a w e l l - d i f f e r e n t i a t e d exposition" and an extensive development section, but did not include the primary material i n the recapitula-: 20 t i o n : S t r u c t u r a l l y , the secondary and c l o s i n g sections by themselves cannot s t a b i l i z e the tonic s u f f i c i e n t l y to balance the f o r c e f u l Mannheim exposition and development. A r e c a p i t u l a t i o n of only the secondary and c l o s i n g material may produce too abrupt a conclusion. (P. 445) Stamitz and other Mannheim composers sometimes recognized t h i s and added f u r -ther material to the r e c a p i t u l a t i o n . A r e c a p i t u l a t i o n based more c l o s e l y on the exposition of course followed l a t e r i n the century. In the areas of s t r u c -ture and orchestration "Mozart evidently learnt a good deal from Mannheim" (p. 446). One of the best of the second generation of Mannheim composers was Ernst Eichner (1740-1777): He attained a p a r t i c u l a r l y advanced thematic d i f f e r e n t i a t i o n that not only contrasted secondary sections but also i n d i v i d u a l i z e d the material of t r a n s i t i o n s and c l o s i n g sections; at the same time he was able to embed these ideas i n sentences and paragraphs with strong d i r e c t i o n a l flow. (P. 446) One of the best composers i n London was J . C. Bach (1735-1782), a composer who also had a s i g n i f i c a n t influence on Mozart: His combination of imagination and t e c h n i c a l mastery made possible a wide v a r i e t y and subtle gradation of thematic ideas, which he then distinguished according to expositional functions: even out of context h i s themes sound l i k e primary, t r a n s i t i o n a l , secondary or c l o s i n g material. (P. 448) In summarizing Mozart's s t y l e , LaRue comments on the importance of surface rhythm to structure: He commanded a remarkable rhythmic vocabulary, which may also be a by-product of a larger colour contrast, as part of Mozart's strong c h a r a c t e r i z a t i o n of s t r u c t u r a l areas by the c r e a t i o n of s p e c i a l thematic types; one can usually recognize the precise e x p o s i t i o n a l function of a Mozart theme even when it- i s taken out of i t s context. (P. 450) 2-1 LaRue discusses a p a r t i c u l a r type of expanded c l o s i n g section charact-e r i s t i c of Mozart's mature symphonies: Between the usual cadential themes he introduced a piano penul- timo: a quiet, r e f l e c t i v e theme that enhances the b r i l l i a n c e of the f i n a l cadential trumpeting. This heightened contrast i n the c l o s i n g area lends a s p e c i a l conviction and d e f i n i t e repose to Mozart's conclusions, noticeable i n embryo as early as K134. (P. 452) In h i s discussion of sonata form i n The Rhythms of Tonal Music, Lester takes a frequently-seen p o s i t i o n : Each passage i n a sonata-form movement has i t s own r o l e to play i n the o v e r a l l form and, therefore, i t s own i n t e r n a l structure. The themes that announce each of the key areas i n the exposition, f o r instance, are more often than not presented i n d i s c r e t e phrases, as opposed to t r a n s i t i o n a l , conclusive, or developmental passages that feature more continuous music and e l i d i n g phrases. (P. 229) The d i s t i n c t i o n between two types of phrase structure i s useful and w i l l form part of my a n a l y t i c a l approach i n chapter 2 below. Lester devotes most of h i s consideration of sonata form to the "second theme group" (by which he means a l l the material i n the second key within the exposition), because he believes t h i s area has a structure that can be general-ized more than any other. This section must e s t a b l i s h the new key area, yet must hold o f f a conclusive a r r i v a l on the tonic of the new key as long as p o s s i b l e . For when the second theme group recurs i n the r e c a p i t u l a t i o n , i t generally follows music i n the tonic key (the f i r s t theme group). Premature closure would make the remainder of the r e c a p i t u l a t i o n sound l i k e a perfunctory tag. In order to f u l f i l l these r o l e s , second theme groups, whatever t h e i r length or the number of themes, tend to begin with phrases or a period with extensions or e l i s i o n s delaying the cadence of the consequent phrase. Later i n the second theme group i s usually a series of ever-shorter cadential phrases, each e l i d i n g with the next. The opening phrases e s t a b l i s h the new key without neces-s a r i l y cadencing i n i t conclusively; the l a t e r e l i s i o n s and r e i t -erated cadences project the f i n a l i t y of the section but hold o f f the f i n a l r e s o l u t i o n u n t i l the end. (Pp. 229-230) 22 This i s a good general d e s c r i p t i o n that applies i n large measure to Mozart's sonata forms (a d e s c r i p t i o n p a r t i a l l y amplified i n Caplin's ECP, as noted above). Lester's "ever-shorter cadential phrases" correspond to my model of c l o s i n g sec-t i o n structure. He l a t e r r e f e r s to t h i s again i n context of a s p e c i f i c analysis (Beethoven's Piano Sonata op. 14, no. 2, f i r s t movement), where the c l o s i n g section i s "cast i n short, r e p e t i t i v e phrasing u n i t s " (p. 232). Note Lester's c a r e f u l use of the term "phrasing u n i t , " as opposed to "phrase," to d i s t i n g u i s h the material here. He also uses the f i r s t movements of Mozart's Piano Sonata K. 545 and S t r i n g Quintet K. 515 to i l l u s t r a t e h i s approach to second theme groups (pp. 233-235). In discussing r e c a p i t u l a t i o n s , Lester notes that whereas f i r s t theme groups are often rewritten, "second theme groups maintain the structure described e a r l i e r " (p. 240). Further references to Lester's book w i l l a r i s e i n chapter 2 i n discussion of timespans and c l o s i n g sections. Several writers discuss the view that pieces of music never come to an absolute conclusion, that they are pieces of something bigger, i . e . , of music. For example, i n Musical Morphology, Leverie and Levy write: "By nature, musical flow i s continuous, i n d e f i n i t e . The end of a piece i s never quite free of a c e r t a i n a r b i t r a r i n e s s " (p. 198). Regarding the ending of tonal music, they write, for example: In the terminal cadences of the high period of t r i a d i c t o n a l i t y , the energetic character, the f o r c e f u l dynamics, and the i n s i s t e n t r e i t e r a t i o n s that often form a chain are a l l means aimed at r e -ducing the generative power of the perfect t r i a d , i s o l a t i n g the "piece" from the i n d e f i n i t e , and affirming the end of the move-ment. Metric r e g u l a r i t i e s contribute. (Pp. 140-141) Their " i n s i s t e n t r e i t e r a t i o n s that often form a chain" and "metric r e g u l a r i t i e s " 23 are supportive of features of my c l o s i n g model. In "Texture as a sign i n C l a s s i c and early Romantic music," Levy des-cribes a number of conventionalized t e x t u r a l signs, one of which i s the unison (including octave doublings). Unisons are frequently used "as a u x i l i a r y signs of close. . . . The e f f e c t may be one of d i s s o l u t i o n " (p. 519). The unison i s also often used to " s i g n a l the close of the exposition" (p. 519). Among her examples are a number by Mozart. Lorince, i n "A study of musical texture i n r e l a t i o n to sonata-form as evidenced i n selected keyboard sonatas from C. P. E. Bach through Beethoven," finds that Mozart distinguishes sections of sonata-form movements by t e x t u r a l means ( i n a d d i t i o n to other means such as key). He finds Mozart's c l o s i n g sections "characterized by simpler t e x t u r a l s e t t i n g s . . . . Sixteenth-note scale passages with a wide melodic range are t y p i c a l as are short repeated passages emphasizing contrast" (pp. 283-284). He considers a v a r i e t y of factors i n the area of texture, such as contour, register,, dynamics, and v e r t i c a l span (or range). For instance, he finds that the widest v e r t i c a l span i n Mozart's works occurs i n the c l o s i n g section (pp. 289-290). In Emotion and Meaning i n Music, Meyer suggests that closure i s p a r t i a l l y dependent on the l i s t e n e r ' s knowledge of when a melody w i l l close (pp. 78-79, 138). In other words, i f a l i s t e n e r hears a cue f o r the beginning of a standard c l o s i n g process, then that c l o s i n g process w i l l be more s a t i s f y i n g than one i n which the l i s t e n e r was unaware that i t was a c l o s i n g process. 24 Most of Meyer's chapter 4, " P r i n c i p l e s of pattern perception: completion and closure," i s relevant to the topic of t h i s d i s s e r t a t i o n . For example, he suggests that form ("shape and pattern") i s the cause of both continuity and closure (p. 130). In discussing s a t u r a t i o n — a process r e s u l t i n g from r e p e t i t i o n , leading to the expectation of change—he notes that the expectation may be d i f -ferent according to the formal context: A repeated pattern at the end of a work need not give r i s e to saturation, since at t h i s point the l i s t e n e r understands . . . the s i g n i f i c a n c e of the r e p e t i t i o n : That i s , because t h i s i s the end of the piece, lack of forward motion, a composed fermata, i s expected and d e s i r a b l e . Thus the law of saturation i s c o n d i t i o n a l : In a s i t u a t i o n where r e p e t i t i o n i s not normal and understandable, the longer a pattern or process p e r s i s t s , the stronger the expec-t a t i o n of change. (P. 136) This i s p a r t i c u l a r l y relevant to my d i s s e r t a t i o n because the c l o s i n g model i s composed of a series of repeated u n i t s . (Meyer's "s a t u r a t i o n " applies to the thematic sections of Mozart's sonata form, i n p a r t i c u l a r to the sentence model discussed i n chapter 2 below.) Further support for my c l o s i n g model i s found i n Meyer's discussion of the law of return: The law of return appears to operate most e f f e c t i v e l y where the given sound term i s l e f t incomplete. Since the sound term i s a Gestalt which sets up forces toward a p a r t i c u l a r kind of closure, the only way i t can be closed i s by repeating i t with a new and more f i n a l ending. (P. 153) Many examples of the c l o s i n g model incorporate such a process, often i n which repeated units are paired, the second of which i s more closed than the f i r s t i n the manner of a simple period. The r e p e t i t i o n i n c l o s i n g sections i s often very exact; t h i s i s supported by Meyer's statement that "the more closed a sound term i s , the more i t s recurrence i s l i k e l y to be exact or almost exact" (p. 153). 25 In Explaining Music, Meyer considers closure throughout the music at various l e v e l s . C l o s u r e — t h e a r r i v a l at r e l a t i v e s t a b i l i t y — i s a r e s u l t of the a c t i o n and i n t e r a c t i o n among the several parameters of music. Because melody, rhythm, harmony, texture, timbre, and dynamics are r e l a t i v e l y independent v a r i a b l e s , some may act to create closure at a p a r t i c u l a r point i n a work, while others are mobile and on-going. (P. 81) The structure of a composition i s something which we i n f e r from  the hierarchy of closures which i t presents. . . . The end of a movement i s . . . the point at which a l l parameters move con-gruently to create the s t a b i l i t y of closure. (P. 89) Meyer's general approach to analysis of tonal melody—the i m p l i c a t i o n -r e a l i z a t i o n model discussed at length i n Explaining Music—would lead him to categorize c l o s i n g sections as normally lacking i n melodic imp l i c a t i o n s . In his analysis of the S t r i n g Quartet i n D Major, K. 575, second movement, f o r ex-ample, he considers the c l o s i n g section, or coda (mm. 61-73), as an extension of the repeat of the main theme: "Since the extension i s e s s e n t i a l l y a melodic prolongation of the t o n i c , A, moving through three octaves, no i m p l i c a t i v e r e l -ationships are generated" (pp. 233-235). This c l o s i n g section i s s i m i l a r to my c l o s i n g model. Ratz, EinfUhrung i n die musikalische Formenlehre, i s p r i m a r i l y a study of eighteenth-century instrumental music. Ratz bases his approach to c l a s s i c a l period music, and on Beethoven i n p a r t i c u l a r , on the a n a l y t i c a l p r i n c i p l e , seen elsewhere, of d i f f e r e n t l y - f u n c t i o n i n g sections. His two p r i n c i p l e s of formal organization are "(1) t i g h t k n i t organization, which includes the main theme and to a c e r t a i n extent the codettas, and (2) loose organization, which includes the subordinate theme, t r a n s i t i o n , r e t r a n s i t i o n , [and] development" (p. 21 i n the German o r i g i n a l ; a l l t r a n s l a t i o n s are done by Professor William E. Caplin of M c G i l l U n i v e r s i t y ) . Although Ratz includes the subordinate theme i n h i s cate-26 gory of loose organization, i t i s not as loose as the other sections included i n t h i s category. In my study I am categorizing both themes as r e l a t i v e l y t i g h t k n i t , at l e a s t i n comparison with other sections. Ratz describes the c l o s i n g section i n t h i s way: Codettas (Closing Section). The essence of the codettas con-s i s t s i n motivic l i q u i d a t i o n and i n cadential formations that are made incr e a s i n g l y c l o s e r u n t i l f i n a l l y nothing more than the I degree remains: e.g., (2x4) + (2x2) + (2x1) + (2xi) + 1. (P. 30) The "motivic l i q u i d a t i o n , " the " i n c r e a s i n g l y cl o s e r cadential formations," the p a i r i n g of s i m i l a r u n i t s , and the reduction i n unit length from four bars to two to one to one-half are a l l features very c l o s e l y r e l a t e d to my c l o s i n g model. In The C l a s s i c a l S t y l e , Rosen considers at some length the issue of the c l a s s i c a l composers' use of t o n a l i t y to generate large-scale dissonance i n son-ata form (e.g., pp. 68-71). The use of contrasting keys i n the second h a l f of the exposition, and i n the development, had i t s repercussions elsewhere i n the form: "The s t a b i l i t y and c l a r i t y of the opening and c l o s i n g pages of a c l a s s i c a l sonata are e s s e n t i a l to i t s form, and they make the increased tension of the middle sections p o s s i b l e " (p. 70). One reason, then, f o r the use of a c l o s i n g section was to assure tonal s t a b i l i t y f o r the form. This feature of c l o s i n g sections, shared with the f i r s t theme, i s somewhat s i m i l a r to Ratz's requirement of tonal s t a b i l i t y (at l e a s t i n the sense of not modulating) f o r the t i g h t k n i t construction of the main theme and the codettas. Much of Rosen's Sonata Forms i s relevant to t h i s d i s s e r t a t i o n , e s p e c i a l l y i n that Rosen concentrates on eighteenth-century sonata forms and analyses many of the same works considered here (e.g., the Symphony i n D Major, no. 38, pp. 194-217). Rosen considers the usual exposition model, " F i r s t Group, Bridge 27 Passage, Second Group, and Concluding Theme," to be "rare i n the eighteenth century, as the move to the dominant i s often i n i t i a t e d without a break from the statement or counterstatement [of the F i r s t Group], and the concluding theme may be a b r i e f appendage to the second group: i n t h i s case, we have a two-part exposition" (p. 98). While some of Mozart's shorter expositions may be analysed as b i p a r t i t e , I f i n d that many others can be seen s u c c e s s f u l l y as based on the four-section model. (I w i l l not use the same terms as Rosen has; f o r example, he uses "theme" i n a more general way than I do, and I prefer " c l o s i n g s e c t i o n " to "Closing Theme".) Like some other w r i t e r s , such as Ratz and Schoenberg, Rosen discusses d i f f e r e n t l y - f u n c t i o n i n g elements and how they contribute to the form,, although he does so i n a d i f f e r e n t way from them: In the sonata form, the meaning of a phrase depended on i t s place i n the.work as a whole, on i t s p o s i t i o n i n the general movement from p o l a r i z a t i o n [of keys] to r e s o l u t i o n . The forms, therefore, demanded c l e a r l y separable elements whose a l t e r e d functions could be c l e a r l y recognized as they appeared at d i f f e r e n t points of the work. (P. 194) This i s c e r t a i n l y an approach I agree with, as I hope to demonstrate that what happens i n a c l o s i n g section i s d i f f e r e n t from what happens elsewhere i n the work. Rosen's chapter on "Exposition" i s quite u s e f u l , as he summarizes a number of ways that t h i s section i s organized, many of the ways being used by Mozart. Although Schenker does not discuss the structure or function of c l o s i n g sections, or closure i n general, h i s theory as i t applies to these matters can be surmised from h i s approach to sonata-form analysis as found i n Free Composi- t i o n (primarily chapter 5, section 3, paragraphs 311-316). The governing p r i n -c i p l e f o r the analysis of a l l sonata forms i s the i n t e r r u p t i o n . "Only the prolongation of a d i v i s i o n (interruption) gives r i s e to sonata form" (p. 134). 28 Diagram 1 One Model of Sonata Form (af t e r Schenker) •7 7^=;—: r 1 ' ' : ~k>-—j H --if—*—J-^ Exposition Development Recapitulat " ^ v 1 J ion - Q r f — < J - Q * f V V The two types of i n t e r r u p t i o n found i n sonata form are those where the fundamen-t a l l i n e begins with scale degrees 3 and 5. Diagram 1 i s based on fig u r e 23 from Free Composition, and i l l u s t r a t e s the f i r s t type. (The second type i s s i m i l a r except that the fundamental l i n e begins on S\ returning there at the s t a r t of the r e c a p i t u l a t i o n ; i n the minor mode the s i t u a t i o n changes i n that I I I or v i s used instead of V, and the f i r s t ^ a r r i v e s only at the end of the development; see figures 24 to 26 i n Free Composition.) I am not i n a p o s i t i o n to state whether a l l of Mozart's sonata-form move-ments can be analysed using t h i s and Schenker's other models f o r sonata form, although c e r t a i n l y many could be. The modulatory scheme at l e a s t f i t s a l l of Mozart's sonata-form expositions, the prolongation of the dominant harmony begin-ning e i t h e r during the t r a n s i t i o n or at the s t a r t of the second theme, depending on the p a r t i c u l a r movement. The development section of most of Mozart's sonata-form movments can be seen as dominant prolongations, the r e c a p i t u l a t i o n s as a return to the tonic along with a subsequent tonic prolongation. The Schenkerian view of the c l o s i n g section, both i n the exposition and r e c a p i t u l a t i o n , i s that i t has no fundamental l i n e motion; instead, i t prolongs 29 one or more already established tones and harmonies ( i n the major mode, the A . . A . background 2 and V i n the exposition, 1 and I i n the r e c a p i t u l a t i o n ) . In the exposition, the 2 i s prolonged by means of a f i f t h - p r o g r e s s i o n descending from i t , descending e i t h e r before or during the c l o s i n g section. (For examples, see Free Composition, f i g u r e 154, 1: Mozart, Piano Sonata i n C Major, K. 279, f i r s t movement; and f i g u r e 47,2: Beethoven, Piano Sonata i n G Major, op. 14, no. 2, f i r s t movement.) Schoenberg's Fundamentals of Musical Composition contains much that i s re l a t e d to my a n a l y t i c a l approach. The emphasis on formal a n a l y s i s , the d i s t i n c -t i o n between primary and secondary sections, the focus on c l a s s i c a l period music, and the use of the terms period and sentence f o r thematic types are a l l s i m i l a r to my approach. He categorizes the sonata-form c l o s i n g section as often being a "group of codettas," sometimes based on the main theme ("adapted to cadential harmonies") (pp. 202, 204). His use of the term "codetta" i s s i m i l a r to mine (his "group of codettas" i s what I w i l l c a l l a "codetta-complex"). Codettas are p r i m a r i l y cadences. They serve as reaffirmations of the ending of a sec t i o n . Harmonically, they may consist of the most rudimentary cadence, V-I; or they may be highly complex. M o t i v a l l y , they may range from simple r e p e t i t i o n s of small e l e -ments to rather independent formulations.1 . . . ^-Usually, i f more than one codetta appears, the l a t e r ones are shortened, often i n the manner of a l i q u i d a t i o n . (P. 155) The technique of l i q u i d a t i o n . . . [involves] gradually depriv-ing the motive-forms of t h e i r c h a r a c t e r i s t i c features and d i s s o l -ving them into u n c h a r a c t e r i s t i c forms, such as scales, broken chords, etc. (P. 152) As suggested by the above quotations, a common c l o s u r a l technique i s l i q u -i d a t i o n , the purpose of which i s "to counteract the tendency toward unlimited extension" (p. 58). Such a technique could be used to end a phrase or a section. Supporting my view of Mozart's c l o s i n g sections i s Schoenberg's statement that 30 "the l i q u i d a t i o n i s generally supported by a shortening of the phrase" (p. 58). And c l o s i n g sections often feature "scales, broken chords, e t c . " Smith's Poetic Closure has been re f e r r e d to by several of the authors c i t e d i n t h i s chapter; f o r example, Meyer and Agawu have both c i t e d Smith's book as an influence on t h e i r own work. However, I have not used i t much i n my d i s s e r t a t i o n : nevertheless, i t may be mentioned here because other writers on music have found some i n s p i r a t i o n i n i t , because Smith makes various compar-isons between music and poetic closure, and because, as one of the few thorough studies of closure i n any a r t form i t may be of some i n t e r e s t to readers study-ing the subject of closure. For Smith, "the sense of closure i s a function of the perception of structure" (p. 4). One of her analogies with music i s concerned with explaining the dual nature of poetic structure: The p r i n c i p l e s of poetic and musical structure are comparable i n -sofar as both forms of a r t produce experiences which occur over a period of time and are continuously modified by successive events. Because language, however, has semantic or symbolic as well as physical properties, poetic structure i s considerably more complex. A sonata consists only of an organization of sounds, but a sonnet consists of an organization of symbols as w e l l . (Pp. 4-5) Musical structure i s thus analogous to formal structure i n poetry, the l a t t e r defined as "the systematic r e p e t i t i o n or patterning of various elements" (p. 6). Missing from musical structure i s an analogy to thematic structure i n poetry, a structure including "everything from reference to syntax to tone" (p. 6). (Many the o r i s t s would l i k e l y disagree with her r e s t r i c t i v e view of musical meaning.) One reason I have avoided reference to Smith's study i s that there i s t h i s basic d i f f e r e n c e i n structure between poetry and music. However, f o r an attempt to apply her approach to music, see Agawu's a r t i c l e , as discussed above. 31 Smyth's d i s s e r t a t i o n "Codas i n c l a s s i c a l form: aspects of large-scale rhythm and pattern completion" i s e s p e c i a l l y relevant to my study, as he inves-tigates a s i m i l a r repertory to mine (including works of Haydn, Mozart, and Beethoven, and a l l movements of works, but not including works other than piano sonatas, s t r i n g quartets, and symphonies), and because he studies closure i n general, not j u s t codas, i n these works. In his chapter 2 he summarizes a number of previous studies dealing with closure and codas. One of these, which I have not seen, i s a d i s s e r t a t i o n by Bohdan J . Kuschnir, "Zur Frtlhgeschichte des Kodaprinzips," (Erlangen, 1947); Smyth comments on one f i n d i n g of t h i s d i s s e r t a t i o n worth noting here: With the r i s e of instrumental music during the baroque period, c e r t a i n c l o s u r a l techniques were c a r r i e d over from e a r l i e r p r a c t i c e . One was "echo-technique": r e p e t i t i o n i n v o l v i n g dynamic contrast a r t i c u l a t e s p a i r s of segments which constitute a greater whole, which i s closed by v i r t u e of the r e p e t i t i o n . (Pp. 10-11) The feature of p a i r s of repeated units i s c l e a r l y r e l a t e d to my c l o s i n g model fo r Mozart, and may be seen as a h i s t o r i c a l forerunner that may have led i n part to the development of the c l o s i n g model i n the c l a s s i c a l period. Also noteworthy here i s the observation that l a r g e r - s c a l e closure r e s u l t s from t h i s lower-level r e p e t i t i o n . Smyth uses the term "codetta" f o r the c l o s i n g section, which he notes i s characterized by a decrease i n harmonic complexity (many employ pedal point) and i n melodic i n t e r e s t (sometimes to the point of including only cadential c l i c h e s and conventional passage work), and rhythmic and t e x t u r a l s i m p l i f i c a t i o n . Previously heard motives might be gradually l i q u i d a t e d , or, a l t e r n a t i v e l y , a short burst of cad-e n t i a l energy might erupt. In e i t h e r case, the "sense of an ending" w i l l most often be quite c l e a r . (Pp. 18-19) Smyth's d e s c r i p t i o n of the c l o s i n g section i s very s i m i l a r to mine. 32 Smyth devotes some discussion to d e f i n i t i o n of terms such as cadence, phrase, and coda. He sees the cadence as e s p e c i a l l y important (even though he defines most segments by i n i t i a t i o n rather than by ending), and i n f a c t demon-strates that, " i n a very important sense, the coda and the codetta are p r e c i s e l y 'extensions of the cadence'" (p. 18). Smyth includes an e n t i r e chapter devoted to sonata forms, a chapter that incorporates a useful survey of approaches to the analysis of t h i s form type. In general, he says "formal closure i s achieved when the o v e r a l l pattern of tension/resolution i s completed" (p. 178). His a n a l y t i c a l technique focusses on how "grouping structures [e.g.,, the formal categories of themes, t r a n s i t i o n s , and c l o s i n g sections] can underlie sonata forms and contribute to a 'symmetrical r e s o l u t i o n of opposing f o r c e s ' " (p. 180; h i s quotation i s from Rosen). E s s e n t i a l l y , Smyth i s concerned with demonstrating how formal closure r e s u l t s from h i g h - l e v e l patterning. To do t h i s he produces graphs of movements which include lengths of various sections; then- he compares and discusses the lengths of these sections p r i m a r i l y as to how they balance. "Overall formal closure i n c l a s s i c a l instrumental music involves pattern completion and d u p l i -cation of grouping structures on a much larger scale than most previous analysts have considered" (p. 219). In The Symphonies of Johann Stamitz: A Study i n the Formation of the  C l a s s i c Style, Wolf includes one of the best theories of phrase and movement structures applicable to the c l a s s i c period (see e s p e c i a l l y h i s chapters 8 and 9). He finds that phrase-level r e p e t i t i o n — " ( a + a ) " — i s e s p e c i a l l y c h a r a c t e r i s t i c of second themes and c l o s i n g sections. "Most of Stamitz's c l o s i n g (K) themes make use of r e p e t i t i o n i n order to s t a b i l i z e the end of the exposition or recap-33 i t u l a t i o n " (p. 108). In view of the s i m i l a r type of r e p e t i t i o n I f i n d i n Mozart's c l o s i n g sections, Wolf's study i s p a r t i c u l a r l y relevant here. Wolf discusses some eighteenth-century theories of phrase structure, including Riepel's Grundregeln zur Tonordnung insgemein. One of the ways Riepel notes f o r expansion of sections i s " r e p e t i t i o n of the cadential units (Verdoppelung der Cadenzen, pp. 61-63 [of R i e p e l ] ) " (p. 115 [of Wolf]), a method corresponding to an aspect of my c l o s i n g model. Wolf bel i e v e s , i n gen-e r a l , that Riepel's "compositional theory incorporates many of the actual pro-cedures that contributed to the evolution of C l a s s i c phrase syntax" (p. 115). Wolf summarizes c l o s i n g material as follows: Whether area or section, K i n Stamitz often includes l i t e r a l r e p e t i t i o n at the broadest l e v e l present within the exposition as a means of providing cadential s t a b i l i z a t i o n . In addition, Stamitz commonly precedes and/or follows t h i s r e p e t i t i o n with one or more small-scale r e p e t i t i o n s based on cadential harmonic formulas, regular chord rhythm, and perhaps pedal point. (P. 151) These features are c e r t a i n l y often found i n Mozart's c l o s i n g sections. Wolf also i d e n t i f i e s a d i f f e r e n t type of exposition structure i n which the second theme i s followed by a section or sections t r a n s i t i o n a l i n s t y l e that lead to the c l o s i n g section i t s e l f (p. 151). This too i s seen i n several of Mozart's movements (e.g., the Piano Sonata i n B - f l a t Major, K. 333, to be discussed l a t e r ) ,. where such sections resemble t y p i c a l t r a n s i t i o n s i n terms of melodic material, texture, and rhythmic organization, though generally not with regard to harmonic function, since they do not modulate. 34 2 Concepts, Models, and Features In t h i s chapter I w i l l be p r i m a r i l y concerned with explaining my view of those c h a r a c t e r i s t i c s of Mozart's f i r s t movement sonata forms relevant to my study of closure i n these works. E s s e n t i a l l y , t h i s w i l l e n t a i l a d e f i n i t i o n and discussion of those features that d i s t i n g u i s h the d i f f e r e n t sections of the son-ata forms, the ultimate goal being the i d e n t i f i c a t i o n of features that promote closure of these works and that are c h a r a c t e r i s t i c of c l o s i n g sections. Discus-sion of areas of sonata forms other than the c l o s i n g section i s necessary because comparing the c h a r a c t e r i s t i c s of d i f f e r e n t areas w i l l better reveal those of the c l o s i n g section, and because the function of the c l o s i n g section within the en-t i r e work must be examined. It should already be apparent that I regard the discussion of the formal function of the t r a d i t i o n a l l y analysed sections of sonata form—themes, t r a n s i -t i o n s , c l o s i n g sections, developments—as a c e n t r a l concern i n my study of these works of Mozart. Having considered other a n a l y t i c a l viewpoints, such as the Schenkerian one, i n which the long-range harmonic and l i n e a r plan i s the c e n t r a l issue, I am convinced that the most valuable approach to the study of closure i n these works i s that of d i v i d i n g the piece into sections, according to the fea-tures found i n each—features defined on the basis of melody, harmony, rhythm, texture, e t c . — a n d then seeing how the d i f f e r e n t sections combine and r e l a t e on 35 the basis of these same features. My approach i s not dogmatic i n the sense of applying one formal model to a l l of these works: many pieces cannot e a s i l y be heard as comprised of sections, or at l e a s t cannot be divided into the same sorts of sections found i n the usual typology of sonata form. The formal, thematic, and phraseological models I pro-pose below must be seen as applying to a greater or l e s s e r extent to these pieces, with no value judgment implied. That i s , a piece which does not conform to a p a r t i c u l a r model must not be understood as deviant: another way must be found to analyse such a piece. This problem i s only one of many i n the use of models f o r musical a n a l y s i s , some of which may be b r i e f l y mentioned here. How homogeneous does a p a r t i c u l a r repertory have to be f o r consideration as a d i s t i n c t repertory, having i t s own models? Id e n t i f y i n g accurate models involves a lengthy feedback process: I began my research by studying a number of randomly chosen works by Mozart, then i d e n t i -f i e d models that applied to some of them. This encouraged me to widen the reper-tory. As more and more pieces were included i n my study, the previously defined models were changed to r e f l e c t the new repertory to which they applied, and new models were developed to explain other newly analysed pieces. This process of r e v i s i o n and development of models could be continued u n t i l a l l of Mozart's music was analysed, as well as compared with music written by other composers working at the same time as Mozart. Although I have not analysed a l l of Mozart's music, nor even a l l of h i s sonata-form music, I am reasonably convinced that the models I present here may be used to explain enough aspects of the music under consid-eration to give the models v a l i d i t y . R e s t r i c t i n g the repertory f o r t h i s d i s s e r t a t i o n c h r o n o l o g i c a l l y i s a r b i -t r a r y because no j u s t i f i c a t i o n can be found f o r a beginning date. Do the l a t e 36 works begin with the year 1775, 1780, 1781, or some other year? Historians cannot agree on what the various s t y l e periods of Mozart are, and even i f they could (or should), and I defined my repertory on t h i s b a s i s , many pieces would not f i t i n f e r r e d s t y l i s t i c norms of a period because they would be written i n e a r l i e r s t y l e s or i n combinations of e a r l i e r s t y l e s and the current, defined s t y l e (e.g., the Piano Sonata i n C Major, K. 545, written i n 1788 but having obvious features of e a r l i e r s t y l e s ) . ^ Furthermore, there are many s t y l e s that were i n vogue i n the 1780s—for example, opera buffa, e c c l e s i a s t i c a l , Mannheim instrumental, concerto—and they a l l f i g u r e to a greater or lesser extent i n the repertory by Mozart that I have chosen f o r a n a l y s i s . That i s , some pieces are more influenced by opera buffa than by concerto s t y l e , some vice versa, and so on. How could one model possibly account for a l l these s t y l i s t i c influences and differences? Much w r i t i n g i n music theory contains as i m p l i c i t the assumption that the analysis of the structure of music i s the analysis of music i t s e l f . This concern with structure i s p r i m a r i l y a feature of twentieth-century w r i t i n g , whereas nine-teenth-century writers were more concerned with the aesthetics of music. The structure and aesthetics of music are two of the concerns writers have had i n the past. By focussing on the a p p l i c a t i o n of models to Mozart's music I place myself among those who see structure as primary. However, I do so with the reservation that the analysis of structure, v i a models, leaves other areas, such as aesthe-2 t i c s , untouched. Despite the various problems and l i m i t a t i o n s i n the use of models for mus-i c a l a n a l y s i s , the use of models seems to me to be e s s e n t i a l i n discussing a large number of r e l a t e d works that may i n some senses appear to form a d i s t i n c t repertory. Eighteenth-century music i s often regarded as being s u i t a b l e f o r 37 theories based on norms of structure. In the eighteenth-century i t s e l f , music c r i t i c i s m focussed on the r e l a t i o n of the i n d i v i d u a l work toith e norm of which i t was an example. Dahlhaus comments on t h i s : The general concept or i d e a l type of a musical form (sonata or fugue), which gradually faded to a schema i n the l a t e nineteenth century and eventually degenerated to a l a b e l , s t i l l possessed h i s t o r i c a l substance around 1800. I t was musically r e a l . ^ While i d e n t i f i c a t i o n of norms of structure i n t h i s repertory i s the primary goal, I am also concerned with e x p l i c a t i n g the unique properties of these pieces to the extent that these properties are revealed by c l o s i n g pro-cesses. In Narmour's terms, I am analysing both s t y l e structures and i d i o s t r u c -4 tures. From Dahlhaus's point of view, I am w r i t i n g a "theory based on analyses and also w r i t i n g analyses which "do j u s t i c e to the p a r t i c u l a r and unrepeatable." The presentation of models w i l l be done systematically according to the length of the unit of musical material. These d i s c r e t e , r e l a t e d models occur i n a v a r i e t y of h i e r a r c h i c a l grouping l e v e l s or formal contexts. The concept of hierarchy that I am using here i s not the same as, f o r example, that used by Schenker, where the length of an event on the musical surface i s not n e c e s s a r i l y a determinant of the s i g n i f i c a n c e of that event on subsequent l e v e l s . In my system, each h i e r a r c h i c a l l e v e l i s p r i m a r i l y defined by the length of i t s char-a c t e r i s t i c unit ( r e l a t i v e to the lengths of the units of the other l e v e l s i n a given work), and by the formal context of i t s c h a r a c t e r i s t i c u n i t . To a large extent, I w i l l uge the terms " h i e r a r c h i c a l l e v e l , " " l e v e l , " "formal context," and "context" interchangeably. The various contexts I am considering are arranged i n table 2 from low to high l e v e l . A further problem a r i s e s here as to method of presentation: i s i t better to begin with the low-level categories and proceed towards the e n t i r e movement, 38 Table 2 Levels, Formal Contexts, and Normative Lengths Level Contexts & formal names Approx. normal lengths (a) segments (motivic segments, grouplets, 2 measures and cadences; i . e . , surface phenomena) (b) phrases and groups 4 to 8 measures (c) small sections (themes, t r a n s i t i o n s , 8 to 40 measures c l o s i n g sections, etc.) (d) large sections (exposition, 40 to 100 measures development, r e c a p i t u l a t i o n ) (e) e n t i r e movements (sonata form) 150 to 250 measures or to reverse the process and s t a r t with the e n t i r e movement and work down? This i s not a small matter, since i n order to discuss, f o r example, phrases, i t may be necessary to discuss the contexts they "occur i n — f o r example, themes. A phrase i n a theme may not have exactly the same model structure as one i n a t r a n s i t i o n . That i s , should phrases be discussed, while mentioning i n t r i n s i c phrase-level features, i n terms of the larger context they occur i n — f o r exampl themes, or should themes be discussed i n terms of the lower-level content they e x h i b i t — f o r example, phrases? As long as the model f o r each l e v e l includes consideration of l e v e l s both above and below the one being d e f i n e d — t h a t i s , i n forming a model f o r , l e t us say, phrases, both segment and small-section l e v e l s and possibly higher l e v e l s too, are incorporated—proceeding from high to low or from low to high w i l l probably y i e l d s i m i l a r r e s u l t s , although v i a d i f f e r e n t routes. My general approach w i l l be to begin with the low l e v e l s , working tow-• 6 ard models of the e n t i r e movement. 39 The approximate normal lengths i n table 2 f o r each context are intended only as guidelines. They are more accurate f o r lower than f o r higher l e v e l s . Some movements w i l l have these lengths doubled (e.g., 4-measure l e v e l [a]) due to tempo, etc. I w i l l begin the discussion of each formal context by d e f i n i n g that con-text i n a general way, that i s , without reference to higher l e v e l s . For example, a phrase would be f i r s t defined using a general model that would apply to a l l h i g h e r - l e v e l contexts i n which a l l phrases would be found. In the discussion of subsequent l e v e l s , the d e f i n i t i o n of phrases would be r e f i n e d to r e f l e c t spe-c i f i c types of phrases found i n each context at each higher l e v e l ; that i s , the thematic phrase, the t r a n s i t i o n a l phrase, etc., would each have more d e t a i l e d d e f i n i t i o n s than the general one found i n the discussion of the phrase l e v e l . However, there w i l l be c e r t a i n contexts i n which an accurate general def-i n i t i o n i s not possible without immediate reference to higher l e v e l s . For ex-ample, at the smallest l e v e l one way of i d e n t i f y i n g whether a segment i s motivic rather than being a grouplet or a cadence i s by the presence of connections be-tween segments that might not be perceived as motivic when seen on t h e i r own (because t h e i r s i m i l a r i t y i s tenuous), but that are perceived as motivic be-cause they are analogously placed i n larger contexts. An event occurring at the beginning of the development might be seen as m o t i v i c a l l y r e l a t e d to another at the beginning of the exposition, whereas the same segments might not be seen i n t h i s l i g h t were they both i n the exposition. Since my use of l e v e l s i s p r i m a r i l y a convenience f o r the presentation . of d e f i n i t i o n s of terms, concepts, and models that w i l l be used i n subsequent chapters dealing with t h e o r e t i c a l and a n a l y t i c a l aspects of c l o s i n g sections, rather than a t h e o r e t i c a l end i n i t s e l f , I w i l l neither be concerned with formal 40 generation of each l e v e l nor with f u l l discussion of a l l p a r t i c u l a r s of each l e v e l . Moreover, since i t i s the middle l e v e l s — ( b ) and ( c ) — a s well as the exposition and r e c a p i t u l a t i o n of l e v e l (d) that are most important to my d i s -cussion of c l o s i n g sections, I w i l l devote most of t h i s chapter to a consider-a t i o n of those l e v e l s . The d e f i n i t i o n process w i l l involve as many as three aspects, depending on the p a r t i c u l a r term under examination and the l e v e l being considered. F i r s t , the features from lower l e v e l s that combine to form the l e v e l being defined w i l l be discussed: f o r example, a phrase would be defined p a r t l y i n terms of types of motivic &nd cadential combinations. Second, i n some cases i t i s necessary to i n -voke higher l e v e l s than the one being defined i n order to obtain a general d e f i n -i t i o n . A t h i r d part consists i n i s o l a t i n g those t r a i t s c h a r a c t e r i s t i c of each l e v e l . Such t r a i t s can be noted i n terms of patterning i n four basic parameters ( i . e . , channels of s t r u c t u r e ) : (1) harmony, (2) melody ( l i n e a r p i t c h ) , (3) rhythm and meter, and (4) texture and timbre. I w i l l assume a general understanding of these basic concepts as they apply to tonal music. Precise meaning f o r these terms w i l l emerge i n the d e f i n i t i o n of each l e v e l . In summary, then, the d e f i n i t i o n process w i l l c o n sist of c h a r a c t e r i s i n g each l e v e l by the harmonic, melodic, rhythmic, metric, t e x t u r a l , and timbral features found i n each l e v e l as well as de f i n i n g the r e l a t i o n s h i p between l e v e l s . Level (a): Segments Motivic segments, grouplets, and cadences are the three types of segments found i n l e v e l (a). There may be more than one, and more than one type, i n a 41 given segment. This 2-bar l e v e l , the lowest I am considering, i s comprised of shorter motives and grouplets, f o r example, 1-bar motives and 1-bar grouplets, which i n turn are comprised of i n d i v i d u a l pitches and i n t e r v a l s . Motives and motivic segments A motive usually features a small number of l i n e a r ( i . e . , non-overlapping) pitches that form a unit due to t h e i r proximity i n time and r e g i s t e r . The p i t -ches usually form a d i f f e r e n t i a t e d rhythmic pattern, they are expressed i n a single texture and timbre, and they express one or two harmonies. A motive i s commonly one bar long; a motivic segment usually has two 1-bar motives. (There i s another type of motive several measures long—comprised of long notes—which often leads to the f i r s t type of motive; e.g., Symphony no. 41, fourth movement.) A necessary c h a r a c t e r i s t i c of motivic segments i s that they are subject to r e p e t i t i o n and v a r i a t i o n . While t h i s happens to grouplets and cadences as well as to blocks of material on other l e v e l s , i t happens there to a l e s s e r ex-tent, and i s a primary feature only of motivic segments. In the case of exact or near-exact r e p e t i t i o n i t i s c l e a r that such a le v e l - ( a ) event w i l l be motivic. The less obvious the r e p e t i t i o n , the more the need f o r reference to higher l e v e l s to demonstrate r e l a t i o n s h i p between motive-forms. A motivic segment, l i k e most surface phenomena i n Mozart's music, i s usu-a l l y found i n the predominating top voice of a complex of voices. The types of textures i n which motives are found are more varied than those of other surface phenomena. I t i s possible f o r a motivic segment to occur i n several voices and even to b~e used p o l y p h o n i c a l l y — f o r example i n i m i t a t i o n . Some motivic segments may be used p r i m a r i l y as accompaniment while at times assuming a s i g n i f i c a n t melo-dic r o l e . Melodic and accompanimental motivic segments may or may not be r e l a t e d . 42 A segment i s motivic i f : (1) i t i s immediately repeated and/or varied so as to give prominence to a p a r t i c u l a r melodic/rhythmic pattern; (2) a non-immediate r e p e t i t i o n occurs at (a) analogous places at higher l e v e l s , f o r example, at the s t a r t of two phrases, two small sections, or two large sections, i n which case the motive may be s u b s t a n t i a l l y v a r i e d , or (b) non-analogous places at higher l e v e l s and the r e p e t i t i o n i s exact or near-exact ( i . e . , compensation f o r non-immediate r e p e t i t i o n occurs e i t h e r by contex-t u a l a s s o c i a t i o n of s i m i l a r l o c a t i o n within higher l e v e l s , or by close i d e n t i t y ) ; or, (3) i t i s transformed to f u l l y occupy a timespan at a higher l e v e l through some operation that preserves the e s s e n t i a l melodic/rhythmic pattern of the mo-t i v e — f o r example, by augmentation. An i l l u s t r a t i o n of type (1) above i s found i n example 2, the Serenade i n C Minor, K. 388. The segment from m. 5(3) to m. 7(2) becomes motivic through immediate sequence a t h i r d higher (oboe 1). Each segment i s divided into two 1-bar suspension motives. The grouping of these suspension motives into motivic segments i s created by several f a c t o r s : (1) the second and fourth motives contain resolutions to tonic t r i a d members, making them harmonically more important than the f i r s t and t h i r d motives; and (2) several d e t a i l s of orchestration contribute to 2-bar grouping, f o r example, the octave leap i n bassoon 2. An i l l u s t r a t i o n of motive type 2(a) i s found i n the opening e v e n t — a p h r a s e — o f example 2, i n mm. 1-5(2), which contains, i n e f f e c t , two motivic seg-ments, i n mm. 1-3(2) and 3(3)-5(2). These segments become motivic through var-i a t i o n at mm. 22-26(2), where new motives are added; t h i s i s the s t a r t of a new small s e c t i o n — t h e t r a n s i t i o n . They are also motivic by reference to 43 mm. 130-134(2), the s t a r t of the r e c a p i t u l a t i o n . The presence of exact repe-t i t i o n as well as the use of the motive at the s t a r t of a section at m. 130 make t h i s occurrence more motivic than the v a r i a t i o n at m. 22. Part of the concluding segment i n t h i s phrase, i n mm. 4-5(2), becomes motivic when transposed, harmonised, and v a r i e d with the ad d i t i o n of a t r i l l i n mm. 13-14 and 15-16. This i s an i l l u s t r a t i o n of type 2(b) above. Here, a concluding motive becomes an opening one at m. 13. The v a r i a t i o n of t h i s motive at mm. 10-12(1) i s remote because i t i s an opening as opposed to a c l o s i n g event and because i t i s varied i n both p i t c h and rhythm. This i s a type (3) motive because of the lengthening of and ad d i t i o n to the motive i n mm. 12(2-3): i t i s transformed into a level-(b) e v e n t — t h e phrase i n mm. 10-12. (The rests i n mm. 9 and 12 i s o l a t e t h i s event i n the manner of a phrase, not of a motivic segment.) Grouplets A grouplet i s a l e v e l - ( a ) segment which i s e i t h e r not repeated or i s repeated only i n a l o c a l context and i n an obvious way, in v o l v i n g sequence and s i m i l a r pattern formation. A motivic segment has long-range s i g n i f i c a n c e and a pervasive melodic influence. A grouplet, on the other hand, i s only a l o c a l event and need not even be repeated. Whereas a motivic segment i s normally characterised by a v a r i e t y of rhythms and pitches, set off by rests from sur-rounding events, a grouplet usually has fewer note values (often either only one or a prominent one among two or three) and fewer s i g n i f i c a n t p itches. (Although there may be many pitches, they are often merely scale or arpeggio patterns.) Also, grouplets often occur i n immediate r e p e t i t i o n without separa-t i o n by r e s t s . In general, a motivic segment i s more i n t e r e s t i n g than a grouplet 44 both i n t r i n s i c a l l y and also i n how i t i s used. Whereas i t i s possible to speak of motivic segments as being normally two bars long, grouplets are more v a r i a b l e i n length, within a range of one to three measures. A grouplet i s t y p i c a l l y composed of s t i l l smaller sub-groups, delineated by melodic or rhythmic f a c t o r s . The d i s t i n c t i o n between a motivic segment and a grouplet i s not always obvious. While there are many segments which w i l l be c l e a r l y one or the other, at times a segment may have some c h a r a c t e r i s t i c s of a motive and some of a grouplet. For example, a segment might have the i n t r i n s i c features of a grouplet but be used i n a more developmental way c h a r a c t e r i s t i c of a motivic segment. In short, there i s a range of possible types of l e v e l - ( a ) non-cadential segments between the common extremes of motivic segment and grouplet.^ In example 3, from the Piano Sonata i n B - f l a t Major, K. 333, a l l of the non-cadential segments i n the f i r s t ten bars are motivic. Here the segments are separated by r e l a t i v e l y long note v a l u e s — t h a t i s , the dotted quarter-notes i n the f i r s t three bars, or by subsidiary l i n k material ( i n mm. 6 and 8) rather than by rests between motives, only one of which i s found here, i n m. 4. A gradual s h i f t to grouplets begins i n mm. 10(4)-14(2). The sixteenth-note l i n k i n g mat-e r i a l , a s t r i n g of equal note values, i s used i n t h i s v a r i a t i o n of the opening four bars to weaken the motivic nature of mm. 12(3)-14, while at the same time there i s no doubt that these bars are a v a r i a t i o n of a previously-heard motive. The statement of a motive three times i n mm. 14(4)-17 i s a d i f f e r e n t kind of weakening of motivic character. Here, although these three segments are i n t r i n s i c a l l y motivic, t h e i r o v e r a l l motivic character i s weakened because they are almost i d e n t i c a l , immediately adjacent without being separated by rests or 4 6 long notes, and used with a s i m i l a r , simple cadential progression (F: - I ). This i s a r e l a t i v e l y l o c a l i n d i c a t i o n of the f a c t that one must often go beyond 45 the segment l e v e l to determine motivic character. Each i n d i v i d u a l segment i s motivic but the way these three segments are used i n the larger unit i s not. A segment which has some features of motives and some of grouplets may be termed a motive/grouplet segment. This i s how I would describe the segments i n mm. 14(4)-17. (The material here i s discussed i n d e t a i l i n note 30 i n r e f e r -ence to t r a n s i t i o n structure.) The weakening of the motivic character of t h i s area of the movement i s further accomplished by the two grouplets i n mm. 18-22. Each of the previous motivic segments and motive/grouplet segments began with an anacrusis and had a beginning and ending that were c l e a r , except f o r the ending of the motive/ grouplet segment i n mm. 16(3)-18(1). The two grouplets i n mm. 18-22 have no anacrusis and have beginnings and endings that are e x t e r n a l l y created rather than i n t e r n a l l y by cadences. That i s , each of these two grouplets begins on a downbeat and ends on a downbeat three bars l a t e r (except f o r the extension here of the second grouplet through m. 22), overlapping with the s t a r t of the second grouplet i n m. 20. Although these units have more features of grouplets than those i n mm. 14-17, they are not as completely so as the model grouplets i n mm. 39-40 and 41-42 (the l a t t e r are completely self-contained, i n that they end on I, whereas the former can end only with the downbeat harmony, and thus involve overlapping, a feature not present i n mm. 39-42). Also c h a r a c t e r i s t i c of these grouplets i s the use of only two note values (and these not i n combination but i n separate bars), and the use of common f i g u r a t i o n patterns, that i s , the pas-sage-work i n mm. 18 and 20, which i s found i n many pieces. The use of low-level sequencing of the f i g u r e i n mm. 18 and 20, forming a series of 1-beat long sub-grouplets, and the use of p a r a l l e l tenths throughout are also common features. (Outer-voice p a r a l l e l i s m i s a feature of grouplets because i t i s the opposite 46 of the standard motive/accompaniment texture found i n motivic segments; p a r a l l -ism i s thus a way of generating the equalized texture c h a r a c t e r i s t i c of grou-l e t s . ) O v e r a l l , then, there has been a gradual change from motivic segments 8 to grouplets over these bars, mm. 11-22. Cadences Cadences are s p e c i a l types of g r o u p l e t s — c l o s i n g g r o u p l e t s — t h a t follow motivic segments. They are normally conventional formations, conventional i n harmonic and melodic senses. Expansions of cadence norms are p o s s i b l e , as are expansions of other segment norms. Such expansions usually occur i n the context of an expansion at l e v e l (b): f o r example, a phrase might be expanded from four to eight bars, with i t s cadence segment being expanded from two to four bars. Cadences may have motivic associations and may be preceded by (neutral) grouplets. Coordination of harmony, melody, rhythm, and texture i s necessary for there to be a cadence. There are a l i m i t e d number of harmonic and melodic c l o -sural patterns, mentioned below, that are used at cadences. Rhythmically, caden-ces occur at the end of h i g h e r - l e v e l u n i t s . The f i n a l chord i s usually metric- _•-a l l y strong, often on a downbeat (although, somewhat c i r c u l a r l y , m etrical strength at cadences, and meter i n general, are p a r t l y defined by cadential accent and placement). The dimension of texture and timbre i s the l e a s t v a r i a b l e at cadences. E s s e n t i a l l y , one texture and one timbre must be maintained through-out the cadence. A change of texture or timbre during a cadence w i l l not t o t a l l y destroy the cadence but w i l l , weaken i t to a c e r t a i n extent. This l a t t e r statement indicates that cadences are generally perceived to have varying degrees of strength or weakness, depending on the extent of coordin-at i o n of the various dimensions and on the actual length of the cadence. A cad-47 ence that uses only two harmonies over two beats i n a common-time a l l e g r o w i l l not be as strong as a cadence that uses several harmonies over several beats, or even, i n extended cases, over several measures. Some examples w i l l serve to i l l u s t r a t e these c h a r a c t e r i s t i c s ; further examples w i l l be seen l a t e r . A perfect authentic cadence (PAC) i s found i n mm. 9-10 of example 3. An imperfect authentic cadence (IAC) i s found i n mm. 8-9 of example 2. Half cadences (HC) are found i n mm. 29-30 of example 3 ( i n F major), and i n mm. 110-111(1) of example 1. Other types of cadences 9 are rare. Discussion of a l l segment types While the discussion of cadential and non-cadential endings w i l l assume greater s i g n i f i c a n c e at higher l e v e l s , a few more musical examples and compari-sons with motivic segments and grouplets w i l l help to c l a r i f y j u s t what i s , and what i s not, a cadence. The c e n t r a l point i s that cadences are endings. In general, the weaker the cadence, the more open-ended i s the h i g h e r - l e v e l u n i t . A l l segments may be regarded as having some cadential properties, because a l l segments must have some kind of ending i n order to be perceived as d i s c r e t e events. Normally, however, the term cadence w i l l be applied only to those level-(a) endings that e x h i b i t coordinated closure i n most dimensions. In example 1, the opening segment of the a l l e g r o , i n mm. 14-15(1), i s motivic rather than cadential because the harmonic motion i s very weak and be-cause i t begins a new theme i n a new tempo. The next segment, i n mm. 15(1)-17(2), i s s t i l l p r i m a r i l y motivic but has some cadential features: the change of texture i n m. 17 from the end of one segment to the s t a r t of another makes stronger the ending of the segment i n mm. 15(l)-17(2).. However, t h i s t e x t u r a l change occurs 48 a f t e r the segment ends and therefore contributes to closure only by hindsight. (If the bass had F - B - f l a t i n octaves on beats one and two of m. 17 the ending would be much stronger.) There i s a h a l f cadence at mm. 20-21 of example 1 because (1) there i s /\ A . strong harmonic motion: the bass pattern 3-4-5 i s frequently heard at strong 6 6 h a l f and authentic cadences, with the harmonies I - IV(or i i ) - V; (2) the melodic sequence i n m. 20 a r r i v e s at ^ c o o r d i n a t e with the a r r i v a l of the dom-inant harmony, and the sequence breaks o ff at t h i s point, the melody d i s s o l v i n g into a common passage-work f i g u r e ; (3) the dominant harmony a r r i v e s on a down-beat, s p e c i f i c a l l y , the downbeat of the eighth bar of the a l l e g r o (higher-level coordination w i l l be discussed l a t e r ) ; (4) these two bars are t e x t u r a l l y u n i f i e d ; and (5) the single'bass note i n m. 21 punctuates the cadence.^ The musical surface may be seen as a series of segments of various kinds. Most segments have some degree of both melodic and harmonic a c t i v i t y : that i s , i t i s rare to f i n d a segment which has no melodic or no harmonic function. There i s , instead, a melodic-harmonic continuum i n which some segments have more mel-odic d i s t i n c t i v e n e s s than harmonic, some segments about the same strengths of these two aspects, and some segments more harmonic than melodic strength. E s s e n t i a l l y , those segments that are pr i m a r i l y melodic are l i k e l y to be motives or grouplets, and those which are p r i m a r i l y harmonic are l i k e l y to be cadences. It should be apparent that the motivic segment i n mm. 14-15(1) of example 1 i s prim a r i l y melodic rather than harmonic. A motivic segment may be defined as an event on the musical surface that i s pr i m a r i l y melodic as opposed to harmonic. Almost any segment, or fragment of musical material, may be motivic. As discussed above, motives tend to have a v a r i e t y of note values and pitches, but sometimes the barest of material may be made motivic (e.g., the opening mo-49 t i v e of example 2). The c h a r a c t e r i z a t i o n of a segment as motivic depends both on i n t r i n s i c q u a l i t i e s — i s the material i n t e r e s t i n g enough to be m o t i v i c ? — and on e x t r i n s i c r e l a t i o n s — w h e r e does the motive occur i n higher l e v e l s ; f o r example, does i t begin a p h r a s e ? ^ An achievement of the c l a s s i c a l s t y l e l i e s i n the balance between elements of the musical texture. The texture i s neither devoid of motivic r e l a t i o n s h i p s nor i s i t saturated with them. A t y p i c a l work by Mozart w i l l have a v a r i e t y of motives which w i l l be used i n a v a r i e t y of ways, never dominating the texture. Local and long-range motivic r e l a t i o n s h i p s w i l l be present, but w i l l form only one aspect of the texture. Rarely w i l l even a small section of a work be dom-inated by one motive or by motives i n general. Usually a combination of new and old motives, grouplets, and cadences w i l l e x i s t i n a balanced texture, the sort 12 of texture c h a r a c t e r i s t i c of the l a t e c l a s s i c a l s t y l e . Level (b): Phrases, Groups, and Timespans Phrases The simplest model for a phrase i n t h i s music i s that of a motivic segment leading to a cadence. Sometimes there may be more than one motivic segment, eith e r l i n e a r l y or v e r t i c a l l y joined. In addition, i n i t i a t i n g motives may be worked into the cadence. Usually, however, the motivic segment i s of prime i n t e r e s t i n a phrase, while the cadence serves to close o f f motivic continuation. That i s , i n the simplest case, where a phrase consists of a motivic segment and a cadence, one melodic function of the cadence i s often to l i q u i d a t e the pre-ceding motives. This can best be seen i n an i l l u s t r a t i o n i n which the cadence 50 i s a lengthy one. In example 1, the phrase from m. 41(3) to m. 50(1) includes a sequence of a 1-bar motive (I x 3) , a repeat of another 1-bar motive ( 1 x 2 ) , and a 5-bar cadence from m. 46 to m. 50. This cadence begins with some undis-t i n c t i v e f i g u r a t i o n which has some s l i g h t connection to previous motives, and concludes with a completely non-motivic bar of t r i l l . Of course, the cadence functions melodically to close the en t i r e phrase, whether or not there are any motivic connections with the previous motive. This cadential function, as d i s t i n c t from p r i o r motivic functions, i s best i l l u s t r a t e d by a case i n which the motive and cadence are separated by a re s t or a l i n k . In example 3, the phrase from m. 4(4) to m. 10 i s made up of a 2-bar motivic segment, repeated with s l i g h t v a r i a t i o n s , and the cadence, i n mm. 9-10, which i n t h i s case contains a varied form of the motive. See diagram 2. Here the cadence melodic-a l l y closes the phrase by s t a t i n g the motive an octave higher i n the soprano voice, which previously had only an implied pedal tone on scale degree 5. Diagram 2 Piano Sonata K. 333: Analysis of measures 4(4) to 10(1) phrase 9.1 •---)••• t e ~ — —~M ai f— —-m ~M -I t f t Lr r f r f £~T f f —f =f= y , f f f f T -\ f-• * ' — i — — f f f T f m f -\ «V.i b A r>— J ^ -J f , f 1-2 s — • i i s-3 s 3 1 motivic segment motivic segment • i cadence (remote v a r i a t i o n of motivic segment) 51 In ad d i t i o n to the motivic segment and cadence of a phrase being d i f f e r -entiated by motivic and generally by melodic means, there i s usually d i f f e r e n -t i a t i o n by harmonic means. In the phrase discussed i n the previous paragraph, i t i s c l e a r that the f i r s t two statements of the motivic segment are non-cadential not only because of the F (5) l e f t "hanging" i n the soprano voice, but also because the harmonic motion i s weak due to the use of inversions. The t h i r d statement puts the f i n a l dominant and tonic chords into root p o s i t i o n , thereby making the cadence perfect authentic, and i t does so i n the normal bass r e g i s t e r , i n contrast to the two previous statements which were an octave higher. The phrase represented i n diagram 2 i s a good example of a phrase that 13 may be seen as an expansion of a 4-bar one. Here the expansion occurs as a r e s u l t of the r e p e t i t i o n of the 2-bar motivic segment. Omitting mm. 6 and 7 would produce a p e r f e c t l y acceptable 4-bar phrase (mm. 4[4] combined with mm. 8-10) that would f i t i n well with the larger thematic context. The demarcation of the end of a phrase by the cadence i s normally unequiv-oca l . A rest i n one or more voices w i l l even follow the cadence. The beginning of a phrase i s usually also c l e a r l y indicated, often by a rest preceding the phrase. Normally a phrase i s i n one key, and has c l e a r l y defined tonal and 14 melodic motions, the cadence being almost always authentic or h a l f . The normal motivic or cadential r e l a t i o n s h i p s may be a l t e r e d when a motive i s used at a cadence. In such cases the models for the normal uses of motives, cadences, and phrases are i n a p p l i c a b l e . Another case re q u i r i n g new models occurs when cadential material becomes motivic: when cadential segments become motivic, when material previously heard i n a piece as cadential i s used as motivic, or when material normally used i n the s t y l e as cadential becomes moti-v i c . A well-known example of the l a t t e r case i s the opening of the t r i o from 52 the Symphony no. 41 ( J u p i t e r ) , reproduced as example 4. Here the cart i s put before the horse, so to speak: a motive masquerading as a cadence i s heard f i r s t , and a motive incorporating a r e a l cadence second. This would have been a p a r t i e s u l a r l y good example of the phrase model of "motivic segment plus cadence" i f mm. 2(3)-6(l) were taken as the phrase. In order f o r Mozart's joke to be c l e a r to the l i s t e n e r , the motive and the cadence must be more c l e a r l y distinguished as such than i n the average phrase. That i s , the average phrase has a process of gradual l i q u i d a t i o n of motivic features leading from the motivic segment to the cadence, "motivic segment plus cadence" being somewhat a s i m p l i f i c a t i o n of the phrase model.^ An example of material previously heard as cadential subsequently becoming motivic i s found i n example 1, at the opening of the development section, i n mm. 66-69. The two 2-bar sequences are based on the f i n a l c a d e n tial bar of the c l o s i n g section. What was f i r s t heard as ending a phrase (and section) i s now heard as opening a phrase (and s e c t i o n ) . Because i t now opens (and closes) as opposed to only c l o s i n g , t h i s material acquires more motivic s i g n i f i c a n c e , and the l i s t e n e r i s more l i k e l y to hear the melodic t h i r d s , f o r example, F - A - f l a t - F , and the octave leaps i n the bass as motivic, that i s , as based on motives i n mm. 14-17 from the opening of the main theme. Groups and timespans A group i s a level-(b) unit that incorporates two grouplets and i s not punctuated by a cadence. Whereas phrases are i n t e r n a l l y closed, groups are open-ended and are often d i s t i n g u i s h a b l e p r i m a r i l y by a s s o c i a t i o n with imme-d i a t e l y adjacent g r o u p s — p a r t i c u l a r l y when a group i s repeated—because groups lack the strong i n t e r n a l closure of cadences. See example 3, mm. 39-42, which 53 contains two i d e n t i c a l grouplets. In order to c l a r i f y the term group, and to d i s t i n g u i s h i t from phrase, I w i l l introduce a t h i r d term—the timespan—which i s not l e v e l - s p e c i f i c . Although i t i s possible to speak of timespans occurring at any l e v e l , i t i s at l e v e l s (b) and (c) that they are of most value i n a n a l y s i s . A timespan at l e v e l (a) would usually be equivalent to two measures. One may think of time-spans as the next higher l e v e l of metric p a r t i t i o n i n g beyond the measure: as measures are divided into beats, so timespans are divided into measures; as measures have pe r i o d i c a l t e r n a t i o n of strong and weak beats, so timespans have pe r i o d i c a l t e r n a t i o n of strong and weak measures; as measures have phenomenol-o g i c a l accents on t h e i r weak beats (syncopated beats), so timespans may have accented weak-measure downbeats. Measures usually occur i n a series where a l l measures are the same length ( i . e . , a movement i s usually written i n one meter throughout). Occasionally a bar or series of bars w i l l be a l t e r e d , a u r a l l y i f not v i s u a l l y on the score, such that not a l l bars w i l l be of equal length. Similar a l t e r a t i o n s i n timespan s e r i e s 1 are more common. As w i l l be seen l a t e r i n the discussion of l e v e l ( c ) , a series of timespans which features compression or expansion of i t s length 16 may at times be normative. A timespan i s more than j u s t a c o l l e c t i o n of adjacent measures: i t i s a frame within which phrases and groups move. In these works of Mozart, timespans are delineated by a v a r i e t y of f a c t o r s . T y p i c a l l y , i t i s middleground harmonic c r i t e r i a — t h a t i.s, at l e v e l s (b) and ( c ) — t h a t are the most important factors i n creating timespans. One important reason f o r introducing the concept of timespan here i s that timespans are often more prominent i n c l o s i n g sections than i n other small sections. In p a r t i c u l a r , the r e l a t i o n between the events 54 and the timespans i n c l o s i n g sections i s often one that i s unique to the c l o s i n g section. Since many of these pieces have s i m i l a r r e l a t i o n s h i p s within the c l o s i n g section, discussing timespan r e l a t i o n s h i p s i s a way of focussing on some of the unique features of c l o s i n g sections. Although the main a t t r i b u t e of phrases, and to a l e s s e r extent of groups, i s a ser i e s of events, phrases and groups also have length, a length not neces-s a r i l y i d e n t i c a l to or coincident with the timespans of those phrases and groups. Phrases and groups w i l l therefore be symbolized by lower case l e t t e r s whether t h e i r events or t h e i r length are being discussed. Timespans w i l l be sumbolized by c a p i t a l l e t t e r s . Timespan A would be that associated with phrase or group a. The d i s t i n c t i o n between the length of a phrase or group and that of i t s associa-ted timespan, while appearing at f i r s t to be a t r i v i a l one, i s i n f a c t quite useful f or the analysis of t h i s music. This should become c l e a r l a t e r i n the d i s s e r t a t i o n . In example 1, the c l o s i n g section timespan of mm. 50-65 i s a 16-bar tonic u n i t : i t i s the f i n a l tonic prolongation. (The previous timespan concludes at the end of m. 49 and w i l l be discussed l a t e r . ) Other movements have c l o s i n g sections i n which the f i r s t phrase or group begins d i r e c t l y on the f i r s t beat of the f i r s t bar of the c l o s i n g section timespan. That i s , the timespan and group begin simultaneously, unlike i n example 1, where the phrase begins on beat three of m. 50. The timespan i s more obvious here than i n other small sections of t h i s movement because i t begins independently of the melodic structure. Compare the beginnings of the other small sections of t h i s movement. In the introduction, the timespan and events begin together (m. 1), as also i n the main theme (m. 14). The subordinate theme begins at m. 30 with a melodic anacrusis i n m. 29. However, m. 29 i s p r i m a r i l y the end of a 16-bar unit begun i n m. 14, 55 and therefore i t i s not l i k e l y that m. 29 would be heard as part of the sub-ordinate theme timespan, which instead begins with m. 30. In m. 50, on the other hand, there i s a d i f f e r e n t kind of anacrusis, one that takes place a f t e r the timespan has begun.^ The concluding event/timespan r e l a t i o n s h i p i s also often d i f f e r e n t i n each small section of a movement. The main theme of example 1 concludes on beat two of the f i n a l bar of i t s 16-bar timespan, m. 29. The subordinate theme of example 1 concludes i n the f i r s t bars of the succeeding timespan, m. 50. And the c l o s i n g section concludes with the f i n a l bar of i t s 16-bar timespan, m. 65. In summary, each small section i n the exposition of example 1 has a d i f f e r e n t event/timespan r e l a t i o n s h i p . See diagram 3. Diagram 3 V i o l i n Sonata K. 454: Event/Timespan Relationships i n the Exposition Main theme events: timespan:. T5T 16 (mm. 14-29) Subordinate theme events: timespan: h 21 20 (mm. 30-49) Closing section events: timespan: 15i 16 (mm. 50-65) The r e l a t i o n of events to timespans i s a factor i n the d e l i n e a t i o n of 18 function of units at a l l l e v e l s , notably at level"-(c). There are four 4-bar level-(b) units (a, b_, c_, d) i n the c l o s i n g section of example 1, corresponding 56 to the four 4-bar timespans (A, B, C,.D) i n mm. 50-53, 54-57, 58-61, and 62-65 (bar numbers indic a t e timespans). Each unit begins on the t h i r d beat of i t s f i r s t timespan, concluding on the f i r s t and second beats of the following time-span, except f o r the f i n a l u n i t , which ends i n the fourth bar (m. 65) of i t s timespan. There are three types of phrases or groups i n t h i s c l o s i n g section. The f i r s t , found i n the two groups i n mm. 50-58, i s the nearest to being a phrase, i n that i t i s the normal 4-bar phrase length, i t has a discernable melodic shape, i t has some motivic i n t e r e s t , and i t has a weak but d i s t i n g u i s h a b l e cadence—a cadence that brings the preceding material to a close. The second type, found i n the two groups i n mm. 58-62, i s further removed from being a phrase i n that i t i s only two bars long and contains only one bar of the barest of melodic material p r i o r to the 1-bar cadence. The t h i r d type i s the 1-bar cadence formula found four times i n mm. 62-65. The term phrase should obviously not apply to the t h i r d t y p e — t h e 1-bar cadence formula. Neither should i t apply to the second t y p e — t h e 2-bar group. It applies i n a weakened sense to the f i r s t type, and i t does so i n part because the two phrases i n mm. 50-58 form a period. Devising new terminology to s u i t each type of group i s not p r a c t i c a l be-cause there are so many types and because some types have some phrase features and might therefore at times be c o r r e c t l y regarded as phrases, as i n mm. 50-58 of example 1. Instead, I w i l l discuss groups i n terms of the extent to which they have features of phrase structure. I f the thematic phrase i s taken as a norm f o r t h i s s t y l e , then groups become phrases as they acquire more features of normal phrases. There i s thus a continuum of possible group structures, varying with the number of phrase features present. 57 The terms group and phrase r e f e r , i n my approach, to motivic-melodic u n i t s , one d i s t i n c t i o n between the two terms being the extent to which the underlying timespan i s prominent: the r i c h e r the motivic-melodic content, the less evident the timespan, p a r t i c u l a r l y on the musical surface, and the more applicable i s the term phrase. A discussion of a t h e o r e t i c a l case at an extreme end of the group struc-ture continuum w i l l help further to c l a r i f y my terminology. If phrases are characterized by melodic and harmonic a c t i v i t y on the musical surface, then a l l groups are to a c e r t a i n extent phrases, because no musical surface i s com-p l e t e l y devoid of a c t i v i t y . However, the extreme example of a foreground unit without any melodic or harmonic motion would s t i l l possess one musical feature: i t would be a prolongation of a sing l e harmony f o r the duration of that u n i t . In other words, such a group would be a timespan. In a given level-(b) u n i t , the greater the number of phrase features the more applicable i s the term phrase. The smaller the number of phrase features the more applicable i s the term group. Timespans are always present, but t h e i r 19 presence may be masked as the number of phrase features increases. Level ( c ) : Small Sections Phrases and groups combine to form small sections such as themes, trans-i t i o n s , and c l o s i n g sections. The d i v i s i o n of movements into a v a r i e t y of d i f -f e r e n t l y functioning small sections i s more apparent i n music of the c l a s s i c a l period than of other periods. Sonata form could not have ar i s e n without t h i s c h a r a c t e r i s t i c feature. Levels (a) and "(b) of sonata form tend to be perceived 58 i n the context of small sections (notwithstanding prominent exceptions such as motivic r e l a t i o n s h i p s at higher l e v e l s ) . And i n conceptualizing an e n t i r e exposition or r e c a p i t u l a t i o n we tend to r e l a t e the small sections of which i t i s comprised. This s p e c i a l nature of small sections has to do with a higher degree of closure of small sections. Each l e v e l of sonata-form structure i s i t s e l f closed, but because of r e l a t i o n s h i p s between l e v e l s , small sections are more closed than are others. A phrase may i t s e l f be closed, but because i t i s usually adjacent to l i k e phrases, i t i s the u n i t — f o r example, a theme—on l e v e l (c) that i s perceived as being more closed. And because small sections tend not to be adja-cent to other s i m i l a r small sections, closure at l e v e l (d) i s not as great as at l e v e l ( c ) . In summary, l e v e l (c) d i f f e r s from other l e v e l s i n the greater d i f -f e r e n t i a t i o n of i t s u n i t s , a d i f f e r e n t i a t i o n so great that l e v e l (c) has more types of commonly-occurring units—themes, t r a n s i t i o n s , e t c . — t h a n does any other l e v e l . At l e v e l (d) then, within each type of large section there are no s i m i l a r small sections. (For example, an exposition i s comprised of a series of d i f f e r e n t small sections.) A small section i s not closed merely due to a strong cadence at i t s end. It i s the r e l a t i o n between units within a small section that creates the strong-est c l o s u r a l forces. In general, closure of a small section i s dependent upon a strong cadence at i t s conclusion; a strong goal-directed harmonic plan, such as the i n t e r r u p t i o n model of Schenker; and elimination of motivic continuation. The more of these f a c t o r s that are present, the stronger closure w i l l be. I f , f o r example, a theme ends with a h a l f cadence rather than a perfect authentic one, t h i s w i l l obviously weaken the closure of the theme. In such cases, other factors may balance the weakened sense of harmonic closure. At times, closure w i l l be 59 af f e c t e d by r e l a t i o n s h i p s between, and by l o c a t i o n of, small sections: t h i s w i l l be discussed below as to l e v e l (d). Small sections are f u n c t i o n a l l y d i f f e r e n t because of the d i f f e r e n t kinds of units within them and the r e l a t i o n s among those u n i t s . P o s i t i o n - f i n d i n g within sonata-form music i s made possible by d i f f e r e n t l y functioning sections that occur i n standard sequences, coupled with a more-or-less f i x e d tonal plan. I am more concerned with expositions and r e c a p i t u l a t i o n s than with devel-opments because c l o s i n g sections are part of the two outer sections. In addi-t i o n , the development tends not to be divided into small sections as c l e a r l y as the other two large sections are, and Mozart's development sections often tend to be short enough to be the length of small sections. For these reasons I w i l l deal here, with respect to l e v e l ( c ) , with small sections of expositions and r e c a p i t u l a t i o n s . I w i l l leave the issue of r e c a p i t u l a t i o n forms of exposition small sections to the discussion of l e v e l (d), where r e c a p i t u l a t i o n s w i l l be dealt with i n t h e i r e n t i r e t y . The small sections w i l l be discussed i n the following order: themes, t r a n s i t i o n s , r e t r a n s i t i o n s , codettas, c l o s i n g sections, codas, and introductions. It should be noted that i n some pieces these small sections combine to form larger parts that are shorter than large sections. In such pieces there w i l l be a l e v e l between that of the small section and that of the large section. This w i l l be discussed i n connection with l e v e l (d), although some shorter 20 pairings w i l l be mentioned here. Themes Four d i f f e r e n t categories of themes w i l l be considered here: sentences, periods, small t e r n a r i e s , and unique structures. The models I use f o r the f i r s t 60 three are largely based on previous work i n thematic and formal theories of c l a s s i c a l period music, i n p a r t i c u l a r on an approach used mainly by many 21 twentieth-century German and Austrian theorists. Thematic structures are used, obviously, i n those small sections termed main theme (MT), or f i r s t theme, and subordinate theme (ST), or second theme. They are also sometimes used i n varied form i n the other small sections. I t i s important then to distinguish between the thematic models—sentence, period, and small ternary—and the thematic small sections—MT and ST. I w i l l discuss the models i n some d e t a i l here because they are used throughout the sonata form. Two generalizations may be made concerning thematic small sections: (1) modulations do not normally occur i n them, and (2) t o n a l i t i e s may be specified: major mode expositions have the MT i n the tonic, the ST i n the dom-inant,, with the recapitulations having both themes i n the- tonic; minor mode expo-s i t i o n s have the MT i n the tonic, the ST i n the r e l a t i v e major, with the recap-i t u l a t i o n s having both themes i n the tonic. Sentence. The model for the sentence i s shown i n diagram 4. The normal 8-bar length i s sometimes doubled to sixteen bars, and variants occur which i n -volve lengths other than these. Some examples of common motivic structure are noted i n diagram 4. The motive-forms of mm. 3 and 4 of the sentence are often varied with respect to the motives i n mm. 1 and 2 to conform to minimal harmonic alterations which may, at times, give the (false) impression of cadences. That i s , commonly the f i r s t 2-bar unit moves from tonic to dominant with the second unit reversing this motion, the motivic alterations being only those required to have the second unit conform to the change i n harmony. Normally, however, cadential implications w i l l be weakened by the use of inverted harmonies. (A 61 Diagram 4 Sentence Model of Thematic Structure Phrase/group length, l e v e l (b) 4 + 4 Segment length, l e v e l (a) (2 + 2) + (1 + 1 + 2) Motives a a 1 a 1 a b or a 1 a b b c or ab ab ab 1 ab 1 c Harmony and cadences I - V V - I I - - PAC or HC common bass l i n e f o r the f i r s t four bars i s 1-2, 7-1.) This means that the f i r s t h a l f of a sentence may be (1) a phrase, i f the second unit ends with a strong enough cadence, or (2) two 2-bar phrases, i f the cadential implications i n mm. 2 and 4 are both strong, or (3) a group having motives instead of group-l e t s , and therefore being more l i k e a phrase without a cadence. The second h a l f of the sentence, while possessing the c l e a r timespan and motivic d i v i s i o n ( 1 + 1 + 2 ) , i s u n i f i e d into one phrase by harmonic and melodic means. Usually the second ha l f contrasts with the f i r s t by having a more act i v e harmonic structure, i f only because of the strong cadence, and t h i s more act i v e harmony i s usually a r t i c u l a t e d by a more act i v e bass l i n e . Whereas the harmony of the f i r s t h a l f of the sentence i s usually characterized by the mere i n t e r -change of tonic and dominant, the harmony of the second h a l f i s usually strongly goal-directed. Whereas the f i r s t h a l f presents the main motive i n two c l o s e l y -r e l a t e d forms, the second h a l f develops the motive, often i n fragmentation, that i s , as (1 + 1 ) , or presents contrasting material. A good i l l u s t r a t i o n of a sentence i s given i n example 5, the main theme from the String Quartet i n A Major, K. 464. The doubled l e n g t h — s i x t e e n bars 62 instead of e i g h t — i s mitigated by the shorter bar length—3/4 instead of the usual 4/4—and by the obvious grouping of bars into 2-bar timespans (mm. 1-2, 3-4, e t c . ) , so that the theme could e a s i l y be heard as eight bars of 6/4. M o t i v i c a l l y , t h i s theme could be represented as follows: ( 4 + 4 ) + (2 + 2 + 4 ) ^ u , i 1 1 2 a + b a + b a a a The a^  and b_ motives are combined i n the f i r s t h a l f , forming two 4-bar phrases which alternate tonic and dominant as i n the model, having very weak cadences. The a motive i s separated from b and sequenced i n a varied form i n mm. 8(3)-12(l) and i s used i n a lengthened v a r i a t i o n i n mm. 12(3)-16. The bass of the second h a l f of the sentence i s more active than the f i r s t , i l l u s t r a t i n g a common . A A A pattern i n which i t r i s e s stepwise from 1 to 5, cadencmg on 1.. The second 22 h a l f of t h i s sentence i s one phrase. Period. The second type of thematic structure I am considering as archetypal i s the period. See diagram 5. The e s s e n t i a l features of a period are (1) the balance between, and s i m i l a r structure of, the two phrases, created by p a r a l l e l motivic structure (a . . . + a_ . . . ) and equal length of phrases, and (2) the use of two cadences, the second of which i s stronger than the f i r s t . There are a number of d i f f e r e n t p o s s i b i l i t i e s f o r motivic and timespan structure within phrases, some of which are shown i n diagram 5, However, more important as an e s s e n t i a l feature than the i n t e r n a l structure of each phrase i s the motivic p a r a l l e l i s m between the beginnings of the two phrases, i f not between the e n t i r e two phrases. Like the sentence, the period i s sometimes found doubled or otherwise a l t e r e d i n length. In some of these cases, there may be four 4-bar phrases 63 Diagram 5 Period Model of Thematic Structure Phrase length 4 + 4 Motives a 1 a a b or a b b^ " (or a . . . c) Harmony and cadences I HC I PAC instead of two 8-bar ones; such structures may be termed double periods. In these cases the f i r s t and t h i r d phrases w i l l have weaker cadences than the sec-ond phrase, which w i l l i n turn have a weaker cadence than the fourth phrase. (See example 3, mm. 23-38.) Unlike the sentence, the period i s a more stable, less developmental structure. This i s due to the period's p a r a l l e l phrase structure; the sentence, on the other hand, has a b u i l t - i n imbalance of timespan, motivic, and harmonic structures. The r e p e t i t i o n of motives i n the period occurs over eight bars (a . . . + a. . .. . ); the sentence does t h i s i n four bars and then develops or contrasts t h i s (aa, or b). The f i r s t h a l f of a sentence i n f a c t often r e s -embles a period. (See example 1, mm. 1-4, which i f taken out of context might be considered to have many of the features of a period.) A further cause of s t a b i l i t y i n the period i s the usual presence of an 23 i n t e r r u p t i o n ( i n the Schenkerian sense). That i s , the melodic-harmonic s t r u c -ture of the two phrases i s normally as follows: /N A A A /\ 3 - 2 3 - 2 - 1 I - V I - V - I This creates strong c l o s u r a l forces at the small section l e v e l , forces usually absent from the sentence, which r a r e l y has such i n t e r r u p t i o n structure. This 64 correlates with my observation that sentences are more c h a r a c t e r i s t i c of main themes than of subordinate themes and that periods are more c h a r a c t e r i s t i c of subordinate themes than of main themes; i n other words, the more open structure — t h e s e n t e n c e — i s more common at the s t a r t of an exposition, while the more closed s t r u c t u r e — t h e p e r i o d — i s more common towards the end of the exposition. (My observations regarding d i s t r i b u t i o n of thematic types are c i t e d i n note 28.) An i l l u s t r a t i o n of the period model w i l l be found i n example 6, the theme 24 of the Piano Sonata i n A Major, f i r s t movement, K. 331, mm. 1-8. This theme embodies most of the features of the period as discussed above. (The period i s found i n mm. 1-8; the remainder of the theme quoted i n example 6 w i l l be discus-sed shortly.) The i n t e r n a l structure of the two phrases i s as follows: 1 a a b 1 + 1 + 2 a a b 1 + 1 + 2 25 The antecedent-consequent construction i s very c l e a r . Small ternary. The t h i r d type of thematic structure i s the small ternary form. This i s not seen nearly as often i n sonata-form movements as the period and the sentence, i t being more commonly used as the form of the theme i n theme and v a r i a t i o n movements, and as the form of minuets and of t r i o s . See diagram 6. The f i r s t A-subsection i s often a period, sometimes a sentence, usually ending with a PAC i n the dominant or i n the ton i c . The B-subsection contrasts both harmonically and m o t i v i c a l l y with the A-subsection, always ending on the dominant, i f not being e n t i r e l y dominant prolongation (but not modulating to the dominant, or to any other key). The A^"-subsection i s usually a repeat of part or a l l of the A-subsection, and nearly, always begins on the ton i c , thus emphasizing the return to the tonic and to the o r i g i n a l motive-forms. The small ternary i s 65 Diagram 6 Small Ternary Model of Thematic Structure 8 4 4 (4 + 4) 4 4 I V V - I (or I) therefore d i f f e r e n t from the period and the sentence i n that i t i s normally twice as long as the other two types. In addition, the B-subsection contains more of a contrast than i s found within e i t h e r the period or the sentence. In p a r t i c u l a r , the B-subsection may contrast t e x t u r a l l y with the A-subsection, and such contrast i s normally missing from the other types of themes. An i l l u s t r a t i o n of the small ternary form i s found i n example 6. The A-subsection, i n mm. 1-8, i s a period as discussed above. The B-subsection, i n mm. 9-12, contains the bare minimum of motivic and harmonic contrast to the A-subsection. One reason f o r the small harmonic contrast i n B i s that A was i t s e l f e n t i r e l y d i a t o n i c , even ending on the tonic as opposed to ending on the dominant as i s seen more often. Therefore, the f a c t that B ends on the dominant, weakly t o n i c i z e d with the only chromatic note i n the theme, i s s u f f i c i e n t con-t r a s t here. The A^"-subsection i s s i m i l a r to the second phrase of the period, and a 2-bar codetta, or cadential extension, based on mm. 15-16, i s added. The A^==subsection d i f f e r s from the model i n that i t i s hot four bars long, although i t i s c l e a r here that the f i n a l two bars are an extension ( i . e . , A''" i s [4 + 2]). A wide range of v a r i a t i o n i n A''" i s found i n the small ternary form: i t may be a 26 f u l l repeat of A, sometimes even with an extension. 66 Unique themes. Thematic structures which are not sentences, periods, or small ternaries, or r e l a t i v e l y close variants of these three, f a l l into my fourth category, that of unique, or o r i g i n a l structures. Obviously, a l l of Mozart's themes are unique and o r i g i n a l i n the broad meanings of the terms, but those which are not based on one of the three models perhaps deserve the terms unique and o r i g i n a l i n a special sense. In addition, this category i n -cludes those themes which are remote variants of the three models and those which are based only i n part on the models. Of course there i s no model for t h i s fourth category: there i s instead a wide range of possible structures, a l l of which are closed, but looser i n structure than the three models. They must be closed i n order to be thematic. This category applies only to the two them-a t i c small sections (MT and ST); the other three types may be found i n other small sections. The f u l l range of thematic structures i s summarized i n table 3. Table 3 Summary of Thematic Structures Period Sentence Small ternary Unique themes Thematic Thematic Used as model function MT, ST x X Used only as MT, ST Also used in other small sections x x x x 67 Most main themes are based c l o s e l y on the thematic models. However, subordinate 28 themes depend less on models and have a wider range of possible structures. Transitions T r a n s i t i o n s d i f f e r from thematic small sections i n that t r a n s i t i o n s are subsidiary as opposed to primary small sections, and also i n that there are no models that account f o r t h e i r melodic, rhythmic, and harmonic features. Trans-i t i o n s have a subsidiary function because t h e i r features are looser i n construc-t i o n than are those of themes. (This i s p a r t i c u l a r l y apparent i n that t r a n s i -tions follow main themes, which have closed constructions.) The f a c t that t r a n s i t i o n s cannot be explained by models means that i t i s more d i f f i c u l t to present an o v e r a l l view of t r a n s i t i o n s . The looser construction of t r a n s i t i o n s i s generated by the following normative features: (1) In those cases where a thematic model i s used f o r a l l or part of a t r a n s i t i o n , the model w i l l i n v a r i a b l y be r a d i c a l l y a l t e r e d i n i t s p r o j e c t i o n into a t r a n s i t i o n . Regardless of whether any thematic model i s used, the seg-ment structure w i l l be looser because (a) both motivic segments and grouplets w i l l be used, together with both phrases and groups (there w i l l often be a s h i f t from one to the other, usually motivic segments and phrases becoming, re s p e c -t i v e l y , grouplets and groups), and (b) motivic associations within the t r a n s i t i o n w i l l be weaker, to the point where each phrase/group may have d i f f e r e n t motives/ grouplets, and there may be motivic associations with both the preceding main theme and the succeeding subordinate theme. In short, the t r a n s i t i o n usually 29 has a series of motives/grouplets based on unrelated materials. 68 (2) Transitions include a modulatory function, although t h i s function i s often attenuated i n the r e c a p i t u l a t i o n form of the t r a n s i t i o n . (The f a c t that there are often two quite d i f f e r e n t forms of the t r a n s i t i o n — a n exposition form and a r e c a p i t u l a t i o n f o r m — i s another reason why there are no models for t r a n s i t i o n s . ) Whatever the nature or extent of the modulation, such modulation means that the t r a n s i t i o n w i l l be open-ended, as opposed to closed, as i s the norm f o r thematic small sections. A l l t r a n s i t i o n s are open-ended, no matter how weak or strong the modulation i s . This open-ended feature i s usually pre-served i n r e c a p i t u l a t i o n forms of t r a n s i t i o n s : where the t r a n s i t i o n ends on V/V i n the exposition, i t w i l l u s ually end on V i n the r e c a p i t u l a t i o n ; where i t ends on V i n the exposition ( i . e . , where there i s no modulation), i t w i l l usually be rewritten i n the r e c a p i t u l a t i o n so that i t s t i l l ends on V. Rarely w i l l such a t r a n s i t i o n not be a l t e r e d i n the r e c a p i t u l a t i o n , even though there i s no appar-30 ent need f o r such a l t e r a t i o n . (3) The timespan structure i s not uniformly p e r i o d i c ("periodic" here meaning successions of equal-length u n i t s ) . Whereas the thematic models employ timespans that are p e r i o d i c at both the 2- and 4-bar l e v e l s , t r a n s i t i o n s are not e n t i r e l y governed by such patterning on any timespan l e v e l . Normally, a r e g u l a r i t y i s established, often at the 2-bar l e v e l , at the beginning of a t r a n s i t i o n (for example, based on the main theme opening). This r e g u l a r i t y i s then upset at some point, and i s followed by a series of unequal timespans, i n a d d i t i o n possibly to some short successions of s i m i l a r timespans. In summary, the melodic structure, the harmonic structure, and the time-span structure of t r a n s i t i o n s are a l l i n t r i n s i c a l l y i r r e g u l a r , at l e a s t i n that they a l l contrast with the more regular structure of the f i r s t theme. This complex of i r r e g u l a r structures i s responsible f o r the loose, open nature of 69 t r a n s i t i o n s . Retransitions Retransitions are short, subsidiary small sections that connect a small section i n the secondary key (or other non-tonic key) to a small section i n (or s t a r t i n g in) the tonic key. One type occurs immediately a f t e r the exposition's c l o s i n g section. A second type i s found at the end of the development section, leading to the main theme i n the r e c a p i t u l a t i o n . The f i r s t type occurs infrequently, but i s of most relevance here because i t follows immediately upon the c l o s i n g section, often being connected to the c l o s i n g section i n some ways. It i s normally very short, and hardly rates the designation small section. However, i t s function i s an important one, and i t c l e a r l y does not belong to e i t h e r of the adjacent small sections. Normally, i t occurs before the repeat sign of the exposition, and may have two d i f f e r e n t end-ings, one to return to the tonic key and the repeat of the main theme, the second to proceed to the opening key area of the development section. In the r e c a p i t u -l a t i o n , such r e t r a n s i t i o n s are e i t h e r omitted or rewritten to lead to a coda. Neither example 1 nor example 2 has such r e t r a n s i t i o n s . In example 7, from the String Quartet i n C Major, K. 465, the r e t r a n s i t i o n i s found between mm. 99 and 106. In addition to having the usual harmonic function of converting the tonic of G major into the dominant of C major, i t includes a development of the opening main theme motive, here sequenced i n the bass vo i c e . The r e t r a n s i -t i o n begins by overlapping the end of the c l o s i n g section; however, i t i s not part of the c l o s i n g section and i s not c l o s u r a l i n function because i t i s not i n the same key as the c l o s i n g section ( i n f a c t i t i s not i n one key; rather, i t modulates), and because i t i s d i s t i n c t from the c l o s i n g section by v i r t u e of 70 d i f f e r e n t motive-forms and texture (e.g., the c e l l o solo i n mm. 99-104 and the monophonic texture i n mm. 104-106 are unique to the r e t r a n s i t i o n ) . This r e -t r a n s i t i o n does not have two endings because the development section begins not on the usual dominant but on a dominant of the subdominant, replacing the tonic opening of the main theme. In the r e c a p i t u l a t i o n (not included i n ex-ample 7), the r e t r a n s i t i o n i s transposed to the tonic, a l t e r e d s l i g h t l y at i t s 32 end, and leads to a coda. Three types of c l o s i n g music Before discussing each type of c l o s i n g music i n d e t a i l , a b r i e f summary of the terms involved may be h e l p f u l . Obviously, the small section known as the c l o s i n g section may end both exposition and r e c a p i t u l a t i o n . Closing sections are often composed of codettas, which i n turn often combine forming a codetta-complex. Closing sections are normally composed of a codetta-complex, but may at times include material based on the thematic models. Codettas and codetta-complexes are also used elsewhere i n the sonata form, that i s , as appendages to themes, i n the development section, and i n codas. Codas occur a f t e r the recap-i t u l a t i o n and are usually formed of codettas. Closing sections, codettas, codetta-complexes, and codas are a l l l e v e l - ( c ) u n i t s ; codetta-complexes are simply larger l e v e l - ( c ) units composed of two or more codettas. These types w i l l be discussed i n the following order: codettas and codetta-complexes, c l o s i n g sections, and codas. Codettas and codetta-complexes Codettas and codetta-complexes are subsidiary small sections, normally of short length i n the case of codettas (about eight to sixteen bars), and 71 somewhat longer i n the case of codetta-complexes (about sixteen to thirty-two bars). They function i n one of two ways, depending on t h e i r p o s i t i o n i n the sonata form: (1) they may occur s i n g l y , as appendages to primary sections, normally as codettas to themes; and (2) a codetta may combine with other cod-ettas to form l a r g e r , more independent small sections c a l l e d codetta-complexes, possibly i n place of or following a subordinate theme, and as part or a l l of a c l o s i n g section or coda. The i d e n t i f i c a t i o n of a codetta or codetta-complex i s dependent upon i t s i n t e r n a l features and on i t s r e l a t i o n to (1) the theme i t follows, or to (2) other codettas with which i t combines. (One example w i l l demonstrate how codettas depend on other sections: i f , i n function [1], the theme ends on the dominant, the subsequent material might be regarded as part of the theme; but i f the theme ends on the t o n i c , the subsequent material might be regarded as a codetta, other factors being the same.) A necessary component of codettas i s a l e v e l of harmonic s t a b i l i t y usually greater than that of themes, to the point where codettas are often char-acteriz e d e i t h e r i n whole or i n part by a pedal. Internal harmonic motion i s usually l i m i t e d to simple progressions, often merely a l t e r n a t i o n of tonic and dominant. A feature of many codettas i s t o n i c i z a t i o n of the subdominant, often over a tonic pedal. T o n i c i z a t i o n of the dominant i s not found i n codettas. (This distinguishes codettas to main themes from t r a n s i t i o n s that follow main themes: a main theme codetta might t o n i c i z e IV but not V, whereas a t r a n s i t i o n would t o n i c i z e V.) The timespan and group structure i s usually very regular, that i s , i n units of two and four bars. Pairings of groups of s i m i l a r timespans and motivic/ grouplet structure i s common. Groups are more commonly used than are phrases. 72 And while grouplets are more commonly used than are motivic segments, motivic associations with the previous theme or adjacent codettas are common. However, the character of a codetta as determined by i t s i n t e r n a l features i s the most s i g n i f i c a n t factor i n determining i t s function as a codetta. The grouplets used are normally c a d e n t i a l , short, and r e p e t i t i v e . Closing sections and codas are often made up e n t i r e l y of a series of codettas. In such cases the codettas function as b u i l d i n g blocks of complete small sections. Often i n such cases the codettas are used i n s p e c i f i c patterns, as w i l l be discussed below. Codetta-complexes sometimes become amalgamated with other small sections. That i s , the codetta function i s present as part of a m u l t i - f u n c t i o n small sec-t i o n instead of having expression i n a d i s c r e t e small section of i t s own. This occurs p a r t i c u l a r l y i n the small sections of the second key area. I l l u s t r a t i o n s of codetta-complexes follow, beginning with an instance of the type noted i n the previous paragraph. In example 2, the codetta-complex i n mm. 67-94 i s comprised of an 8-bar codetta, repeated with an extension, that i s , 8 + (8 + [4 + 4] + 4). I t i s i n t e r e s t i n g that although the two 8-bar codettas have some features of the sentence m o d e l — f o r example, t h e i r i n t e r n a l structure i s (2 + 2) + (1 + 1 + 2 ) — t h e y are not thematic i n function because they involve throughout a heavy emphasis of the subdominant, and because they lack s u b s t a n t i a l melodic-motivic material. The f i r s t sixteen bars are based on only one motivic idea, with many r e s t s : i t i s c l e a r that these measures could not serve a thematic function. However, these codettas do show how thematic models may acquire d i f -ferent functions, according to how they are used. The issue i n mm. 67-94 i s whether the codetta-complex functions as a subordinate theme codetta-complex or as a c l o s i n g section. In t h i s case i t has 73 both functions. These measures do form the f i n a l small section of the exposi-t i o n , and to that extent they form the c l o s i n g section. There are other reasons why they are a c l o s i n g section, as w i l l be discussed below. They form a subor-dinate theme codetta-complex because they d i r e c t l y follow the subordinate theme, which lacks the usual expanded cadential progression. The codettas are also somewhat more act i v e than would be the case i n a normal c l o s i n g section, i n part because the sentence model i s used. (Sentences are not common i n c l o s i n g sec-tions.) And the subdominant t o n i c i z a t i o n i s more common to codettas following themes than to codettas i n c l o s i n g sections. An i l l u s t r a t i o n of a codetta-complex forming a c l o s i n g section i s found i n example 1, i n mm. 50-65. As discussed above i n connection with groups and timespans, there are four 4-bar units that form t h i s c l o s i n g section. The f i r s t two, i n mm. 50-58, are phrase/groups that form a codetta by v i r t u e of t h e i r sim-i l a r content and by the nature of that content (as previously discussed). The second two, i n mm. 58-65, are a series of successively shorter grouplets ( f i r s t 2- then 1-bar long), forming one codetta by v i r t u e of very s i m i l a r melodic-motivic content and harmonic-rhythmic patterning. An i l l u s t r a t i o n of a t y p i c a l conclusion to a movement i s also found i n example 1. The c l o s i n g section i n the r e c a p i t u l a t i o n i s expanded with respect to the exposition form: mm. 135-146 are s i m i l a r to mm. 50-61, and the remaining measures of the r e c a p i t u l a t i o n are an expansion of the c l o s i n g s-ection with a further series of codettas. New codetta-function features of t h i s form of the 33 c l o s i n g section include a tonic pedal and subdominant t o n i c i z a t i o n . 74 Closing sections This part of chapter 2 w i l l serve as an introduction to the internal structure of closing sections. A discussion of the r e l a t i o n of the closing sec-tion to other small sections i n the exposition and recapitulation w i l l be found i n Level (d): Large Sections, l a t e r i n this chapter. Subsequent chapters w i l l focus on analysis of several closing sections and the functions of closing sec-tions within expositions, recapitulations, and entire movements. Generally speaking, on the one hand there are certain recurring patterns and features i n many closing sections, and on the other hand some movements have unique closing sections. I have c l a s s i f i e d closing sections into four types, on the basis of recurring internal structural patterns: (1) The closing model. See the discussion of this type i n chapter 1, pp. 7-8. The following adds to that discussion. It i s important to note that a l l units i n the closing model ( i . e . , l e v e l [b] units) are groups. Obviously, the units of the f i r s t p a i r — a a — a r e groups. While b_ and c_ are shorter, they too are groups—of reduced length—rather than grouplets or subgrouplets on l e v e l (a). The closing model thus incorporates a s h i f t i n perception of normal group length, thereby contributing to closure by reducing the length of timespans (and reinforcing this reduction through repe-t i t i o n ) and reducing the m a t e r i a l — t h a t i s , the groups—in the timespans. The closing section of example 1 was discussed e a r l i e r i n order to show the different types of level-(b) structures. While i t i s possible to see four 4-bar level-(b) units and timespans here, the view from l e v e l (c) shows c l e a r l y not only the pairing of groups but also the reduction i n group and timespan length: material that was four bars long i s compressed into two bars, then into one bar. I t i s preferable to see a series of progressively shorter units rather 75 than four equal-length ones here. The c l o s i n g section of example 2, i n mm. 66-94, also functions as a sub-ordinate theme codetta. (This was discussed i n connection with "Codettas" above.) Part of the reason i t functions as a c l o s i n g section i s that the sense of closure 34 i s enhanced through use of the c l o s i n g model. See diagram 7. This c l o s i n g section d i f f e r s from the model i n i t s doubled length, i n the relatedness of the second p a i r of groups to the f i r s t p a i r , and i n the d i f f e r e n t structure of the t h i r d " p a i r . " Diagram 7. Serenade K. 388: Closing Section Measures : 66 74 82 86 90 K. 388: (8 + 8) + (4 + 4) + (1 + 1 + 1 + 2) 1 2 2 . a a a a b b b b 1 Model: (4 + 4) + (2 + 2) + (1 + 1) a a b b c c (2) The c l o s i n g codetta. This type i s usually only a few bars long, and often functions more as a f i n a l codetta to the e n t i r e subordinate theme area than as a separate small section. Longer examples may have a more independent status. This type has the features of codettas, as discussed above. A c l e a r i l l u s t r a t i o n w i l l be found i n example 8, from the Piano Sonata i n C Major, K. 309. The sub-ordinate theme, i n mm. 35-54(1), incorporates a s i g n i f i c a n t and t y p i c a l expansion i n mm. 43-54(1) using three statements of an expanded cadential progression. Note also the increase i n surface rhythmic a c t i v i t y and the t r i l l (m. 53). The c l o s i n g section, i n mm. 54(2)-58, i s comprised of two statements of a simple cad-76 e n t i a l pattern. I t might be possible to see t h i s c l o s i n g section as a highly truncated c l o s i n g model: instead of three pairings as i n the model, here there i s only one. The r e c a p i t u l a t i o n form of the c l o s i n g section i s also shown i n example 8 i n mm. 148(2)-155. Aside from the t r a n s p o s i t i o n and one chromatic a l t e r a t i o n (m. 150[2]), there i s an i n s e r t i o n of (a) a reference to the opening motive of the main theme, i n mm. 152-153(3), a motive which was heavily used i n the dev-elopment section, and (b) a d d i t i o n a l cadential material, i n mm. 153(4)-155. (3) The c l o s i n g theme followed by the c l o s i n g codetta. In t h i s uncommon type, there i s a short, simple period with a shorter codetta added to i t . The d i s t i n c t i o n between t h i s type and the c l o s i n g model i s that here there are nor-mally only four phrases or groups, not s i x , and the f i r s t two phrases are d i s -t i n c t l y more theme-like—that i s , they are phrases, not groups—than the f i r s t two groups of the c l o s i n g model. In addition, the c l o s i n g codetta i s c l e a r l y an addition to the c l o s i n g theme—a c l o s i n g theme c o d e t t a — a s well as a codetta within the c l o s i n g section. In order f o r the theme to be a c l o s i n g theme as opposed to a second subordinate theme, i t must occur a f t e r the expanded cadential progression. There w i l l often be a reduction i n surface rhythmic a c t i v i t y mark-ing the beginning of the c l o s i n g theme. Most of these features are seen i n the c l o s i n g section of example 9, from the Piano Sonata i n B - f l a t Major, K. 570, mm. 70-79. The timespan and events of the subordinate theme conclude with m. 69, and the c l o s i n g section comprises a simple 8-bar period, (4 + 4), followed by a 3-bar codetta, ([1 + 1] + 1). The r e c a p i t u l a t i o n form i s the same, except of course for the necessary t r a n s p o s i t i o n . (4) Unique procedures. A number of works eit h e r have c l o s i n g sections that do not f i t any of the previous three categories, or have c l o s i n g sections 77 that are extreme variants of one of these types. Often these unique procedures are found i n connection with unusual subordinate themes; that i s , the e n t i r e second-key area w i l l be unique i n such works (e.g., the Symphony no. 35, d i s -cussed i n connection with Level (d): "Expositions," and i n chapter 6.) Codas As discussed above i n "Three types of c l o s i n g music," codas may occur a f t e r the r e c a p i t u l a t i o n section. In such cases, they are usually found a f t e r the development-recapitulation repeat sign. That i s , i n the instances where the repeat structure i s || E x p o s i t i o n : || :Development-Recapitulation: || , the coda i s not repeated. In such cases, the r e c a p i t u l a t i o n ends with the trans-posed c l o s i n g section, the coda following immediately or a f t e r a b r i e f l i n k . When the coda follows the repeat sign i t w i l l usually be a s u b s t a n t i a l new small section of about twenty bars length. Mozart's codas are always small rather than large sections. They are never the si z e of, and they never have the function of, f o r example, some of Beethoven's codas (such as that i n the f i r s t movement of the Piano Sonata i n C Major [Waldstein], op. 53, where the coda i s a large s e c t i o n ) . Extensions of the c l o s i n g section i n the r e c a p i t u l a t i o n are sometimes found: these w i l l be quite short and not true small sections. They w i l l be discussed here because of t h e i r s i m i l a r i t y to codas. Such extensions vary from one or two a d d i t i o n a l tonic chords to one or two a d d i t i o n a l groups. The material w i l l be c l e a r l y s i m i l a r to the c l o s i n g section material, i f not a c t u a l l y being r e p e t i t i o n s of the f i n a l c l o s i n g section groups. Anything longer than two groups, having material not so c l o s e l y r e l a t e d to the c l o s i n g section, w i l l l i k e l y be a coda proper. 78 There are also movements i n which the second key area i s rewritten i n the r e c a p i t u l a t i o n such that i t i s d i f f i c u l t to i d e n t i f y what might constitute a coda. One of the functions of a coda (as well as of both c l o s i n g section extensions and rewritten second key areas) i s to give the r e c a p i t u l a t i o n a d i f -ferent ending from that of the exposition, t h i s being one way i n which the two large sections are d i f f e r e n t i a t e d . R e l a t i v e l y few movements—perhaps about one-quarter—have codas. To a ce r t a i n extent the presence of a coda seems to depend on genre: f o r example, codas are more common i n the s t r i n g quartets than i n the piano sonatas. Of the ten s t r i n g quartets, h a l f have codas; of the twelve piano sonatas, only 35 one—K. 457—has a coda. A l l four s t r i n g quintets have su b s t a n t i a l codas. Of the ten symphonies (nos. 31-41, omitting no. 37),. eight have ei t h e r a coda or a c l o s i n g section extension, the l a t t e r being more frequent. (Numbers 35 and 38 have neither.) Some movements involve a rewritten second key area with some sense of a coda (e.g., nos. 31 and 34), and two have an extended c l o s i n g section that i s close to being a coda (nos. 39 and 40). That true codas are not common i n the sym-phonies may have some connection with the repeat structure of the movements: numbers 31-35 have no repeat signs; numbers 36, 39, 40, and 41 repeat only the exposition. A separate coda small section i s more common i n works which repeat both the exposition and the development-recapitulation, such as i n three of the four s t r i n g quintets (K. 516, 593, and 614). Where the development-recapitula-t i o n i s repeated, the cl o s i n g section must be written so as to lead back f i r s t to the development: any suggestion of a coda must therefore be avoided u n t i l a f t e r the repeat sign. Where the development-recapitulation i s not repeated, the c l o s i n g section can be extended f o r greater c l o s u r a l e f f e c t , and a separate 79 coda i s not as l i k e l y i n these cases. Here the revised c l o s i n g section a t t a i n s some of the function of a true coda because s i m i l a r features are found i n both. In movements where a coda follows the c l o s i n g section, the c l o s u r a l function i s found i n both of these small sections. In such movements the coda does not replace the c l o s u r a l function normally found i n the c l o s i n g section, but adds to i t : such codas stand s l i g h t l y outside of the large sections of the movement and, i n f a c t , close the whole movement. I t might be suggested that, i n such cases, the c l o s i n g section functions only to close the large section: however, the c l o s i n g section i n these cases i s not r a d i c a l l y d i f f e r e n t from the cl o s i n g section i n movements without a coda, where the c l o s i n g section e f f e c -t i v e l y closes both the large section and the whole movement. There are a few d i f f e r e n t l y constructed movements i n which the c l o s i n g section i s absent, or nearly so, from both the exposition and r e c a p i t u l a t i o n , and i n which a coda f u l -f i l l s the missing c l o s u r a l function (e.g., the Symphony no. 39). Codas and extended c l o s i n g sections have s i m i l a r features: codas simply have more of the same codetta features than do extended c l o s i n g sections. These features are the ones usually found i n codettas and c l o s i n g sections: tonic pro-longation, r e p e t i t i o n of simple cadential patterns, regular p e r i o d i c timespan structure, use of groups rather than phrases, and l i m i t e d use of motivic r e f e r -ence . Example 10 includes the c l o s i n g . s e c t i o n from the exposition, followed by the c l o s i n g section from the r e c a p i t u l a t i o n , and'then the coda, from the Piano Sonata i n C Minor, K. 457. The two forms of the c l o s i n g section are very sim-i l a r , i n mm. 59-71(1) and 156-168(1). The 18-bar coda i s one of the more sub-s t a n t i a l ones, not only i n length but also i n content. I t features an im i t a t i v e development of the opening main theme motive, a development that was prefigured 80 i n the r e t r a n s i t i o n , i n mm. 71-74, and i n the revised t r a n s i t i o n , i n mm. 118-120 (not shown i n example 10). The exposition, development, r e c a p i t u l a t i o n , and coda a l l begin with t h i s arpeggio motive on C, and t h i s lends more weight than i s usual to the coda. In ad d i t i o n , i t might be suggested that the length and subs t a n t i a l content of the coda might give i t enough weight to balance the 25-bar development section. (The coda often has t h i s function i n Beethoven's works, as i n the Waldstein Piano Sonata.) This i n t e r p r e t a t i o n i s weakened because the development acquires more importance through i t s r e p e t i t i o n , whereas the coda i s heard only once."^ This coda has the usual codetta and c l o s i n g section features, although the f i r s t eight b a r s — c o n s t r u c t e d as (2 x 4 ) — a r e more act i v e than usual. The following s i x bars, mm. 176-181, are made up of two segments—(3 x 2 ) — a n d the f i n a l four bars are tonic prolongation. The coda supplies one feature missing from the exposition and r e c a p i t u l a t i o n : normally the expanded cadential pro-gression concludes with a bar of t r i l l immediately before the c l o s i n g section. 37 This feature, missing from mm. 58 and 155, i s found i n m. 175. Introductions In the works I have analysed, introductions are separated from the main part of the movement by (1) a d i f f e r e n t tempo (the introduction i s always i n a slow tempo, the subsequent part i n a f a s t e r tempo), (2) a d i f f e r e n t meter (e.g., i n the Symphony no. 36 the introduction i s i n 3/4, the subsequent part i n C), (3) a pause at the end of the introduction, (4) the f a c t that the introduction i s not included i n the repeat of the exposition, and (5) the f a c t that the i n t r o -duction i s not part of the sonata form, and often does not have motives or other features i n common with the sonata form. These factors suggest that introduc-81 tions are not always part of the f i r s t movement, and I w i l l not consider i n t r o -ductions i n any depth, even at l e v e l (e), unless a c l e a r r e l a t i o n i s apparent with the sonata-form part of the movement, and, s p e c i f i c a l l y , unless the i n t r o -38 duction has some connection with the c l o s i n g section. Level (d): Large Sections Expositions The most important four small sections discussed above i n connection with l e v e l (c) combine i n the following order to form the usual model of expo-s i t i o n structure: main theme, t r a n s i t i o n , subordinate theme, c l o s i n g section (MT-TR-ST-CS), a l t e r n a t i n g primary and subsidiary small sections. This model applies well to approximately one-third of the expositions I have studied. These expositions involve a l l four small sections used i n normal ways. The exact r e l a t i o n s h i p between lengths of i n d i v i d u a l small sections i s subject to great v a r i a t i o n , appearing therefore to be one cause of the uniqueness of i n d i -v i d u a l movements. However, a small section w i l l r a r e l y be more than twice the length of any other small section i n a given exposition. More commonly equiv-alent i n length i s the MT-TR pa i r compared with the ST-CS p a i r . The second hal f of the exposition i s often s l i g h t l y longer than the f i r s t h a l f . Exposition length i s not a f a c t o r i n e i t h e r the length of small sections or the degree of a p p l i c a b i l i t y of the model. Absolute length i s , however, only one f a c t o r i n evaluating the s i g n i f i -cance and influence of these small sections. The shorter length of the tonic area i s balanced by the usually t i g h t e r construction of the main theme compared 82 Diagram 8 A Model of Exposition Structure Level Exposition (c) main theme (b) phrases (a) motivic segments t r a n s i t i o n phrases -^groups ^ g r o u p l e t s — second theme phrases motivic segments c l o s i n g section phrases & groups -^grouplets Note: Arrow means "becoming." with the subordinate theme and by the f a c t that i t occurs f i r s t and i s the only small section i n the tonic key. Diagram 8 shows one common model of how units on l e v e l s (a), (b), and (c) vary within the exposition. This pattern also applies i n large part to the r e c a p i t u l a t i o n . It should be emphasized that t h i s i s only one model, and an incomplete one, f o r exposition structure. The two themes, which appear to be equivalent i n the diagram, are distinguished by c e r t a i n other features, such as t o n a l i t y . This f a c t o r , among others, also d i f f e r e n t i a t e s the two subsidiary small sections. The exposition of example 1 may be considered an i l l u s t r a t i o n of t h i s model: the main theme i s eight bars long, i n mm. 14-21; the t r a n s i t i o n eight bars long, i n mm. 22-29; the subordinate theme twenty bars long, i n mm. 30-49; and the c l o s i n g section sixteen bars long, i n mm. 50-65. (This i n t e r p r e t a t i o n d i f f e r s from that on p. 55.) The unusual features here are (1) the close s t r u c -t u r a l i d e n t i t y of the main theme and the t r a n s i t i o n (to the point that these two sections may be heard as one larger theme., a period; see note 25); and (2) the imbalance i n length among the four small s e c t i o n s — h a v i n g a r a t i o of 2:2:5:4— •and between the f i r s t and second p a i r s— 4 : 9 . (This i s perhaps p a r t i a l l y compen-83 sated f o r by the tonic area of the introduction.) The exposition of example 3 i s s i m i l a r to that of example 1 i n some aspects of form. The main theme i s ten bars long, i n mm. 1-10; the t r a n s i t i o n twelve bars long, i n mm. 11-22; the subordinate theme t h i r t y - s i x bars long, i n mm. 23-58; and the c l o s i n g section only f i v e bars long, i n mm. 59-63. The r a t i o of small section lengths does not include as great an imbalance as i n example 1, but i t i s s t i l l unusual—2:2:6:1, and 4:7. The large subordinate theme i s the r e s u l t of a twenty-bar codetta-complex to the actual sixteen-bar theme. The ad d i t i o n of a codetta or a codetta-complex i s common, when, as here, the subordinate theme i t s e l f has no expansion at i t s end, as i s u s a l l y otherwise the case. That i s , the subordinate theme i s a 16-bar period, the subordinate theme codetta-complex supplying the expansion and, i n p a r t i c u l a r , the expanded cadential progression ( i n mm. 52-58) c h a r a c t e r i s t i c of subordinate themes. This codetta-complex i s s u b s t a n t i a l enough to absorb part of the c l o s i n g section function, the c l o s i n g section being merely a c l o s i n g codetta, and a p a r t i c u l a r l y short one at that. The exposition of example 2 may be seen as a normal one i f the f i n a l small section i s regarded as functioning only as a c l o s i n g section, as opposed to both a c l o s i n g section and a subordinate theme codetta-complex (as discussed above i n Level ( c ) : "Codettas"). Here the main theme i s twenty-one bars long, i n mm. 1-21; the t r a n s i t i o n twenty bars long, i n mm. 22-41;:the subordinate theme twenty-five bars long, i n mm. 42-66; and the c l o s i n g section twenty-eight bars long, i n mm. 67-94. The r a t i o of lengths i s c l o s e r to the norm compared with the two previous examples; here 4:4:5:6, and 4:5. The i r r e g u l a r , unique structure of the main theme of example 2 i s d i s -cussed i n note 27. The t r a n s i t i o n begins as a variant of the main theme opening, 84 a variant which i n i t i a t e s a process of r e g u l a r i z i n g the lengths of groups and phrases by adding one bar to the main theme's 5-bar opening phrase (mm. 1-5, mm. 22-27). There are two more 6-bar phrases i n the t r a n s i t i o n , followed by a 2-bar l i n k to the subordinate theme, which also features prominent use of 6-bar phrases. The c l o s i n g section normalizes lengths even more i n i t s use of 8-bar groups, c l o s i n g section timespans beginning i n m. 66. These are the timespans: MT: (5 + 4) + 3 + (2 + 2) + (1 + 1 +• 2) + 1 TR: (6 x 3) + 2 ST: ( 6 x 4 ) CS: (8 x 2) + (4 x 2) + 5 This exposition may therefore be viewed as having a process of p e r i o d i z a t i o n : the main theme sets up a dissonance of timespans that resolves i n succeeding small sections. In these three expositions the t r a n s i t i o n always begins as a varia n t of the opening of the main theme. This sort of connection between small sections weakens the independence of these small sections ( i n that t h e i r openings share s i m i l a r motivic material) while at the same time forming l a r g e r - s c a l e connections and units (on a l e v e l between [c] and [d]). The MT-TR connection seen i n these three movements i s a common one. The thematic connection, however, contrasts with the harmonic and s t r u c t u r a l differences between these two small sections. As i n K. 388, harmonic and thematic associations between the main theme and the t r a n s i t i o n d i s s i p a t e i n unison soon a f t e r the t r a n s i t i o n begins. The three expositions discussed so f a r — t h o s e i n examples 1, 2, and 3 — may be interpreted i n more than one way according to the p r i n c i p l e s I have set fo r t h here. (Other i n t e r p r e t a t i o n s of these expositions w i l l be mentioned shortly.) Although i t i s common f o r pieces to be subject to such d i f f e r i n g 85 i n t e r p r e t a t i o n s , there are some expositions which have e s s e n t i a l l y only one in t e r p r e t a t i o n i n my approach. I l l u s t r a t i o n s of such c l e a r l y normative expo-s i t i o n s can be found, f o r example, i n the following works: the Symphony no. 40 (see chapter 3), the V i o l i n Sonata K. 481 (see chapter 5), and the Stri n g Quar-tet K. 387 (see chapter 3). Many expositions incorporate some modification of the standard four-small-section model. Such expositions may be categorized into two general classes: those in v o l v i n g minor modifications to the model and i n which the model may s t i l l apply, possibly with a l t e r n a t i v e a n a l y t i c a l i n t e r p r e t a t i o n s using the model; and those in v o l v i n g extreme modifications of the model, i n which the model may apply only i n part, and i n which a l t e r n a t i v e analyses w i l l u s ually be po s s i b l e , some not i n v o l v i n g the model. There i s , then, a s l i d i n g scale of the degree of a p p l i -c a b i l i t y of the exposition model: at one extreme, some pieces w i l l e x h i b i t a l l t r a i t s of the model; at the other extreme, some pieces w i l l have few, i f any, t r a i t s of the model; and i n between f a l l s the majority of pieces, that involve 39 some degree of modification to the model. The vast majority of a l t e r a t i o n s to t h i s exposition model take place a f t e r the t r a n s i t i o n . Some works do involve a l t e r a t i o n s to the t r a n s i t i o n and i t s con-nection with subsequent material, and a few involve a l t e r a t i o n s i n the MT-TR r e l -ationship, such as there being one MT-TR small section rather than two d i s c r e t e ones ( i . e . , instead of separate MT and TR sec t i o n s ) . Another common a l t e r a t i o n involves the addition of a f i f t h small section to the exposition. Occasionally the reverse happens, and a small section w i l l be omitted from the exposition, or at le a s t severely truncated. Other a l t e r a -tions involve connecting two small sections, t r a n s f e r r i n g normal functions of one small section to another, and avoiding sections a l t o g e t h e r — r e p l a c i n g them 86 with continuous material that i s not p a r t i t i o n e d into l e v e l - ( c ) u n i t s . (Ex-amples of a l l of these types of a l t e r a t i o n s w i l l be seen i n subsequent chapters.) The a l t e r a t i v e analysis of example 1 involves i n t e r p r e t i n g mm. 14-29 as one small section (see note 25). This means that there i s no d i s t i n c t t r a n s i -t i o n small section, the t r a n s i t i o n function being absorbed into the end of the 40 thematic small section which modulates to the dominant. Instead of four small sections, then, t h i s exposition has only three: MT sixteen bars, ST twenty, CS sixteen, having a r a t i o of 4:5:4. This r a t i o i s more balanced than i s the one i n the i n t e r p r e t a t i o n of t h i s exposition i n v o l v i n g four sections with the r a t i o 2:2:5:4. The introduction, i f considered part of the exposition, may have some of the functions of the missing fourth small section: f i r s t , i t i s the f i r s t of four sections, and second, i t does have the modulation from tonic to dominant that would be found i n the t r a n s i t i o n . In t h i s work the introduction does help to explain why there are only three small sections i n the exposition. In example 2 i t has been noted that i t i s possible to consider mm. 66-94 as containing e i t h e r a subordinate theme codetta or a c l o s i n g section. However, i t i s better to consider these measures functioning i n both ways. They have the former function i n part because they supply the expanded cadential progres-sion missing from the subordinate theme, which has no cadence using e i t h e r the A. A bass progression 3-4-5 or an expansion. The codetta-complex to the theme begins with two segments, i n mm. 66-70, i n which the bass ends o n ^ (G), the p i t c h c l a s s that was missing from the bass of the second h a l f of the theme. The bass continues i n a s l i g h t l y varied form of the expanded cadential progression i n mm. 71-74. This i s then repeated i n mm. 74-81. The dynamic and cadential i n t e r -ruption at m. 82 emphasizes again the 3, and the expanded cadential progression i s ornamented through m. 85 where these measures are repeated. 87 The exposition of example 3 was above considered a normal exposition with a somewhat larger than usual subordinate theme area, due to the subordinate theme codetta-complex i n mm. 39-58, which also has some c l o s u r a l function. An a l t e r -native a n a l y s i s , suggested by the imbalance of small sections, an imbalance due l a r g e l y to the 36-bar subordinate theme area, i s to consider the subordinate theme ( i n mm. 23-38) one small section, and the codetta-complex ( i n mm. 39-58) another. This has the advantage not only of r e s o l v i n g the imbalance within the four-small-section i n t e r p r e t a t i o n , but also of acknowledging that the codetta-complex i s melodically and harmonically somewhat more su b s t a n t i a l than most codetta-complexes and therefore deserves to be considered an independent small section. The r a t i o of small section lengths i s then 3:3:4:5:1$. In t h i s i n t e r -p r e t a t i o n mm. 38-58 function i n three ways: (1) they form a codetta-complex functioning as a subsidiary small section that includes new melodic material as well as development; (2) they function as a codetta-complex to the subordinate theme, incorporating the missing expanded cadential progression; and (3) they begin the process of closure that i s confirmed i n the c l o s i n g section that f o l -lows, a c l o s i n g section too short to include a l l the c l o s u r a l function. This i n t e r p r e t a t i o n of example 3 i s preferable to that mentioned above i n t h i s section. A number of other expositions w i l l be discussed i n d e t a i l i n subsequent chapters. Examples of works varying i n some way from the model are c i t e d below, with annotations i n d i c a t i n g aspects of these v a r i a t i o n s . ( A l l of these works w i l l be discussed i n subsequent chapters. None are quoted as musical examples.) (1) The Symphony i n D Major (Haffner), no. 35. Some unusual features of the exposition ( i n mm. 1-94) of t h i s work have been mentioned e a r l i e r i n t h i s chapter. The exposition model does not apply well here f o r the following rea-sons: (a) This exposition i s unusually continuous, due to a great deal of over-88 lapping of small sections and to the lack of breaks i n the texture. (b) There are many more than four small sections, the functions of which are not always c l e a r , at le a s t not i n the sense of primary, or thematic, versus subsidiary small sections. That i s , the primary/subsidiary d i s t i n c t i o n i s b l u r r e d , p a r t l y because the thematic models are not used (or are used as extreme v a r i a n t s ) . (c) The modulation i s accomplished i n a very unconventional way. A move to the dominant begins i n m. 24 but i s arrested i n m. 41 with a prominent return of the tonic and the main motive. A stronger move to the dominant follows, (d) A s i n -gle motive dominates the melody, and there i s no strong candidate f o r second 41 theme. From m. 13 to m. 94 there are several small sections that have them-a t i c , t r a n s i t i o n a l , and c l o s u r a l functions. (2) The Symphony i n C Major ( J u p i t e r ) , no. 41. Like the Haffner Symphony, thi s work also features a very continuous exposition, although the greater de-gree of cont i n u i t y comes about here i n a d i f f e r e n t way and i n sp i t e of the breaks between small sections. The main theme, although long, i s unusual i n that i t i s open-ended (ending on the dominant i n m. 23). The re s t i n m. 80 ap-pears to signal the end of the subordinate theme codetta, which ended inconclu-s i v e l y the bar before. The following section, i n mm. 81-100, i s a continuation of the subordinate theme codetta into a codetta-complex having a more s i g n i f i c a n t function than that of a codetta, ending as in c o n c l u s i v e l y as the previous section and with a re s t i n m. 100. The following c l o s i n g section i s the only small sec-t i o n to end with a perfect authentic cadence. Each of the four or f i v e small sections has i t s i d e n t i t y and function weakened due to i t s open-ended nature, 1 ending on the dominant of the following section (except f o r the c l o s i n g section). (3) The Sonata f o r V i o l i n and Piano i n F Major, K. 377. The main theme, i n mm. 1-17, i s s i m i l a r i n form and function to that of example 1; both are 89 16-bar periods that end on the dominant. (The motion to V i n K. 377 i s not as strong, however, as i n K. 454.) In K. 377 the t r a n s i t i o n and subordinate theme functions are combined i n one small section, i n mm. 18-36. The normal c l o s i n g section follows i n mm. 37-51. There are thus only three small sections, of about equal length, the middle one having a double function. (4) The Piano Sonata i n C Major, K. 545. This work has the shortest exposition of a l l those works I am considering. Its twenty-eight bars are made up of only a 12-bar main theme that ends on the dominant, a 1-bar l i n k to the 12-bar subordinate theme, and a 3-bar codetta. The type of exposition composed of only two small sections i s obviously r e l a t e d to an h i s t o r i c a l l y e a r l i e r , and 43 shorter, model of sonata form. (5) The S t r i n g Quintet i n C Major, K. 515. This work has the longest exposition I have encountered—about 145 bars. The main theme area i s composed of a number of small sections t o t a l l i n g about s i x t y bars and includes some foreign key areas that prefigure the t r a n s i t i o n . The precise s t a r t of the t r a n s i t i o n i s d i f f i c u l t to determine, as i t seems to grow out of the chromati-cisms that characterize the end of the main theme area, i n mm. 57-69. The subordinate theme and c l o s i n g section are r e l a t i v e l y normal aside from t h e i r expanded length, i n mm. 86-114 and 115-143. The exposition i s somewhat s i m i l a r to that of the Haffner Symphony i n that the modulation i s accomplished i n stages i n more than one small section, here i n the main theme and t r a n s i t i o n : t h i s i s one reason why there i s no c l e a r separation of main theme and t r a n s i t i o n func-tions or sections i n t h i s work. 90 Developments The essential function of the development s e c t i o n — t o act as a te x t u r a l , formal, harmonic, melodic, and rhythmic contrast to the exposition—usually i s realized i n a r e l a t i v e l y small number of bars. The average length i s forty bars, with the exposition:development r a t i o commonly about 2:1. Whatever the form of a given development, divisions at l e v e l (c) are usually weak due to the lack of strong cadences and the use of overlapping. This continuous nature of the development, coupled with i t s r e l a t i v e l y short length, are the reasons why this section i s often on a le v e l between that of (c) and (d). When thematic models are used, they are found i n substantially modified form. Detailed d i s -44 cussion of developments i s unnecessary here. Recapitulations The norm for the recapitulation section i s the repeat of the exposition section, with the exception of the necessary transposition of the secondary key material into the tonic. The form of the recapitulation i s therefore usually the same as that of the exposition, except for the transposition. That i s , the type and order of level-(c) sections i s normally the same i n both exposition and recapitulation, although at times there are small differences between the two forms of a section, such as might res u l t from expansion or contraction. There are a few movements i n which there are s i g n i f i c a n t differences between the expo-s i t i o n and recapitulation at l e v e l (d). However, the percentage of movements having differences between exposition and recapitulation rises somewhat when viewed from levels (a) and (b): for example, embellishments or other s l i g h t variations of a motive or phrase are not uncommon. 91 Comparison of level-(d) units would seem to be appropriate i n the d i s -cussion of l e v e l (e), but because of the close i d e n t i t y of exposition and recap-i t u l a t i o n I w i l l do some of t h i s here. An examination of the ten symphonies and the ten s t r i n g quartets w i l l serve to i l l u s t r a t e the extent and type of d i f -ferences between expositions and r e c a p i t u l a t i o n s . F i f t e e n of these twenty works have s i m i l a r expositions and re c a p i t u l a t i o n s at l e v e l s . ( c ) and (d). (The excep-tions are the Symphonies nos. 31, 32, 34, and 38, and the Quartet K. 465.) If codas and c l o s i n g section extensions are considered as s i g n i f i c a n t a l t e r a t i o n s to l e v e l s (c) and (d) within the r e c a p i t u l a t i o n , then several more movements would be regarded as having r e c a p i t u l a t i o n s d i f f e r e n t from t h e i r expositions. (See "Codas" above, f o r a discussion of t h i s with respect to the symphonies and s t r i n g quartets.) A l t e r a t i o n s to r e c a p i t u l a t i o n s at l e v e l s (a) and (b) are com-mon: a l l works have some such changes. A l i s t of the types of r e c a p i t u l a t i o n v a r i a t i o n s follows, with some examples of each type, s t a r t i n g with a l t e r a t i o n s at lower l e v e l s . (1) Two works having almost no a l t e r a t i o n s are the Quartets K. 458 and 499. Both have s l i g h t a l t e r a t i o n s permitting the t r a n s i t i o n to remain i n the tonic. (2) Differences i n orchestrating the same material are sometimes found. This involves e i t h e r giving the material to a d i f f e r e n t instrument, possibly i n a new r e g i s t e r , or a l t e r i n g the doubling of or accompaniment to a melody. Assigning material to d i f f e r e n t instruments i s a feature of quartet s t y l e , es-p e c i a l l y i n the three St r i n g Quartets (Prussian), K. 575, 589, and 590. Some-times t h i s can have a s i g n i f i c a n t e f f e c t . For example, i n K. 575, the c l o s i n g section i n the exposition begins with a 2-bar group i n v i o l i n II answered by a 2-bar group i n v i o l i n I; t h i s i s repeated an octave lower i n the following four 92 bars: -___b b T T 3 (rest) . II a_ (rest) In the r e c a p i t u l a t i o n c l o s i n g section t h i s i s changed so that i m i t a t i o n i s sug-ested. New accompaniments are also added i n v i o l i n I I : b a , I > (rest) II xxxxxxxxxx,xxxxxxxxxx (rest) Va (rest) S i g n i f i c a n t l y , group a_ i n the diagrams above i s a diminution of the opening mo-t i v e of the main theme of t h i s movement. (3) The a d d i t i o n of embellishments and other surface ornamentation and v a r i a t i o n i s sometimes found. For example, i n the Quartet K. 387 the endings of the f i r s t two segments of the main theme are chromatically embellished i n the r e c a p i t u l a t i o n . (4) The few minor mode works usually have a greater v a r i a t i o n to the r e c a p i t u l a t i o n than do major mode works. (A prominent exception to t h i s i s the Symphony no. 40, where the exposition and r e c a p i t u l a t i o n are very s i m i l a r . ) The second theme of the Quartet K. 421 has many changes i n i t s melody (mm. 25—32, 94-102); the c l o s i n g section of t h i s work has even more such a l t e r a t i o n s (mm. 32-40, 102-111). (5) The t r a n s i t i o n i s the one section that i s frequently a l t e r e d i n some respect. Variations range from no a l t e r a t i o n s beyond t r a n s p o s i t i o n to the tonic (e.g., Quartet K. 499), to a nearly t o t a l r e writing of the t r a n s i t i o n (e.g., Symphony no. 41, where, although the t r a n s i t i o n ends with the same material, the f i r s t part, from m. 212, i s harmonically very d i f f e r e n t ; and Quartet K. 421, where the t r a n s i t i o n i s rewritten-—mm. 14-24 as compared to 83-94). A l t e r a t i o n s 93 i n v o l v i n g i n t e g r a t i o n of the t r a n s i t i o n with other small sections are noted below. (6) A l t e r a t i o n s i n lengths of small sections are sometimes seen. An i n t e r e s t i n g one that i s perhaps not as t r i v i a l as i t f i r s t appears—because i t a l t e r s the metric p o s i t i o n of the e n t i r e subsequent small s e c t i o n — i s i n the t r a n s i t i o n of the Quartet K. 421. As noted i n the preceding paragraph, t h i s t r a n s i t i o n i s greatly rewritten: part of the a l t e r a t i o n involves a half-bar expansion i n length from ten-and-a-half to eleven bars. This s h i f t s the f o l -lowing theme so that i t s melody begins on the t h i r d beat (of m. 94) instead of on the downbeat (of m. 25). Another i n t e r e s t i n g movement that includes l e v e l - ( c ) r e c a p i t u l a t i o n expansions i s i n the Symphony no. 40: the t r a n s i t i o n , subordinate theme, and c l o s i n g section a l l feature expansions with respect to t h e i r exposition forms. (7) A s p e c i a l case of expansion or contraction as development may occur towards the end of the main theme, and sometimes includes part or a l l of the . . 45 t r a n s i t i o n . An i l l u s t r a t i o n has been seen i n the V i o l i n Sonata K. 454, ex-ample 1, where the second h a l f of the 16-bar main theme i s replaced i n the r e -c a p i t u l a t i o n by a sequential development i n mm. 98-111, and by a dominant pedal i n mm. 111—114. In the Symphony no. 34, the 20-bar main theme and 20-bar trans-i t i o n are replaced i n the r e c a p i t u l a t i o n by a s i n g l e 19-bar small section i n mm. 158-176 that at f i r s t resembles the main theme, then incorporates some sequential development, and ends with a dominant pedal, a transposition of the end of the t r a n s i t i o n (which had ended on a dominant of the dominant pedal); some of the missing material i s r e c a p i t u l a t e d l a t e r i n the r e c a p i t u l a t i o n . Sim-i l a r contractions of the main theme and t r a n s i t i o n into one small section are seen i n the Symphony no. 38' and the Quartet K. 465. This procedure i s obviously 94 a r a d i c a l one, i n that i t gives the r e c a p i t u l a t i o n a d i f f e r e n t form at l e v e l s (c) and (d) ; there are often other factors that should be taken into account, however, such as the subsequent r e c a p i t u l a t i o n of missing material i n the Symphony no. 34, and the p r i o r r e c a p i t u l a t i o n of missing material i n the Sym-phony no. 38. (This l a t t e r work, the Prague Symphony, i s a rare example of a movement i n which the tonal and melodic r e c a p i t u l a t i o n processes are separated. The tonic key i s reached almost i n c i d e n t a l l y i n m. 177, with codetta material repeated from the main theme and t r a n s i t i o n being used. The tonic key and expo-s i t i o n material are maintained through the r e s t of the development and the [new] r e t r a n s i t i o n prepares f o r the main theme r e c a p i t u l a t i o n i n m. 208.) (8) Some re c a p i t u l a t i o n s begin with the second theme, the main theme following l a t e r . This i s also a r a d i c a l a l t e r a t i o n of level-(d) form compared • • 4 6 to the exposition. (9) A few r e c a p i t u l a t i o n s are s i g n i f i c a n t l y a l t e r e d at l e v e l s (c) and (d) throughout. That i s , they have whole small sections omitted, added, or rear-ranged to d i f f e r e n t places i n the r e c a p i t u l a t i o n s r e l a t i v e to the expositions. Most of the symphonies, and i n p a r t i c u l a r the s t r i n g quartets, do not involve t h i s type of a l t e r a t i o n . The Symphony no. 31, however, does have many such a l t e r a t i o n s , too many to c i t e here. Some other examples may be c i t e d . (a) The Serenade K. 375 has a new theme i n the r e c a p i t u l a t i o n i n mm. 151-171. (b) In the F l u t e Quartet K. 285 the main theme i s shortened, the t r a n s i t i o n and subo'r-diate theme are combined to form one small section, and the c l o s i n g section i s lengthened to include some of the missing subordinate theme. (c) In the Piano Sonata K. 576 the exposition has the unusual form MT-TR1-TR2-ST. In the recap-i t u l a t i o n the main theme and the f i r s t t r a n s i t i o n are combined into one small section that also has the features of a secondary development. The second theme 95 follows, with the second t r a n s i t i o n concluding the r e c a p i t u l a t i o n . However, because the second t r a n s i t i o n i s now i n the tonic, because of i t s nature, be-cause of i t s new ending, and because of i t s new p o s i t i o n , i t now has a new function: that of subordinate theme codetta and c l o s i n g section. In short, 47 the r e c a p i t u l a t i o n here normalizes the form of an unusual exposition. Level (e): Complete Movements The e n t i r e movement i s always comprised of the three large s e c t i o n s — exposition, development, and r e c a p i t u l a t i o n — a n d the outer two of these often have the same form, with the exception of the necessary t r a n s p o s i t i o n of the second key material to the t o n i c . Although I believe most of Mozart's sonata-form movements may be heard as t r i p a r t i t e at t h i s l e v e l , some may be analysed . 4 8 as b i p a r t i t e . Most movements have the r e p e t i t i o n pattern |] E x p o s i t i o n : |J Development-Recapitulation: || . The r a t i o of lengths of the three large sections i s on aver-age about 2:1:2. Absolute lengths i n common time a l l e g r o f o r the sections aver-age about 80, 40, and 85 bars r e s p e c t i v e l y , without r e p e t i t i o n s taken into ac-- 4 9 count. The r e l a t i v e importance of the exposition (and r e c a p i t u l a t i o n ) as compared with the development i s c l e a r l y implied by i t s greater length, by the greater v a r i e t y i n i t s length, and by the greater v a r i e t y of i t s l e v e l - ( c ) sections. O v e r a l l , then, the exposition sets up a tonal dissonance, continued by the development, and resolved i n the r e c a p i t u l a t i o n . 96 3 The Closing Model Each of chapters 3, 4, 5, and 6 deals with one of the four types of c l o s i n g sections discussed i n connection with l e v e l (c) of chapter 2. A sim-i l a r procedure w i l l be followed i n each of these four chapters; that i s , a con-s i d e r a t i o n of a l l movements which use a p a r t i c u l a r type of c l o s i n g section, with some analysed i n depth. Only by analysing a large number of works w i l l the wide v a r i a t i o n i n use of each type become apparent. Some movements w i l l appear i n more than one chapter because some c l o s i n g sections may be analysed i n more than one way: such discussion of a l t e r n a t i v e approaches to a given movement should ill u m i n a t e both the music and the a n a l y t i c a l strategies I am employing. T y p i c a l l y , a d e t a i l e d analysis of a movement w i l l begin with a consideration of the form of the exposition, continue with an examination of the c l o s i n g section, and conclude with a comparison of the r e c a p i t u l a t i o n forms of these areas, including an analysis of any coda. Works which are not analysed i n d e t a i l w i l l be commented on b r i e f l y , i f only to ind i c a t e the type of c l o s i n g section each has. The c l o s i n g model i s the most frequently seen type of c l o s i n g section: about s i x t y percent of a l l works can be analysed with t h i s model. In addition, aspects of the c l o s i n g model are found i n the other f o r t y percent of movements, as w i l l be seen i n l a t e r chapters. The model was outlined i n chapter 1, pp. 7-8, 97 and i n chapter 2, pp. 74-75. For purposes of discussion and analysis i n each chapter, I w i l l usually group the works according to genre, following the order i n the w o r k - l i s t i n table 1, pp. 4-6. Symphony no. 36. The c l o s i n g sections of s i x symphonies may be analysed with the c l o s i n g model (nos. 31, 32, 33, 34, 36, and 40). The c l o s i n g section nearest the model i s that of the Symphony i n C Major ( L i n z ) , no. 36, a work I w i l l consider i n d e t a i l here. The form of the exposition of the f i r s t movement, summarized i n diagram 9, corresponds to the normal exposition model a f t e r the introduction. Diagram 9 Symphony no . 36: Exposition Intro. ||: MT TR ST CS Retr.: Measures: 1-19 20-41 42-72 72-87 88-119 120-122 Timespans: 19 bars (10 + 12) 30 (8 + 8) (8 + 16 + 8) 4 Harmony: I - V I-V I-I I - I/V vi/V-I/V I/V I/V-V Period Unique theme Closing model The introduction . i s a normal one. The main theme i s based on the period model, with some expansions. Measure 42 i s at once the end of the theme's f i n a l phrase and the beginning of the f i r s t group and timespan of the t r a n s i t i o n . Like many t r a n s i t i o n s , t h i s one begins as i f i t were a main theme codetta, but r a p i d l y leaves the tonic area and introduces new motives. This t r a n s i t i o n i s somewhat unusual, however, i n that i t i s longer and more i n t e r e s t i n g than many t r a n s i t i o n s , and ends with a perfect authentic cadence—rather than a h a l f cad-98 e n c e — i n the dominant key. That the t r a n s i t i o n i s a substantial one, modulating convincingly to the dominant and ending with so strong a cadence, may be ex-plained i n part by an unusual feature of the subordinate theme, which begins i n m. 72 i n the r e l a t i v e minor of G major. I t would not be possible for this theme to begin i n this way i f the new key had not been previously well-estab-lished. The subordinate theme i s neither a period nor a sentence, but i s based on a (1 x 4) + (4 x 1) pattern, here repeated with some variations.''" There are no expansions or codettas i n t h i s theme, although the r e p e t i t i o n may be considered a substitute for such material. In p a r t i c u l a r , there i s no expanded cadential progression, although the harmonies and bass l i n e for the ECP are present i n the v a r i a t i o n , i n mm. 84-87. The v a r i a t i o n has a stronger cadence than the o r i g i n a l — a c h i e v e d by increasing the dynamic l e v e l , adding instruments, and using a 1^ (bass ^) i n m. 84 (not present i n m. 76) as part of the unex-panded cadential progression—and thereby closes the subordinate theme area. The 32-bar closing section—one of the longest i n these w o r k s — f u l f i l l s the expansion function missing from the subordinate theme: there are expansions i n the b_^  and groups. A second v a r i a t i o n i n the use of the closing model here i s that the bb^ " subsection i s longer than the aa''" subsection. A t h i r d v a r i a t i o n , necessitated by the length of t h i s closing section, i s that the material i s more dynamic than that found i n shorter closing sections. For example, the surface harmony i s considerably more interesting than the mere tonic-dominant interchange ch a r a c t e r i s t i c of the closing section i n example 1. Nevertheless, a l l s i x groups here do end on the tonic, and the harmony remains ess e n t i a l l y diatonic. The timespan and group structure i s summarized i n dia-gram 10. 99 Diagram 10 \ Symphony no. 36: Exposition Closing Section Measures: Groups: Timespans: Bars i n timespans: 86 87 88 '89 90 91 92 93 Measures: Groups: Timespans: Bars i n timespans: 94 95 96 97 98 99 100 101 bL " l 10 1 Measures: Groups: Timespans: Bars i n timespans: 102 103 104 105 106 107 108 109 2 3 4 5 5a 5b 5c 5d Measures: Groups: Timespans: Bars i n timespans: 110 111 _c_ 112 113 114 1 c 115 116 117 118 119 P 6 3 1 2 — ~> 3 1 2 3 3a 3b ECP-100 The aa p a i r are t y p i c a l of the c l o s i n g model. Each group begins d i r -e c t l y a f t e r the preceding cadence, each i s four bars long, each i s strongly c a d e n t i a l , and there i s not a great deal of v a r i a t i o n from £ to a^, except f o r the weaker cadence of aS whereas a^ begins a f t e r the cadence of a, the b group begins simultaneously with i t s timespan on the f i r s t beat of m. 95, thereby weakening the cadence of a^ _. The b_^  group begins i n the same way as b_. Whereas IJ i s subdivided as (3 + 3), B^ i s expanded to (3 + 7). As shown i n diagram 10, i t i s the f i f t h bar of which i s expanded to a t o t a l of f i v e bars, thus making B^ four bars longer than B_. This cadence i s s l i g h t l y weakened by the f o r t e and brass entry on the tonic chord (beat one of m. I l l ) , which s i g n a l a new beginning. An uninterrupted cadence occurs only at the end of t h i s c l o s -ing section, i n mm. 116-119. The cc^ groups return to the same type of r e l a t i o n s h i p with t h e i r time-spans as found i n the aa"*" p a i r . The cadences of the four groups are also sim-i l a r (except f o r the i n t e r r r u p t i o n of a^) . The cc'*" p a i r d i f f e r from the model i n three ways: the tonic pedal i s not used throughout, t h i s subsection i s long-er than usual, and there i s an extension i n the group. The s i g n i f i c a n t var-i a t i o n i n c^ i s the novel use of an echo i n the winds, i n m. 117, and then a repeat with a l l instruments i n m. 118. This adds the two extra b a r s — 3 a and 3b-—grouping t h i s p a i r as (3 + 5). Measures 116-119 include a type of ECP. Diagram 11 l i s t s the timespans of t h i s c l o s i n g section as written, a hypothetical c l o s i n g section s i m i l a r to t h i s one without expansions i n b^ and c \ and the c l o s i n g model. In s p i t e of the expansion of the BJB p a i r r e l a t i v e to the model, the r a t i o of BB_ to C£ i s the same here as i n the model, that i s , 2:1. Furthermore, the r a t i o of B_ to B_^  i s the same as of £ to C_\ that i s , 3:5. These observa-101 Diagram 11 Symphony no. 36: Expansion of Closing Section A A 1 B B 1 Closing model: (4 + 4) + (2 + 2) + (1 + 1) (No. 36) without expansions: (4 + 4) + (6 + 6) + (3 + 3) Symphony no. 36: (4 + 4) + (6 + 10) + (3 + 5) tions suggest that expansions are not merely l o c a l events but are controlled by some larger sense of balance. Why does t h i s closing section have a larger second subsection? The ma-j o r i t y of closing sections which have expansion of the closing model use a nor-mal length AA p a i r — ( 4 + 4)—-and then expand subsequent groups. This suggests that shorter r e p e t i t i v e units signal the start of the closing section, and that s i g n i f i c a n t expansion can take place only after t h i s s i g n a l l i n g of the closing section beginning. The expansion of EB^ here i s then balanced by CC"*" being i n the same r a t i o to BB^ as i n the model. That this closing section i s unusually long may be partly due to the fact that the subordinate theme i s short and i s not as tonally unified as i s normal: i t o s c i l l a t e s between vi/V and V. Since one of the functions of the closing section i s the continuation of the key of the subordinate theme, this closing section, by i t s very length, balances the tonal i n s t a b i l i t y of the subordinate theme. A short r e t r a n s i t i o n leads f i r s t to the repeat of the exposition and then to the development, i n mm. 123-162. The form of the recapitulation i s s i m i l a r to that of the exposition. The main theme i s exactly the same, the t r a n s i t i o n i s altered s l i g h t l y to end on the tonic, the subordinate theme has a few surface a l t e r a t i o n s , and the closing section i s the same except for a 102 few d e t a i l s , mainly i n mm. 241-251. The coda, i n mm. 265-287, begins l i k e the r e t r a n s i t i o n , i n mm. 119-122, and continues to use the r e t r a n s i t i o n motive i n a manner s i m i l a r to i t s use i n the development, i n mm. 128-137. In the coda, however, t h i s r e t r a n s i t i o n motive has cadences added to i t , g i v i ng i t a c l o s u r a l rather than a t r a n s i t i o n a l function, f o r example, i n mm. 270-274. The opening ten bars form a period, followed by a repeated 2-bar codetta i n mm. 275-278. See diagram 12. The f i r s t timespan begins i n m. 265 according to the usual c r i t e r i a of tonic a r r i v a l at the end of a cadence and because a new group begins there. In a d dition, t h i s passage i s s i m i l a r to that at the end of the exposition, where the r e t r a n s i t i o n timespan begins i n m. 119. The f i r s t group, i n mm. 265-269, may be subdivided as ( 2 + 2 + 1 ) i n terms of both harmony and grouplets. The second group i s subdivided e i t h e r as ( 2 + 2 + 1 ) , i n that i t . p a r a l l e l s the grouplet structure of the f i r s t group, or as (3 + 1 + 1) on har-monic grounds. A more r a d i c a l d i v i s i o n of these ten bars according to harmony would be ([2 + 2] + 4 + 1 + 1); that i s , the harmony i s I - V^/IV - i i 6 - V - I, an unusual design f o r a period. However, the thematic p a r a l l e l i s m overrides t h i s : hence the d i v i s i o n as (5 + 5) i n diagram 12. A d i f f i c u l t y with t h i s i n t e r p r e t a t i o n of timespans as (5 + 5) i s that the succeeding timespan must begin i n m. 275, which means that the b_ group now begins with an upbeat i n m. 274. In other words, the repeated 2-bar cod-ettas i n mm. 274-278 ought to r e l a t e to t h e i r corresponding timespans i n the same way as the two 5-bar groups do, because a l l four groups begin with the same fi g u r e and with tonic harmony a r r i v a l . That i s , p a r a l l e l i s m of treatment of the same material together with a p p l i c a t i o n of the same a n a l y t i c c r i t e r i a ought to r e s u l t i n a l l four groups being analysed the same way as regards time-103 Diagram 12 Symphony no. 36: Coda Measures: 265 275 279 Timespans: (5 + 5) + (2 + 2) + (2 + [2 + 2]) + (1 + 1 + 1) Groups: a b b^ " c c^ " d d span/group r e l a t i o n s h i p : e i t h e r a l l groups begin i n the f i r s t bar of t h e i r r e s -pective timespans or a l l begin with an upbeat f i g u r e leading into the f i r s t bar of t h e i r respective timespans. . However, t h i s view would mean that the f i r s t two groups would have (5 + 4) timespans, thus reducing t h e i r thematic p a r a l l e l i s m . In add i t i o n , m. 275 sounds l i k e a be g i n n i n g — o f a 2-bar timespan—due to the entrance of so many instruments. A furth e r f a c t o r r e i n f o r c i n g timespan beginnings from m. 275 i s that 2-bar timespans continue from here to the end of the coda. If m. 274 contains material functioning as an anacrusis to m. 275 and m. 276 s i m i l a r l y to m. 277, then m. 278 should function the same way to m. 279. However, m. 279 and m. 280 repeat m. 278 with octave doublings, e t c . , making the material i n mm. 278-280 an extended upbeat to the next timespan p a i r , mm. 281-284. In other words, mm. 281-284 form the basic timespan and group material, with an extended upbeat. This supports the i n t e r p r e t a t i o n of the two b_ groups as having upbeats; that i s , the same material used as upbeats to the b groups i s used i n extended form as an upbeat to the c^  group p a i r . Aspects of the c l o s i n g model can be seen i n th i s coda, namely i n the use of repeating groups and progressively shorter timespans. Over the course of the coda the groups become progressively more ca d e n t i a l , with the retrans-i t i o n motive playing less and less of a r o l e , u n t i l i t i s f i n a l l y eliminated 104 i n m. 281. Despite some motivic s i m i l a r i t i e s with the development section, t h i s coda does not have a developmental function: rather, i t s function i s p r i m a r i l y c l o s u r a l , as generated by the c l o s i n g model. The need f o r a coda i n t h i s move-ment may be explained by the unusually a c t i v e nature of the c l o s i n g section, as noted above. I t would appear that, i n general, the longer the c l o s i n g sec-t i o n , the less the need f o r a coda. However, the reverse i s true here: the unusually long c l o s i n g section can be sustained only by dynamic mat e r i a l , which i n turn weakens the c l o s u r a l nature of the section, and a coda i s therefore demanded. By i t s exceptional character, t h i s c l o s i n g section i l l u s t r a t e s why most c l o s i n g sections are shorter than t h i s one: ten to twenty bars i s the norm f o r c l o s i n g sections because that range of lengths i s not merely s u f f i -c i e n t , but i s indeed optimal, f o r an e x c l u s i v e l y c l o s u r a l section. The e f f e c t s of lengthening the c l o s i n g section are seen i n t h i s symphony; the e f f e c t s of shortening the c l o s i n g section w i l l he, seen l a t e r , p r i m a r i l y i n chapter 4. Symphony no. 40. The other symphony using the c l o s i n g model with only s l i g h t v a r i a t i o n s i s the Symphony i n G Minor, no. 40. In the discussion of l e v e l (d) i n chapter 2 I noted that the exposition of t h i s movement i s a nor-mative one. The main theme—a sentence—ends on the dominant i n m. 20. The t r a n s i t i o n begins as i f part of the theme but quickly modulates to the r e l a t i v e major and eliminates the theme's motives. The t r a n s i t i o n also ends on a dom-imant, t h i s time of the secondary key. The subordinate theme i s comprised of an 8-bar period i n mm. 44-51, i t s v a r i a t i o n i n mm. 52-66, and a codetta to the theme i n mm. 66-72. The codetta i s motivated by the absence of $ from the bass of the extended cadential progression, and, indeed, from that of the e n t i r e 105 second phrase of the v a r i a t i o n i n mm. 56-66. The codetta features t h i s missing D prominently i n m. 66, and also i n m. 69. I t also forms an e f f e c t i v e bridge between the theme and the c l o s i n g section. However, the codetta i s p r i m a r i l y attached to the theme and not to the c l o s i n g section because i t completes the expanded cadential progression and because i t uses motives from the theme (e.g., the chromatic ascent motive i n mm. 66-68 i s an inversion of that i n mm. 56—58). An unusual feature of t h i s codetta i s that i t weakens the cadence ending i n m. 66 (by s t a r t i n g so quickly and abruptly i n m. 66) and does not i t s e l f end with a strong cadence. As noted above, the two previous small sections also end with weaker cadences (both h a l f cadences). A major function of the c l o s i n g section, then, i s to supply unequivocal perfect authentic cadences, i n I I I i n the exposition, i n the tonic i n the r e c a p i t u l a t i o n . In f a c t , caden-t i a l material does form a large part of t h i s c l o s i n g section. The c l o s i n g model i s varied here i n that the f i r s t two timespans of the model—AA—are each expanded to eight bars, the second two groups are expanded (unequally), and the l a s t two groups of the model are reduced to one long group. See diagram 13. Despite the odd-numbered timespans, then, the model i s b a s i c a l l y doubled i n length from fourteen to twenty-eight bars i n t h i s c l o s i n g section. The f i r s t group i s e s s e n t i a l l y repeated (mm. 72-87), the t h i r d i s expanded by one bar (mm. 88-94), and the f i f t h i s made up of a 1-bar cadential grouplet heard three times and then compressed.to a half-bar and repeated (mm. 95-98). The f i r s t two groups also feature i n t e r n a l r e p e t i t i o n , that i s , pf t h e i r i n i t i a l 2-bar grouplets (mm. 72-75, 80-83). Two i n t e r e s t i n g features of t h i s c l o s i n g section deserve some comment. F i r s t , the 3 missing from the subordinate theme i s s t i l l being compensated f o r 106 Diagram 13 Symphony no. 40: Exposition Closing Section Measures: 72 80 88 91 95 99 No. 40: ([2 + 2 + 4] + [2 + 2 + 4]) + (3 + 4) + (3 + 1) 2 (Model x 2): ( 8 + 8 ) + (4 + 4) + (2 + 2) Model: ( 4 + 4 ) + (2 + 2) + (1 + 1) Retr. i n the c l o s i n g section: the f i r s t four groups of the c l o s i n g section a l l feature prominent use of D i n t h e i r bass l i n e s . Second, the opening main theme motive i s used i n the f i r s t two groups, although i n a new c l o s u r a l context. Closure i s enhanced by the return to the opening motive, i n much the same way as closure i s generated by the return of the opening material i n a small or large ternary form. In t h i s movement, the sense of return i s coupled with a transformation of the. opening motive into a c l o s i n g one. Several other movements have a s i m i l a r use of main theme motives, as discussed below. A 2-bar r e t r a n s i t i o n leads f i r s t to the repeat of the exposition and then to the development i n mm. 101-163. Aside from the e f f e c t i v e overlapping of the end of the development with the s t a r t of the r e c a p i t u l a t i o n , the main theme i s repeated exactly i n mm. 164-183. The t r a n s i t i o n , i n mm. 183-226, i s doubled i n length. The changes take the form of a development of the trans-i t i o n m o t i v e s — t h a t i s , a secondary development—and a r e d i r e c t i o n of the harmony to end on V / i rather than V/III. As noted i n chapter 2, t h i s movement i s exceptional among minor mode works i n that the t r a n s p o s i t i o n and change of mode of the second key material do not prompt Mozart to rewrite t h i s material. The second theme, i n mm. 227-254, i s not changed except f o r the transposition, the d i f f e r e n t p o s i t i o n of the pedal i n mm. 241-245 (now 3 instead of 4, as i n 107 mm. 58-62, thereby strengthening the ECP), and the expansion i n mm. 246-254. The codetta to the theme, i n mm. 254-260, i s not a l t e r e d . The c l o s i n g section, i n mm. 260-299, i s e s s e n t i a l l y very s i m i l a r to i t s exposition form except for an extension. An i n t e r e s t i n g d e t a i l i s the change i n t o n i c i z a t i o n at the end of the f i r s t two groups, i n mm. 265-266 and 273-274: i n the exposition, mm. 77-78 and 85-86, v i / H I was t o n i c i z e d , thereby providing 3 i n the bass as part of the ECP as noted above, as well as allowing the E-flat-D motive to be used. If t h i s were transposed to G minor i n the re c a p i -t u l a t i o n , the semitone motive would be changed to a whole t o n e — C - B - f l a t . Mozart therefore rewrote t h i s passage, t o n i c i z i n g i v / i , which permits the semi-tone A - f l a t - G to be used. This, however, removes 3 from the bass voice of mm. 265 and 273; on the other hand,. 3 was used i n the subordinate theme p e d a l — i n mm. 241-245—where i t was not i n the corresponding place i n the exposition, as noted i n the previous paragraph. These f i r s t two groups i n the c l o s i n g section are otherwise l i t t l e changed. The next two timespans, previously ( 3 + 4 ) , are expanded to ( 3 + 8 ) , i n mm. 276-286. Diagram 14 includes a sketch of the second of each of these two groups as they appear i n the exposition and r e c a p i t u l a t i o n . To a c e r t a i n extent, the added material i n the r e c a p i t u l a t i o n i s an expansion of that which i t replaces i n the exposition. The most obvious expanded element i s the second hal f of m. 94, which becomes mm. 285-286: both harmony and melody have been expanded to two bars. The r e l a t i o n of mm. 281-284 to mm. 93-94(2) i s not so ob-vious; however, i t i s possible to hear an inner voice i n mm. 281-283—indicated i n diagram 14 within brackets—based on the melody of mm. 93(2)-94(l) trans-posed to G minor. 108 Diagram 14 Symphony no. 40: P r i n c i p a l Voices i n mm. 91-95 and 279-287 ^—r-T! " \ 1 T ,V T i II 13 r f IV ^ ^ fFfff J --i=n -4 -Q. •J— —« • M i JD fftrr —m—\- ~ T t ~ S " f E 0 0 =2= 1 — - - —*= 4 t=t= 7^--1—• The end of t h i s expansion overlaps with a new group—but not a new time-s p a n — i n mm. 287-293, based on i m i t a t i o n of the main theme motive over a tonic pedal. The use of a tonic pedal and the subdominant t o n i c i z a t i o n i n mm. 287-289 (and i n the f i r s t two groups i n mm. 265-266 and 273-274) are features of c l o s i n g sections that strengthen closure here because they were absent from the expo-s i t i o n c l o s i n g section. The f i n a l group, i n mm. 293-299, i s unchanged except f o r the addi t i o n of two bars of tonic chords. Three of the four small sections of the r e c a p i t u l a t i o n feature expansions r e l a t i v e to t h e i r exposition forms, as noted i n chapter 2. In the case of the c l o s i n g section, the expansion/extension i s p a r t i a l l y prompted by the addition 109 of previously missing normative features. The resultant longer c l o s i n g section may be termed a c l o s i n g section extension, although the new material i n mm. 285-292 gives i t some of the character of a coda. One f i n a l point should be mentioned regarding t h i s c l o s i n g section. In discussing the c l o s i n g section of the previous work—the Linz Symphony—I noted that, at thirty-two bars, i t was unusually long, that t h i s length resulted i n changes to the nature of the c l o s i n g section material, and that a coda was thereby demanded. At twenty-eight bars, the exposition form of the c l o s i n g section i n the Symphony no. 40 i s nearly as long as that of the L i n z . This length i s p a r t i a l l y compensated f o r by the f a s t e r tempo (molto a l l e g r o i n no. 40, a l l e g r o i n no. 36), and by the close adherence to the c l o s i n g model (more so than i n the case of no. 36). The material of the c l o s i n g section i n no. 40 i s somewhat more ac t i v e than that of the average c l o s i n g section, a l -though less active than that of the c l o s i n g section i n the Linz Symphony. The c l o s i n g section of no. 40 i s more normative—that i s , more c l o s u r a l — than i s that of no. 36, although s t i l l longer than usual. One more reason f o r the addi t i o n of standard c l o s u r a l material to the r e c a p i t u l a t i o n i s to compensate f o r any weakness i n the c l o s u r a l function of the c l o s i n g section. Symphony no. 31. Four other symphonies may be analysed with the c l o s i n g model, although a l l employ extreme variants of i t , and two may be analysed i n other categories. I w i l l b r i e f l y discuss each, p r i m a r i l y to explain the nature of the v a r i a t i o n i n use of the c l o s i n g model. The Symphony i n D Major ( P a r i s ) , no. 31, has a very long exposition (119 bars) brought about mainly by a long, loosely organized subordinate theme area. The main theme i s a sentence v a r i a n t , i n mm. 1-26, with a codetta i n mm. 26-32. The t r a n s i t i o n i s r e l a t i v e l y short 110 and weak, i n mm. 32-51. The subordinate theme area i s composed of two unique themes connected by a contrasting area. The f i r s t of t h e s e — i n mm. 5 2 - 6 5 — i s composed of a (1 + 4 + 2) phrase, repeated. Measures 66-73 function as a har-monic contrast by introducing a pedal on the dominant (of A major), and as a melodic contrast by introducing new motives. The second theme within the sub-ordinate theme a r e a — i n mm. 74-104—resembles the small ternary form model: mm. 74-83 use the opening main theme "rocket" motive i n i m i t a t i o n , ending with an interrupted cadence; mm. 84-92 function as a contrast, and there i s a return to the i m i t a t i o n idea i n mm. 93-104. This l a t t e r subsection i s extended two bars and so.has some of the features of an ECP. The c l o s i n g section begins i n m. 105 with a ( 2 + 2 + 2 ) group based on the main theme codetta, repeated exactly from m. 111. In mm. 117-118 a 1-bar grouplet i s repeated leading to a f i n a l statement of the opening main theme motive, the f i r s t bar of which—119—concludes the c l o s i n g section and overlaps with the s t a r t of the development. The c l o s i n g model applies only i n that there i s one p a i r of repeated g r o u p s — a a — a n d not three. The remainder of the c l o s i n g section, i n mm. 117-119, i s not based on the c l o s i n g model. Several factors connect t h i s c l o s i n g section with the preceding small section, despite the already great length of the subordinate theme area. (1) The employment of 2-bar grouplets and ( 2 + 2 + 2 ) groups, begun i n m. 74, continues almost to the end of the c l o s i n g section. (2) The small segments of mm. 74-104 are more l i k e grouplets than motives, despite the f a c t that a var-i a t i o n of the opening main theme motive i s used; therefore, t h i s section i s connected to the c l o s i n g section because grouplets are used through both sec-tio n s . The c l o s i n g section does, however, include a s i m p l i f i c a t i o n of the texture by removing the i m i t a t i o n c h a r a c t e r i s t i c of the previous section. I l l (3) In mm. 228-295 of the r e c a p i t u l a t i o n these two sections are integrated and new material i s added. Symphony no. 32. In the Symphony i n G Major, no. 32, the main theme— a p e r i o d — i s i n mm. 1-12, the t r a n s i t i o n i n mm. 12-32, the subordinate theme— also a p e r i o d — i n mm. 33-49, and the c l o s i n g section i n mm. 49-69. See diagram 15. The ji subsection i s unusual i n i t s v a r i a t i o n four times of one motive i n i m i t a t i o n , over a pedal, and with a crescendo. The b_ subsection d i f f e r s from the model i n i t s doubled length and more complex structure. The c_ grouplet i s based on the o v e r a l l structure of the a subsection, that i s , a r i s i n g scale. new tempo, i n a new meter, and with new material. In t h i s sense i t i s not a r e c a p i t u l a t i o n , but a contrast, although i n the tonic key (mm. 110-207). The return to the f i r s t tempo and meter i s i n m. 208, with what i s e s s e n t i a l l y t r a n s i t i o n m a t e r i a l , ending i n m. 219 on the dominant. The subordinate theme returns i n the tonic i n mm. 220-236, and the c l o s i n g section i n mm. 236-256, with few changes. A coda i n mm. 256-274 i s based on some of the missing main theme and t r a n s i t i o n material, now i n a c l o s u r a l context. Diagram 15 Symphony no. 32: Exposition Closing Section Measures: 49 57 65 The r e c a p i t u l a t i o n of t h i s movement i s unusual i n that i t begins i n a Timespans: ( 2 x 4 ) + (2 + 2) + (2 + 2) + (2 + 2) + 1 Grouplets: 1 2 3 a a a a c c 112 Symphony no. 33. In the Symphony i n B - f l a t Major, no. 33, the main theme—a sentence v a r i a n t — i s i n mm. 1-25, the t r a n s i t i o n i n mm. 25-54, the subordinate theme—a long, unique s t r u c t u r e — i n mm. 55-96, and the c l o s i n g section i n mm. 96-138. The subordinate theme ends with a s u b s t a n t i a l expanded 3 4 5 cadential progression i n mm. 89-96. See diagram 16. Note that a , a , and a 1 2 are variants by i n v e r t i b l e counterpoint of a, a_, and a_ r e s p e c t i v e l y , or, o v e r a l l , mm. 108-128 are variants with extensions of mm. 96-107. In other words, these two subsections can be seen as an expansion of the f i r s t two g r o u p s — a a — o f the c l o s i n g model. The f i n a l subsection, i n mm. 129-138, more c l o s e l y resembles the end of the c l o s i n g model—c£—with extensions using the tonic chord. In the r e c a p i t u l a t i o n there are extensions of several groups (mm. 323-324, 336-337, 342-357, and 364-365). Diagram 16 Symphony no. 33: Exposition Closing Section Measures: 96 108 Timespans: ( t l x 4] + [2 x 2] + 4) + ([1 x 2] + [2 x 2] + 3 + Grouplets: a a a a 1 1 2 a a a 3 3 a a 4 4 5 a a a Measures: 117 129 Timespans: [ 2 x 3 ] + 2 + [2 x 2]) + ([2 x 2] + [ l x l ] + 4) Grouplets: b b 1 b 2 c d d 1 e e 1 1 ' e e 113 Symphony no. 34. The f i n a l symphony that may be analysed with the cl o s i n g model i s that i n C Major, no. 34. The main theme—a unique s t r u c t u r e — i s i n mm. 1-16, with a l i n k to the t r a n s i t i o n , the l a t t e r i n mm. 20-40. The subordinate theme i s composed of an 8-bar unique theme i n mm. 40-48, varied with an e x t e n s i o n — i n c l u d i n g an E C P — i n mm. 48-64. See diagram 17. This c l o s i n g section i s s i m i l a r to that of the Symphony no. 32 i n i t s f i r s t two subsections, that i s i n the use of a 2-bar grouplet i n i m i t a t i o n over a tonic pedal with a crescendo i n mm. 64-74, and i n the use of a repeated (2 + 2) pat-tern i n mm. 74-82. The t h i r d subsection begins with a 6-bar cadential group i n mm. 82-86, vari e d with a long extension, and with a more su b s t a n t i a l ECP than was i n the subordinate theme i n mm. 86-104. The f i n a l subsection, i n mm. 104-112, more c l o s e l y resembles the end of the model, as i n the Symphony no. 33. In the r e c a p i t u l a t i o n the main theme i s al t e r e d , shortened, and ends on the dominant instead of the tonic (mm. 158-176). This permits the subordinate theme to follow immediately, f o r the t r a n s i t i o n i s e n t i r e l y omitted. The cl o s i n g section i s also a l t e r e d s u b s t a n t i a l l y : the f i r s t — i m i t a t i v e — s u b s e c t i o n i s omitted, the c l o s i n g section beginning instead i n m. 200 with the (2 + 2) + 2 groups. The t h i r d subsection follows with only i t s f i r s t four bars, that i s , (2 x 2), i n mm. 233-236. Then the main theme returns i n i t s o r i g i n a l form i n mm. 237-249, but with a stronger cadence, and the movement concludes with sev-e r a l bars of cadential f l o u r i s h e s i n mm. 249-264. 114 Diagram 17 Symphony no. 34: Exposition Closing Section Measures: 64 74 82 104 Timespans: (2 x 5 ) + ([2 + 2] x 2) + (6 + 16) + ([2 x 2] + [1 x 4]) ^ • i «. 1 2 3 4 , ,1 , , 1 1 . .1 Grouplets: a a a a a b b b b c c d d Eine k l e i n e Nachtmusik. The Serenade i n G Maj or (Eine k l e i n e Nachtmusik), K. 525, has an exposition of only 55 bars, short enough that i t i s i n f a c t com-pri s e d of only two small sections, each having two functions, and each about the same length. The f i r s t , i n mm. 1-27, has a unique main theme, i n mm. 1-18, and a subsection that begins as a main theme codetta but t o n i c i z e s pedals, f i r s t on V, then on V/V, i n mm. 18-27. The second section, i n mm. 28-55, begins with an 8-bar period. The material s t a r t i n g i n m. 35 has some features of a sub-ordinate theme codetta, some of a c l o s i n g section, and some of a sentence. See diagram 18. The structure of the repeated 8-bar unit,, i n mm. 35-42 and 43-50, resembles the sentence model i n i t s timespans, but not i n the character of the material, which i s comprised of grouplets as opposed to motivic segments. On the other hand, some of the material i s too a c t i v e f o r a c l o s i n g section or codetta, i n p a r t i c u l a r the (1 + 1) segments. Nevertheless, the f a c t that the 8-bar unit i s repeated gives t h i s subsection a feature of the c l o s i n g model. A 5-bar cadential codetta concludes the exposition. The analysis of short movements i s often more d i f f i c u l t than that of longer ones because d i f f e r e n t functions are combined into fewer sections, and some standard features may even be absent. For example, t h i s exposition does not have an expanded cadential progression, one of the most common features of 115 Diagram 18 Eine kleine Nachtmusik: Exposition Second-Key Area Measures: 35 43 51 Timespans: ([2 x 2] + [1 + 1 + 2]) x 2 (1 x 3) + 2 Grouplets: a a b b c e second-key areas. I t i s true that the second-key area does have a c l e a r l y defined theme—the period i n mm. 28-34—but the material that follows has thematic, codetta, and closural functions, a l l i n one subsection. In the recapitulation, the main theme—in mm. 76-93—is unchanged; the t r a n s i t i o n — i n mm. 93-100—has i t s second tonicized pedal—the one on V/V— simply omitted, so that the t r a n s i t i o n now ends on V; the subordinate theme i s b a s i c a l l y unchanged, now i n the tonic, i n mm. 101-107; and the closing sec-t i o n — i n mm. 108-137—has i t s f i n a l group expanded, so that the closing section i s now more related to the closing model. See diagram 19. I t i s the addition of two new 2-bar grouplets i n p a i r s , together with other closural features such as more cadences and a tonic pedal, that substantiates use of the closing model i n the analysis of this passage. Diagram 19 Eine kleine Nachtmusik: Recapitulation F i n a l Section Measures: 124 132 Grouplets: Timespans: ([1 x 3] + [2 x 2] + 1) + (2 x 2) + 2 . . 1 j 2 1 2 . _ d d d e e f f g 116 The Serenade i n C Minor, K. 388 (example 2), has been considered i n de-t a i l i n chapter 2: pp. 72-73, 75, 83-84, 86; notes 27, 28, 31, 32, 34, and 47. C l a r i n e t Quintet. In the Quintet f o r C l a r i n e t and Strings i n A Major, K. 581,. the main theme ( i n mm. 1-19) and the t r a n s i t i o n ( i n mm. 19-41), are more strongly connected than i s usual, forming a section on a l e v e l between (c) and (d). One reason f o r t h i s strong connection i s the smooth, gradual nature of the modulation, the t r a n s i t i o n concluding on the V/V pedal i n mm. 34-41. The main theme i s a unique structure and the subordinate theme i s a sentence coupled with a v a r i a t i o n , i n mm. 42-65, a p a r t i a l expanded cadential progression ending the v a r i a t i o n . The c l o s i n g section, i n mm. 65-79, i s based on the c l o s i n g model to the extent that there i s one p a i r of r e p e t i t i v e groups, and t h i s i s followed by a sin g l e cadential group, that i s , xx^y, o v e r a l l . The A 1 element missing from the ECP—the bass tone 3 — i s used i n the xx groups i n mm. 67 and 71. The f i n a l group, i n mm. 75-79, i s based on the opening main theme motive, here used i n i m i t a t i o n . The form of the r e c a p i t u l a t i o n i s s i m i l a r to that of the exposition, although many d e t a i l s on l e v e l s (a) and (b) are changed. Parts of the two themes are omitted and the c l o s i n g section, i n mm. 169-197, i s extended. The extension comes i n the second of the repeated groups; see diagram 20. In other words, the grouplet that was expanded i n the second group, that i s , b_ to b\. i s the subject of even greater expansion i n the r e c a p i t u l a t i o n . This e f f e c t i s seen i n some other c l o s i n g sections. The expansion includes a much longer ECP, i n mm. 185-193. 117 Diagram 20 C l a r i n e t Quintet: Closing Section Exposition c l o s i n g section: ([2 + 2] + [2 + 4] + 5 (mm. 65-79) a b a b^ c Recapitulation c l o s i n g section: ([2 + 2] + [2 + 18] + 5 (mm. 169-197) a b a b c S t r i n g Quintet K. 515. Three of the four s t r i n g quintets may be success-f u l l y analysed with the c l o s i n g model. I w i l l consider a l l three i n d e t a i l be-cause each has i n t e r e s t i n g v a r i a t i o n s of the model. The exposition of the S t r i n g Quintet i n C Major, K. 515, was discussed on p. 89, and therefore I w i l l analyse only the c l o s i n g section here. I noted i n chapter 2 that t h i s expo-s i t i o n was very long, and t h i s length a r i s e s i n part by the use of extensions within the four small sections. The 28-bar c l o s i n g section, i n mm. 115-143, employs three methods of extension. (1) The group i s two bars longer than a_. (2) The bb'*' p a i r i s (3 + 3) rather than (2 + 2) , and the cc^ p a i r i s (4 + 4) rather than (1 + 1). (3) There i s an a d d i t i o n a l p a i r of groups beyond 2 2 the normal s i x : c c grouped as (2 + 2). See diagram 21. This c l o s i n g section i s preceded by the usual expanded cadential progres-sion and t r i l l , ending at m. 115, which i s also the f i r s t bar of the f i r s t c l o s i n g section timespan. The &~ v a r i a t i o n , i n mm. 119-125, employs a 2-bar extension of i t s t h i r d bar, m. 121, prolonging the D i n v i o l i n I into the b_ subsection and weakening the cadence of The and b_ groups overlap i n m. 125, thereby j o i n i n g aa^" to b b \ It i s the p a i r i n g of bb'*" that separates these groups from aa/J": i f b_ were omitted i t would be c l e a r that b_^was not a 118 Diagram 21 String Quintet K. 515: Exposition Closing Section Measures: 115 125 131 139 Timespans: (4 + 6) + (3 + 3) + (4 + 4) + (2 + 2) 1 v v 1 1 2 2 Groups: a a b b c c c c separate group but was instead an extension of a . Although the two b groups overlap—m. 128 i s harmonically the end of the b_ group and also the beginning of the b_^  group—there i s not so s i g n i f i c a n t a melodic overlap here because m. 128 i s p r i m a r i l y a beginning, as i s made evident from the exact repeat of m. 125, the leap i n the f i r s t v i o l i n (A to D, mm. 127-128), and the dynamic change (piano to f o r t e , mm. 127-128). A d i f f e r e n t kind of overlap i s found i n the connection between b^ and c i n t h i s example: t h i s can be c a l l e d accompaniment overlap. Although the melody of c_ begins i n m. 132, the accompaniment pattern of c_ begins a bar e a r l i e r , i n the same bar that the b ^ group concludes. In other words, a l l of m. 131 i s com-mon both to groups b_^  and c_—to melodically and harmonically, and to c_ ac-companimentally and harmonically. 2 The c_ groups are i d e n t i c a l , each now beginning during the f i r s t bar of t h e i r respective timespans, overlapping with the f i n a l notes of t h e i r respective preceding groups (mm. 139, 141). The £ subsection i s greatly expanded with respect to the model, normally (1 + 1). In spite of t h i s expansion, i t i s cle a r from the tonic p e d a l — c h a r a c t e r i s t i c of the f i n a l s u b s e c t i o n — t h a t t h i s i s indeed the f i n a l part of the c l o s i n g section. Nearly h a l f of th i s c l o s i n g section i s taken up by a tonic pedal. The c_ 1 . 2 and c_ subsections are constructed as (1 + 1 + 2) groups, with c echoing the 119 Diagram 22 String Quintet K. 515: Recapitulation Closing Section Measures: 305 315 322 327 Timespans: (4 + 6) + (3 + 3) + 1 + ([2 + 1 + 2] + [2 x 3]) + Groups: a a b b 3 . . c i m i t a t i o n Measures: 333 341 353 Timespans: ([2 x 4] + [2 x 6]) + ([4 + 4] + [2 + 2 + 2] + 2) Groups: ST material 1 2 2 2 c c c c c end of the c_ v a r i a t i o n . The length of th i s c l o s i n g s e c t i o n — a n d i n p a r t i c u l a r the length of the tonic p e d a l — i s perhaps not s u r p r i s i n g because t h i s exposition i s one of the longest Mozart wrote. In spite of the a l t e r a t i o n s here to the cl o s i n g model, there remains an o v e r a l l a c c e l e r a t i o n i n timespan lengths from four to three to two bars, with a regression to four bars between those of three and two bars. The r e c a p i t u l a t i o n i s s i m i l a r i n form to the exposition. The c l o s i n g section i s the small section that i s most changed: i t i s expanded to the point where i t has some coda function. In diagram 22 the symbols r e f e r to the same material as i n the exposition (diagram 21). E s s e n t i a l l y , t h i s c l o s i n g section i s expanded by the i n s e r t i o n of two types of material. F i r s t , i n mm. 321-332, a motive based on £ i s used i n fugal i m i t a t i o n , resembling the £ subsection of the c l o s i n g section i n the exposition. Second, i n mm. 333-352, material from the subordinate theme—see mm. 273-305—is reworked i n a cadential context. In mm. 353-368 the £ subsection i s recapitulated and extended with an ad d i t i o n a l 2 c group and two bars of tonic. 120 S t r i n g Quintet K. 516. There are a number of i n t e r e s t i n g features i n the String Quintet i n G Minor, K. 516, not the l e a s t of which i s the close r e l -ationship between the t r a n s i t i o n material, i n mm. 30-48, and the subordinate theme, i n mm. 49-64. It i s much more common fo r the t r a n s i t i o n to be based on the f i r s t theme than on the second. In those rare instances where the t r a n s i -t i o n and subordinate theme share the same material, the impression i s that the theme i s based on the t r a n s i t i o n ; t h i s procedure reverses the normal primary/ subsidiary d i s t i n c t i o n , and makes the t r a n s i t i o n seem more important than the subordinate theme. The c l o s i n g section has an unusually dense texture, espe-c i a l l y i n the f i r s t subsection, aa (based on the f i r s t motive of the main theme). See diagram 23. The c l o s i n g model i s operating on two l e v e l s here: at the 8-bar theme level—mm. 72-84 are based d i r e c t l y on mm. 64-71, with an expanded cad-e n t i a l progression added, and at the group l e v e l — t h e codetta i n mm. 85-90. The c l o s i n g section s t a r t s o f f l i k e bb^ " (2 + 2) of a. c l o s i n g model but evolves into a sentence which i s repeated. The r e c a p i t u l a t i o n i s s i m i l a r i n form to the exposition, and the c l o s i n g section i n p a r t i c u l a r i s very s i m i l a r to i t s exposition form. A f t e r the r e -t r a n s i t i o n , a coda begins i n m. 235 with main theme material i n i m i t a t i o n . The c l o s i n g model i s used f o r the next subsection i n mm. 243-254, based on the sub-ordinate theme, that i s , (3 + 3) + (2 + 2) + 2. Diagram 23 S t r i n g Quintet K. 516: Exposition Closing Section Measures: 64 72 85 91 Timespans: ([2 x 2] + [1 + 1 + 2]) + ([2 x 2] + [1 + 1 + 7]) + (3 + 3) 1 1 1 1 2 2 2 Grouplets: a a b b c a a b b c a a Retr. 121 String Quintet K. 593. The String Quintet i n D Major, K. 593, has an introduction that recurs i n the coda. This unusual feature means that the introduction must be considered part of the movement and perhaps part of the exposition i n p a r t i c u l a r . The sections i n mm. 34-63 and 64-75 have some trans-i t i o n and subordinate theme features but are based p r i m a r i l y on main theme ma-t e r i a l . Due to these unusual f a c t o r s , the models of exposition and e n t i r e -movement forms are not s u f f i c i e n t to analyse t h i s movement. Even a cursory view of the o v e r a l l form would require very extended discussion; therefore, I w i l l consider only the c l o s i n g section, which, despite the unusual features of the movement, i s e a s i l y i d e n t i f i a b l e and even r e l a t i v e l y normal, i n mm. 75-97. By comparison with the c l o s i n g model, t h i s c l o s i n g section i s expanded with respect to i t s t o t a l length—22 b a r s — a n d contracted with respect to the number of g r o u p s — f o u r . It i s the b_b subsection of the model which i s here omitted. The aa^ p a i r i s expanded to ( 6 + 8 ) , and then the tonic pedal appears. (An explanation of the posited v a r i a t i o n r e l a t i o n s h i p of these groups w i l l be offered shortly.) Since the tonic pedal i s normally associated with the f i n a l p a i r i n g , these two f i n a l groups might be named cc^" as i n the model. However, to avoid possible misunderstanding, I have shown them as bb'*" i n diagram 24. They are expanded here i n comparison with the model to (4 + 4). This c l o s i n g section has some i n t e r e s t i n g differences from some of the previous examples. The end of the subordinate theme has a strong cadence, but not a f u l l ECP. The a-group begins simultaneously with i t s timespan, unlike some of the previous examples. This overlap i n m. 75 i s better described as an i n t e r r u p t i o n because new material begins the instant the tonic chord appears, thus weakening the a s s o c i a t i o n between the tonic and the previous dominant: the extent to which the cadence i s therefore weakened i s the extent to which an i n -122 terruption occurs. This closing section can then be seen as a progression to-wards a stronger cadence. The a^ group begins with an interruption as did the a_ group; hence there i s no cadential f u l f i l l m e n t here. This cadence i s further weakened due to the replacement of the expected major tonic with a minor one i n m. 81. I t i s the cadence at mm. 87-89—with i t s prominent descending-fifth A, l i n e and 3 i n the bass, both absent from previous cadences—which s a t i s f i e s the need for a strong cadence. The b_ group now begins after i t s timespan does, thus further strengthen-ing the cadence by allowing the tonic harmony to be associated with the a~ group. The pedal also adds to the weight of tonic harmony: i n f a c t , the need for extended tonic harmony may explain why the pedal i s used here, i n place of the usual bb pair found i n the model. Another reason for the omission of the middle pair of the model i s that the aa"*" pair i s unusually long. Yet another difference here i s the character of and r e l a t i o n between the a_ and a^_ groups. One of the archetypal features of closing sections i s that groups are primarily cadential, often employing only tonic and dominant harmon-ies. The f i r s t two groups here are not so strongly cadential, partly because each i s longer than the normal 4-bar a-group length. The aa^ " pair i s somewhat more dynamic i n character than i n a normal closing section. This pair i s also remarkable for the remoteness of the v a r i a t i o n from a^  to a^_: whereas the a group i s based on a descending-thirds sequence, bar by bar, the a_^  group em-ploys f i r s t a (2 x 2) sequence and then a ( i x 8) quasi-sequence. Another difference i s that a. and a^ are not the same length—something quite unusual. And whereas^the a group i s one 6-bar u n i t , the a^ group may ea s i l y be heard as (4 + 4). The a''" group may also be heard as (6 + 2), the f i n a l two bars being an extension necessitated i n part by the redirection of the harmony i n 123 Diagram 24 String Quintet K. 593: Exposition Closing Section Measures: 75 89 Timespans: ( 6 + 8 ) + ( 4 + 4 ) Grouplet lengths: ( 1 x 6 ) + ([2 x 2] + [1 x 4]) + (2 x 2) + (2 x 2) Groups: a a"*" b b''" m. 86, where the second chord i s a V2 rather than a root p o s i t i o n dominant. (That i s , the cadence could e a s i l y have occurred i n mm. 86-87 i f the bass had been D-sharp-E or D-E i n m. 86.) The two groups therefore are s i m i l a r i n that a}~ i s an extension of a group the same length as a_. They are also s i m i l a r from a t e x t u r a l point of view, i n that each has a primary melody of constant eighth notes. The motives of the two groups are somewhat s i m i l a r , f o r example, as i n mm. 75 and 82. The group has the stronger cadence and so the two groups may be heard as a simple period, the r e l a t i o n between many group-pairs i n c l o s i n g sections. The b_ and groups may be heard as (2 + 2) imitations of a 2-bar motive. The v a r i a t i o n technique of borrowing p i t c h classes from the p a r a l l e l minor mode i s common to both the bb^ p a i r and the aa^" p a i r . Many of the c l o s i n g sections discussed e a r l i e r used the opening main theme motive; t h i s c l o s i n g section does not. In f a c t , there i s no overt r e f -erence to any previous material, probably because main theme m o t i v e s — p r i m a r i l y those i n mm. 20(4)-22(3) and 30-33(1)—have dominated so much of the exposition up to the c l o s i n g section. In the r e c a p i t u l a t i o n the c l o s i n g section i s rewritten to a c e r t a i n ex-tent. The aa"*" p a i r , i n mm. 200-216, has i t s main voice/accompanying voices 124 inverted with respect to the exposition, together with some further rewriting. The group i s extended by two bars, that i s , i t i s now (2 x 3) + (1 x 4). The bb'*" p a i r i s extended into a r e t r a n s i t i o n preparing f o r the coda, which, as noted above, begins with the larghetto, and concludes with part of the main theme at tempo I. Stri n g Quartet K. 387. Six of the ten s t r i n g quartets use the c l o s i n g model i n some way. Rather than go into d e t a i l on a l l or even some, I w i l l o f f e r only b r i e f remarks on the nature of the v a r i a t i o n i n the use of the c l o s i n g model i n each. The c l o s i n g section of the St r i n g Quartet i n G Major, K. 387, may be summarized as i n diagram 25. The shorter length of a l l the sections i n t h i s movement explains why the c l o s i n g section begins with 2- rather than with 4-bar u n i t s . In other words, t h i s c l o s i n g section i s based on a reduction of the c l o s i n g model to h a l f the usual length. (At the same time, a case could be made for hearing t h i s movement i n 2/4 as opposed to the notated common time, thus doubling the number of bars i n the c l o s i n g section. This would help explain why the c l o s i n g section,, unusually, begins on the t h i r d beat. However, more important i n the model than the absolute length of units i s the r e l a t i o n s h i p between the lengths of u n i t s , whether 4:2:1 or 2:1:$. Diagram 25 Str i n g Quartet K. 387: Exposition Closing Section Measures: 38(3) 42(3) 49(3) Timespans: (2 + 2) + (2 + 5) + (1$ + 1$) + ( $ + J ) + 2 „ 1 1 T- T - 1 1 1 j Grouplets: a a b b c c c c d 125 The bb p a i r of the model i s doubled i n length and expanded i n th i s c l o s i n g section; a l t e r n a t i v e l y , one could see the bb^ " subsection as an i n s e r -t i o n into the model: without these groups the lengths of the others are pro-g r e s s i v e l y reduced, i n a manner s i m i l a r to that of the model. The f i n a l 2-bar g r o u p — c i — i s a curious addition, of a type seen only i n one or two other move-ments. In the r e c a p i t u l a t i o n the aa"*" subsection i s expanded by three bars, the bb^ subsection i s also expanded by three bars, and the c^c^" subsection i s expanded by one bar. Str i n g Quartet K. 421. The St r i n g Quartet i n D Minor, K. 421, l i k e the Quartet i n G Major, has shorter than usual sections and has a c l o s i n g section that beings on the t h i r d beat. See diagram 26. The lengths of groups i s the v a r i a t i o n here i n the use of the c l o s i n g model.. The use of exact r e p e t i t i o n i n each p a i r — e x a c t aside from, the consistent use of octave s h i f t s — i s a l i t t l e unusual. As noted on pp. 92-93 t h i s movement has some i n t e r e s t i n g expansions i n lengths of small sections i n the r e c a p i t u l a t i o n . The unusual l£-bar lengths of the aa p a i r are "normalized" to two bars i n mm. 102-105, and the second b_ group i s expanded by a half- b a r , i n m. 109. This emphasis on half-bar units means that the movement could be considered i n 2/4, another s i m i l a r i t y with the Quartet i n G Major. The r e t r a n s i t i o n material, i n mm. 111(3)-112, i s used Diagram 26 Str i n g Quartet K. 421: Exposition Closing Section Measures: Timespans: Groups: 32(3) 35(3) 39(3) (1$ + l i ) + (2 + 2) + ( i + i) a a b b c c 126 here to lead f i r s t to the repeat of the development-recapitulation sections, and the second time to the coda. St r i n g Quartet K. 458. There are a number of unusual features i n the Stri n g Quartet i n B - f l a t Major, K. 458, notably the combination of t r a n s i t i o n and subordinate theme functions i n one small section i n mm. 18-77. A f t e r the ECP i n mm. 71-77, the c l o s i n g s e c t i o n — l o o s e l y based on the c l o s i n g model on two l e v e l s — i s heard i n mm. 77-90. See diagram 27. On l e v e l (b) there are only two groups, the second an expansion of the f i r s t . On l e v e l (a) the group-1 2 l e t s mm form a p a i r ; m_ begins as i f repeating m but leads to a new g r o u p l e t — n; n i s s i m p l i f i e d to n^ and repeated. In the r e c a p i t u l a t i o n there i s a s l i g h t v a r i a t i o n i n the n^n^" p a i r , i n -eluding s u b s t i t u t i o n of 3 f o r 6 m the bass of m. 228, which makes f o r a strong-er f i n a l cadence. One reason f o r the presence of a substantial coda involves the development sec t i o n , the l a t t e r conditioned by the need to begin with a theme i n compensation f o r the lack of a true theme i n the dominant i n the expo-s i t i o n . Following t h i s theme i s "new" material, based on a slow (half-speed) inversion of the opening motive. The development never deals at a l l with the opening music, the s t r e t t o p o s s i b i l i t i e s of which are so obvious. This i s Diagram 27 Stri n g Quartet K. 458: Exposition Closing Section Measures: 77 81 83 89 Timespans: (2 x 2) + (2 + [2 x 3] + 2) 1 Groups: a a i - 1 2 1 1 Grouplets: m m m n n n 127 probably why Mozart writes a coda beginning with the f i r s t theme i n s t r e t t o , 2 hence speeded up, rather than slowed down as m the development. Stri n g Quartet K. 464. The main theme of the String Quartet i n A Major, K. 464, was discussed as a model sentence i n chapter 2, pp. 61-62. The close connection between the end of the subordinate theme and the beginning of the c l o s i n g section, i n mm. 68-69, means that the c l o s i n g section may be considered a subordinate theme codetta. Like the Quartet K. 458, t h i s c l o s i n g section has p a i r i n g of units on both l e v e l s (a) and (b); see diagram 28. Most c l o s i n g sections begin with some degree of overlap with the end of the subordinate theme: here the overlap i s so extreme that the tonic harmony i s omitted altogether and the group begins with i t s timespan on the f i r s t beat of m. 69. In f a c t , the cadence i s e l i d e d : i t i s i n c o r r e c t to speak of t h i s as a deceptive cadence, despite the harmonies i n mm. 68-69: (For a b r i e f d i s -cussion of the DC, see chapter 2, note 9.) Grouplet m i s based on the opening motive of the main theme. This pro-cedure i s common to many c l o s i n g sections: here, however, the exact pitches from the v i o l i n I l i n e i n mm. 1-2 are used i n the same instrument i n mm. 69-70, despite the new key. Grouplet o i s a var i a n t of n as well as of the cadential Diagram 28 String Quartet K. 464: Exposition Closing Section Measures: 69 73 79 83 Timespans: 4 + ([2 x 3] + [2 x 2]) + 4 + 1 1 Groups: a a b 1 2 3 1 4 2 Grouplets: mn m m m o o m o 128 grouplet at the end of the subordinate theme, i n mm. 67-68. Variant o_ i s a variant because i t s main n o t e s — B and D-sharp—are the same as those of o, and because i t i s used i n the same p o s i t i o n — a t a cadence—as o. In the r e c a p i t u l a t i o n , the a^ group i s expanded by eighteen bars and the _b group by four bars. In summary, t h i s c l o s i n g section i s distinguished by i t s r i c h motivic a s s o c i a t i o n s , both within the c l o s i n g section and between the c l o -sing section and other sections, p r i m a r i l y the main theme. This means that many of the segments could be re f e r r e d to as motive/grouplet segments; that i s , many grouplets assume more motivic s i g n i f i c a n c e than i s usual. S t r i n g Quartet K. 499. The S t r i n g Quartet i n D Major, K. 499, has an unusual subordinate theme area which includes a canon i n A major i n mm. 40-56, a passage that begins as i f i t were a theme i n F-sharp minor i n mm. 57-64, ano-ther p a s s a g e — i n F major i n mm. 65-70, and f i n a l l y a cadence i n A major i n mm. 70-73. A r e l a t i v e l y normal c l o s i n g section follows—normal i n the sense that i t i s based on the c l o s i n g model; see diagram 29. The v a r i a t i o n here i s i n the use of a d d i t i o n a l groups and d i f f e r e n t lengths of groups than i n the model. Nevertheless, t h i s c l o s i n g section i l l u s -trates well two of the standard features of the model, that i s , the progressive reduction i n group length ( i n the model, 4-2-1; here 5-4-2-1), and the consis-Diagram 29 Stri n g Quartet K. 499: Exposition Closing Section Measures: 73 83 91 95 Timespans: (5 + 5) + ([4 x 2] + [2 x 2] + [1 x 2] + 2) Groups: a a''" b b b^ b^ b^ b^ 129 tent p a i r i n g of groups. The subsection i n mm. 83-98 could e a s i l y be viewed as based exactly on the c l o s i n g model: t h i s i s supported by the a s s o c i a t i o n of groups within these bars; that i s , a l l the groups are based on the same mater-i a l — b — a n d group lengths are i d e n t i c a l to those i n the model— (4 + 4) + (2 + 2) + (1 + 1). (The f i n a l two bars, mm. 97-98, are a common extra prolongation of the tonic.) The r e c a p i t u l a t i o n i s s i m i l a r to the exposition, and, except for a few d e t a i l s at l e v e l (a), the c l o s i n g section i n p a r t i c u l a r i s not a l t e r e d (see mm. 215-240). The coda, beginning i n m. 241, i s based on an extension of the r e t r a n s i t i o n — i t s e l f based on the f i n a l group of the c l o s i n g section. In mm. 249-266 the main theme motive i s added and used i n cadential contexts. Although there are no strong motivic r e l a t i o n s h i p s between the c l o s i n g section and previous sections, and i n p a r t i c u l a r none with the main theme ( t h i s perhaps due to the use of the main theme motives i n the subordinate theme area, thus demanding contrast i n the c l o s i n g s e c t i o n ) , the coda does combine the material i n the f i n a l group of the c l o s i n g section with main theme material ( t h i s also occurred i n the development section, which the coda resembles i n some respects). S t r i n g Quartet K. 590. Unlike many of the preceding quartets, the form of the S t r i n g Quartet i n F Major, K. 590, i s normal, as i t follows the four-small-section model i n both the exposition and r e c a p i t u l a t i o n . The c l o s i n g section i s based on a reduced c l o s i n g model; see diagram 30. Instead of s i x groups, here there are only four, and a l l are based on the same material from the opening of the main theme. The c l o s i n g section i n the r e c a p i t u l a t i o n i s almost unchanged, i n mm. 174-183. It leads into the r e t r a n s i t i o n material, as i n the exposition, 130 Diagram 30 String Quartet K. 590: Exposition Closing Section Measures: 63 69 Timespans: (3 + 3) + (2 + 2) Grouplets: 1 2 2 a a a a and into a coda that i s very s i m i l a r to the opening of the development section, i n mm. 184-198. This coda does not include any reference to the main theme, as i s common i n codas (compare the Quartet K. 499). In the coda the material i s of course transformed—primarily h a r m o n i c a l l y — s o as to be e n t i r e l y c a d e n t i a l . This i l l u s t r a t e s w ell the p r i n c i p l e that the function of a given section i s de-termined more by how the material i n that section i s used rather than by the na-ture of that material. St r i n g T r i o . The Divertimento f o r V i o l i n , V i o l a , and C e l l o i n E - f l a t Major, K. 563, has a very long subordinate theme area that can be analysed i n more than one way according to formal function. The i n t e r p r e t a t i o n I w i l l con-side r here involves hearing the c l o s i n g section begin at m. 44, thereby making i t — a t thirty-one b a r s — a very long c l o s i n g section. This view i s supported i n part by the ECP i n mm. 40-43, which closes the subordinate theme. See diagram 31. This c l o s i n g section has some s i m i l a r i t i e s with that i n the Quartet K. 499: that i s , the use of 5-bar groups i n the f i r s t p a i r , aa"*"; the use of ascending 1-bar sequences i n the f i r s t three bars of the <a group, followed by a 2-bar cadence; and the use of i n v e r t i b l e counterpoint i n the v a r i a t i o n from a_ to However, here the a"*" group i s greatly expanded due to extensions i n mm. 53-57— adding a cadence s i m i l a r to that i n mm. 42-43—and due to an a d d i t i o n a l ECP i n 131 Diagram 31 String T r i o K. 563: Exposition Closing Section Measures: 44 49 58 62 68 Timespans: (5 + [9 + 4]) + (3 + 3 ) + (1 + [ 2 x 2 ] + 1) Groups: a a b b c c mm. 58-61. Unusually, a bar with no material beyond a sustained tonic harmony and an accompaniment pattern—m. 68—precedes the f i n a l p a i r ; t h i s bar could also be seen as added to the previous t i m e s p a n — — t h e r e b y making i t four bars long. The c l o s i n g section i n the r e c a p i t u l a t i o n i s almost unchanged. V i o l i n Sonatas K. 304, 377, and 454. Of the f i v e sonatas f o r keyboard and v i o l i n which I am considering, three use the c l o s i n g model. In f a c t , a l l three use the model with very l i t t l e v a r i a t i o n , and I w i l l therefore comment only b r i e f l y on each. The Sonata f o r V i o l i n and Piano i n E Minor, K. 304, has unusual thematic sections: the main theme i s one of the few examples of a small ternary, and the subordinate theme, i n mm. 28-59, i s an extreme vari a n t of a sentence. This l a t t e r theme incorporates a good example of an ECP, mm. 51-58 being an expansion of the previous s i x bars. The c l o s i n g section, i n mm. 59-77,. has timespans of (4 + 4) + (3 + 3) + (2 + 2) , and groups of aaVb^cc. In the r e c a p i t u l a t i o n the c l o s i n g section, i n mm. 159-183, i s lengthened by the add i t i o n of two more c_ groups and a further 2-bar group. A f t e r the r e -t r a n s i t i o n the main theme reappears as the coda: t h i s may be due to the short-ened and a l t e r e d form of the main theme used at the s t a r t of the r e c a p i t u l a t i o n . 132 The exposition of the Sonata f o r V i o l i n and Piano i n F Major, K. 377, was discussed on pp. 88-89. The t h i r d small section, i n mm. 37-51, has time-spans of (3 x 2) + (2 x 2) + (2 x 2) + 1, and groups aa^'bbcc'*". The r e c a p i t u -l a t i o n i s unusual f o r i t s rearrangement of l e v e l (c) and (b) u n i t s ; the c l o s i n g section does not escape t h i s rearrangement, although at l e a s t i f remains i n t a c t as a small section and remains i n the same level-(d) l o c a t i o n — t h a t i s , at the end—as i n the exposition. However, whereas i n most works any change i n the r e c a p i t u l a t i o n c l o s i n g section usually involves expansion, i n t h i s movement the opposite occurs: the b_b p a i r i s omitted. Contraction of the c l o s i n g sec-t i o n i s a very unusual procedure. The Sonata f o r V i o l i n and Piano i n B - f l a t Major, K. 454, has been d i s -cussed i n chapter 2: pp. 47-48, 50, 52, 54-56, 63, 73-75, 82-83, 86; notes 9, 10, 25, 28, 32, 37, and 38. Piano Sonatas K. 284, 311, 310, 330, 457, and 533. This chapter w i l l conclude with b r i e f remarks on the s i x piano sonatas that feature the c l o s i n g model. The exposition of the Piano Sonata i n D Major, K. 284, divides p r i m a r i l y into two sections at nr. 21. Closing material begins at m. 38, although t h i s material i s strongly connected to the preceding thematic statement. The c l o s i n g model applies only to the f i r s t two groups; the o v e r a l l timespan structure i s ( 3 x 2 ) + 6 + 2 , with group structure aabc, where b_ i s an ECP. In the r e c a p i t u l a t i o n the a p p l i c a t i o n of the c l o s i n g model i s stronger 1 2 due to the replacement of the sin g l e b_ group with two variants of i t — b b ; a 4-bar compression of b_ i n mm. 116-119 i s followed by a 6-bar v a r i a t i o n . 1 2 . This expansion of b_ to b_ strengthens the impression of an ECP, which, coupled 1 . 1 2 with the a d d i t i o n a l cadence ( i n b ) and the a d d i t i o n a l p a i r i n g ( b b ), streng-133 thens closure. The Piano Sonata i n D Major, K. 311, begins with a 16-bar section com-bining main theme and t r a n s i t i o n functions. An 8-bar subordinate theme i s then followed by another 16-bar section that combines subordinate theme codetta and c l o s i n g section functions, as well as introducing a prominent m o t i v e — i n mm. 28-29—that i s used extensively i n t h i s and i n subsequent sections. See diagram 32. The bb'*" p a i r acquires more s i g n i f i c a n c e because i t i s repeated and because i t has some motivic features. The d group i s an extra one s i m i l a r i n function to that at the end of the c l o s i n g section i n the String Quartet K. 387. The r e c a p i t u l a t i o n i s rearranged at l e v e l s (b) and ( c ) : mm. 79-86 vary the second theme; mm. 87-99 r e c a p i t u l a t e mm. 24-36 of the c l o s i n g section; and mm. 99-112 form one small section incorporating part of the main theme with a new continuation, ending with a v a r i a n t of the c; and d_ groups from the c l o s i n g section. Diagram 32 Piano Sonata K. 311: Exposition Closing Section Measures: 24 28 36 Timespans: (2 + 2) + ([2 + 2] x 2) + 2 + 2 Groups: a a''" b b^ " b b^- c d The c l o s i n g model i s used i n a shortened form i n the Piano Sonata i n A Minor, K. 310: instead of s i x groups there are four, (5 + 5) + (2 + 2) + 1, aa^ bb'*", i n mm. 35-49. Here b_ i s based on the opening motive of the main theme. In the r e c a p i t u l a t i o n a cadential extension of three bars i s added to b^; other-wise the c l o s i n g section, i n mm. 116-133, i s only s l i g h t l y rewritten, and the 134 few small a l t e r a t i o n s are l i k e l y due to the change of mode. In the Piano Sonata i n C Major, K. 330, i d e n t i f i c a t i o n of the t r a n s i t i o n , the subordinate theme, and the c l o s i n g section i s problematic. The section i n mm. 19-34 has some thematic features but could also be considered a t r a n s i t i o n . The period i n mm. 34-42 i s thus e i t h e r the f i r s t or the second subordinate theme. Because expansion has not taken place and codettas have not occurred, the section i n mm. 42-58 could be seen as a codetta-complex to the period. How-ever, i t could also function as a c l o s i n g section based on the c l o s i n g model: (6 + 6) + (2 + 2) + 1, aa^bb^. The 6-bar groups feature i n t e r n a l grouplet p a i r i n g i n t h e i r f i r s t halves: (1 + 1) + ( J + £), xxyy. In the r e c a p i t u l a t i o n the c l o s i n g section i s s i m i l a r except f o r a change to the x grouplet and the a d d i t i o n of a new codetta. The c l o s i n g section of the Piano Sonata i n C Minor, K. 457, i s s i m i l a r to that of the preceding sonata i n that there are only two, and not three, pairs of groups; that i s , i n mm. 59-70, (4 + 4) + (2 + 2), aa^bb^. In the r e c a p i t u l a t i o n the bb'*' p a i r i s a l t e r e d i n order to lead into the coda, which i s discussed on pp. 79-80. The c l o s i n g section of the Piano Sonata i n F Major, K. 533, comes a f t e r a long expanded cadential progression that ends i n m. 89. This c l o s i n g section i s a c l e a r i l l u s t r a t i o n of the model, and i s also a good example of the type i n which a l l groups are based on the same material, so that with each successive 1 1 2 2 2 p a i r the material i s reduced: (3 + 3) + (2 + 2) + ( 1 + 1 + 1 + 1 ) , aaa a a a a . In the r e c a p i t u l a t i o n several sections are somewhat rewritten, but the c l o s i n g section remains b a s i c a l l y the same. 135 Having discussed a l l of the works that are based on the c l o s i n g model, i t would seem appropriate to o f f e r some generalizations on the use of t h i s model and on closure as generated by t h i s model i n these works. I w i l l defer such discussion u n t i l chapter 7, by which point I w i l l have examined the r e -maining movements, the ones based on other models. The c l o s i n g model i n f a c t has some a p p l i c a t i o n to the other models, as w i l l be seen i n subsequent chap-te r s , and t h i s i s another reason I wish to wait to make generalizations con-cerning t h i s model. In addition, I want to discuss closure o v e r a l l i n these works of Mozart, and t h i s i s best l e f t u n t i l a l l movements have been mentioned: I can then not only summarize the c l o s i n g model and the other models, but also compare and contrast t h e i r a p p l i c a t i o n , prevalence, v a r i a t i o n , r e l a t i o n s h i p , and c l o s u r a l strength. I t should at l e a s t be apparent that the c l o s i n g model i s used i n a large number, and a large percentage (60%) of pieces. The v a l i d i t y of the c l o s i n g model i s revealed not j u s t because a large number of pieces may be analysed with i t , but also because i t applies to so many pieces that are d i f f e r e n t . That i s , no two pieces use the c l o s i n g model i n the same way, yet the c l o s i n g model s t i l l applies to a l l of them without being so watered-down and vague a model that i t t e l l s us nothing about each piece. Only by considering a large number of pieces has i t been possible to observe t h i s . 136 4 The Closing Codetta A second type of c l o s i n g section may be named the c l o s i n g codetta. The t y p i c a l representative consists of a s i n g l e codetta, of length four to eight bars. In form i t i s often l i k e a shortened c l o s i n g model, containing only one p a i r of s i m i l a r groups; that i s , (2 + 2) or ( 4 + 4 ) . Such codettas hardly rate the designation "small s e c t i o n , " but, while many are not true small sections, they have some independence i n the sense that they are neither e x c l u s i v e l y codettas to the previous subordinate theme nor parts of subsequent r e t r a n s i t i o n s or developments. Such c o d e t t a s — o n a l e v e l between (b) and ( c ) — u s u a l l y function as codettas to subordinate themes and as c l o s i n g sections. (I w i l l r e t a i n the term " c l o s i n g s e c t i o n " despite the short length of t h i s type.) The c l o s i n g codetta commonly occurs i n two kinds of contexts r e l a t i v e to the subordinate theme, contexts which I w i l l term (x) and (y): (x) This type involves a subordinate theme followed d i r e c t l y by the c l o s i n g codetta. There are few examples of t h i s type, and most are r e l a t i v e l y short i n length. (y) More common i s the longer type i n v o l v i n g a subordinate theme followed by a codetta-complex that normally includes an ECP, then by the c l o s i n g codetta. 137 With type (y), closure i s often d i s t r i b u t e d between the end of the subordinate theme and the various codettas, unlike i n the case of works using the c l o s i n g model, where the c l o s i n g section's r o l e i n generating closure i s more exclusive and self-contained. (This observation provides a d i f f e r e n t way to c l a s s i f y c l o s i n g sections, i . e . , on the basis of how the c l o s u r a l function i s d i s t r i b u t e d : i n one section, i n two sections, or i n a series of codettas that do not form c l e a r l y - d e f i n e d sections.) Type (y) often occurs with expositions that have long second-key areas, i n which i t may not always be possible to d i s t i n g u i s h thematic from codetta material. In other words, such second-key areas have a serie s of small sec-tions which have both thematic and c l o s u r a l functions. The codetta material i s usually c l o s u r a l i n function no matter whether i t occurs as a codetta to the theme or as a c l o s i n g codetta. The d i s t i n c t i o n between a codetta to the theme and a c l o s i n g codetta i s made according to the presence of features c h a r a c t e r i s t i c of one or the other of these sections. For example, the expan-ded cadential progression w i l l be found i n a codetta to the theme but not i n a c l o s i n g codetta; and p a i r i n g of s i m i l a r groups (as i n a truncated c l o s i n g model) w i l l be more common i n a c l o s i n g codetta than i n a codetta to the theme. Sometimes there i s no subordinate theme and the second-key area i s made up of a serie s of codettas grouped as one or more codetta-complexes. Expositions i n which the c l o s i n g model i s used f o r the c l o s i n g section normally have a c l e a r separation between the subordinate theme and the c l o s i n g section. This i s not the case with the c l o s i n g codetta: there i s more variance i n movements using t h i s type of c l o s i n g section than i n the c l o s i n g model works. It might be u s e f u l , then, f o r the reader to review the discussion of thematic small sections i n chapter 2, note 28. 138 Detailed discussion must be given to more of the movement i n cases where the c l o s i n g codetta i s used, because i t i s obvious that i n these works closure i s i n i t i a t e d p r i o r to the c l o s i n g section. Therefore, although a s u b s t a n t i a l number of works may be considered to have t h i s type of c l o s i n g section, I w i l l not be able to analyse i n d e t a i l as many works as were so examined i n the pre-vious chapter. In f a c t , I have selected only four works f o r extended discus-sion. In the cases of the Quartet K. 575 and, to a l e s s e r extent, the Quintet K. 614, I have used p i t c h reduction i n the a n a l y s i s , p a r t l y because i t seemed appropriate f o r these works and because i t provides an opportunity to analyse closure from a d i f f e r e n t perspective as well as to evaluate t h i s perspective. A f t e r these four works have been analysed, b r i e f mention w i l l be made of the remaining works which may be considered to have c l o s i n g codettas. Symphony- no. 39. A work that has not yet been discussed i s the Symphony i n E - f l a t Major, no. 39. There i s an introduction, followed by the main theme i n mm. 26-54, the t r a n s i t i o n i n mm. 54-97, the subordinate theme i n mm. 97-135, and the c l o s i n g section i n mm. 135-142. The subordinate theme area divides into two sections, the f i r s t — t h e theme p r o p e r — i n mm. 97-119 ( i t s e l f comprised of a sentence i n mm. 97-109 and a period i n mm. 110-119), and the second i n mm. 119-135. This second section i s not so much a codetta to the previous thematic material as i t i s a separate section. It i n i t i a t e s closure due to the increase i n t e x t u r a l density ( r e s u l t i n g from the a d d i t i o n of instruments and the change to a f o r t e dynamic), and also due to the ECP ( e s p e c i a l l y the repeated cadential group i n mm. 125-129 and 130-134). 139 Diagram 33 Symphony no. 39: Exposition and Recapitulation Closing Sections Closing model: (4 + 4) + (2 + 2). + (1 + 1) CS (Exposition) measures: 135 139 timespans: (2 x 2) + (1 x 2) + 2 CS (Recapitulation) measures: 292 299 303 timespans: (2 + 5) + (2 x 2) + (1 x 3) + 4 The c l o s i n g codetta i n mm. 135-142 has a stronger than usual connection with the previous codetta, l a r g e l y due to the use of a s i m i l a r v i o l i n motive (mm. 121, 135, e t c . ) . This weakens the independence of the c l o s i n g codetta, making i t function as an extension of the previous material. Elements of the c l o s i n g model are c l e a r l y present, that i s , i n the p a i r i n g of s i m i l a r groups having timespans (2 + 2) + (1 + 1) + 2. (Such elements are also found i n the previous codetta i n mm. 125-134.) The f i n a l 2-bar group i s an obvious r e f e r -ence to a t r a n s i t i o n motive (mm. 89-90, e t c . ) . The reference to the t r a n s i t i o n i s i n f a c t quite strong, as the e n t i r e c l o s i n g codetta may be seen as based on mm. 83-90. The development section then continues along l i n e s s i m i l a r to the subsequent bars of the t r a n s i t i o n . These factors of connection—with the preceding section and with the transition—mean that mm. 135-142 are weakened i n terms of motivic independence. At the same time, t h i s codetta i s important harmonically i n that i t provides several measures of s t a b i l i t y on the tonic i n contrast to, and i n r e s o l u t i o n of, the preceding codetta. Here, therr, i s the main reason for the presence of the c l o s i n g codetta (not only f o r t h i s work but, generally, i n many others too): the preceding codetta c l e a r l y aims towards closure as implied by the l o c a l to-140 n i c , and the c l o s i n g codetta substantiates the implication by extending the tonic harmony. That several measures of tonic are needed i s obvious a f t e r the dominant harmony of the t y p i c a l expanded cadential progression: replacing mm. 135-142 with a single bar of tonic would be u n s a t i s f a c t o r y . That the main function of the c l o s i n g codetta i s harmonic i s not imme-d i a t e l y obvious from t h i s work. However, many c l o s i n g codettas are i n f a c t composed of r e l a t i v e l y i n s i g n i f i c a n t m a t e r i a l — t h a t i s , short groups and grouplets without motivic r e f e r e n c e — c o u p l e d with tonic prolongation. See example 3, the Piano Sonata i n B - f l a t Major, K. 333, where the c l o s i n g codetta i s i n mm. 59^63. In somewhat exceptional works such as the Symphony no. 39, on the other hand, Mozart adds motivic references to the c l o s i n g codetta, giving t h i s s ection a melodic function as well as harmonic and rhythmic functions (the l a t t e r that of prolonging a harmony f o r a required length of time).^ The two codettas i n mm. 119-135 and 135-142 bear some resemblance to c e r t a i n features of the c l o s i n g model. It w i l l be r e c a l l e d that the c l o s i n g model incorporates a reduction i n harmonic and melodic a c t i v i t y — n o r m a l l y the f i n a l p a i r or the l a s t two p a i r s of the model i s / a r e b u i l t on a tonic pedal. In t h i s sense, the two codettas here form an expanded c l o s i n g model. Further-more, the second codetta reduces the group length, a feature also found i n the model. (The c l o s i n g section cannot be considered to begin i n m. 119 because the subordinate theme area normally ends with the expanded cadential progression. Expansion i n p a r t i c u l a r i s not a feature of c l o s i n g sections of any type.) In t h i s work, then, one may. say that closure i s i n i t i a t e d i n the f i r s t codetta, understanding that the c l o s i n g model i s not r e s t r i c t e d to the c l o s i n g 141 section proper. The two codettas share c l o s u r a l processes and may be consid-ered together to be an extreme variant of the c l o s i n g model. In the r e c a p i t u l a t i o n the c l o s i n g codetta i s more than doubled i n length, i n mm. 292-309. The additions here r e s u l t i n greater independence f o r t h i s section,, and i t now functions more c l e a r l y as a c l o s i n g . s e c t i o n , and even has something of the character of a coda. See diagram 33. F l u t e Quartet K. 285. The Quartet f o r F l u t e , V i o l i n , V i o l a , and C e l l o i n D Major, K. 285, i s one of the e a r l i e s t works I am considering here. (The manuscript i s dated Dec. 25, 1777.) The early date may explain the d i f f i c u l t y of establishing, unequivocal formal functions f o r the d i f f e r e n t sections of the movement. More than i n most of the works I am considering here, t h i s one i s subject to d i f f e r e n t i n t e r p r e t a t i o n s according to the method of formal analysis I am using. At any rate, the p a r t i c u l a r i n t e r -p r e t a t i o n on which I have s e t t l e d — o u t l i n e d i n diagram 34—provides a framework fo r discussion of the movement. The main theme, i n mm. 1-12, appears to begin as an expansion of the sen-tence model: that i s , mm. 1-4 double the usual 2-bar opening motivic segment of the sentence, and mm. 5-8 form the balancing second s e g m e n t — — o f the model, also doubled i n length. (That these eight bars do not form a period i s c l e a r from the lack of strong harmonic motion i n mm. 1-4, by the lack of a strong cadence i n these measures, and by the melodically weak cadence i n mm. 7-8. Indeed, note how these eight bars function melodically to sustain A.) The t h i r d phrase, i n mm. 9-12, brings the sentence to an end prematurely— i n that a 16-bar sentence was expected based on the implications of the content of mm. 1-8—with a stronger cadence that includes melodic closure. 142 Diagram 34 F l u t e Quartet K. 285: Exposition and Recapitulation Measures: 1 13 25 43 51 58 Sections: MT(1) . MT codetta MT(2) TR(1) ST(1)[25-32] TR(2)[33-43] ST(2) + codettas CC Measures: 100 124 132 139 146 Sections: MT(l)[l-8] MT(2)[14-17] TR(2)[33-43] ST(2) + codettas CC (coda) [13 + 25] This premature closure has implications f o r the subsequent section. Instead of functioning as a straightforward t r a n s i t i o n , the section s t a r t s i n m. 12(4) as a codetta to the main theme: t h i s i s suggested by the subdominant t o n i c i z a t i o n i n mm. 14-15 c h a r a c t e r i s t i c of such codettas as well as by the need f o r furt h e r material i n the tonic key due to the shortened main theme. Ad d i t i o n a l connections with the main theme as well as suggestions of thematic status f o r t h i s section r e s u l t from the use of 4-bar timespans arranged as (2 + 2) motivic segments, and from the t o n i c i z a t i o n of IV i n the f i r s t phrase followed by the t o n i c i z a t i o n of V i n the second (expanding on the weaker use of these—and only these—harmonies i n the f i r s t and second phrases r e s p e c t i v e l y i n the main theme). As a theme, t h i s section might be heard as a vari a n t of the period model, with mm. 13-16 as antecedent and 17-25(2) as extended consequent ( i n c l u d i n g a repeated unit i n mm. 17-19, 20-22). T r a n s i t i o n functions are represented by i n i t i a t i o n of i r r e g u l a r timespans i n mm. 17-19, 20-21, 22-25, and by repeated t o n i c i z a t i o n s of the dominant, the section ending with t h i s harmony. 143 Despite the multiple functions of the section i n mm. 13-25, i t i s reas-onably c l e a r that i t ends p r i m a r i l y as a t r a n s i t i o n . This, of course, helps to c l a r i f y the function of the following s e c t i o n — o r at l e a s t the beginning of the following s e c t i o n — a s the subordinate theme. The eight bars i n mm. 25(2)-33(l) are based on the sentence model with the exception of the ending: i t i s more common f o r themes to end on the t o n i c , and i t easy to 2 imagine how t h i s one could have ended on I of A major i n m. 33. In addition, the overlap to non-thematic codetta material i n m. 33 i s unusual, and weakens the perception of mm. 25-33 as a thematic statement because of the lack of a cadence. Measures 33-43 do not function as an extension of the theme, as i n the manner of, for example, the t y p i c a l extensions or expansions often found i n second-key areas (such as the ECP). Instead, the sudden increase i n surface a c t i v i t y to sixteenth-notes, the p a i r i n g of i d e n t i c a l groups (mm. 33-34, 35-36), the lack of cadences ( u n t i l mm. 41-43), and the pedal on the dominant of the dominant a l l suggest a second t r a n s i t i o n . O v e r a l l , then, the section i n mm. 25-43 i s comprised of an incomplete theme connected to a subsection having some of the functions of a (second) t r a n s i t i o n . A second t r a n s i t i o n i s perhaps needed due to the weak modulation (or lack of modulation) i n the f i r s t t r a n s i t i o n , although such weak mod-ulations are common i n e a r l i e r works of Mozart. That the f i r s t t r a n s i t i o n had a weak modulation i s i n turn possibly due to the need f o r further material i n the tonic caused by the shortened main theme. Of course, t h i s second trans-i t i o n i s only functioning as such because i t strengthens the modulation to the dominant. In f a c t , mm. 33-43 could e a s i l y have followed d i r e c t l y a f t e r m. 24 ( i f the fourth beat of m. 24 were changed to tonic harmony): from t h i s 144 viewpoint, mm. 25-32 function as a thematic i n t e r p o l a t i o n within a larger t r a n s i t i o n complex. A second subordinate theme—this one a p e r i o d — f o l l o w s i n mm. 43(3)-51(l). This i s i n f a c t the f i r s t thematic statement c l e a r l y based on one of the thematic models. Another d i f f e r e n c e with previous themes i s that i t i s harmonically more act i v e and the only tonic harmony occurs at the very end (m. 51). The f i r s t subordinate theme, i n mm. 25-33, i s on the other hand centered around the A major harmony. Obviously, the f i r s t subordinate theme must focus on A because t h i s key has been only t e n t a t i v e l y established, whereas the second subordinate theme does not have such a constraint because the key of A major has by t h i s time been unequivocally established. The subsection i n mm. 51-58(1) i s based on the (1 x 4) + (4 x 1) model. Here, the f i r s t four bars are paired (2 + 2) due to the i m i t a t i o n , and the second four bars reduced to a timespan of three bars length due to the overlap i n mm. 57-58. The codetta-type material, the use of tonic and dominant har- r / A A A monies, and the strong cadence (note the repeated 3-4-5 bass motion), a l l of which contrast with the preceding theme, suggest a subsidiary function fo r t h i s subsection. It might appear that the codettas beginning i n m. 51 have a r e l a t i o n to the preceding theme s i m i l a r to that of the codettas beginning i n m. 33 to the theme beginning i n m. 25. However, the boundary at mm. 50-51 i s i n f a c t very d i f f e r e n t from the one at mm. 32-33. F i r s t , the cadence i n mm. 50-51 i s much stronger than the one i n mm. 32-33; and a l l instruments cadence i n m. 51, whereas i n m. 33 they immediately go on to new material despite reaching the pitches of the dominant cadence harmony. Then, while there i s an overlap of material i n m. 51, i t i s appreciable only by hindsight: the half-note A 145 i n m. 51 ( f l u t e ) i s heard f i r s t as the end of the previous phrase, but i s reinterpreted as the beginning of a 2-bar group a f t e r the i m i t a t i o n begins i n m. 52. In other words, the nature of the overlap i n mm. 50-51 i s such that closure of the previous 8-bar theme i s accomplished, where i t was not i n mm. 32-33. The overlap at mm. 57-58 i s s i m i l a r to the one j u s t discussed. As the subsection i n mm. 51-58 was subsidiary i n comparison with the immediately preceding one, so t h i s next subsection, i n mm. 58-65, i s subsidiary i n com-parison with the one preceding i t . This c l o s i n g codetta i s comprised of a 2-bar group, repeated, then compressed to one bar, repeated, and a f i n a l two bars of tonic chords. In other words, there are no i n t e r n a l l y contrasting groups within t h i s codetta. Melodic and harmonic motion decreases, then, i n two stages a f t e r the second subordinate theme, which enhances t h i s decrease by being the most highly organized melodic s e c t i o n — t h e only one based e n t i r e l y on a thematic model—and by being the most harmonically active section. The codettas i n mm. 51-58 retrace the melodic motion of the period i n A major) and use mainly tonic and dominant harmonies i n that key. The c l o s i n g codetta melodically decorates the tonic note A, and uses only a tonic pedal (or V 7/IV - IV - V - I over t h i s pedal). The rearrangement of t h i s exposition material i n the r e c a p i t u l a t i o n was b r i e f l y discussed i n connection with r e c a p i t u l a t i o n s i n chapter 2: l e v e l (d), p. 94. The f i r s t two phrases of the main theme are repeated exactly i n mm. 100-107. Part of the t h i r d phrase i s combined with part of the second main theme material i n mm. 108-114. This leads d i r e c t l y into a transposed and rewritten form of mm. 33-43 i n mm. 115-124(1), supporting the view of 146 t h i s material as t r a n s i t i o n . E s s e n t i a l l y , then, mm. 100-124 form one section based on most of the f i r s t main theme, and on some of the second t r a n s i t i o n . The second subordinate theme, i t s codetta-complex, and the c l o s i n g codetta follow i n mm. 124(3)-146, with a few a l t e r a t i o n s , a l l at l e v e l (a). The following section, i n mm. 146-154, i s based on part of the second main theme (m. 1 2 [ 4 ] f f . ) , and part of the f i r s t subordinate theme previously omitted from the r e c a p i t u l a -t i o n (mm. 25[3]-26[l]). These materials are, however, rearranged i n new ways to form a section not heard i n the exposition, a section that functions as a short coda. This section i s composed of two pa i r s of s i m i l a r g roups—that i s , xx^yy--and to t h i s extent resembles the c l o s i n g model. Stri n g Quintet K. 614. Three of the four s t r i n g quintets were analysed i n chapter 3. The fourth, the.String Quintet i n E - f l a t Major, K. 614, i s unlike the others i n that i t has a type 2(y) c l o s i n g section. The main theme i s i n mm. 1-19 and the t r a n s i t i o n i n mm. 19-38. Refer to diagram 35 f o r the following discussion. The f i r s t subordinate theme i s a double period, i n mm. 38(3)-54(l), and provides a welcome r e l i e f from the almost constant use of the opening motive — f r o m mm. 1 - 2 — i n the preceding two sections. Although m. 54 i s the s t a r t of the next theme's timespan, i t i s also the end of the l a s t phrase of the f i r s t ST. The second ST returns to the opening motive, t h i s time used to form a sin g l e 8-bar phrase composed of four 2-bar motivic segments i n mm. 54-62(1). This theme i s then va r i e d i n mm. 62-78(1). The v a r i a t i o n i s at f i r s t quite close to the o r i g i n a l (e.g., the Vn. II l i n e i n mm. 62-68[l] i s i d e n t i c a l to the Vn. I l i n e i n mm. 54-60[l]), but becomes more remote with the ECP i n mm. 70-78. The c l o s i n g section i s a 6-bar tonic unit (mm. 78-83), with three a d d i t i o n a l bars (84T86) as r e t r a n s i t i o n . The groups i n t h i s section a l l begin on the t h i r d 147 Diagram 35 Str i n g Quintet K. 614: Exposition Dominant-Key Area Measures: 39 47 54 62 68 72 78 84 Phrases/groups: Timespans: ([4 + 4] + [4 + 3]) (8 + [6 + 4 + 6]) ([2 x 2] + [1 x 2]) + 3 1 2 v t * 1 1 a a a a b b ECP c c c c Small sections: ( ST 1 ) ( ST 2 ) ( Closing codetta ) Retr. eighth-note of the bar, and they are arranged as a p a i r of length ( 1 + 1 ) and a succeeding, compressed p a i r of length ( $ + $ ) • This c l o s i n g codetta may be seen as based on the c l o s i n g model to the extent that there are two p a i r s of groups. Three features suggest m. 54, a l t e r n a t i v e l y , as the s t a r t of the c l o s i n g section, an expanded c l o s i n g model. (1) I t i s common f o r the c l o s i n g model to begin i n the bar of tonic i n which the subordinate theme f i n a l cadence ends; that i s , the overlap i n m. 54 i s c h a r a c t e r i s t i c of c l o s i n g section beginnings. (2) The near-exact r e p e t i t i o n ( i n the sense of the simplest of sequences) of 2-bar units within mm. 54-61 i s suggestive of grouplet/group structure rather than motivic segment/phrase structure. I f the motivic segment used here were not so strongly based on the opening main theme motive, then the (a) and (b) l e v e l units might be regarded as grouplets and groups, r e s p e c t i v e l y . Even with the motivic reference, there i s s t i l l a suggestion that they are on the borderline between the two types of units on both of l e v e l s (a) and (b). (3) The i n i t i a t i o n of r e p e t i t i o n of these eight bars suggests an expanded c l o s i n g model; that is,.mm. 54-61 begin to be repeated i n m. 62, suggesting an (8 + 8) p a i r i n g that would be the f i r s t two units of the c l o s i n g model expanded by a f a c t o r of two. With the ECP, however, i t becomes c l e a r that 148 such i s not the case and that m. 78 i s the end of a separate theme or codetta having the primary function of closure. The closing codetta, then, has the function of prolonging the l o c a l tonic harmony, as did the closing codetta i n the Symphony no. 39. The s i m i l -a r i t y between these two works also extends to the function of the preceding two sections; that i s , i n both works the dominant-key area i s comprised of three sections: (ST) (ST2 or ST codetta [ECP]) (CC). The recapitulation i s very si m i l a r to the exposition except for the nec-essary transposition. The closing section, i n mm. 204-212, i s lengthened by two bars with the addition of a t h i r d (1 + 1) group i n the f i r s t subsection: instead of repeating, each of the three 2-bar groups i n mm. 204-210 i s now on a d i f f e r -ent tonal l e v e l , the goal being the t o n i c i z a t i o n of the dominant i n preparation for the repeat of the exposition-development, and then for the coda. This tonal a l t e r a t i o n of the closing section makes i t end as i t did i n the exposition, i n -stead of ending on I as i t would have had i t been transposed exactly. The analysis of timespans i n the coda i s d i f f i c u l t due to c o n f l i c t i n g features. One interpretation i s shown i n diagram 36. By analogy with the end of the exposition, mm. 212 and 214 are beginnings (of 2-bar timespans). How-ever, by analogy with the start of the development, as well as with the sta r t of the exposition (and, for that matter, with the start of the recapitulation in m. 125), m. 215 would be a beginning (and not the second bar of a timespan from m. 214). Two-bar timespans begin at m. 215, then, and continue to m. 222: here, the second bar of the timespan beginning i n m. 221 i s reinterpreted as a f i r s t bar. One reason supporting the hearing of 2-bar timespans i n mm. 217-218 and 219-220 i s the repeated octave-doubled motive i n the v i o l i n s : m. 216 i s an anacrusis to mm. 217-218—confirmed by the repeat of 217-218 i n 219-220—and the 149 Diagram 36 Stri n g Quintet K. 614: Coda Measures: 215 224 Timespans: (2 + [ 2 x 2 ] + 1 + 2) + ( [ 1 + 1 ] x 3) + 3 1 1 2 1 1 Grouplets: m m m m PAC n n absence of downbeat attacks i n 218 and 220 makes them weak. This motive i s con-densed to one bar i n m. 221—suggesting a reduction of timespan length—and the G octave now a r r i v e s on the downbeat (of m. 222) : both of these features work towards i n t e r p r e t i n g m. 222 as a beginning. In addition, mm. 222-223 i n i t i a t e an ECP which ends on the downbeat of m. 224 with tonic a r r i v a l . Two-bar time-spans continue to the end ( i n part by analogy with mm. 78-83). The main reason a coda i s present here i s that the c l o s i n g section i s so short that further closure i s needed.- The c l o s i n g section i s s u f f i c i e n t to close the exposition, but not the e n t i r e work. If mm. 204-223 are omitted and mm. 224-232—the transposed c l o s i n g s e c t i o n — a r e substituted, i t i s apparent that t h i s proposed ending i s not quite adequate. Furthermore, rewriting the c l o s i n g section i n mm. 204-214 so that i t ends on the dominant has the added benefit of e f f e c t i n g a smooth t r a n s i t i o n (1) to the repeat of the development and r e c a p i t u l a t i o n , i n a manner s i m i l a r to that of the end of the exposition, and (2) to the coda. In e f f e c t , the harmonic changes to mm. 204-214 give t h i s section the function of a r e t r a n s i t i o n , as well as of re-opening the music a f t e r temporary closure at m. 204(1). The coda begins as a variant of the main theme, following l o g i c a l l y a f t e r the r e t r a n s i t i o n group i n mm. 212-214. (This r e t r a n s i t i o n group was used p r i o r to a l l statements of the main theme—i.e., i n the exposition 150 Diagram 37 String Quintet K. 614: P i t c h Reduction of Closing Section and Coda and r e c a p i t u l a t i o n — e x c e p t , of course, for the very f i r s t statement.) The variant only begins l i k e the theme, then has a d i f f e r e n t continuation. This continuation supports harmonic closure through r e p e t i t i o n of V-I progressions, and by suggesting and then stating an ECP; that i s , the 4 6 2 " 3 motions i n mm. 217-218, 219-220, and 221-222 lead to the f i r s t bass element — t h e G—of the ECP, which i s completed i n mm. 222-224(1). The second subsection of the coda i s e s s e n t i a l l y a "correct" statement of the closing section; that i s , i t presents the closing section i n the tonic key throughout, unlike the statement i n mm. 204-211. A difference with the o r i g i n a l closing section i s that there are three statements of the (1 + 1) unit here and not two as i n the exposition. This may be to balance the three statements at the end of the recapitulation (mm. 204-209); however, the l a t t e r 151 came about f o r harmonic reasons, and the three statements i n the coda are harmonically i d e n t i c a l . They are more varied r e g i s t r a l l y than both previous sets were; i t i s as i f they are being used to close o f f a l l r e g i s t e r s of the work. A p i t c h reduction of the c l o s i n g section and coda i s shown i n diagram 37. This shows that, a f t e r the strong harmonic and melodic closure at m. 204, the music i s kept open harmonically, by the sequences i n mm. 204-210 and by the inversions i n mm. 215-222; melodically, by the r i s e to B - f l a t a f t e r which the soprano descends to 1 i n c o n c l u s i v e l y i n m. 215 (inconclusive because i n the wrong r e g i s t e r and not supported by a root p o s i t i o n tonic chord), and conclusively i n m. 224; and rhythmically, because the V-I progressions are at f i r s t beginning-accented rather than end-accented. Stri n g Quartet K. 575. In the St r i n g Quartet i n D Major, K. 575, neither theme i s strongly based on any of the thematic models. The main theme (mm. 1-17[1]) i s constructed of a 6-bar phrase having a very weak cadence and a 2-bar extension, the whole repeated with some additions and v a r i a t i o n s . The t r a n s i t i o n begins as i f i t were a codetta to the theme (mm. 17[3]-21[2]), but t h i s beginning i s repeated and extended, and ends with a dominant pedal. The subordinate theme (mm. 32[3]-49[l]) resembles a double period. The f i n a l phrase (mm. 44[3]-49[l]) i s extended by one bar i n comparison with the previous three phrases, which are a l l four bars long. A l l cadences i n t h i s theme are weak, even the l a s t one. The codetta to t h i s theme (mm. 49[2]-64[l]) i s substantial enough to be considered a separate small s e c t i o n . I t i s comprised of a phrase and i t s extension and v a r i a t i o n , and i s thus s i m i l a r to the t r a n s i t i o n i n construe-152 t i o n . However, whereas the t r a n s i t i o n ended with a dominant pedal, the codetta ends with an ECP. Motivic references are p a r t i c u l a r l y abundant i n t h i s movement. For example, the subordinate theme begins with a vari a n t of the main theme's f i r s t motive, a vari a n t already used i n the main theme i t s e l f (m. 13). The sub-ordinate theme codetta opens with the same motive-pair as i s used to close the two halves of the main theme. But the most obvious motivic reference i s the use of the f u l l opening motive (mm. 1-5[1]) i n diminution as the basis of the c l o s i n g section, that i s , i n mm. 64-66(1), repeated two bars l a t e r . The other motive used i n the c l o s i n g section, i n v i o l i n I, may be heard as based on a motive from the subordinate theme (e.g., i n mm. 33[2]-35[l]) to the extent that both are descending scale patterns and use staccato bowing. In addition, both function i n a s i m i l a r way, that i s , as a response subsidiary to an immediately preceding motive. The c l o s i n g section i s therefore based on elements of the two themes, the element from the subordinate theme being secondary to the element from the main theme. I t resembles the c l o s i n g model i n that there i s one p a i r of repeating groups (4 + 4), but i s i n e f f e c t so short that i t should be seen as a c l o s i n g codetta, type (y). A longer than average r e t r a n s i t i o n follows i n mm. 72-77. This c l o s i n g section i s unusual not only i n i t s strong motivic references but also i n how i t i s subsequently used. Although i t i s common f o r grouplets from the c l o s i n g section to appear i n the f i r s t few subsections of the devel-opment, the appearance of the e n t i r e c l o s i n g section, here i n mm. 105-113(1), followed by four bars of r e t r a n s i t i o n material, i s so unusual that I cannot r e c a l l i t happening elsewhere i n Mozart's oeuvre. A f t e r the chromatic dominant 153 preparation i n the bars preceding 105, the use of the c l o s i n g section at the same p i t c h l e v e l as i n the exposition means that i t functions i n mm. 105-113 as the r e t r a n s i t i o n of the development section. Although one small section i s being used at the end of two large sections, i n each case i t i s functioning i n a d i s t i n c t manner: i n the f i r s t case to close the exposition, i n the second, to return to the tonic key and the main theme. Another unusual feature of t h i s movement i s the extent to which the r e c a p i t u l a t i o n i s s i m i l a r to the exposition. Except f o r the necessary trans-p o s i t i o n , a few l e v e l - ( a ) changes, and a s l i g h t l y a l t e r e d end to the c l o s i n g section, the r e c a p i t u l a t i o n i s the same as the exposition. Even the t r a n s i t i o n , which almost always undergoes some re w r i t i n g , i s not a l t e r e d : because i t ends on a dominant, without modulating to or even t o n i c i z i n g that dominant, the subordinate theme can follow, transposed to the tonic key (compare mm. 32 and 48). This p o s s i b i l i t y e x i s t s wherever a non-modulating t r a n s i t i o n ends on V. Mozart r a r e l y takes the opportunity f o r l i t e r a l restatement of the t r a n s i t i o n , at l e a s t to t h i s extent. Appearances of the c l o s i n g section thus f a r were followed by a smaller subsection made up of r e l a t e d material; i n p a r t i c u l a r , the development concludes with material s i m i l a r to that i n the f i n a l bars of the r e c a p i t u l a -t i o n (mm. 113-116, 190-192). This creates an i m p l i c a t i o n that the f i n a l appearance of the c l o s i n g section w i l l be followed by something, but since the r e t r a n s i t i o n at the end of the exposition i s not usable here, a d i f f e r e n t ending i s necessary. Mozart a l t e r s the f i n a l two bars of the c l o s i n g section proper—186-187—to put more emphasis on the dominant, and adds s i x bars based on the eighth-note scale motive. When t h i s motive i s inverted i n mm. 190-192, a further reference to the opening main theme motive i s apparent, Diagram 38 String"Quartet K. 575: Pi t c h Reduction (1) MT (8 + 8) TR(4 + 7 + 4) ST(4 + 4 + 4 + 5 ) n i l 78 i 86/ ^ 94 .—29 102 „ | ll)5 , D: G^/vi v i V/vi lIV i i i bVI G 5 'v Dev. 8 + 8 + 1 1 + ( 8 + 4 ) 165 171 177 180 186 190 ST cdta(6 + 6 + 3) CS(4+2+4 + 4) 155 that i s , a f i l l i n g - i n of the t r i a d i n m. 190 i n the same rhythm (d i J ) as i n m. 180. Also, one more reference to th i s motive i s added i n the v i o l a part of m. 188. The a l t e r a t i o n s and extensions which replace the r e t r a n s i -t i o n add authentic cadences which were absent from the o r i g i n a l c l o s i n g sec-t i o n . A summary of melodic and harmonic motion, form, and timespans i s provided i n diagram 38. A number of conclusions can be drawn from t h i s diagram. Harmonically, there i s a gradual increase i n a c t i v i t y coincident with changes i n small sections: the main theme has very l i t t l e harmonic a r t i c u l a t i o n ; the t r a n s i t i o n introduces the dominant; the subordinate theme i s i n the dominant and includes some harmonies within that key as well as a r t i c u l a t i n g each phrase with a d i f f e r e n t p a i r of chords; and the sub-ordinate theme codetta has the most varied harmonic surface of any section thus f a r , with only i t s most important harmonies being shown i n the diagram. The c l o s i n g section returns to harmonic s t a b i l i t y ; t h i s i s a sim-i l a r i t y with the main theme which i s supported by the unusual motivic par-a l l e l i s m s as noted above, as well as by the p e r i o d i c i t y of timespans—the main theme and the c l o s i n g section are the only two sections having exclu-s i v e l y i d e n t i c a l - l e n g t h , paired timespans. A further s t r u c t u r a l s i m i l a r i t y between these two sections i s that both are s i m p l i f i e d periods i n the sense that the second h a l f of each i s based c l o s e l y on the f i r s t h a l f of each: that i s , i n both cases t h e i r structure i s aa^. The timespan and phrase structures are connected i n that the melodic diminution of the main theme motive i n the c l o s i n g section i s coupled with a halving of the timespan length. 156 Melodically, i n the exposition, after the stable 1 i n the main theme, the t r a n s i t i o n r i s e s to ^, at f i r s t supported by I, then by V. Now i n the dominant key, the subordinate theme melodic motion i s e s s e n t i a l l y /5-%-/3, while the subordinate theme codetta motion i s ov e r a l l S-^-T. The closing section prolongs 1, and the r e t r a n s i t i o n introduces natural-7 * 4 m the tonic key. In the exposition, then, the levels of melodic a c t i v i t y p a r a l l e l those i n the harmonic sphere. The development section alternates active and stable areas, harmonically, melodically, and rhythmically. The two stable areas are (1) a new theme-like statement i n G major (mm. 86-94[l]), and (2) the restatement of the closing section as the r e t r a n s i t i o n (mm. 105-116). This suggests that the main har-monic motion of the development i s IV-V, and that i n p a r t i c u l a r the IV acts as a lower neighbor to the two dominant-key sections. The connection between the ends of the exposition and development i s especially strong i n this work because of the i d e n t i t y of both material and key. While i t i s true that harmonic i d e n t i t y i s common between these two areas of Mozart's sonata form movements, i t i s not usual for such a large part of the development to be given to r e t r a n s i t i o n (12 of 39 bars, nearly one-third). This connection between the exposition and development explains why there i s no repeat of the dev.-recap.: the harmonic and melodic neighbor motion would be absent. With the transposition i n the recapitulation, the association of formal functions and s p e c i f i c melodic motions i s more evident than i n the exposition: the ascent to A i n the t r a n s i t i o n , the descent from A to F-sharp i n the sub-ordinate theme, the descent from F-sharp to D i n the subordinate theme codetta, and a sustained D i n the closing section—extended now v i a a neighbor note supported by a dominant—that balances the D of the main theme. 157 Diagram 39 String Quartet K. 575: P i t c h Reduction (2) (16 + 15 + 17 + 15 + 14) (27 + 12) (16 +15 + 17 + 15 + 14) MT TR ST STcdta CS Dev r e t r MT TR ST STcdta CS A h i g h e r - l e v e l summary of the movement i s given i n diagram 39. In both diagrams 38 and 39 the G of the development melody—sustained from the end of the e x p o s i t i o n — r e s o l v e s to F-sharp at the s t a r t of the main theme (m. 117). Both the D and the F-sharp are important i n the main theme melody, and a case can be made f o r e i t h e r being the primary tone. E i t h e r a d i f f e r e n c e can be permitted i n the soprano tones f o r the two versions of the main theme— perhaps on the basis of the necessity of a r e s o l u t i o n f o r the sustained G of the development—or the soprano tone of the i n i t i a l statement can be changed to 1 A feature of the sketch shown i n diagram 39 i s that i t i s not highly p i e c e - s p e c i f i c . In other words, many of Mozart's sonata-form movements could . . 3 be shown to have s i m i l a r structures at t h i s l e v e l . On the one hand, t h i s would be evidence f o r p o s i t i n g a si n g l e model of melodic-harmonic structure f o r Mozart's sonata forms; on the other hand, such a model would not r e f l e c t and explain the great d i v e r s i t y of these works. For c l o s i n g sections i n p a r t i c u l a r , the m a j o r i t y — a n d perhaps a l l — would have the same melodic and harmonic functions as indicated i n diagram 39. 158 That i s , melodic and harmonic closure are nearly always reached immediately p r i o r to the c l o s i n g section, the functions of the c l o s i n g section i n these areas being to sustain these goals to balance the main theme and to contrast with the a c t i v i t y between the two stable areas. If any demonstration of the need f o r s t a b i l i t y and contrast i s needed, i t can be shown by imagining the omission of the main theme and c l o s i n g section: t h i s i s at l e a s t remotely possible i n terms of diagram 39 , as t r a n s i t i o n s — l i k e the one- h e r e — o f t e n begin i n the tonic key, and melodic and harmonic goals are reached before the c l o s i n g section. The d i s r u p t i o n i n tonal balance, and the f a i l u r e to simply expose e s s e n t i a l motivic and thematic material that would r e s u l t from the omission of these sections, should make i t apparent that they must be r e -tained, despite t h e i r apparent lack of melodic and harmonic motion. Schenker might maintain that the absence of melodic and harmonic mo-t i o n within sections i s evidence f o r dismissing the analysis of music i n 4 terms of formal functions and sections. I would counter that t h i s lack of motion i s a fundamental feature of these sections. If a l l of Mozart's sonata-form movements have t h i s feature, then there i s no point i n pursuing t h i s a n a l y t i c a l approach with other movements. Although I have analysed t h i s movement i n terms d i f f e r e n t from those used f o r the previous works i n t h i s chapter, s i m i l a r conclusions have been reached regarding c l o s i n g section function. In a l l four works the subor-dinate theme i s followed by a section containing an expanded cadential pro-gression and then by a short type (y) c l o s i n g codetta. In t h i s work, the c l o s i n g codetta also has strong thematic connections as well as formal and harmonic connections with other sections of the movement. 159 Symphonies nos. 32 and 34; Eine k l e i n e Nachtmusik. A number of works analysed i n chapter 3 as type (1) c l o s i n g sections may be r e i n t e r p r e t e d as of type (2). I w i l l give one example i n d e t a i l and r e f e r only b r i e f l y i n what follows to other works which may be s i m i l a r l y r e i n t e r p r e t e d as well as to works not yet considered. In chapter 3 I considered the c l o s i n g section of the Symphony i n C Major, no. 32, to begin at m. 49 and to be an extreme vari a n t of the c l o -sing model. An a l t e r n a t i v e analysis would see mm. 49-64 as a codetta to the subordinate theme, and mm. 65-69 as a c l o s i n g codetta. This i n t e r p r e -t a t i o n i s supported by the following points: (1) The subordinate theme does not end e i t h e r with a p a r t i c u l a r l y strong cadence or with an expanded cadential progression, thereby making stronger the connection with the subsequent material as codetta to the theme. (2) The codetta i n mm. 49-64 f u l f i l l s the expansion and cadential func-tions missing from the end of the subordinate theme. (3) Features of the c l o s i n g model appear only i n mm. 49-64, too short a span f o r convincing a p p l i c a t i o n of the model. (4) The cadence ending on the downbeat of m. 65 i s one of the strongest i n the movement, as a r e s u l t of which subsequent bars are heard as a unit d i s -t i n c t from the previous codetta. Measures 65-69, viewed as a c l o s i n g codetta, are seen to represent the common type based on a reduction of the c l o s i n g model to one p a i r of repeated groups. The-Symphony i n C Major, no. 34, can also be seen as having a type (y) c l o s i n g codetta. Instead of beginning at m. 64, the c l o s i n g section i n t h i s new i n t e r p r e t a t i o n begins at m. 104, ending as before i n m. 112(1). 160 In t h i s case mm. 64-103 function as a codetta-complex to the subordinate theme. This c l o s i n g codetta i s based on a shortened form of the c l o s i n g model, as was that i n the Symphony no. 32. In the serenade Eine k l e i n e Nachtmusik, K. 525, the repeated codetta i n mm. 35-51(1) could be heard as p r i m a r i l y a codetta to the subordinate theme rather than as part of the c l o s i n g section. In t h i s case, the remaining measures of the exposition—51-55—would be a type (y) c l o s i n g codetta. As was noted i n chapter 2, the codettas i n mm. 35-51(1) function i n several ways: determining which function i s primary i s a matter of i n t e r p r e t a t i o n . S t r i n g Quartets K. 428 and 589; St r i n g T r i o K. 563. The St r i n g Quartet i n E - f l a t Major, K. 428, has an unusual exposition form only i n d i r e c t l y r e l a t e d to the usual model incorporating four small sections. However the two sections i n mm. 12-24 and 24-40 are analysed, a theme i s heard i n mm. 40-56 followed by a codetta to i t i n mm. 56-64. The c l o s i n g codetta i s i n mm. 64-68. In the r e c a p i t u l a t i o n , the two sections i n mm. 12-40 are combined, the r e s t remaining almost unchanged. The i n t e r e s t i n g main theme and i t s codetta i n the St r i n g Quartet i n B - f l a t Major, K. 589, were remarked on i n chapter 2, note 33. The t r a n s i t i o n here i s very strong. A f t e r the subordinate theme, the type (x) codetta i s i n mm. 61-71. The f i r s t phrase i n mm. 61-71(1) i s harmonically and melodically more a c t i v e than would be found i n most codettas, and therefore has some thematic features. (This CS might almost be considered i n chapter 5: the c l o s i n g theme followed by the CC.) In the discussion of the Divertimento, or St r i n g T r i o i n E - f l a t Major, K. 563, i n chapter 3, I noted that the second-key area may be analysed i n more than one way according to formal function. I there considered the sub-161 ordinate theme and i t s codetta to be i n mm. 26(4)-43(l), and the c l o s i n g section to be i n mm. 43(2)-73. An a l t e r n a t i v e i s to see the codettas i n mm. 43-62(1) as a separate codetta-complex small section, or as further codettas to the subordinate theme. This i n t e r p r e t a t i o n i s supported by the s i m i l a r cadences i n mm. 41(4)-43(1) and 55(4)-58(l). The cadence forming the subsequent codetta (mm. 58-62[l]) i s e s s e n t i a l l y a strengthening of the previous cadence. I t follows, according to t h i s a l t e r n a t i v e , that the c l o s i n g s ection i s i n mm. 62-73 and i s of a more common length than the 30-bar type (1) noted i n my e a r l i e r i n t e r p r e t a t i o n . Here, then, i t i s a type (y) c l o s i n g codetta. Piano Sonatas K. 284, 309, 311, 333, 545, 570. In chapter 3 I consid-ered the c l o s i n g s ection of the Piano Sonata i n D Major, K. 284, to begin at m. 38. However, because mm. 38-50(1) are strongly r e l a t e d to the preceding thematic statement, they may be considered a codetta to the theme, leaving mm. 50-51 as a c l o s i n g codetta.. It would be reasonable to see a l l of mm. 22-51 as a si n g l e section, l a r g e l y because there i t has only one complete cadence. It i s apparent that t h i s long section has both thematic and c l o s u r a l functions (the dual function feature being the reason why t h i s section i s somewhat loose i n s t r u c t u r e ) . Closure i s generated mainly by the repeated codetta i n mm. 38-43 and by the subsequent ECP, In the Piano Sonata i n C Major, K. 309, the main theme—a period, extended with a codetta—ends at m. 21(1). The t r a n s i t i o n ends at m. 32 and i s followed by a 2-bar l i n k to the subordinate theme. The c l o s i n g section of t h i s exposition, a type (x) c l o s i n g codetta, follows immediately a f t e r the ST. In the absence of the usual codetta between the subordinate theme and the 162 c l o s i n g section, the subordinate theme i s here lengthened to include an ECP ( i . e . , one section does what i s more commonly done i n two). The subordinate theme and c l o s i n g section, as well as the r e c a p i t u l a t i o n form of the c l o s i n g section, are discussed on pp. 75-76 and shown i n example 8. In the discussion of the Piano Sonata i n D Major, K. 311, i n chapter 3, mm. 24-39 were considered one section that combined subordinate theme codetta and c l o s i n g section functions. An a l t e r n a t i v e analysis would see mm. 24-36(1) as p r i m a r i l y a subordinate theme codetta, and mm. 36-39 as a type (y) c l o s i n g codetta. This i n t e r p r e t a t i o n i s supported by some motivic associations be-tween the theme and i t s codetta (e.g., the cadences i n mm. 31-32 and 35-36 are s i m i l a r to the cadence ending the theme i n mm. 23-24). In add i t i o n , the theme i s short and i s without expansions. Support f o r t h i s second i n t e r -p retation i s found i n the r e c a p i t u l a t i o n , which, as I noted i n chapter 3, i s considerably d i f f e r e n t from the exposition. In p a r t i c u l a r , mm. 24-36(1) are separated from the c l o s i n g codetta, the f i r s t theme being heard between the two; that i s , the r e c a p i t u l a t i o n form i s : subordinate theme and codetta-complex (mm. 79-98), main theme (mm. 99-108), c l o s i n g codetta (mm. 109-112). Here i t i s obvious that the codetta-complex i s associated p r i m a r i l y with the subordinate theme. The main theme has a new ending, i n which a p a i r of s i m i l a r 2-bar groups (mm. 105-108) lead d i r e c t l y into the c l o s i n g section. The Piano Sonata i n B - f l a t Major, K. 333, was discussed at various points i n chapter 2.^ In p a r t i c u l a r , I draw the reader's attention to pp. 83 and 87 of chapter 2, where the form of the exposition was analysed i n two d i f f e r e n t ways. In both i n t e r p r e t a t i o n s the c l o s i n g section i s i n mm. 59-63 and i s a type (y) c l o s i n g codetta. Despite the f a c t that some aspects of the c l o s i n g model are found i n the codetta-complex i n mm. 39-59(1), 163 the closing section cannot be considered to begin i n m. 39; nor can i t begin somewhere between m. 39 and m. 59, since mm. 39-59 form one section. This section does, however, i n i t i a t e closure with some closing model features. Aside from an expansion i n the codetta-complex and some alterations to the t r a n s i t i o n , the recapitulation i s sim i l a r to the exposition. The exposition of the Piano Sonata i n C Major, K. 545, was discussed i n chapter 2, p. 89 and note 43. A few comments here w i l l elaborate on that previous summary. There are a number of interesting s i m i l a r i t i e s between the two themes, i n pa r t i c u l a r the fact that both are twelve bars long and are constructed with ( 4 + 4 + 4 ) timespans. Measure 13 has the function, then, of breaking up the otherwise smooth flow of 4-bar timespans, and takes the place of a t r a n s i t i o n . Measures 26-28 function both as a sub-ordinate theme codetta and as a type (x) closing codetta. The exposition timespan summary i s thus: ( 4 + 4 + 4 ) + 1 + (4 + 4 + 4) + 3. Measures 13 and 26 to 28 add up to one more 4-bar unit; these bars are the two subsidiary "sections." These two short, i r r e g u l a r units serve to highlight the two themes by contrasting with the more periodic nature of the themes: i n other words, even though they are not sections, they re t a i n the contrasting function of such subsidiary sections. The irregular length of the closing codetta also sets off the exposition from the development, which i s constructed with (4 + 4 + 4) + 1 timespans, based at f i r s t on the closing-codetta material. Here again the primary part of the development i s the same length as the two themes, and there i s an additional irregular unit setting off the dev-elopment, i n turn, from the r e c a p i t u l a t i o n . ^ In the Piano Sonata i n B - f l a t Major, K. 570, the main theme i s i n mm. 1-20, the t r a n s i t i o n i n mm. 21-40, the subordinate theme i n mm. 41-69(1), 164 and the c l o s i n g section i n mm. 69-79. The c l o s i n g section melody begins a bar a f t e r i t s f i r s t 4-bar timespan, but the new accompaniment f i g u r e s t a r t s immediately i n m. 69. This c l o s i n g section i s based on the c l o s i n g model i n that there are two pa i r s of repeated groups, having timespans (4 + 4) + (1 + 1) + 1. This c l o s i n g section may be considered a type (x) c l o s i n g codetta because the subordinate theme and i t s codetta form one section; that i s , to the extent that the theme ends i n m. 69, the c l o s i n g codetta i s of type ( x ) . 8 There i s a greater degree of uniformity i n the nature of type (2) c l o s i n g sections than i n those of type (1), p r i m a r i l y due to the short length of c l o s i n g codettas. Most c l o s i n g codettas are based on shortened forms of the c l o s i n g model, the most common having one or two pairs of repeated groups. This short length means that s i g n i f i c a n t closure i s i n i t i a t e d p r i o r to the c l o s i n g section i n most works which have the c l o s i n g codetta. Of course, i n most works—no matter what type of c l o s i n g section i s u s e d — closure i s i n i t i a t e d before the c l o s i n g section: as has been seen, the cadence or ECP concluding the subordinate theme area i s normally one of the strongest i n the movement. The short length of the c l o s i n g codetta, however, means that closure takes place p r i m a r i l y before, rather than during, the c l o s i n g section, e s p e c i a l l y i n the shortest c l o s i n g sections. That t h i s i s true i s confirmed by the prevalence of type (y) c l o s i n g codettas, those with a codetta-complex between the subordinate theme and the c l o s i n g section. The codettas of t h i s complex ei t h e r function as extensions of the subordinate theme area, or they group together as a sep-arate small section (there may be some of both types i n a given work); 165 also, they i n i t i a t e closure, p r i m a r i l y through the use of the expanded cadential progression and p a i r i n g of repeated groups (many such codetta-complexes res-emble the c l o s i n g model). Although the i n t e r n a l structure of c l o s i n g codettas i s f a i r l y uniform, the contexts i n which they are found vary widely. 166 5 The Closing Theme Followed by the Closing Codetta The features of the c l o s i n g theme followed by the c l o s i n g codetta were outlined i n chapter 2: l e v e l ( c ) : c l o s i n g sections, p. 76, which the reader may wish to review. Five of the works I have analysed f a l l i nto t h i s category of c l o s i n g section. Symphony no. 41. The exposition of the Symphony i n C Major ( J u p i t e r ) , no. 41, was discussed i n chapter 2: l e v e l (d): expositions, p. 88. Expansion i s a feature of the several subsections of the subordinate theme area: (1) The theme p r o p e r — a period i n mm. 56-71(1)—has i t s second h a l f expanded by three bars; that i s , the theme i s constructed with (6 + 9) timespans. (2) The f i r s t codetta-complex, i n mm. 71-89(1), has i t s second group— s t a r t i n g i n m. 75 as a repeat of m. 7 1 — g r e a t l y expanded, and even interrupted i n m. 80; that i s , the timespans of t h i s subsection are (4 + [6 + 8 ] ) . The 8-bar group i s an ECP. (3) The following codetta, i n mm. 89-100, has i t s second group expanded by two bars; that i s , the timespans are ( 5 + 7 ) . The unique ending of t h i s l a t t e r codetta deserves some comment: no other c l o s i n g section examined here involves such an approach. Normally, 167 codettas end with cadences or at least with tonic harmony, often with tonic pedals: the group i n mm. 89-94(1) i s t y p i c a l . The group i n mm. 94-100 i s therefore not functioning as a codetta to the extent that i t has a weaker cadence than the preceding group. (This pair of groups thus reverses the normal cadential patterning found i n such codettas; i . e . , when the cadences of group pairs are not i d e n t i c a l , the second one i s usually stronger than the f i r s t . Often the second one i s or has an ECP.) One effect of t h i s unusual codetta ending i n m. 100 i s that the closing section i s strongly a r t i c u l a t e d . The harmonic motion, the change of melodic material, the change of dynamic l e v e l , the change of instrumentation, and the use of rests contribute to this formal a r t i c u l a t i o n . A reason for t h i s special treatment of this d i v i s i o n i s that the closing section begins i n m. 101 with material that i s more theme-like than usual. If standard codetta material were to be used i n m. l O l f f . , then the ending of the previous codetta would be inappropriate. (For example, imagine the omission of mm. 101-111[1] with the codettas i n mm. 111[2]-120 d i r e c t l y following m. 100.) The nature of the closing section has i n part determined the structure of the preceding section, i n p a r t i c u l a r the unusual ending of the codetta preceding the closing section. As an alternative to seeing m. 101 as the start of the closing section, m. 89 might be considered the start because (1) the subordinate theme and i t s codetta have taken place, (2) the ECP ends on the downbeat of m. 89, and (3) mm. 89-100 form a closural pair of si m i l a r groups. The main factor working against t h i s interpretation i s the strong formal d i v i s i o n i n mm. 99-101 which makes the material s t a r t i n g i n m. 101 appear as a new section. 168 Diagram 40 Symphony no. 41: Exposition Closing Section Measures: 101 107 111 117 Timespans: ([2 x 3] + [2 x 2]) + (3 x 2) + (1 x 3) + 1 Groups: a a a b b c c d d d The c l o s i n g theme (CT) i s i n mm. 101-111(1) and i s not obviously based on a thematic model. However, i t has the character of a theme because (1) of the way i t i s prepared by the preceding codetta, as discussed above, (2) of the introduction of new motives not obviously r e l a t e d to any preceding material, (3) of the dynamic and t e x t u r a l change: the CT i s u n i f i e d and distinguished from i t s surroundings by a piano dynamic and d i f f e r e n t texture, and (4) thematic statements are usually given by s t r i n g s , with the melody i n the v i o l i n s , as i s the case here. See diagram 40. C e r t a i n l y there are some resemblances to the c l o s i n g model here, espe-c i a l l y i n the p a i r i n g of s i m i l a r groups and the move towards material that has more features of codettas. The c l o s i n g model contains such a progression, i n part because of the shortening of group length: the shorter the group the less space f o r motivic material. In the case of the CT followed by the c l o s i n g co-detta, t h i s progression i s amplified by the more thematic nature of the f i r s t subsection. It w i l l be r e c a l l e d that the f i r s t p a i r of groups i n the c l o s i n g model i s often l i k e a s i m p l i f i e d period: the c l o s i n g theme-closing codetta may thus be viewed as a modification or s p e c i a l case of the c l o s i n g model i n which the f i r s t subsection i s more thematic than usual.''" The three a groups are very s i m i l a r except f o r a few d e t a i l s , f o r ex-ample, the oboe entrance i n m. 103, and the bassoon doubling i n m. 105ff. The 169 l a t t e r r e c a l l s the subordinate theme; see m. 62ff., where the bassoon i s used i n a s i m i l a r way, that i s , to double the v i o l i n melody two octaves lower, i n v a r i a t i o n of preceding material. The two b_ groups are very s i m i l a r except f o r the add i t i o n of the f l u t e doubling of the melody i n the second b_ group. This again i s s i m i l a r to the addition of the f l u t e i n the subordinate theme, m. 67ff. The a and b_ groups are more connected than i n the c l o s i n g model, l a r g e l y because of the way the b_ group begins i n m. 107 as a continuation of the a_ group, and because of s i m i l a r i t i e s i n harmonic rhythm and texture. The two £ groups, although three bars long, are made up of two sequenced 1-bar u n i t s , followed by a 1-bar cadence. They are c l e a r l y separated from the preceding material by the r e s t , sudden f o r t e , a d d i t i o n of brass i n s t r u -ments, and change i n texture i n m. 111. The implications of the s i m i l a r i t i e s i n orchestration noted above between the subordinate theme and c l o s i n g section are worth considering because the unusual s i m i l a r i t i e s seem more than c o i n c i d e n t a l . Diagram 41 i s incomplete i n that i t omits the f a c t that i n both sections the bassoon and f l u t e are added as doublings of the melody i n v a r i a t i o n of immediately preceding m a t e r i a l . In the case of the subordinate theme—which here f o r convenience I take to include the codettas up to m. 100—the process of add i t i o n of winds and brass to a b a s i c a l l y s t r i n g texture i s begun gradually, but then interrupted i n mm. 71-80, and then i s abruptly completed with the unexpected f o r t e entrance of the f u l l orchestra i n m. 81. In the case of the c l o s i n g section, however, the addition of instruments, begun the same way as i n the subordinate theme, i s completed without i n t e r r u p t i o n . 170 Diagram 41 Symphony no. 41: Orchestration of Exposition Subordinate Theme and Closing Section Measures: Instrumentation: Dynamics: f o r t e Measures: Instrumentation: 81-99 CS: 101 105 109 111 to 120 f l u t e — f winds oboe winds bsn. brass brass Dynamics: strings-f o r t e — -strmgs--piano -f orte-P a r t l y because of t h i s o r c h e s t r a t i o n a l r e l a t i o n s h i p between the two sections, the c l o s i n g section may be heard as brought to a more s a t i s f y i n g close than the subordinate theme. This r e l a t i o n s h i p i s somewhat l i k e that of a period, i n which two subsections begin: the same way, but only the second, by completing what was implied i n the f i r s t , i s heard as closed. Support for t h i s view i s also found i n the f a c t that the subordinate theme ends, unusually, with dom-inant harmony ( i n mm. 99-100); t h i s i s , of course, s i m i l a r to the usual ending of the f i r s t h a l f of a period. A great deal of the development section i s based on the c l o s i n g theme. A f t e r a 2-bar introduction modulating to E r f l a t , the c l o s i n g theme i s i n f a c t stated completely i n t h i s new key i n mm. 123-132(1). One reason the key of E - f l a t sounds so convincing here i s that the c l o s i n g theme melody has a pro-171 Diagram 42 Symphony no. 41: Closing Theme i n Exposition and Development j 2 1 1 = 3 ^ 1 3 2 1 0 -e- o o o w BO 4W- r y . — _ ^ y CT (e.g., mm. 101-103[1]).and codetta (e.g., mm. 113-114[1] modulation mm. 121-123 n : CT i n Dev. (e.g., mm. 123-125[1]) n- ° — o — H — g ° b z - — vo , b n hit . • YV mment use of 3-2-1, and the 3 of E - f l a t i s the tonic of the previous t o n a l i t y . The modulation i n mm. 121-123 i s based on t h i s same 3-2-1 progression; the 2 theme's melody i s thus heard as an echo of the modulation. See diagram 42. Motives from the CT are used i n the development up to the f a l s e r e c a p i t u l a t i o n s t a r t i n g i n m. 161 and they recur again towards the end of the r e t r a n s i t i o n , mm.. 181-188. The main theme i s repeated without change i n mm. 189-211. The t r a n s i t i o n i s rewritten to a c e r t a i n extent: the changes p r i m a r i l y involve s t a r -t i n g i n C minor rather than i n C major, and a l t e r i n g m. 235ff. to stay on G as pedal. One 8-bar codetta of the subordinate theme i s rewritten: mm. 269-276 are s i g n i f i c a n t l y d i f f e r e n t from mm. 81-88. The c l o s i n g section i s b a s i c a l l y unchanged, i n mm. 289-313. The cadence at the end of the c l o s i n g theme i s extended by one bar, mm. 304-306(1), and f i v e bars of tonic arpeggios i n mm. 309-313 replace the one bar of tonic i n m. 120. Some aspects of orchestration are a l t e r e d i n the subordinate theme and c l o s i n g section. Both have a s l i g h t l y thicker texture due to the addition of horns i n the subordinate theme, and trumpets and timpani i n the c l o s i n g section. Although the sequence of add i t i o n of instruments i s not the same i n both sections as i t was i n the exposition, there are s t i l l s i m i l a r i t i e s i n how the two sections are orchestrated. 172 Str i n g Quartet K. 465. The a l l e g r o of the St r i n g Quartet i n C Major, K. 465, begins with a 22-bar main theme i n mm. 23-44. Despite i t s length, t h i s theme i s t i g h t l y organized i n i t s use of both period and sentence models. In other words, the e n t i r e theme i s constructed as a period (8 + 14), and each subsection as a sentence (4 + 4) + (4 + 10). Obviously, the second subsection has an extension i n the manner of a codetta. The t r a n s i t i o n follows i n mm. 44-55,. overlapping the f i n a l bar of the main theme. Although the t r a n s i t i o n i s s h o r t — i t i s h a l f the length of the preceding t h e m e — i t has a f a i r l y strong modulation to the dominant because i t moves very quickly towards V and because i t ends on a V/V pedal. The subordinate theme i s a 15-bar sentence i n mm. 56-71(2). The f i r s t subsection i s the standard (2 + 2) pattern, but the second i s considerably extended with sequences and an ECP. The c l o s i n g theme i s a normal 8-bar period i n mm. 71(3)-79(1). The c l o s i n g section then continues with a series of codettas to m. 99. (The r e -t r a n s i t i o n i n mm. 99-106 was discussed on pp. 69-70.) See diagram 43. Various in t e r p r e t a t i o n s of the timespan lengths are possible i n t h i s section. For ex-ample, the c l o s i n g theme timespan could be started at m. 72 (with an overlap at m. 79); however, I have decided on m. 71 on the basis of harmony—m. 71 being a prominent tonic a r r i v a l — a n d on the basis of p r i o r establishment of 4-bar time-spans at m. 67. Whatever the d e t a i l e d view of timespans here, the o v e r a l l pat-tern i s (8 + 12 + 8). Diagram 43 String Quartet K. 465: Exposition Closing Section Measures: 71 79 87 91 Timespans: (4 + 4) + ([5 + 3] + 4) + (4 + 4) 1 b d 1 Groups: a a c e e 173 This i s one of the few closing sections i n which there i s almost no use of any features of the closing model. The only group pairs are the period a a \ and the f i n a l pair ee^ " (this l a t t e r pair based on the opening main theme motive). There i s some rep e t i t i o n i n each of the b_, c_, ci, and e_ groups, that i s , at the 1-bar l e v e l . However, there i s no overall pattern of reduction of group length. In the recapitulation the main theme and t r a n s i t i o n are combined to form one section i n mm. 155-175. The f i r s t seventeen bars of the theme are repeated with a number of surface alterations to which are added the f i n a l four bars of the transposed t r a n s i t i o n . The subordinate theme follows i n mm. 176-191(2): although i t i s the same length and has the same material as i n the exposition, some det a i l s are rewritten, especially i n mm. 182-190 (e.g., the i n t e r v a l of transposition i s changed to direct the theme towards the key of F major). The closing theme i s then repeated i n C major without a l t e r a t i o n . The remainder of the closing section follows i n mm. 199-219 with some surface changes. In p a r t i c u l a r , the cadence i n mm. 208-211 i s strengthened due to the use of 3-4-#4-5-l as the bass voice, compared to b7-6-#4-5-l i n mm. 88-91. The r e t r a n s i t i o n i n mm. 219-226 i s sim i l a r to that i n the exposition, and so moves towards the key of F major ( i . e . , as the r e t r a n s i t i o n i n the exposition moved from G major to C major, so i n the recapitulation i t moves from C major to F major). The f i n a l b a r — 2 2 6 — i s altered so that the coda w i l l begin as the development does, with a variant, i n F major, of the begin-ning of the main theme. This main theme motive i s quickly liquidated and a cadence closes off further motivic development i n mm. 227-235(1). A pair of si m i l a r 3-bar groups i n mm. 235-240 i s followed by a pair of active 2-bar groups over a tonic pedal i n mm. 241-245, then by a bar of tonic arpeggio. Overall, 174 the timespans i n the coda are 8 + (3 + 3) + (2 + 2) + 2. The p a i r i n g of s i m i l a r groups and the reduction i n timespan length are both features of the c l o s i n g model, features that were not strongly present i n the c l o s i n g section. To an extent, then, the coda supplies c l o s u r a l features absent from the c l o s i n g section. V i o l i n Sonata K. 481. The exposition of the Sonata f o r V i o l i n and Piano i n E - f l a t Major, K. 481, was c i t e d i n chapter 2: l e v e l (d), p. 85, as an example of normative small section structure. The main theme, i n mm. 1-24, i s a sentence v a r i a n t with a codetta, that i s , (6 + 6 + 4) + (4 + 4). The t r a n s i t i o n , i n mm. 25-36, forms a strong contrast with the preceding theme by v i r t u e of t o n a l i t y , motives, and surface rhythm. The subordinate theme, i n mm. 37-68, contrasts strongly with the preceding sections f o r these same reasons. In a d d i t i o n , the subordinate theme—a modified p e r i o d — h a s a s e r i e s of extensions to i t s second h a l f culminating i n an ECP i n mm. 63-68. See d i a -1 1 4 gram 44. Groups cdc d -ECP form a secondary u n i t within the theme. The c l o s i n g theme, i n mm. 69-84(1), i s a double p e r i o d— 8 + 8 — i n which motives and surface rhythm again are responsible f o r creating strong contrast with the preceding sections. O v e r a l l , then, t h i s exposition has a high degree of contrast between the four small sections. The c l o s i n g theme and Diagram 44 V i o l i n Sonata K. 481: Exposition Subordinate Theme Measures: 37 41 45 49 53 57 61 Timespans: (4 + 4) + (4 + 4 + 4 + 4 + [2 + 6]) Phrases: a b a* c d c"*" d^ ECP 175 Diagram 45 V i o l i n Sonata K. 481: Exposition Closing Section Measures: 69 73 77 81 85 Timespans: ([4 + 4] + [4 + 4]) + ([2 + 2] + [1 + 1]) Phrases/groups: a b 1 a b 1 c c 1 1 c c Cadences: HC IAC HC PAC c l o s i n g codetta may be summarized as i n diagram 45. Phrase b i s a vari a n t of a_ ( i . e . , where a. ends on V, b_ ends on I ) , but rather than l a b e l b_ as a^ i t i s more important to i n d i c a t e that the two phrases i n mm. 77-84(1) are variants of the two preceding ones. (In 1 1 . . 1 2 3 other words, aba b i s more informative than aa a a .) The c l o s i n g model applies to a s u b s t a n t i a l extent to t h i s c l o s i n g section: a l l phrases and groups are paired with s i m i l a r ones ( i . e . , mmnnoopp) and there i s a reduction i n timespan bar length of 4 to 2 to 1. A 2-bar r e t r a n s i t i o n i n mm. 90(2)-92 converts the B - f l a t harmony to a dominant. The main theme i s rec a p i t u l a t e d i n mm. 140-155(1), with the 8-bar co-detta omitted and replaced with a sequence of the f i n a l phrase of the theme, i n mm. 155-159. This sequence t o n i c i z e s the subdominant, permitting the t r a n s i t i o n to be transposed up a fourth so that i t now ends on V instead of on V/V. This i n turn allows the subordinate theme to appear i n the toni c ; there are very few a l t e r a t i o n s to t h i s theme. The c l o s i n g theme i s repeated i n E - f l a t without change i n mm. 204-219(1). The c l o s i n g codetta i s , however, replaced by a new section i n mm. 219-229(1) that begins with sequences based on the 2-bar c l o s i n g codetta group. A f t e r t h i s section cadences, the missing codetta to the main theme i s heard i n 176 Diagram 46 V i o l i n Sonata K. 481: Recapitulation Ending Measures: 220 230 238 245 Timespans: (2 + 2 + 2 + 4) + (4 + 4) + 7 + (2 + 2) + (1 + 1) + 2 1 2 3 , ,1 j j A A Groups: a a a a b b c d d d d mm. 229(2)-237(l); the only changes here are the addition of a new anacrusis f i g u r e i n m. 229 and the overlap with the succeeding section i n m. 237. The l a t t e r , extending to m. 245, i s a new section based on the material i n the ce n t r a l section of the development, mm. 104-121; whereas i n the development t h i s material i s used i n modulatory sequences, i n the r e c a p i t u l a t i o n i t i s used i n an e s s e n t i a l l y d i a t o n i c way with the key of E - f l a t . F i n a l l y , the c l o s i n g codetta returns with a new accompaniment and a s l i g h t l y changed ending i n mm. 245-252. The sections from m. 219 to m. 252 form an ending "to the r e c a p i t u l a t i o n d i f f e r e n t from that of the exposition; they do not form a coda, although some functions of a coda are present. (If there were a coda 'here, l o c a t i n g i t s beginning would be d i f f i c u l t . ) See diagram 46. One of the strongest c r i t e r i a f o r timespan i n i t i a t i o n i s harmonic a r r i v a l . Often, however, other factors work i n concert to override harmony: t h i s occurs frequently i n the present movement, and i s i n f a c t a c h a r a c t e r i s t i c feature of i t . Various factors are seen to counteract the normal tendency of the f i n a l chord and bar of a phrase to be accented, factors which, while occurring i n other works, are more frequent here. For example, the 6-bar phrase lengths i n the main theme permit the f i n a l cadential harmony to a r r i v e a bar early ( i . e . , i n mm. 5 and 11), thus making the f i n a l bar of each phrase unaccented. (Omitting mm. 3-4 and 9-10 would make the theme harmonically "square" and 177 would make the cadential harmonies a r r i v e too early.) Instead of subsequent phrases continuing with the p r e v a i l i n g harmony or overlapping with the pre-ceding phrase, phrases often s t a r t with a new harmony or have a r e s t between phrases or other a r t i c u l a t i o n such as texture separate the two phrases. For example, see m. 17 which i s strong compared with m. 16, and s i m i l a r l y m. 25 compared with m. 24. The f i r s t d i s r u p t i o n to timespans s t a r t i n g on odd-numbered bars occurs i n the ECP, where mm. 64 and 66 are accented ( i . e . , mm. 63-68 are 1 + 2 + 2 + 1 ) . The alignment of harmony with timespans i s a f a c t o r i n the strength of t h i s cadence. The c l o s i n g theme, however, returns to timespans beginning on odd-numbered bars i n m. 69. And, despite the change of dynamics and texture i n m. 84, that measure remains unaccented and functions as an upbeat bar to m. 85. Whether or not odd-numbered, bars continue to.be accented through the r e t r a n s i t i o n and introduction to the development (mm. 90-96), i t i s c l e a r that the main part of the development has, 2-bar timespans s t a r t i n g on odd-numbered bars (mm. 97-118). Note i n p a r t i c u l a r mm. 104-105, where a r r i v a l of A - f l a t major tonic harmony and i n i t i a t i o n of a new texture i n m. 104 do not create an accent: that timespans begin i n m. 105 i s c l e a r p r i m a r i l y from the left-hand octaves and subsequent v i o l i n a r t i c u l a t i o n s . (This subsection i s also grouped at a higher l e v e l into 4-bar timespans—105-108, e t c . — b y the rests i n the v i o l i n l i n e , creating a 4-note motive that often has been c i t e d as one of Mozart's f a v o r i t e s , r e c u r r i n g i n other works such as the f i n a l e of the Symphony no. 41.) A s i g n i f i c a n t change occurs i n mm. 119-121: t h i s i s a 3-bar timespan, extended by one bar from the 2-bar norm by the hemiola i n mm. 120-121. This c l e a r l y puts a strong accent on m. 122, i n i t i a t i n g 2-bar timespans now on 178 even-numbered bars, and i t functions to a r t i c u l a t e the r e t r a n s i t i o n subsection i n mm. 122-139. (Bar 122 i s one l o c a t i o n where timespan i n i t i a t i o n i s i n f l u -enced by harmonic a r r i v a l , of course i n concert with other factors such as v i o l i n a r t i c u l a t i o n and rhythm.) The r e c a p i t u l a t i o n thus d i f f e r s from the exposition by having timespans s t a r t on even-numbered bars, a f a c t which i s remarkable only by v i r t u e of the extreme consistency of the 2-bar hypermeter l e v e l . This pattern continues — t h e r e c a p i t u l a t i o n otherwise c l o s e l y r e l a t e d to the exposition, as noted above—to the subsection i n mm. 238-244. I t i s within these eight bars that a s h i f t back to timespans beginning on odd-numbered bars begins. Bar 238 i s strong by continuation of even-numbered bars accentuation and by analogy with m. 104ff. The bass and v i o l i n a r t i c u l a t i o n s are not, however, the same continuing from m. 238 (compare m. 105). The v i o l i n changes from a 3-bar a r t i c u l a t i o n to two 2-bar ones i n mm. 238-240, 241-242, 243-244. The bass pattern i s not c l e a r on i t s own except that m. 240 i s l i k e m. 239, suggesting an extension supporting the v i o l i n ' s 3-bar grouping, and that mm. 243-244 form a 2-bar u n i t based on s i m i l a r a r t i c u l a t i o n and patterning. The harmony supports the 2-bar units i n 241-242 and 243-244, and therefore these eight bars i n mm. 237-244 have timesparts of, from m. 236, ( 2 + 3 + 2 + 2 ) . The s h i f t back to accentuation of odd-numbered bars would seem to be negated i n m. 245, which, by analogy with m. 84, should be unaccented. However, a comparison of the subsections i n mm. 245-252 and mm. 84-90 reveals differences which reduce t h e i r s i m i l a r i t y to the point where they have opposite timespan patterning. . F i r s t , the preceding material i s not the same for both subsections: i n the exposition, mm. 81 and 83 are accented, leading to accentuation of 85 and 87; i n the r e c a p i t u l a t i o n , mm. 241 and 243 are accented, supporting accentuation 179 of 245, 247, etc. Second, the bass supports di f f e r e n t 2-bar patterns i n each case: i n the exposition, patterns begin on the second and fourth bars (mm. 85, 87); whereas, i n the recapitulation, patterns begin on the f i r s t and t h i r d bars (mm. 245, 247). Third, the endings of each subsection are d i f f e r e n t : i n the exposition, a change to even-numbered bar accentuation i s possible i n mm. 88 and/or 90; i n the rec a p i t u l a t i o n , no such change i s l i k e l y , odd-numbered bar accentuation continuing to the end. Whereas much of the movement i s characterized by timespan i n i t i a t i o n that i s not influenced by harmonic a r r i v a l , the f i n a l sections of the move-ment reverse t h i s feature to have timespan i n i t i a t i o n and harmonic a r r i v a l i n synchrony. This i s further supported by dynamics, which change i n m. 245 with the new timespan and harmonic unit. Piano Sonata K. 332. The Piano Sonata i n F Major, K. 332, i s char-acterized by a large number of thematic statements; that i s , there are themes and theme-like constructions i n places where such statements are not normally found. The main theme, of unique construction, i s i n mm. 1-12(1) and i s followed by i t s codetta—a s i m p l i f i e d p e r i o d — i n mm. 13-22. As i n the v i o l i n sonata just discussed, the t r a n s i t i o n here strongly contrasts with the preceding theme and codetta. To the extent that t h i s t r a n s i t i o n introduces and prominently features new motives—that i s , i n mm. 2 3 - 2 6 — i t i s more thematic than usual for a t r a n s i t i o n . (For example, compare the t r a n s i t i o n i n the previously-discussed v i o l i n sonata, consisting largely of sixteenth-note patterns.) These motives are liquidated as the t r a n s i t i o n moves to the dominant of the p a r a l l e l minor of C, ending i n m. 40. 180 Diagram 47 Piano Sonata K. 332: Exposition Closing Section • Measures: 71 82 86 90 Timespans: ([6 + 6] + [2 + 2]) +.(2 + 2) + 4 Phras es/groups: a a^ b b^ " c c^ d The subordinate theme, a double period ( 4 x 4 ) , follows i n mm. 41-56(1). The next section, i n mm. 56-70, returns to the key of C minor, uses sequence, and ends with a dominant pedal. In these respects i t resembles a second t r a n s i t i o n . The c l o s i n g theme then follows i n mm. 71-82(1) and the c l o s i n g codetta i n mm. 82-93. See diagram 47. The c l o s i n g theme i s i n the form of a s i m p l i f i e d period i n which the f i r s t h a l f ends with an imperfect authentic cadence (mm. 75-76), the second with an implied perfect authentic cadence (mm. 81-82). The e l i s i o n of the expected tonic i n m. 82 i s the beginning of the f i r s t codetta ( 2 x 2 ) , which could also be considered an extension of the c l o s i n g theme, as i t leads to the tonic c h o r d — i n m. 8 6 ( 1 ) — t h a t was expected i n m. 82(1). The c l o s i n g theme uses a motive that i s a s i m p l i f i c a t i o n of one i n the subordinate theme; that i s , mm. 71-72 resemble mm. 41-42 i n the use of a repeated note i n the f i r s t bar and a descent by a whole tone on the t h i r d beat of the next bar. In addition, the codetta i n mm. 82-85 resembles the second t r a n s i t i o n (following the subordinate theme). From diagram 47 i t i s apparent that the p a i r i n g of s i m i l a r groups r e s -embles the c l o s i n g model. However, the b_ and a_ groups form a larger u n i t , and the timespan lengths do not correspond to those i n the model. Another possible i n t e r p r e t a t i o n of t h i s c l o s i n g section i s as a type (2)(y); that i s , mm. 71-86 181 would be a second subordinate theme and the remainder would be the c l o s i n g section (a c l o s i n g codetta). The development section begins with yet another theme i n mm. 94-109(1). This one resembles the CT, but i t i s transformed i n various ways, becoming here a sentence, repeated. Aside from a few d e t a i l s , the r e c a p i t u l a t i o n i s very s i m i l a r to the exposition. Piano Sonata K. 570. The Piano Sonata i n B - f l a t Major, K. 570, was considered i n chapter 4 to have a c l o s i n g codetta i n mm. 69-79. I t i s possible to hear the f i r s t two groups, i n mm. 69-77(1), as a simple period to the extent that the groups are phrases and have motives rather than grouplets. A much shorter c l o s i n g codetta would follow i n mm. 77-79.^ An explanation f o r t h i s r e i n t e r p r e t a t i o n i s suggested by the f a c t that the subordinate theme i s based on the opening motive of the main theme. The c l o s i n g theme then forms the more contrasting theme i n the dominant key. The c l o s i n g theme i s a further contrast i n that i t i s a period whereas the previous two themes were sentences. A s i m i l a r i t y with the previously-discussed work, the Piano Sonata K. 332, i s the large number of themes. Even the t r a n s i t i o n , a f t e r i t s two introductory bars, has a more theme-like statement than i s normal f o r a subsidiary section. Note, however, that Mozart compensates for t h i s abundance of themes by ending each of the four small sections with a codetta or co d e t t a - l i k e material. This paradigm of theme/codetta f o r small sections continues even i n the devel-opment section and through the r e c a p i t u l a t i o n . See table 4. 182 Table 4 Piano Sonata K. 570: Theme/Codetta Paradigm at Level (c) Small Section Theme: mm. Codetta: mm. Main theme Sentence: 1-12(1) 12(2)-20 T r a n s i t i o n 23-34 35-40 Subordinate theme Sentence: 41-57(1) 57-69(1) Closing section Period: 69(2)-77(l) 77-79 Dev. sec. (1) (TR): 81-94 95-100 (2) (ST): 101-116 117-132 Main theme Sentence: 133-144(1) 144(2)-152 T r a n s i t i o n 155-164 165-170 Subordinate theme Sentence: 171-187(1) 187-199(1) Closing section Period: 199(2)-207(1) 207-209 In comparison with types (1) and (2), c l o s i n g sections of type (3) are not common. This i s due to the prevalence of the exposition model i n which p r i m a r y — t h a t i s , t h e m a t i c — s e c t i o n s alternate with subsidiary ones, the c l o s i n g section normally thus being a s u b s i d i a r y — t h a t i s , non-thematic— section. It i s i n t e r e s t i n g therefore to note that some of the type (3) c l o s i n g sections use themes throughout the exposition (e.g., the two piano sonatas), the CT thus occurring as part of an o v e r a l l thematic design. Elements of the c l o s i n g model, however, continue to be used i n the CT-CC type of c l o s i n g section. The use of p a i r i n g of s i m i l a r groups and/or the use of reduction of timespan length are found i n most of the works con-sidered i n t h i s chapter. 183 6 Closing Sections Not Based on Models This fourth and f i n a l type of c l o s i n g section i s i n f a c t not a type at a l l , but i s a category f o r c l o s i n g sections which do not f i t any of the pre-vious three types. In other words, i n t h i s chapter I w i l l consider c l o s i n g sections which are the most a t y p i c a l , i n the same sense of a t y p i c a l that I applied to those themes that were thematic without being based on any of the thematic models (see chapter 2: l e v e l [ c ] : themes, p. 66). This category also includes those works i n which the c l o s i n g section i s d i f f i c u l t to i d e n t i f y as well as those i n which the c l o s i n g section combines with other sections. A few works discussed i n the previous three chapters had one of other of these features, although not to the extent that the works to be discussed here have them. For example, several works were considered i n more than one chapter because they could be analysed i n more than one way regarding c l o s i n g section l o c a t i o n (e.g., Symphonies 32 and 34 were analysed i n chapters 3 and 4); however, at l e a s t i n those cases evidence could be found f o r supporting each i n t e r p r e t a t i o n . The present category also includes those cases i n which no c l e a r c l o s i n g section emerges. Although few of the movements considered i n the previous chapters have expositions that do not conform to the four-small-section model ( l e v e l [d]), most of the works to be analysed here do have unusual exposition forms. 184 As w i l l be seen, then, most of these works have unusual features on a v a r i e t y of l e v e l s , and not j u s t i n t h e i r c l o s i n g sections. F i n a l l y , there are very few works having c l o s i n g sections which do not follow any of the models. In f a c t , only s i x of the forty-seven works I have analysed f o r t h i s d i s s e r t a t i o n w i l l be considered i n t h i s chapter. Symphony no. 35. The exposition of the Symphony i n D Major (Haffner), no. 35, was discussed on pp. 86-87 as an example of a work i n which the four-small-section model does not apply very w e l l . Reasons were given there as to why the exposition model applies weakly; here I w i l l discuss what the form i s , rather than what i t i s not.^" The only p r i m a r i l y thematic statement i n the movement i s the main theme i n mm. 1-13. This theme i s a v a r i a n t of the- sentence model: instead of having timespans (2 + 2) + (1 + 1 + 2), the theme has p a r t i a l l y doubled timespans of ( 3 + 2 ) + ( 2 + 2 + 3 ) . Measures 13-23 may be seen as a codetta to the theme, or, more l i k e l y , as the f i r s t part of the t r a n s i t i o n . (Codettas are usually not variants of preceding thematic material, whereas t r a n s i t i o n s often are. Furthermore, the addition of instruments coupled with the sudden f o r t e i n m. 13 are signals that the t r a n s i t i o n i s beginning. [This common feature of t r a n s i -tions i s discussed i n Batt, "Function and structure of t r a n s i t i o n s ; " see also the Symphony no. 39, i n which the t r a n s i t i o n begins i n m. 54.]) A f t e r the dominant i s t o n i c i z e d i n the following b a r s — 2 4 - 3 5 — a second theme could emerge. (There may not be a strong modulation, but i t i s not un-usual f o r a second theme to follow so weak a move towards the dominant.) Instead, the dominant, which might have become a t o n i c , retains i t s dominant function with the a d d i t i o n of the G-naturals, and a prominent return to the 185 Diagram 48 Symphony no. 35: Exposition Measures: Timespans: Keys : Small sections: Orchestration: Dynamics: (5 + 4 + 3) I main theme t u t t i ; s t r i n g s t u t t i f ; P . f 13 35 (6 + 4 + 6 + 6) (6 + 7) I (V) MTcdta/TRl 48 (11) I V MTvar.1/TR2 MTvar.2/TR3 s t r . ; t u t t i s t r i n g s P ;f P Measures: 59 67 74 Timespans: ( 4 + 4 ) ( 4 + 3 ) ( 6 + 4 + 4 + 7 ) Keys: Small sections: MT var.3 var. of MT var.3 CS Orchestration: t u t t i winds t u t t i Dynamics: f p f Note: The i n i t i a l move towards the harmonic area of V i s tentative; hence the use of parentheses. tonic ensues i n m. 41. That t h i s area i s d e f i n i t e l y not leading immediately to a second theme i s confirmed by the equally conspicuous return of the opening main theme motive. (Mozart's second themes are r a r e l y based on main theme motives.) The return of the opening motive i n the tonic key i n m. 41ff., although prominent, i s s h o r t - l i v e d . A sequence of the motive leads to a dominant-of-the-dominant pedal i n mm. 48-57. Nevertheless, the main theme motives are s t i l l u s e d — i n the v i o l a p a r t — a l t h o u g h with a new counter-melody i n the v i o l i n s . At the end of t h i s pedal we expect the second theme. An i n d i c a t i o n 186 that we are not going to get i t (yet) i s that the pedal ends with a cadence: normally, t r a n s i t i o n s end on the dominant, not the toni c , of the secondary key, that i s , the pedal would continue r i g h t up to the s t a r t of the theme, where the tonic would appear. When the theme does s t a r t , i n m. 59, i t i s once again on a D-major harmony. This time, however, the D-major chord i s heard as IV/V, not as I / I ; that i s , i t i s part of a pla g a l progression i n the dominant key. Never-theless, there i s a c e r t a i n weakness to the recent modulation to the dominant when, so soon a f t e r t h i s modulation, a new section begins on the previous to n i c . Furthermore, t h i s 8-bar theme—a s e n t e n c e - v a r i a n t — i s based, once more, on the opening main theme motives. This theme i s weakened as such by beginning on the subdominant, by i t s strong r e l a t i o n to main theme motives, and by i t s context:-when so many sections are based on the same material, none but the f i r s t stands out as p a r t i c u l a r l y thematic; The following 8-bar section, i n mm. 67-74, i s a varia n t i n the p a r a l l e l minor mode of the preceding theme. Whereas the f i r s t statement used the f u l l o r chestra,.forte, the va r i a n t uses mainly winds, piano; whereas the f i r s t statement ended without overlap i n m. 66, the second overlaps i n m. 74 with the s t a r t of the next section. The f i n a l section, i n mm. 74-94, i s a long codetta-complex divided into four subsections (codettas). I t i s one u n i f i e d section l a r g e l y due to (1) consistent use of the f u l l orchestra and f o r t e dynamic, and (2) use of only one cadence, that ending i n m. 88. The f i r s t subsection i s the r i s i n g scale f i g u r e i n octaves i n mm. 74-80(1); the second i s a repeated 2-bar cadential f i g u r e i n mm. 80-83; the t h i r d i s a stronger cadential codetta i n mm. 84-88(1); and the fourth i s the pedal that prolongs the cadential t o n i c , i n mm. 88-94, 187 and that includes a p a i r of repeated groups i n mm. 88-91. This f i n a l s e ction functions as a c l o s i n g section i n s p i t e of the almost complete absence of the usual models or procedures, f o r the three reasons as noted below: (1) This i s the only section not based on main theme motives. This makes i t notJso much a c l o s u r a l as a contrasting section. (2) Its o v e r a l l harmonic plan i s strongly oriented towards, and i s e n t i r e l y within, the tonic (A major), unlike most of the previous sections, many of which were p a r t l y i n D major (or minor) and p a r t l y i n A major. The f i r s t codetta r i s e s strongly to the dominant (to: m. 80), the second prolongs the dominant while implying a perfect authentic cadence (to m. 83), the t h i r d i s e s s e n t i a l l y c a d e n t i a l (to m. 88), and the fourth prolongs the tonic with a pedal (to m. 94). (3) The fourth subsection resembles a c l o s i n g codetta i n i t s p a i r i n g of 2-bar groups and use of a tonic pedal. This o v e r a l l view of the exposition form i s summarized i n diagram 48. In deciding the boundaries of small s e c t i o n s — a process more d i f f i c u l t i n t h i s movement than i n most I am considering h e r e — I added orchestration and dynamics to the usual c r i t e r i a of cadences, motivic unity, thematic construction, etc. It seems that orchestration and dynamics work i n unison to a s s i s t i n shaping the form of the exposition, replacing to a large extent the usual factors of theme and key. Of course, i n most works orchestration and dynamics are important—the former e s p e c i a l l y i n works scored f o r larger ensembles—but i n t h i s work they are more important than usual as form-generating elements. In p a r t i c u l a r , changes of orchestration and dynamics strongly a r t i c u l a t e the boundaries of small sections, and only two sections have such changes 188 i n t e r n a l l y . I t might be argued that d i f f e r e n t section boundaries could be formulated with emphasis put on other c r i t e r i a ; f o r example, mm. 88-94 might be regarded as a separate small section ( i . e . , a c l o s i n g codetta). However, the c o r r e l a t i o n between orchestration, 'dynamics, cadences, thematic models, etc., i s strong enough to support d i v i s i o n as noted i n diagram 48 and i n the paragraphs above. And, as stated i n chapter 2, t h i s movement i s so continuous — t h a t i s , lacking i n strong section demarcation—that any d i v i s i o n w i l l be ten t a t i v e . The key of the dominant i s weakened by the f a c t that r e l a t i v e l y few phrases or groups begin on tonic harmony i n the dominant key, and i n p a r t i c u l a r that the f i r s t phrase to begin on I i n A major with a t u t t i and f o r t e dynamic s t a r t s only at m. 74, the beginning of the c l o s i n g section. In other words, although a s u b s t a n t i a l amount of t i m e — a t l e a s t h a l f the e x p o s i t i o n — i s spent i n the key of the dominant, t h i s key i s weaker than i n expositions of comparable length i n other works f o r these reasons and because there i s no recognizable theme i n the dominant. Replacing t h i s lack of a theme i n V i s the development of the opening main theme motive, which i s used i n a v a r i e t y of ways without cessation u n t i l the c l o s i n g section begins. Replacing the normally strong dominant key i s the expectation of the dominant's a r r i v a l : educated l i s t e n e r s i n the c l a s s i c a l period as well as i n modern times expect works i n sonata form to modulate to the dominant; t h i s piece plays with our expectation of such a modulation. The development section begins, unusually, with a subsection i n mm. 95-104 that seems to have the function of a r e t r a n s i t i o n , at l e a s t harmonically. The dominant pedal would appear to be preparing a return to the tonic and the main theme. However, i n movements of such large dimensions as t h i s one 189 the l i s t e n e r w i l l know that the main theme cannot return i n the tonic so soon. In other words, to l a b e l mm. 105ff. a f a l s e r e c a p i t u l a t i o n would be an error because a r e c a p i t u l a t i o n would never occur at t h i s point i n a long sonata form movement, and one would not mistake the F-sharp chord at m. 105 f o r the t o n i c . A f t e r the subsection i n the mediant, i n mm, 105-116, a sequence i s used to return to the tonic i n m. 129. This return i s too abrupt, too e a s i l y made, for i t to be heard as the s t a r t of a true r e c a p i t u l a t i o n : the tonic appears i n m. 129 merely as one element of a c i r c l e of f i f t h s , and i s not properly prepared with a r e t r a n s i t i o n . This suggests e i t h e r (1) that the opening sub-section of the development was the r e t r a n s i t i o n and that mm. 105-128 form an i n s e r t i o n between the r e t r a n s i t i o n and the r e c a p i t u l a t i o n (or an extension of the r e t r a n s i t i o n ) , or (2) that m. 129 i s the s t a r t of a f a l s e r e c a p i t u l a t i o n . These p o s s i b i l i t i e s are unconvincing, however, as the r e t r a n s i t i o n i s too e a r l y , as noted above, and there i s no prominent subsequent a r r i v a l of the tonic and main theme that would constitute a r e a l r e c a p i t u l a t i o n beginning. At the very l e a s t , however, i t can be concluded that the r e c a p i t u l a t i o n s t a r t i n g i n m. 129 i s less important than the usual type of r e c a p i t u l a t i o n ; that i s , the boundary between the development and r e c a p i t u l a t i o n sections i s less s i g n i f i c a n t here -, 2 than i s normal. This diminished importance of the development/recapitulation boundary correlates with the decreased s i g n i f i c a n c e of boundaries between small sec-t i o n s . The boundary between the exposition and development i s also less important than usual because (1) there are no repeats, (2) there i s no expo-s i t i o n - r e t r a n s i t i o n , (3) the development continues the same dominant pedal as i n the l a s t subsection of the exposition, and (4) the development continues the same a l t e r n a t i o n of t u t t i / s t r i n g s and forte/piano as characterized the 190 exposition. (The boundary between the exposition and the development would be more evident i f mm. 95-104 were removed and m. 105ff. followed d i r e c t l y a f t e r the c l o s i n g section.) In general, then, t h i s movement features more continuity than d i v i s i o n at both of l e v e l s (c) and (d). The main theme i s repeated exactly i n mm. 129-141(1). The main theme co d e t t a / t r a n s i t i o n (1) i s rewritten so as to lead towards the subdominant, ending i n mm. 154-165 with a dominant pedal, which corresponds to the V/V pedal i n mm. 48-58 ( i . e . , MT var. [2]/TR [3]). The material beginning at m. 165 might have sounded l i k e the r e a l r e c a p i t u l a t i o n of the main theme except that the pedal i s cadenced (mm. 163-164), and m. 165ff. begins with IV, not I. The remainder of the r e c a p i t u l a t i o n i s s i m i l a r to the exposition except that the f i n a l codetta of the c l o s i n g section i s a l t e r e d somewhat— although s t i l l beginning with (2 + 2) repeated groups—and four bars of cadential material are added. Symphony no. 38. The Symphony i n D Maj or (Prague, or Symphony without  Minuet), no. 38, i s included here because the c l o s i n g section i s not based on any model and because i d e n t i f i c a t i o n of the s t a r t of the c l o s i n g section i s d i f f i c u l t . In addit ion, the r e c a p i t u l a t i o n i s unusual i n that i t begins i n the development section, as was discussed i n chapter 2 i n con-nection with r e c a p i t u l a t i o n s , pp. 93-94. This movement i s only s l i g h t l y more d i v i s i b l e into sections than i s the Haffner Symphony. A b r i e f o u t l i n e here w i l l have to s u f f i c e ; the c l o s i n g section w i l l be discussed i n d e t a i l . The movement begins with a substantial and very harmonically active introduction. The main theme begins i n m. 37, but i d e n t i f y i n g i t s ending i s problematic because the theme i s not based on a 191 thematic model and because i t merges into the t r a n s i t i o n . The main part of the theme seems to end at m. 51(1); t h i s i s followed by four bars of connecting material to a t u t t i / f o r t e passage that would appear to s i g n a l the s t a r t of the t r a n s i t i o n , but remains i n the tonic u n t i l i t ends i n m. 71. There i t ends on V and a subordinate theme could follow: instead there i s a trans-p o s i t i o n to V of the main theme opening and the r e a l t r a n s i t i o n follows, 3 ending i n m. 97(3). Unlike the main theme, the subordinate theme i s based on a thematic model — t h e p e r i o d — b u t , l i k e the main theme, i t s ending could be i n one of several places. The f i r s t p a r t — t h e period i t s e l f — i s c l e a r l y i n mm. 97-111, that i s , i t i s arranged as two 8-bar phrases. Rosen considers the subordinate theme to be i n ternary form based on harmonic c r i t e r i a ( i . e . , mm. 97-104 i n major, 105-111 i n minor, and 112-121 i n major), and he appears not to notice the 4 period structure. In f a c t , the harmonic contrast of the tonic minor i s not that strong and i s overridden by the thematic p a r a l l e l i s m inherent i n the period structure, so that, i n e f f e c t , the t h i r d subsection (mm. 112-121[1]) i s functioning as a codetta to the period. This codetta i s i n the form of a sentence, that i s , (2 + 2) + (1 +.1.+ 1 + 2). (An e l i s i o n takes place i n m. 112: the sixteenth bar of the period becomes the f i r s t bar of the sentence. In addition, the beginning of the sentence yet a bar e a r l i e r i s suggested by the bassoon parts: mm. 111-115 resemble mm. 97-101[l]; however, whereas m. 97 i s accented, m. I l l i s not, and therefore m. I l l i s an anacrusis.) The use of a texture, motive ( i n the bassoons), and dynamic i n mm. 112-120 s i m i l a r to those i n the preceding period i s evidence f o r considering these bars a codetta to the period. The c l o s i n g section, then, might begin i n m. 121: t h i s would be supported by the change i n motives, orchestration, and dynamics. 192 Diagram 49 Symphony no. 38: Exposition Closing Section Measures: 121 125 129 136 Timespans: (4 + 4) + (7 + 7) Groups: a b c d Motivic o r i g i n : 55ff. 66ff. 37ff. 63-65 On the other hand, there i s no expanded cadential progression p r i o r to m. 121 and no use of standard closing: model features from m. 121. The subsection i n mm. 121-129 r e c a l l s the l a s t part of the main theme area, that i s , mm. 55-71, although the cadence ending i n m. 129 i s stronger than any i n the main theme, and i s one of the strongest i n the exposition. See diagram 49. The second subsection, i n mm. 129-142, i s based f i r s t on the opening motive of the main theme, considerably transformed, and then on a short motive from the end of the main theme i n mm. 63-65. Rosen notes that t h i s c l o s i n g section i s thus comprised of elements from the t u t t i / f o r t e area of the main theme, that i s , from mm. 55-71: "What i s most o r i g i n a l here, however, i s the permutation of the elements." In p a r t i c u l a r , the c l o s i n g section ends with the most " s t a b l e " of these elements—the one i n mm. 63-65, now i n 136-142.^ Both Rosen and Larsen (see note 5) overemphasize the connection with-the main theme. There i s a great d i f f e r e n c e between the e n t i r e theme or even subsections of i t being re-used—something which does not happen here, and never does i n Mozart's e x p o s i t i o n s — a n d i s o l a t e d motives or at most phrases being re-used--and t h i s happens quite often. What i s unusual here i s that so many elements ( i . e . , motives of the main theme) are used to form the c l o s i n g section, and that they should be rearranged to s u i t the d i f f e r e n t formal 193 function of the c l o s i n g section. This c l o s i n g section i s not a restatement of the main theme, as both Rosen and Larsen imply: rather, i t i s a new small section which uses motives from the main theme i n new ways. In other words, i t i s a question of the l e v e l of r e p e t i t i o n : t h i s c l o s i n g section incorporates some l e v e l (a) and possibly some l e v e l (b) r e p e t i t i o n of equivalent main theme un i t s , but no l e v e l (c) r e p e t i t i o n . If the cadence ending at m. 129 i s considered the equivalent of an ECP, then the subsection i n mm. 121-129 might be heard as a further codetta to the subordinate theme or as a separate small section. This would mean the c l o s i n g section would s t a r t i n m. 129. This view i s supported by the material used i n mm. 125-135: when t h i s material was used e a r l i e r i n the exposition, there was a major d i v i s i o n at m. 71 (here m. 129), between the main theme and the t r a n s i t i o n ; therefore, one might p o s i t a s i m i l a r d i v i s i o n at m. 129. On the other hand, there was a s i g n i f i c a n t change of texture and dynam-ic s i n m. 71, a change which strongly influenced the formal d i v i s i o n ; t h i s change i s absent from m. 129. The i n t e r e s t i n g and unusual r e c a p i t u l a t i o n processes here are discussed i n chapter 2, as noted above. In addition, both Rosen and Larsen discuss the r e -c a p i t u l a t i o n . ^ The c l o s i n g section, i n mm. 270-302, undergoes some expansion (e.g., group a i s repeated), but i s otherwise s i m i l a r to i t s exposition form. The c l o s i n g model i s now suggested by some r e p e t i t i o n and l i q u i d a t i o n of material. C l a r i n e t Quintet. A number of previously-discussed works might also be considered here because models might not have applied convincingly to these works or because a l t e r n a t i v e views present themselves. I w i l l only consider one such work here, the Quintet f o r C l a r i n e t and Strings i n A Major, K. 581. 194 In chapter 3 I analysed t h i s work as based on the c l o s i n g model to the extent that there i s one p a i r of s i m i l a r groups ( i . e . , i n mm. 65^75). This i s followed by a s i n g l e group i n mm. 75-79 based on the main theme motive. Two important a t t r i b u t e s of the c l o s i n g model—reduction i n group length and con-s i s t e n t p a i r i n g of s i m i l a r groups—are absent here, bringing into question the a p p l i c a t i o n of the model. This c l o s i n g section cannot be seen as a type ( 2 ) — a c l o s i n g c o d e t t a — because i t i s too long. However, i t i s j u s t possible to consider i t as a type ( 3 ) — a c l o s i n g theme followed by a c l o s i n g codetta. The f i r s t two groups have s u f f i c i e n t features of phrases to be considered a rudimentary period. Replacing the expected strong cadence at the end of the second group ( i . e . , i n mm. 74-75) i s an overlap which leads to an extension i n the form of a 1—group codetta ( i . e . , i n mm. 75-79) which supplies the missing cadence. This c l o s i n g section can thus be considered as an extreme v a r i a n t of ei t h e r type.(l) or type (3); i n t h i s case, "extreme v a r i a n t " means that neither approach i s convincing as an a n a l y t i c a l method. The point i s that, i n seeing how these models apply to t h i s c l o s i n g section, I have, in'effect,, discussed the features of i t . To consider t h i s c l o s i n g section without r e f e r -ence to any model ( i . e . , as a type [4]) would be to a r r i v e at much the same r e s u l t as considering i t as extreme variants of two models, because features such as the group p a i r i n g and the f i n a l group functioning as a codetta or extension to the p a i r would have to be discussed. A further reason why t h i s c l o s i n g section may be considered of type (4) i s that i t s r e c a p i t u l a t i o n form i s s i g n i f i c a n t l y v a r i e d : a 12-bar expansion together with further rewriting (e.g., the ECP and t r i l l are moved from the ST to the CS) r e s u l t s i n the c l o s i n g section approaching the status of a coda. 195 Piano Quartet K. 478. The Quartet f o r V i o l i n , V i o l a , C e l l o , and Piano i n G Minor, K. 478,. has a most unusual exposition form: put simply, a f t e r the main theme and a b r i e f t r a n s i t i o n , there i s a subordinate theme and a c l o s i n g section followed by another subordinate theme and c l o s i n g section. See diagram 50. The main theme i s a good i l l u s t r a t i o n of a sentence, ( 4 + 4 ) +8, with each 4-bar phrase divided as (2 + 2), and the second h a l f divided as (2 + 2) + 4, resembling another (here, lower-level) sentence. The doubled length of the o v e r a l l sentence ( i . e . , from the 8-bar norm to sixteen bars here) at the outset of the work, gives the impression of 4/2 rather than the notated 4/4 meter (that i s , the main beats are h a l f rather than quarter notes). This impression i s rein f o r c e d by the opening motive, which accents h a l f beats. Subsequent sections e i t h e r continue t h i s emphasis on 2-bar timespans or counteract i t with timespans of d i f f e r e n t lengths: i n other words, the movement may be regarded as a ser i e s of sections that a l t e r a t e l y strengthen and weaken the 2-bar grouping into larger timespans. (This i n t e r e s t i n g hypo-thesis can be only b r i e f l y mentioned here.) The modulation to the r e l a t i v e major i s weakened by the b r e v i t y of the t r a n s i t i o n (mm. 17-22), by the continued use of 2-bar timespans (although the larger grouping i n t o three units contrasts with the previous section, i n which the timespans were grouped evenly), and by the i n i t i a l appearance of I I I as merely one element of the sequence (mm. 17-24). 7 Of course, the section s t a r t i n g i n m. 23 might be regarded as part of the t r a n s i t i o n ; t h i s , however, would be unusual because t r a n s i t i o n s r a r e l y incorporate a pedal on the tonic of the new key, the function of the t r a n s i t i o n normally being to lead to the new key without s t a t i n g i t s tonic (at l e a s t i n so extended 196 Diagram 50 Piano Quartet K. 478: Exposition Measures: 1 17 23 45 57 65 88 Timespans: (8 + 8) 6 (9 + 5 + 8) + 12 (4 + 4) (9 + 14) (8 + 2) + 2 Keys 3: i -» (III) I I I - - - -+ Small sections: MT TR ST1 - cdta CS1 ST2 CS2 Retr. Notes: Arrow indicates modulation; parentheses indicate tentative modulation. a manner as here). The section s t a r t i n g i n m. 23 i s therefore only weakly harmonically indicative of the subordinate theme; i t i s only weakly mel-o d i c a l l y i n d i c a t i v e of the subordinate theme because i t i s not strongly contr-asting with the main theme i n motivic material, because i t i s not cast i n a thematic model, and because i t has no c l e a r l y defined ending. (There i s no cadence u n t i l mm. 44-45.) Bar 37 may be considered the star t of a new section due to the use of tonic harmony ( i n B - f l a t major), this harmony being prepared by the immediately preceding dominant pedal, and by the change i n dynamics. The addition of f u r -ther contrasting motives, stronger surface harmonic motion, and a sentence model strengthen the interpretation of these eight bars—37-45(1)—as the subordinate theme proper. Bars 23 through 36, then, have some t r a n s i t i o n a l and some thematic func-tions, and bars 37 through 45(1) are more strongly thematic. The status of the former section as t r a n s i t i o n a l i s supported further i n that i t introduces the f i r s t disruption i n 2-bar timespans. (Although i t i s an even number of bars long, i t i s arranged i n t e r n a l l y as [ 2 + 2 ] + 1 + 2 + 2 + [2 + 2 + 1 ] J 197 The subsequent theme returns to e x c l u s i v e l y 2-bar timespans. The section i n mm. 45-57(1) functions as a codetta and ECP to the pre-ceding theme. Its status as a codetta i s generated p r i m a r i l y by the i n i t i a l s t a t i c harmony and short r e p e t i t i v e grouping. It becomes somewhat more a n i -mated i n m. 50 and concludes with a s u b s t a n t i a l cadence, one of the strongest thus f a r . Its timespan structure i s i r r e g u l a r ( 5 + 4 + 3 ) . The three small sections i n mm. 23-57 that combine forming a unit on a l e v e l between that of (c) and (d) are u n i f i e d by v i r t u e of the strong f i n a l cadence—which brings the whole to a c l o s e , by: s i m i l a r motives, and by a common harmonic paradigm: a l l three sections begins with, tonic prolongations, t o n i c i z e the subdominant and feature i t prominently, and conclude with the dominant (the f i n a l section ends on I ) . The section i n mm. 57-65(1) functions as a c l o s i n g section because (1) i t follows a thematic statement and a codetta which concluded with an ECP,. (2) harmonically, i t e s s e n t i a l l y features a tonic pedal with f a i r l y weak cadences, and (3) i t i s i n the form of a s i m p l i f i e d period (4 + 4) and so resembles the f i r s t p a i r of the c l o s i n g model. That i t features some rhythmic g i r r e g u l a r i t i e s has been noted by several authors. At m. 65, then, one would expect a continuance of the c l o s i n g model. Instead, a new theme i s heard based on the sentence model ( 2 + 2 + 5 ) , f o l -lowed by i t s v a r i a t i o n ( 2 + 2 + 4 + 6 ) to m. 88(1). This section i s not part of the c l o s i n g section because the sentence model i s not c h a r a c t e r i s t i c of c l o s i n g sections i n general: sentences are normally too developmental to be c l o s u r a l . In addition, t h i s thematic area ends as so many other sub-ordinate themes do, that i s , with an ECP (mm. 82-88). 198 The f i n a l section of the exposition i s the second c l o s i n g section i n mm. 88-98. It i s based on a 2-bar cadential group heard four times, and arranged as (2 + 2) + (2 + 2) by a change i n instruments i n m. 91 and by the contrast generated by the G - f l a t s i n mm. 93 and 95. A feature of the c l o s i n g model i s found i n mm. 96-97, where the group length i s reduced to one bar from the previous two. ( i . e . , there are two 1-bar groups here). This c l o s i n g section ..ends on the downbeat of m. 98, the r e t r a n s i t i o n following i n mm. 98-99. Af t e r an extension of the r e t r a n s i t i o n , the development proper begins with a new theme i n mm. 104-111(1). This theme serves as the basis f o r most of the development. The sections of the r e c a p i t u l a t i o n and the coda may be summarized as follows: (1) mm. 141-156: This section repeats the f i r s t eight bars of the main theme, then has a new continuation connecting with a very abridged version of mm. 17-36, which here ends on the dominant. (2) mm. 157-164: This s e c t i o n 1 i s a t r a n s p o s i t i o n to G minor of mm. 37-44 (ST [1]), with the f i n a l cadence now deceptive. (3) mm. 165-177: This i s s i m i l a r to mm. 45-56—the codetta to ST ( 1 ) — except that i t begins i n the submediant instead of i n the expected t o n i c . The change to the tonic key i n the second group r e s u l t s i n an a d d i t i o n a l bar; that i s , i t i s now ( 5 + 5 + 3 ) instead of ( 5 + 4 + 3 ) . (4) mm. 178-185: This section i s s i m i l a r to the f i r s t c l o s i n g section (mm. 57-64) except f o r the rewriting of the s t r i n g parts (which none of the writers c i t e d i n note 8 seems to have noticed ) . (5) mm. 186-211: This section i s b a s i c a l l y a t r a n s p o s i t i o n of the second subordinate theme (mm. 65-87) with some extensions; that i s , i t i s now (11 + 5) instead of (9 + 14). 199 (6) mm. 212-223: This second c l o s i n g section i s very s i m i l a r to i t s exposition form (mm. 88-97). The 2-bar r e t r a n s i t i o n follows. (7) mm. 224-251: The coda i s based on the main theme motives and i s perhaps occasioned by the shortened versions of the main theme and t r a n s i t i o n i n the r e c a p i t u l a t i o n . I t begins with a statement of the f i r s t eight bars of the theme followed by a development of the new continuation found i n the recap-i t u l a t i o n (mm. 148-150). This contrasting s u b s e c t i o n — a g a i n , s t a r t i n g i n VI (see also m.:. 1 6 5 f f . ) — l e a d s back to a return of the opening motive i n a f i n a l f o r t i s s i m o subsection: (2 + 2) + (2 + 2) + (2 + 1 + 1 + 1). V i o l i n Sonata K. 306. The unusual features of the Sonata f o r V i o l i n and Keyboard i n D Major, K. 306, which cause i t to be included here, are that (1) there i s more of a connection than normal between the subordinate theme area and the c l o s i n g section, and (2) the r e c a p i t u l a t i o n i s s i g n i f i c a n t l y d i f f e r e n t from the exposition. See diagram 51. The main theme i s a good i l l u s t r a t i o n of a sentence (2 + 2) + (1 + 1 + 2), followed by a codetta based on the second h a l f of the sentence. Bar 8 f a l l s within the timespan of the sentence, despite i t s tonic a r r i v a l , because of the strength of the 8-bar model and because m. 9 can c l e a r l y be heard as a beginning parallel..to m. 5 (m. 8 being e s s e n t i a l l y an ending). Such i s not the case with the end of the codetta: m. 12 i s p r i m a r i l y a beginning because i t i s so a c t i v e (compared with m. 8) and because of subsequent p a r a l l e l i s m . In other words, there i s an e l i s i o n at m. 12: what would have been the fourth bar of the c o d e t t a — o r the twelfth bar of the thematic a r e a — i s converted to the f i r s t bar of the t r a n s i t i o n . This close connection between the theme and the t r a n s i t i o n ensures that these two sections are heard more as one 200 Diagram 51 V i o l i n Sonata K. 306: Exposition Measures: 1 12 26 38 53 Timespans: (8 + 3) + 12 (6 + 6) + (8 + 7) (9 + 6 + 7 ) Keys: ' I I V V Small sections: MT TR ST codetta CS larger unit (mm. 1-25). The t r a n s i t i o n may be seen as based on the sentence model: mm. 12-20(1) form a sentence, and,mm. 20-25 a codetta prolonging the dominant harmony. The subsequent p a r a l l e l i s m r e f e r r e d to above begins i n m. 12: that i s , the two s i m i l a r 2-bar groups i n mm. 12-13 and 14-15 e s t a b l i s h m. 12 as a beginning. This 2-bar grouping continues with new material to the end of the t r a n s i t i o n i n m. 25. The modulation i s of course not strong, due to the use of a pedal on 5 (rather than on 5 i n the key of the dominant). In addition to contrasting melodically and harmonically with the previous sections, the subordinate theme contrasts rhythmically with i t s i n i t i a l 3-bar grouping i n mm. 26-31. The theme i s based on the sentence model, p a r t l y doubled: that i s , instead of (4 + 4) + (2 + 2 + 4), i t i s (3 + 3) + (2 + 2 + 2) i n mm. 26-37 (r e t a i n i n g at l e a s t the f a c t o r of equal length i n each of the two subsections, i . e . , 6 + 6 ) . A f t e r the two 3-bar timespans, the sentence then continues with 2-bar timespans through m. 35, and begins a concluding segment, which i n the prototype would be four measures long, i n m. 36. This segment cadences a f t e r two measures, at which point a new section beginning i s o v e r l a p p e d . T h i s section has functions of d i f f e r e n t standard sections, making i t d i f f i c u l t to apply only one formal l a b e l to mm. 38-52: 201 (1) The i n s i s t e n t dominant pedal i s the harmonic feature missing from the t r a n s i t i o n section. (2) The use of r e p e t i t i v e grouplets i n mm. 38-45—the 2-bar structure i s abab—suggests the function of a t r a n s i t i o n or a c l o s i n g section. (3) The close connection with the previous sentence—the cadence i n mm. 37-38 i s very weak—and the subsidiary nature of the material i n mm. 38-52 suggest a codetta function f o r t h i s section ( i t s length making i t a codetta-complex). The structure noted i n (2) also suggests the form of a modified, p a r t l y doubled sentence i n mm. 38-52: xx*y, ( 4 + 4 ) + ( 3 + 3 + 2 ) . This i s supported by the only cadence being at the end. The c l o s i n g section would be expected a f t e r the cadence i n mm. 50-52. The c l o s i n g model i s suggested by the two s i m i l a r 5-bar groups (mm. 52-57[1] and 57-62[l]). Unusually, the next subsection, i n mm. 62-68(1), i s based on part of the preceding codetta-complex ( i . e . , on mm. 48-52); as before, th i s material i s e s s e n t i a l l y cadential i n function. The use of cadences takes on s p e c i a l importance here, because there have been so few cadences i n the exposition. The f i n a l subsection,, i n mm. 68-74, i s l i k e a c l o s i n g codetta. A way to understand the c l o s i n g section here i s i n terms of the rhythmic d i s p o s i t i o n of the s t r u c t u r a l Iv-^-^-^-? l i n e over the course of the sections i n A major, mm. 26-74. (Refer to diagram 52 f o r the following discussion.) The p e c u l i a r feature of t h i s l i n e i s that, whereas the f i r s t four s t r u c t u r a l tones occur i n seven bars (mm. 26-32), the 2 i s prolonged f o r twenty bars, reso l v i n g to the ^ only i n m. 52. Although the s u b s t a n t i a l subsequent pro-longation of the 1l i s normal (for c l o s i n g sections), the £ prolongation i s not. This delay of the 2-1 r e s o l u t i o n sets up the need for something more conclusive i n the way of r e s o l u t i o n beyond the cadence at m. 52. This i s provided by the c l o s i n g section, which'has several l i n e a r descents to ^. 202 Diagram 52 V i o l i n Sonata K. 306: P i t c h and Timespan Reduction of Exposition Measures 26-74 t 4 s 26 I I 29_ | 32 , J 34 36 38 40 42 44 r1- £ 3 P 3 z T 1 4 A: 'I i i - V I f T 6 " - - 'V ST: ( 3 + 3 ) + ( 2 + 2 + 2 ) ([2 + 2] + [2 + 2 ] + 3 f c 49 51 53 55 57 60 m 3 T •2. 5 * + 2 V I I + 2 ) CS: ( 2 + 2 ) + ( 3 + 2 ) + A2_ 66_ 20 22 14. ( 2 + 2 + 2 ) + ( 2 + 2 + 3 Notes: (1) The reduction r a t i o i s J = 1 bar. (2) Note values i n t h i s reduction are represented by inwardly stemmed notes. S t r u c t u r a l notes are shown by outwardly stemmed notes. 203 That most of the s t r u c t u r a l l i n e a r motion takes place i n the f i r s t few bars of the dominant-key area i s not i n i t s e l f s u r p r i s i n g : these measures— 26-38—form the thematic statement of t h i s area and therefore should have ac t i v e s t r u c t u r a l as we l l as surface melodic motion. The next sections are less thematic i n nature, and therefore have less s t r u c t u r a l motion: t h e i r function i s to be prolongational rather than to be s t r u c t u r a l l y a c t i v e ; that i s , the codetta-complex i n mm. 38-52 prolongs the 2, the c l o s i n g section prolongs the 1. Thus there i s a coordination of formal f u n c t i o n s — a primary,, thematic section, followed by two subsidiary codetta-complexes, the second of which i s a c l o s i n g s e c t i o n — w i t h s t r u c t u r a l l i n e a r a c t i v i t y — t h e l i n e a r motion takes place mainly i n the primary section, the f i n a l two tones pro-longed i n each of the two subsidiary sections, r e s p e c t i v e l y . The p r o t r a c t i o n of the 2-1 r e s o l u t i o n sets up the need f o r something more conclusive than the b r i e f cadence at m. 52. (Note how, i n diagram 52, the surface s i g n i f i c a n c e of the cadential descent i s represented by sixteenth-n o t e s — t h e shortest note values i n the diagram and the only ones used i n t h i s f i g u r e to th i s point.) It i s obvious that twenty bars of ^  supported by si x bars of i i ^ followed by fourteen bars of V, w i l l not be s a t i s f a c t o r i l y resolved by a b a r — o r even a few b a r s — o f tonic harmony prolonging / i \ C e r t a i n l y i n the normal (ST-ECP)-CS model there would be some prolongation of the 2, e s p e c i a l l y i n the ECP, prolongation that would f i n d i t s r e s o l u t i o n i n the c l o s i n g section. The prolongation here, however, goes beyond t h i s norm i n length, and therefore t h i s c l o s i n g section i s longer and has s p e c i f i c c l o s u r a l features beyond the norm: (1) The c l o s i n g section i s characterized by several l i n e a r descents to i \ A A notably the f i r s t two i n mm. 53-57, var i e d i n 57-62, from 5 to 1. 204 Diagram 53 V i o l i n Sonata K. 306: Exposition Closing Section Measures: 53 57 62 64 68 Timespans: (4 + 5) + [2 + (2 + 2)] + (4 + 3) Groups: a a''" b c c^ d e (2) The re-use i n m. 62ff. of material from the preceding section—an unusual feature, as noted above—functions as a sort of retrospective i n s e r t i o n , r e c a l l i n g the cadential approach so that i t may be made stronger and more convincing. S p e c i f i c a l l y , mm. 62-63 are:the insertion into the closing model, mm. 64-65 and 66-67 functioning as the second pair of the model by vir t u e of the r e p e t i t i o n . See diagram 53. The cadence at mm. 64-68 i s stronger because the tonic a r r i v a l i n m. 68 i s now i n an accented bar, as opposed to a weak one at m. 52. In addition, the cadential approach i s strengthened i n mm. 66-67 by greatly increasing the length of the and "4* that lead to the ^  i n the bass voice (compare mm. 51 and 65). In diagram 53 i t i s apparent that the entire closing section may be con-sidered a modified closing model, with the f i r s t pair of groups expanded to ([2 + 2] + [3 + 2]), followed by the 2-bar retrospective i n s e r t i o n , the second pair of groups as normal i n mm. 64-67, and the f i n a l pair expanded to a sep-arate codetta not based on the model. Some det a i l s of diagram 52 may be c l a r i f i e d at this point. The timespan organization into a l t e r a t e l y 3/4 and 2/4 ( i . e . , units of three or two bars) i s generally clear except for a few points: (I) The f i r s t two bars are i n threes on the basis of phrase structure; 205 however, on harmonic grounds they might be grouped as ( 2 + 2 + 2 ) . (2) The s h i f t to 3/4 f o r mm. 46-48 i s j u s t i f i e d on the basis of the sequence. (Note that the bass voice continues, i n diminution, the ascending fourths pattern i n mm. 38-41 and 42-45, begun i n mm. 27-28 and 30-31,) (3) The ascending fourths pattern descends by step through m. 48; at the point where i t would end on'l' the sequence breaks o f f , avoiding the cadence. The s h i f t to 2/4 i n m. 49 coincides with t h i s . (4) The tonic a r r i v a l i n the ECP leading up to the c l o s i n g section i s normally accented; here, however, m. 52 i s weak, contri b u t i n g to the uncon-vi n c i n g nature of the cadence here. In the re-use of t h i s cadence i n the c l o s i n g section, the accentuation i s reversed. The 2-bar grouping at m. 62 i s begun by the sixteenth-note sequential pattern on beat 1, whereas i n m. 48 i t began on the t h i r d beat; that i s , the retrospective i n s e r t i o n i n mm. 62-63 reverses the accentuation of the equivalent mm. 48-49; t h i s r e v e r s a l i s con-firmed and continued by the 2-bar cadential pattern i n mm. 64-65 and 66-67, hence m. 68 i s accented. (5) The c l o s i n g model contains s i m i l a r groups accented i n s i m i l a r ways; here t h i s does not happen with the f i r s t p a i r of groups ( i . e . , instead of 5 + 5 from m. 52, i t i s 4 + 5 from m. 53). Reasons for m. 53 and not m. 52 being the s t a r t of the timespan were noted i n (4) above. In terms of the s t r u c t u r a l reduction i n diagram 52, there must be a 3/4 bar at mm. 57-59 because there cannot be a downbeat at m. 59, and the addition of such a bar makes the f i r s t two groups of the c l o s i n g section as nearly s i m i l a r l y accented as p o s s i b l e . The r e t r a n s i t i o n of the development section begins i n m. 107 and ends with a repeat of the f i n a l four bars of the t r a n s i t i o n (mm. 22-25) i n 206 Diagram 54 V i o l i n Sonata K. 306: Recapitulation Main Theme (Coda) Measures: 159 163 168 Timespans: (2 + 2) + (2 + 3) + (2 + 2 + 1) Groups: a a c c 1 mm. 109-112. The r e c a p i t u l a t i o n i s thus able to begin with the subordinate theme, now i n the t o n i c , instead of with the main theme. The subordinate theme and the subsequent codetta section are repeated with only small v a r i a t i o n s i n mm. 113-139(1). The c l o s i n g section then follows i n mm. 139-158 with only one s i g n i f i c a n t a l t e r a t i o n : the f i n a l 3-bar group i s omitted. The main theme begins instead i n m. 159 with a repeat of the f i r s t four bars, continuing with a greatly rewritten form of the remainder of the theme. See diagram 54. Aspects of the c l o s i n g model can be seen here, namely in. the use of repeating p a i r s of groups. In a d d i t i o n , the material i s now i n the form of groups rather than phrases, due l a r g e l y to the shortened length of units and to the use of repeated, short cadential units (such units are not a feature of themes). This f i n a l section, then, functions (1) as a r e c a p i t u l a t i o n of the main theme (more accurately, of part of the main theme), (2) as a c o d a — because i t i s heard a f t e r the r e c a p i t u l a t i o n of the subordinate theme area and c l o s i n g section and because i t i s i n the form of a codetta-complex (char-a c t e r i s t i c of codas), and (3) as a substitute f or a normal c l o s i n g s e c t i o n — because i t uses the c l o s i n g model which was previously not used. 207 Piano Sonata K. 576. Some of the unusual features of the Piano Sonata i n D Major, K. 576,. were noted i n chapter 2: r e c a p i t u l a t i o n s , pp. 94-95. Refer to diagram 55 f o r the following discussion. The main theme i s an 8-bar period followed by a v a r i a t i o n . Like the main theme and codetta i n the V i o l i n Sonata K. 306 discussed above, the eighth bar of the theme i s within i t s timespan, m. 9 being heard as a beginning; however, the eighth bar of the v a r i a t i o n — m . 1 6 — i s heard as the beginning of a new timespan because of subsequent p a r a l l e l i s m . As with m. 12 of K. 306, m. 16 here i s the l o c a t i o n of an e l i s i o n : what would have been the eighth bar of the v a r i a t i o n i s now the f i r s t bar of the next section. In f a c t , l i k e the V i o l i n Sonata, t h i s next section—mm. 16-27(4)—begins as a main theme codetta and continues as a t r a n s i t i o n that weakly moves to the dominant. Instead of a theme i n the following section, mm. 26(6)-41(4), the device of canon i s used, unusually, with the opening motive of the main theme. This leads to codetta-type material i n mm. 34-41 ( i n the form of a sentence but not functioning as a theme), s i m i l a r to the second and t h i r d groups of the t r a n s i t i o n (mm. 20-27, which likewise were sentence-like but not theme-1ike). This section, then, i s a second t r a n s i t i o n , functioning i n part to strengthen the modulation to the key of the dominant. The subordinate theme i s f i n a l l y reached at m. 41(6), continuing to m. 53(1),. and i s i n the form of a modified period; that i s , the second phrase i s a v a r i a n t of the f i r s t , and includes a 3-bar extension. A short c l o s i n g codetta concludes the exposition (2 x 2) + 2. (This movement might have been included i n chapter 4 except f o r the unusual exposition and r e c a p i t u l a t i o n forms.) 208 Diagram 55 Piano Sonata K. 576: Exposition Measures: 1 16 28 42 53 Timespans: (8 + 7) ( 4 + 4 + 4 ) (6 + 8) (4 + 7) 6 Keys: I I V V - -Small sections: MT TR(1) TR(2) ST CS In comparison with most expositions, t h i s one i s unusual i n that the dominant key i s not even suggested u n t i l half-way through the exposition (mm. 26-27): normally, the dominant key would be reached somewhat e a r l i e r . This feature r e s u l t s i n part from the short length of the c l o s i n g section. The presence of two t r a n s i t i o n s and a normal subordinate theme would suggest a c l o s i n g section longer than t h i s one. In other words, closure i s weaker i n t h i s exposition than i n most by Mozart. A possible a l t e r n a t i v e explanation here would be to regard the second t r a n s i t i o n — o r at l e a s t mm. 34-41—as the subordinate theme, with mm. 42-58 as a type (3) c l o s i n g section ( i . e . , a c l o s i n g theme followed by a c l o s i n g codetta). This view i s supported by the close connection between the theme and the codetta; that i s , the l a t t e r can e a s i l y be heard as a codetta to the theme. In addition, the preceding section ends with a perfect authentic cadence rather than a h a l f cadence (subordinate themes, not c l o s i n g sections, occur a f t e r h a l f cadences). Working against t h i s i n t e r p r e t a t i o n i s the f a c t that expansion—the only expansion i n the e x p o s i t i o n — t a k e s place i n t h i s theme, and expansion normally i s a feature of the subordinate theme and i t s codettas (e.g., the ECP). Closing themes, at any rate, are usually simple periods ..and are without the high degree of contrast found i n t h i s theme. 209 In the r e c a p i t u l a t i o n , only the f i r s t eight bars of the main theme are repeated (mm. 99-106). A new 15-bar section begins i n m. 106(6) l i k e the v a r i a t i o n of the main theme ( i n m. 8 f f . ) , ends l i k e the f i r s t t r a n s i t i o n did i n mm. 118-121 (see mm. 24-27), but has a d i f f e r e n t c e n t r a l part i n the manner of a short secondary development. This section, then, replaces the f i r s t t r a n s i t i o n . Instead of the second t r a n s i t i o n , the subordinate theme follows i n mm. 121(6)-129, now i n the normal p o s i t i o n f o r such themes. This theme i s a l t e r e d i n t e r n a l l y as well as i n i t s p o s i t i o n within the r e c a p i t u l a t i o n . O r i g i n a l l y , i t was a (4 + 7) period with an extension i n i t s second h a l f ; now i t i s reduced to a (4 + 4) period, followed by a v a r i a t i o n of the same t o t a l length but ending on V / v i . In the exposition an expansion was necessary because i t was i n a p o s i t i o n where expansion was normal. Here, the normal p o s i t i o n f o r subordinate themes, there i s no need f o r expansion. The ending on V/vi i n m. 137 has the e f f e c t of connecting the v a r i a t i o n to the next section, the canonic second t r a n s i t i o n , which now functions as a codetta-complex to the subordinate theme. This section i s s l i g h t l y rewritten: the i n t e r v a l of t r a n s p o s i t i o n i s not uniform (mm. 137[6]-139 d i f f e r from the other bars), and the cadence i s four bars longer (mm. 153-154 resemble the end of the o r i g i n a l subordinate theme: i . e . , the expansion missing from the recap-i t u l a t i o n form of t h i s theme i s used now—in i t s usual p l a c e — t o lead into the c l o s i n g s e c t i o n ) . The c l o s i n g section then follows without a l t e r a t i o n . One function, then, of the r e c a p i t u l a t i o n i s to normalize the form of an unusual exposition. The exposition form i s MT-TR1-TR2-ST-CS; t h i s i s rearranged i n the r e c a p i t u l a t i o n to MT-TR1-ST-TR2-CS, having the formal functions MT-TR-ST-STcodettas-CS. 210 7 Conclusion An important c r i t e r i o n i n aesthetic judgment of a musical work i s the extent to which closure i s successful. In simple terms, a work i s good i f i t ends i n a s a t i s f y i n g way, bad i f i t ends abruptly or inconclusively. In s l i g h t l y more refined terms, a work i s successful i f i t s structure i s complete, i f i n i t i a l processes are carried through to t h e i r l o g i c a l conclusion, and i f the sense that nothing more need be heard i s projected at the end of the work. This success usually manifests i t s e l f i n the l i s t e n e r becoming aware that the end of a piece i s forthcoming. The boundaries of a piece of music are so pronounced—music as opposed to s i l e n c e — t h a t the l i s t e n e r must prepare himself psychologically for the start of a piece, and the composer must prepare the l i s t e n e r for the end. A d i s t i n c t i o n must then be drawn between the end of the piece and the closural process that leads inexorably to that end ( i n music which has such closural processes). It i s of course the closural process that i s of i n t e r e s t , the end being merely a point that has been prepared by the process. The two main variables i n closural processes may be summarized as follows: (1) Different styles of music u t i l i z e d i fferent methods of closure. For example, some music may locate closure i n s p e c i f i c formal sections (e.g., the closing section i n c l a s s i c a l period sonata form), while other music may 211 more c l o s e l y integrate the c l o s i n g process within o v e r a l l structure (e.g., i n shorter works such as Chopin's Preludes, as Agawu has demonstrated''"). (2) D i f f e r e n t s t r u c t u r a l channels may be used to generate closure. Melody, harmony, rhythm, form, etc., need not a l l be involved i n closure i n a given work. For example, i n L i s z t ' s Les Preludes, the r e c a p i t u l a t i o n of the main theme at m. 405 as the f i n a l section not only i n the tonic key but i n the o r i g i n a l tempo—after many other tempos, most of which.--.are associated with d i f f e r e n t moods and themes—is a strong c l o s u r a l gesture. Use of tempo and mood i n generating closure i s almost unknown i n music of e a r l i e r periods, although, even i n t h i s work, these factors might be seen as enhancing, rather than replacing, the formal process of r e c a p i t u l a t i o n . A fundamental c r i t e r i o n i n assessing the c l o s u r a l process i n a given work i s the l e v e l on which closure i s operative. Although most d i a t o n i c pieces of music end with a perfect authentic cadence i n the tonic key, t h i s i s normally i n s u f f i c i e n t to e f f e c t global closure, unless the piece i s very short (and even then there w i l l normally be other c l o s u r a l processes operating). In general, the higher the l e v e l on which closure occurs, the stronger the sense of closure w i l l be. A work with an e n t i r e f i n a l section devoted to prolongation of ^  with tonic harmony w i l l be more strongly closed than a A work that a r r i v e s at 1/1 very near the end of the work. It i s apparent from the foregoing discussion that an i n v e s t i g a t i o n of c l o s u r a l processes i n music must, i f i t i s not to become unwieldy i n length, or overly general, proceed along s t y l e - s p e c i f i c l i n e s . The studies of closure i n , f o r example, Chopin and Mahler by Agawu and Hopkins, r e s p e c t i v e l y , are 2 evidence of t h i s concern f o r s t y l e and i t s influence on c l o s u r a l types. The present d i s s e r t a t i o n i s of course another such instance. 212 Although I have divided the study and analysis of Mozart's sonata-form closing sections into four chapters, this was done as much for organizational as for a n a l y t i c a l reasons; that i s , while i t i s true that I have found a variety of types of closing sections i n these works, there i s a sense i n which most of the movements analysed share important closural features (especially i n compar-ison with other types of closure i n other s t y l e s ) . An important reason for this uniformity i s the use of a d i s t i n c t closing section having the formal function of closure: a l l of the works analysed here have such a section (or a substitute for i t that functions i n a modified closural way, as i n the Piano Sonata i n C Major, K. 545). Another factor i s that closural processes do not vary according to genre or instrumentation: the same closural process i s as 3 l i k e l y to occur i n , for example, a symphony as i n a s t r i n g quartet. And the use of a closing section normally means that closure i s operative at the same le v e l i n most works, i n that different closing sections usually have roughly equivalent relationships to other sections, at least i n comparison with music of other styles . However, perhaps the most s i g n i f i c a n t factor i n the s t y l i s t i c unity of these movements with respect to closure i s that a si m i l a r closural structure i s used i n most works: the closing model i s found to some extent i n nearly a l l of the movements I have analysed here, and i s used with r e l a t i v e l y l i t t l e v a r i a t i o n i n at least half of the movements. About s i x t y percent of the movements were analysed i n chapter 3 which dealt with works based on the closing model i t s e l f ; the closing codetta, the subject of chapter 4, may be seen as a shortened c l o -sing model (and several of the works analysed i n chapter 3 were also considered i n chapter 4, showing how related these two types are); the closing theme f o l -lowed by the closing codetta, the subject of chapter 5, can be considered as 213 a variant of the c l o s i n g model i n which the f i r s t p a i r of groups are more thematic than i n the model; and even some of the works considered i n chapter 6, where works not based on models were discussed, can be seen as having some elements of the c l o s i n g model. The factors that make the c l o s i n g model c l o s u r a l , together with the various channels of structure involved i n closure i n these works, may now be summarized: (1) Melody. The use i n c l o s i n g sections of groups and grouplets as opposed to phrases and motivic segments reduces the need f o r melodic continuation and generates contrast with thematic sections. Other factors c o n t r i b u t i n g to the reduction of continuation are the use of exact r e p e t i t i o n ( p a i r i n g of groups), and the shortening of group length over the model, which eliminates whatever r e s i d u a l motivic references are contained i n the groups. (2) Linear motion. The model contains no s t r u c t u r a l l i n e a r motion; instead, i t prolongs *t and I i n the r e c a p i t u l a t i o n (2 and V, or 5^  and V, i n the exposition). This absence of s t r u c t u r a l motion makes the c l o s i n g section a section of r e s t i n contrast with other sections, which normally have such motion. The c l o s i n g section may have some lower l e v e l l i n e a r motion; f o r example, i f the subordinate theme had a ? to i l i n e a r descent, the c l o s i n g section might echo that at a lower l e v e l . (3) Harmony. See (2) above. Lower l e v e l harmonic motion i s r e s t r i c t e d to r e p e t i t i v e cadential formulations, usually.perfect authentic, possibly with some simple d i a t o n i c progressions leading up to the cadences. (4) Rhythm and form. Contrast with other sections i s p a r t l y generated by the three factors noted above, but more so by the o v e r a l l hypermetric patterning of the model, which has no equivalent elsewhere i n the sonata form. 214 The reduction i n timespan length through the model establishes rhythmic closure by reducing the normal length of the unit on l e v e l (b) from four bars to two bars to one bar: the next unit length i n t h i s sequence would be zero, and i t s equivalent i s of course s i l e n c e . This reduction i s emphasized by the p a i r i n g of s i m i l a r length timespans (and groups) i n the model: the r e p e t i t i o n estab-l i s h e s one length more f o r c e f u l l y than one statement alone would, and the change to another length i s thus e s p e c i a l l y e f f e c t i v e as a change from an established norm, emphasizing the reduction i n timespan lengths. (This happens twice, from four bars to two bars, and then from two bars to one bar.) (5) Texture, r e g i s t e r , and orchestration. These f a c t o r s contribute to closure mainly i n that there tends not to be a change i n them during the course of the c l o s i n g section. A generally s t a t i c texture p r e v a i l s , usually homophonic with a simple melody i n a moderate range and i n a moderate dynamic. In Mozart's sonata form c l o s i n g sections, then, the channels of structure most s i g n i f i c a n t f o r closure are melody, harmony, and rhythm, as noted above. Leonard Meyer's remarks on general features of closure are appropriate here i n summing up t h i s d iscussion: The slowing down which brings a piece of music to i t s close i s not a slowing down i n the phy s i c a l tempo but a slowing down of the rate of musical process. That i s , though the tones may f l y by with great r a p i d i t y , the melodic, harmonic, and rhythmic changes which create a sense of tendency are brought to a stand-s t i l l . The music no longer progresses; i t s marks time; i t i s s t a t i c . 4 The discussion i n the paragraphs above pertains to the majority of c l o s i n g sections by Mozart that I have analysed. There are of course many variants to the standard c l o s i n g processes, variants too numerous to c i t e here ex-haustively, but that have been noted i n the previous chapters. For example, the introduction of a more active element into a p a r t i c u l a r c l o s i n g section, 215 such as chromatic harmony or a reference to a main theme motive, might be associated with the a d d i t i o n of another formal function to the c l o s i n g section. An important var i a n t that should be mentioned b r i e f l y , one that may be present—apparently p a r a d o x i c a l l y — e v e n with normal c l o s i n g sections, i s that closure may not always be operating i n only one small section of a movement. In f a c t , to the extent that the expanded cadential progression i s a normal feature immediately preceding the c l o s i n g section, a c t i v e c l o s u r a l processes can be said to begin i n the preceding small section. This i s p a r t i c u l a r l y the case where there i s a separate codetta complex between the subordinate theme and the c l o s i n g section, a codetta complex that may function as a codetta to the theme but w i l l most l i k e l y have the main function of i n i t i a t i n g closure through the ECP. The l a t t e r i s c l o s u r a l at a high l e v e l because of i t s focus on a strong, c l e a r , protracted harmonic progression to the p r e v a i l i n g t o n i c — such lengthy cadences being infrequent i n the s t y l e — a n d because the s t r u c t u r a l l i n e a r motion 2-1 normally occurs at t h i s point. (For further discussion, see Caplin's paper on the ECP."') To. the extent that the section preceding the c l o s i n g section has d i r e c t e d l i n e a r and harmonic motion towards 1/1, such a section i s functioning i n a c l o s u r a l way within those channels of structure. An avenue f o r f u r t h e r , r e l a t e d research that I may pursue i s the extent to which the c l o s i n g model and i t s variants are found i n other r e p e r t o r i e s . One.might f i r s t i n vestigate genres of Mozart's works other that those I con-sidered (e.g., concertos and vocal music, as well as other movements i n the works I d i d consider, i . e . , slow movements and f i n a l e s ) . My impression i s that .the use of the c l o s i n g model i s not r e s t r i c t e d to f i r s t movements i n 216 Diagram 56 V i o l i n Concerto K. 216, t h i r d movement, closing section (Allegro 1—y it ' m.418F st r i n g s -mr • > timespans: (4 + 4 ) + dfc= <—> p * - * I—« ' ^"j p — r< —#— r obo« hon • * i s & s t r i r c#" —•— » T/ obo€ horr s s t r i -X—5—S—j P u ngs oboes g y 3 t i l & horns f ' T, 1 y 1 (2 + 2 ) + 4 sonata form. An example of this i s shown i n diagram 56, the closing section from the f i n a l e — a rondo—of the V i o l i n Concerto i n G Major, K. 216 (1775). The closing section here serves a dual purpose: as i n most rondos, the A-section returns at the end of the movement, and must therefore be closed i n t e r n a l l y as well as close the entire movement,(unless a new section or extension of the A-section i s added at the end, which does not happen here). Whereas i n a sonata form the closing section closes the exposition and the recapitulation, i n a rondo the closing section closes the main theme (the A-section) and the 217 movement. The c l o s i n g section here i s based c l o s e l y on the model, the f i n a l (1 + 1) p a i r of the model replaced here with a 4-bar tonic group. This example i s also a simple form of the sentence model: i n t h i s i n t e r p r e t a t i o n , c l o s i n g model and sentence merge. (For an example of the use of the c l o s i n g model i n a slow movement, see the Piano Concerto i n B - f l a t Major, K. 595, mm. 116-130.) A f t e r studying the use of the c l o s i n g model i n other repertories of Mozart (including operas), I would consider music of other c l a s s i c a l period composers, and then other s t y l e s of music altogether, s t a r t i n g with l a t e Bar-oque and Romantic period music. The model of musical forms c o n s i s t i n g of d i s -crete, d i f f e r e n t l y functioning sections applies p r i m a r i l y to music of the c l a s -s i c a l period; therefore, I would expect to f i n d somewhat s i m i l a r types of c l o s i n g sections i n Haydn and Beethoven as i n Mozart. (See, f o r example, a use of the c l o s i n g codetta i n Beethoven, Symphony no. 1 i n C Major, f i r s t movement, mm. 100-106; and a use of the c l o s i n g model i n Beethoven, Symphony no. 5 i n C Minor, f i r s t movement, mm. 110-124.) Baroque music and music a f t e r Beethoven l i k e l y has l i t t l e use of the c l o s i n g model, closure being achieved i n other ways. This i s to be expected because,, as suggested e a r l i e r i n t h i s chapter, one reason s t y l e s of music are d i f f e r e n t i s that they employ d i f f e r e n t means of closure. A r e l a t e d avenue f o r research i s to investigate the h i s t o r i c a l and theor-e t i c a l issues involved i n the development of the c l o s i n g model. Why did the c l o s i n g model develop i n the c l a s s i c a l period, and why i s i t a feature of t h i s style? (This i s perhaps answered i n part by a thorough d e s c r i p t i o n of how i t functions i n c l a s s i c a l period sonata form.) Who were the f i r s t composers to use i t and when did i t become a c h a r a c t e r i s t i c of sonata form? How i s the c l o s i n g model r e l a t e d to the development of sonata form? 218 F i n a l l y , i t may be useful to b r i e f l y evaluate the type of analysis of closure I have taken here. I t seems obvious to me that t h i s music i s very c l e a r l y s e c t i o n a l , to the point where t h i s sectionalism i s an unarguable s t y l i s t i c feature. Any a n a l y t i c a l approach that aims at comprehensiveness must therefore account f o r t h i s feature. In f a c t , i n my view, the issue of form i s appropriately c e n t r a l i n analysis of t h i s music. Other channels of structure such as harmony and melody must be f u l l y appreciated i n a n a l y s i s , of course, but are best considered i n t h e i r r e l a t i o n s to form, as I have done here. I have also shown how aspects of closure operating at d i f f e r e n t l e v e l s are coordinated. S t r u c t u r a l l i n e and harmony are s i g n i f i c a n t f a c t o r s for closure: as has been seen, c l o s i n g sections often begin with l Y l a r r i v a l and serve to prolong these through the section. However, I have also drawn atten-t i o n to lower l e v e l rhythmic and melodic features that are equally important i n promoting closure: the c l o s i n g model i s an expression of these l a t t e r f e a -tures. The c l o s u r a l success of a Mozart c l o s i n g section i s thus dependent upon both lower l e v e l conventionalized formations, such as groups and grouplets, which ensure a unique formal function f o r the section, and on a higher l e v e l s t r u c t u r a l function which coordinates /l"/1 a r r i v a l and prolongation with the unique formal function. 219 Notes to Chapter 2 (Concepts, Models, and Features) "The l i n e of demarcation i n Mozart between the 'youthful' and the 'mature' i s e a s i l y reduced to absurdity. . . . Mozart did not experience a personal development." Blume, "Mozart's s t y l e and influe n c e , " 19, 20. 2 "The focussing on structure implies the concession that t e c h n i c a l analysis of composition reaches aesthetic e s s e n t i a l s . " Dahlhaus, Analysis  and Value Judgment, 17. 3 Dahlhaus, Analysis and Value Judgment, 46. See also pp. 13-14: eighteenth-century music i s "fu n c t i o n a l music" i n Dahlhaus's terms: Whereas i n fu n c t i o n a l music a work i s p r i m a r i l y the exemplar of a t y p e — a n examplar which reaches p e r f e c t i o n when i t projects the marks of the type c l e a r l y and p u r e l y — i n the epoch of aest h e t i c s , i n the nineteenth century, a work bases i t s claim to be considered ar t on exactly the opposite, on i n d i v i d u a l i t y and o r i g i n a l i t y . A d i f f e r e n t view of the use of models i s suggested by Meyer i n Emotion  and Meaning i n Music: Once a work i s recognized as being a type f o r which an abstract, normative cl a s s has been evolved, then that " i d e a l type" becomes the basis f o r expectations. (P. 57) 4 Narmour, Beyond Schenkerism, chapter 11. Dahlhaus, Analysis and Value Judgment, 8. ^ This procedure i s s i m i l a r to that used i n many textbooks of musical form; e.g., Schoenberg, Fundamentals of Musical Composition, i n order from low to high l e v e l , chapters 3, 2, 4-8, 13-20.. ^ Although the extremes are not that common, understanding of a l l units on t h i s l e v e l i s f a c i l i t a t e d by d e f i n i t i o n s of the two basic types that combine i n various ways to form hybrids. (This approach applies also to the next higher l e v e l f o r the terms phrase and group.) 8 The d i s t i n c t i o n between motivic segments and grouplets may be c l a r i f i e d by reference to Rosen, The C l a s s i c a l Style, 71-72, where he discusses " f i l l i n g " 220 and "conventional m a t e r i a l , " i . e . , my grouplets (and at l e v e l [b], groups). Kohs, i n Musical Form, makes a useful d i s t i n c t i o n between themes and "neutral material such as scales and arpeggios" (p. 264), material s i m i l a r to my grouplet (and group). Berry, i n Form i n Music, also distinguishes between these two types (p. 8). Caplin, i n h i s ECP paper (discussed i n chapter 1), uses the term "basic idea" f o r the 2-bar u n i t of a theme, a term roughly equivalent to my "motivic segment" (p. 218; and i n note 16 [p. 254] he discusses the question of terminology f o r t h i s l e v e l , noting that the term "motive" i s normally reserved f o r a lower-level u n i t ) . 9 . . The deceptive cadence involves the harmonic motion V-VI replacing an expected authentic cadence, which normally follows the deceptive one. In t h i s sense the DC i s not a true cadence. See example 1, mm. 149(3)-153(1). Other types of cadences are best analysed i n other ways, for example as sequences of a cadential pattern found i n example 1, mm. 146(3)-149(2). ^ The e f f e c t of t e x t u r a l d i s j u n c t i o n would be seen i f one were to claim that the segments i n mm. 21-22 formed an authentic cadence: although harmonic c r i t e r i a s a t i s f y the requirements of an authentic cadence, the t e x t u r a l and dynamic change i n m. 22 ensures that m. 22 w i l l be heard as a beginning, not as an ending. (Higher-level formal and rhythmic patterning also work against pos-i t i n g a cadence i n mm. 21-22.) ^ Certain material i s probably inherently and always p r i m a r i l y non-motivic. A l b e r t i basses and other standard bass patterns are examples. The bass of the f i r s t phrase of the subordinate theme of example 1, i n mm. 30-33, i s not motivic i n the usual meaning of the term, although h i g h e r - l e v e l patterning r e s u l t s i n part from the a s s o c i a t i o n of t h i s material with the motive above i t and the r e p e t i t i o n of t h i s material, as well as by the octave leap which closes the second phrase and the a s s o c i a t i o n of t h i s leap with the motive i n mm. 14-15. If the r e p e t i t i o n of a common bass pattern gives that pattern some degree of motivic d i s t i n c t i v e n e s s , the r e p e t i t i o n of a r i c h e r t r e b l e pattern i s even more a f a c t o r i n the degree of importance of a motive. (The former i s i l -l u s t r a t e d by the f i r s t two phrases of example 1, which are r e l a t e d by the eighth-note repeated bass pattern [mm. 14-15, 18-19], a r e l a t i o n s h i p missing from the next two phrases.) The extent of r e p e t i t i o n , the kind of r e p e t i t i o n — v a r i a t i o n , development, e t c . — a n d the l e v e l of repetition—immediate through long-range— are important factors i n the s i g n i f i c a n c e of a motive. 12 Caplin, i n h i s ECP paper, describes a cadence as "'conventional' i n the sense that i t s melodic content i s common to many works within the s t y l e , " as opposed to the "basic idea" ( i . e . , my motivic segment; see note 8 above), which "normally contains a ' c h a r a c t e r i s t i c ' melody, one that can d i s t i n g u i s h a given theme from another" (p. 251). He also notes that the cadence i s a "two-measure formula" (p. 216). And, "I regard 'cadential function' as that formal function responsible for bringing formal closure to a given theme" (personal communication, July 5, 1988). Kohs' discussion of cadences i s good, e s p e c i a l l y table 4.2, "Factors a f f e c t i n g the weight of a cadence" (Musical Form, 25-27). The 4-bar phrase may be taken as a norm f o r t h i s s t y l e . See the four 4-bar phrases of the second theme, i n mm. 23-38, of example 3, the f i r s t three 221 of which have weak, short cadences as the f i n a l bar of t h e i r second motivic segment, the fourth of which i s more c l e a r l y "motivic segment plus cadence." The expansion and contraction of phrases that would otherwise be four bars long i s , however, quite common. And, as w i l l be seen l a t e r , s p e c i f i c types of ex-pansion and contraction are c h a r a c t e r i s t i c of s p e c i f i c small sections, so much so that such expansions and contractions may be better analysed as norms i n t h e i r own r i g h t . In a f a s t tempo, a phrase of eight bars may be equivalent to the 4-bar norm, and i n a slower tempo, a phrase of two bars equivalent to the 4-bar norm. In addition, phrases other than ones four bars long may sometimes be seen as normal i n the context of s p e c i f i c small sections ( l e v e l [ c ] ) . 14 The d e f i n i t i o n of phrase that I am using here i s i n f a c t a f a i r l y r e s t r i c t i v e one, i n the sense that few units of any given work by Mozart w i l l e x h i b i t a l l the features of phrases. Instead, many units w i l l e x h i b i t only some of the features of phrases, and many units w i l l be better analysed as groups, as discussed below. The terms phrase and group are as inadequate here as the terms motivic segment and grouplet were for l e v e l (a). However, as d i s -cussed i n note 7, c l e a r l y i d e n t i f y i n g the two extremes on a given l e v e l i s a good s t a r t towards understanding events on that l e v e l . I f we had, f o r example, a term f o r "phrase without cadence" and another term f o r "non-cadenced unit combining with an immediately successive cadenced unit forming a level-(b) statement," then these two terms could be used here, among others, without f u r -ther discussion. Of course, I could invent such terms here, but that would imply inventing a v a r i e t y of other terms f o r phrases that lack features other than cadences or that deviate i n some way from my d e f i n i t i o n of phrase. Consider, i n example 3, the phrase from m. 0(4) to m. 4(2), i n which the cadence i s weak-ened by the double suspension on beat one of m. 4, by the use of the same A l b e r t ! bass f i g u r a t i o n pattern i n a l l four bars, by the eighth-note r e s t on beat one of m. 4, by the motive continuing through the cadence, and by the use of a va r i e d form of the same motive i n mm. 1-2, where there i s no cadence, and i n mm. 3-4. To invent a term to explain a l l of these features would be p o i n t l e s s , since few, i f any, other phrases would e x h i b i t exactly these same features. ^ Although t h i s example i s not taken from a f i r s t movement, i t i s worth including here because i t i l l u s t r a t e s so well c e r t a i n aspects of phrases. Sev- •-. e r a l t h e o r i s t s have also commented on the unusual phrase structure of t h i s t r i o . For example, the apparent displacement of the cadence i s noted by Ratner i n C l a s s i c Music, 39-40. See also Kramer, "Beginnings and endings i n Western a r t music," who discusses how the t r i o "plays witty games with c l o s i n g p r o f i l e versus opening placement" (p. 7). 16 Another often-used term f o r timespan i s hypermeasure. Several theor-i s t s used t h i s term: comparing how two t h e o r i s t s use hypermeasure may help to c l a r i f y my use of timespan. Edward Cone, i n Musical Form and Musical Performance, comes close to de f i n i n g h i s use of hypermeasure as follows: One can f i n d long stretches i n which the measures combine into phrases that are themselves m e t r i c a l l y c o n c e i v e d — i n t o what I c a l l hypermeasures. This i s e s p e c i a l l y l i k e l y to occur whenever several measures i n succession e x h i b i t s i m i l a r i t y of motivic, harmonic, and rhythmic construction. These almost demand to be counted as u n i t s . (P. 79) 222 I t i s not clear whether the "motivic, harmonic, and rhythmic construction" i s a part of the hypermeasure, or whether i t merely helps to create the hyper-measure. That i s , i s Cone's hypermeasure a unit that includes events—what I c a l l a group or a phrase, depending on other f a c t o r s — o r does i t refer only to higher-level metric organization? I use the term timespan only for metric organ-i z a t i o n , bearing i n mind that melodic, rhythmic, t e x t u r a l , and harmonic events create timespans. The events form groups or phrases, which i n turn occupy time-spans. Headlam, i n "A rhythmic study of the exposition i n the second movement of Beethoven's Quartet op. 59, no. 1," goes even farther i n defining large-scale metric organization: A meter may be organized not only into measures, with internal per-iodic beats . . . , but also into hypermeasures—metric units of more than one measure, with internal periodic measures. . . . Since a hypermeasure i s a metric unit, i t needs to be confirmed by r e p e t i t i o n ; the meter resulting from this p e r i o d i c i t y of re-peated hypermeasures i s the hypermeter. (P. 114) Although i n t h i s passage Headlam does not state the c r i t e r i a by which his hyper-measures are formed, he does assert that only a repeated hypermeasure w i l l be considered a hypermeasure. In this respect, my use of the term timespan i s sim-i l a r to Headlam's use of hypermeasure. Although p e r i o d i c i t y i s often a factor i n delineation of timespans, I do not require i t as a factor, as Headlam appears to do. ^ I am not claiming that a l l movements have these relationships between events and timespans: the f i r s t theme of the Symphony i n G Minor, no. 40, for example, begins with a similar event/timespan relationship to that i n the opening of the closing section of example 1. The point i s that different small sections within the same movement begin i n different ways. 18 This issue of events and timespans i s discussed by many theori s t s , a l -though not using the same terminology and meaning as I have used here. For ex-ample, Berry discusses the relationship of phraseology to meter i n Structural  Functions of Music (pp. 322-324). 19 . ' A comparison of my ideas regarding phrase structure with those of a few other theorists may help to c l a r i f y my terminology for l e v e l (b). Berry, i n Form i n Music, includes a good discussion of the phrase; for example, he notes that the phrase i s often comprised of two 2-bar motives (p.. 12; or i n my terminology, two motivic segments). In Structural Functions i n Music, Berry sees the phrase as metrically recessive ( i . e . , beginning-accented),the cadence being strong only at l o c a l levels (e.g.., p. 329; see also note 18 above). Caplin,. i n "The 'expanded cadential progression'," discusses three types of phrases according to t h e i r function i n the larger unit (p. 250). His d e f i n i t i o n s of cadences are very precise (pp. 217-218). Cone, i n Musical Form and Musical Performance, describes the r e l a t i o n of phrase/group to meter and timespan as follows: The beats seem to form a pre-existing framework that i s independent of the musical events that i t controls. One feels that before a 223 note of the music was written, the beats were i n place, r e g u l a r l y divided into appropriate sub-units, and r e g u l a r l y combined into measures. (P. 70) Davis, i n "Harmonic rhythm i n Mozart's sonata form," notes that trans-i t i o n sections have "areas of patterned harmonic rhythm that may occupy merely the dimensions of a phrase " (p. 29). This c l o s e l y p a r a l l e l s my d e s c r i p t i o n of "group." In Beyond Orpheus, Epstein divides musical time into two p a r a l l e l h i e r a r c h i e s , metric and rhythmic, the l e v e l s of which correspond. Chronometric (Metric) Beat Measure Hypermeasure Macroperiodizations of hypermeasure groups Integral (Rhythmic) Pulse Motive (or motive-group) Phrase Macroperiodizations of phrase groups (P. 61) Epstein's theory here implies a dichotomy: the two ways of looking at musical time are mutually exclusive. For example, a phrase i s something that occurs on top of an underlying hypermeasure, suggesting that the hypermeasure e x i s t s inde-pendently of the phrase. My approach d i f f e r s from Epstein's only i n that I am t r y i n g to see how the two c l a s s i f i c a t i o n s of time i n t e r a c t and influence each other, e s p e c i a l l y on the l e v e l of hypermeasure/phrase, or, i n my terms, timespan/ phrase or group. A timespan i s not j u s t a c o l l e c t i o n of adjacent measures; i t i s also a functioning unit of time, not n e c e s s a r i l y begun by an accented bar, as Epstein's hypermeasure i s . F a i r l e i g h , i n " T r a n s i t i o n and r e t r a n s i t i o n i n Mozart's sonata-type movements," discusses the use of " i n s i g n i f i c a n t f i g u r a t i o n " i n t r a n s i t i o n s and notes that "phrase and period constructions are extremely uncommon" i n t r a n s i -tions (p. 26). Green, i n Form i n Tonal Music, includes a general discussion of "phrase" and the d i f f i c u l t y of de f i n i n g i t , a d i f f i c u l t y that I believe i s p a r t i a l l y eased by r e s t r i c t i n g the d e f i n i t i o n to music of a s p e c i f i c s t y l e or composer. Kohs, i n Musical Form, discusses sonata form having d i f f e r e n t types of material; f o r example, the t r a n s i t i o n may have "neutral material such as scales and arpeggios" and a d i f f e r e n t texture (p. 264). Also s i m i l a r to my "group" i s his d e f i n i t i o n of "dissolved phrase . . . a phrase which ends without a cadential c l o s e " (p. 38). Lester, i n The Rhythms of Tonal Music, discusses the factors determin-ing, and r e l a t i o n s between, "Hypermeter, meter, and phrase rhythms," h i s chapter 6. For example, he notes that "hypermeters . . . frequently occur i n c l o s i n g passages, e i t h e r of sections or of movements, where cadences c o n t i n u a l l y e l i d e with the beginning of the next phrase" (p. 186). He gives the c l o s i n g section i n the f i n a l e of Mozart's V i o l i n Concerto i n G Major, K. 216, as an i l l u s t r a -t i o n ( t h i s i s quoted i n diagram 56 i n my chapter 7). Lowinsky, i n "On Mozart's rhythm," notes, as I have, Mozart's use of rests "to c l a r i f y and de l i m i t a phrase" (p. 35) . In the f i e l d of a r c h i t e c t u r e , the modern house, with i t s d i f f e r e n t l y functioning rooms, may be compared with sonata form: t h i s comparison may help 224 to explain why the small-section l e v e l i s most i n t e r e s t i n g . In f a c t , the struc-t u r a l l e v e l s of a house and of sonata form correspond quite c l o s e l y : House Pieces of wood, n a i l s , etc. Panels, window panes Doors, walls, f l o o r s , windows,, c e i l i n g s Rooms, hallways, stairways Complete f l o o r s E n t i r e houses Sonata Form Notes and i n t e r v a l s (a) Segments (b) Phrases and groups (c) Small sections (d) Large, sections (e) E n t i r e movements It i s easy enough to perceive i n d i v i d u a l panels of walls, window panes, doors, etc., but i t i s the space created by e n t i r e rooms that i s most i n t e r e s t i n g to us i n houses. Although i t i s possible to conceptualize the layout of a complete f l o o r and of an e n t i r e house, we tend to think instead of a f l o o r plan i n terms of the d i f f e r i n g and contrasting functions of the rooms on each f l o o r and of the d i f f e r i n g functions of each f l o o r of the house. 21 Arnold Schoenberg, Fundamentals of Musical Composition, 20-81 and 119-140. Erwin Ratz, EinfUhrung i n die Musikalische Formenlehre, 21-25. Ca r l Dahlhaus, "Satz und Periode: Zur Theorie der musikalischen Syntax," Z e i t s c h r i f t fur Musiktheorie, 9/2 (1978), 16-26. Caplin, "The 'expanded cad-e n t i a l progression'," 218-219 and 222-223. 22 . An i l l u s t r a t i o n of one of the many types of v a r i a t i o n s of the sentence model i s found i n the main theme of example 3. This sentence may be.represented as follows: ( 2 a + b + 2 1 ) + (2 + 2 + 2 ) + b The main d i f f e r e n c e with respect to the model i s the extension i n the second h a l f , where the normal ( 1 + 1 + 2 ) construction becomes ( 2 + 2 + 2 ) , as discussed i n connection with diagram 1 i n chapter 2. 23 24 Heinrich Schenker, Free Composition (Der f r e i e Satz), I, pp. 36-40. S t r i c t l y speaking, K. 331 should not be included i n t h i s d i s s e r t a t i o n because i t i s not i n sonata form. However, the objects of my study are f i r s t movements, and t h i s movement i s i n t e r e s t i n g because i t i s one of the very few f i r s t movements not i n sonata form. (It i s a theme and v a r i a t i o n s movement.) In a d d i t i o n , the theme exhibits some archetypal features which are found i n sonata-form movements. 25 Another example of the period i s found i n example 1, i n mm. 14-29(2). Here the main theme i s doubled i n length to sixteen bars. There are only two cadences, ending i n mm. 21 and 29, and therefore t h i s i s not a double period. Nevertheless, each 8-bar phrase i s divided as (4 + 4), mainly by dynamic means (piano-forte alternation) and by motivic contrast. Each 4-bar unit i s divided i n turn into two 2-bar motivic segments. This period has the motivic features 225 necessary for i t to be a true double period, but not the c a d e n t i a l features necessary to d i v i d e the 8-bar units into 4-bar phrases. The f i r s t and t h i r d 4-bar units may be termed phrases without cadences. This theme may be rep-resented as follows: ( 4 + 4 ) + ( 4 + 4 ) (2 + 2) + (1 + 1 + 2) + (2 + 2) + (1 + 1 + 2) a + b c 1 d HC a + b PAC i n V The unusual feature of t h i s period i s that i t modulates (to the dominant). (Modulation i s unusual i n normal thematic small sections but not i n themes used i n other small sections and i n extreme variants of thematic small sections.) An a l t e r n a t i v e analysis of t h i s theme i s discussed i n chapter 2 i n connection with l e v e l (d): "Expositions." 26 Some t h e o r i s t s use the term "rounded binary" f o r what I am c a l l i n g "small ternary." (For example, see Green, Form i n Tonal Music, chapter 6.) Any section of a work having a contrasting subsection that leads to a return of the opening material i n the tonic should, I b e l i e v e , be l a b e l l e d ternary, regard-less of any repeat signs. 27 A theme that i s not based on one of the three models w i l l u s ually be strongly closed i n other ways, usually harmonically. Such a theme i s seen i n example 2. The main theme extends from m. 1 to m. 22(1), overlapping with the subsequent small section. The theme may be summarized as follows: 9 + (5 + 4) + (3 13 + [2 + 2] + [(1 + 1 + 2) + 2]) ab d(bl) I-V V-I V-I V-seq.->IV -»V VI V — I HC PAC IAC DC PAC This theme d i f f e r s from the three models not only i n that i t i s not based on any aspect of the models (except that mm. 13-22 may be based on the sentence model) but also i n that i t presents a more varied motivic structure: more motives and more development of motives than i s usual i s present here. The b_ motive i s dev-eloped i n the second part of the theme—even the d motive may be seen as a f i l l i n g -i n of b_—and t h i s suggests some connection with the sentence model, along with the f a c t that the timespan and motive length are shorter, i n p a r t i c u l a r the (2 + 2) unit from m. 13 to m. 16. More important, perhaps, i s the constant regular reduction i n segment length up to m. 18: 5, 4, 3, 2, and 1 bars. This pattern has no r e l a t i o n to any model, and the u n i t lengths are not expan-sions or contractions of more normative lengths or patterns, except for.the f i n a l s i x bars which are an expansions of the 4-bar phrase due to the deceptive cadence. This r e p e t i t i o n of the cadential pattern puts more weight onto the cadence, thus helping to close the theme. Also remarkable i n t h i s theme i s the large number of cadences. For further discussion of t h i s theme, see M i t c h e l l , "The serenades 226 for wind band," 74; and Lowinsky, "On Mozart's rhythm," 32. 28 The sentence and the period models are the most frequently used i n both MTs and STs,. accounting for 68% of a l l themes. MTs are dominated by sen-tence and period models: 85% of a l l MTs are based on these models. STs make less use than do MTs of the sentence and period models, although 50% of STs are based on them. There i s greater variety i n the nature of STs than of MTs. In p a r t i c u l a r , STs show some—18%—use of double themes ( i . e . , one theme f o l -lowed by another), which are not found i n MTs. (This i s one indi c a t i o n of the general observation that STs are usually longer than MTs.) More than h a l f — 60%—of MTs are sentences, with a further one-quarter being periods. No one category accounts for a majority of STs: one t h i r d are periods, one t h i r d are unique themes, and one-third are sentences or double themes. Periods and unique themes are both more common to STs than to MTs. Double periods are more common to STs than to MTs (indicating again that STs are often longer than MTs). The most extreme case of ST variance from models i s found i n movements in which one cannot even speak of a theme, or at least a d i s t i n c t thematic area, i n the second key area (e.g., the Symphony no. 35). In such cases the t r a n s i -t i o n may also merge into the second key area. One may also f i n d movements i n which non-thematic units are connected to thematic ones i n the second key area. Often one function of such additions, etc., i s to expand the ST area, to a point where one could use the term complex of themes. As well as expansion i n the number of subsections within the ST complex,, expansion of the length of the ST i t s e l f i s normal. This i s accomplished either by increasing the number of phrases (e.g., by the use of a double period) and/or by increasing the length of phrases. Both of these factors characterize the ST (in mm. 42-66) of example 2. Not only does this theme feature expansion of phrases and expansion by r e p e t i t i o n , but the entire theme i s doubled by compari-son with the length of the sentence model. Another common type of expansion i n the ST i s an expansion of the sec-ond half of the theme, whether period or sentence. E s s e n t i a l l y , i t i s an expan-sion of the cadential area of the theme, what Caplin has termed an "expanded cadential progression" (ECP), as discussed i n chapter 1. In example 1, the ST— a period—begins at m. 29(2) and ends at m. 50(1). The f i r s t phrase of the per-iod ends with a half cadence at m. 37, and i s constructed as a sentence. (This i s another way of expanding a 4-bar phrase to an 8-bar one: by not merely doub-l i n g i t s length but also by giving i t the shape of a thematic archetype, often, as here, that of a sentence.) The second phrase, i n mm. 37(2)-50, begins as a repeat of the f i r s t , but i t s f i n a l seven bars are expanded with respect to the f i r s t phrase's f i n a l two bars. The archetypal feature of this ECP i s the har-monic progression 1^ - i i ^ (or IV) - V - I, with the bass voice ^ - ^ - S - l " . The dom-inant i s often decorated with a cadential six-four chord and a t r i l l at the very end,, as here i n mm. 48-49. Normally, as here, each harmony i s f a i r l y long i n com-parison with the previous rate of harmonic change i n the theme. The presence of 3" i n the bass i s a signal that an ECP i s occurring. The long cadence, usually the longest i n the entire movement, has the effect of inducing s i g n i f i c a n t closure at higher l e v e l s , as well as of expanding the theme. (For further discussion, see Caplin's ECP paper. See also Weimer, Opera Seria and the Evolution of C l a s s i c a l  Style, chapter 2, "Harmonic expansion from 1716 to 1784;" see especially p. 33 where he discusses the development of an ECP-like progression.) 227 D i f f e r e n t types of r e p e t i t i o n characterize d i f f e r e n t small sections. Repetition of le v e l - ( a ) units i n mm. 14-17 of example 3 d i f f e r s from that i n , f o r example, the main theme of t h i s movement i n the following ways: (1) there i s no separation between the segments i n mm. 14-17; (2) continuity i s further . established by the continuous eighth-note bass voice, a voice which i s also even less motivic than i n the theme; and (3) the d i s t i n c t i o n between the le v e l - ( a ) units of motivic segments and the next lower l e v e l of motives i s l o s t : the unit i n mm. 14(4)-15(3[1]) i s a compression to one bar of the 2-bar motivic segment i n mm. 4(3)-6(2), and mm. 14(4)-17 are therefore comprised of three s i m i l a r 1-bar compressed segments followed by a half-bar extension to the end of m. 17. So whereas mm. 10(4)-14(3) form a phrase comprised of two motivic segments, mm. 14(4)-17 form a group comprised of three motive/grouplets. One reason f o r t h i s l a t t e r l e v e l - ( b ) unit forming a group rather than a phrase i s that i t i s not cadenced. It might be considered to end on the downbeat of m. 18, thus forming a h a l f cadence i n F major, except that the cadence i s overlapped with the new material i n m. 18. 30 For an i l l u s t r a t i o n of the type of change inv o l v i n g a t r a n s i t i o n ending on V/V, see example 3, where the t r a n s i t i o n i s a l t e r e d i n the r e c a p i t u l a t i o n to end on V (mm. 104-118). For an i l l u s t r a t i o n of a t y p i c a l minor mode example, see the Piano Sonata i n A Minor, K. 310, where i n the exposition the t r a n s i t i o n moves from i to V/III (mm. 9-22), and i n the r e c a p i t u l a t i o n from i to V (mm. 88-103). For an i l l u s t r a t i o n of a major mode t r a n s i t i o n ending on V i n the exposition, see the Symphony i n B - f l a t Major, no. 33, mm. 25-54 and 232-263: both versions of the t r a n s i t i o n end on V, but the r e c a p i t u l a t i o n version takes a c i r c u i t o u s harmonic route i n a r r i v i n g there. 31 . . . Although i t i s not r e a l i s t i c a l l y possible to formulate models that take into account a l l features of t r a n s i t i o n s , i t i s possible to categorize the general function of t r a n s i t i o n s . The modulatory function of t r a n s i t i o n s i s the centr a l one, with melodic contrast to the surrounding small sections being the less e r function. Four broad categories of t r a n s i t i o n procedures can be noted: (1) A very few works have no t r a n s i t i o n small section, or else have an extremely short one—one or two bars. In such works the missing t r a n s i t i o n func-t i o n may be transferred to the main theme, which may, f o r example, end on or i n the dominant; the thematic function w i l l be primary i n such cases. See, f o r ex-ample, the Piano Sonatas i n C Major, K. 545, and D Major, K. 311. (2) The majority of movements have a d i s t i n c t t r a n s i t i o n small section, varying from about eight to twenty-five bars i n length. See, for instance, ex-amples 3 (mm. 11-22), and 2 (mm. 22-39). (3) A few movements have more than one t r a n s i t i o n small section. Each of these has a series of small sections i n which the modulatory function i s d i v -ided so as gradually to s h i f t the tonal focus from the tonic to the new key. For example, the f i r s t of two small sections might end on the dominant, with the sec-ond ending on the dominant of the dominant, as i n the Stri n g Quartet i n D Major, K. 593 (mm. 34-45, 45-63). (4) A few movements combine t r a n s i t i o n and subordinate theme functions i n one or more small sections. For example, see the Symphony i n D Major, no. 35, discussed i n d e t a i l i n chapter 6. For further discussion, see my paper "Function and structure of trans-i t i o n s i n sonata-form music of Mozart," Canadian Univ. Music Review, (forthcoming); 228 this paper also includes summaries of other theoretical writings on tr a n s i t i o n s , including those of Davis, F a i r l e i g h , and Kohs as discussed i n note 19 above. Lowinsky, i n "On Mozart's rhythm," writes: In many compositions increasing motion w i l l be found i n the f i r s t section of a sonata-allegro form up to the moment when the second theme appears, at which point a new wave of gradually increasing motion s t a r t s . (P. 44) 32 The second type of r e t r a n s i t i o n — t h a t occurs at the end of the devel-opment—is found i n nearly a l l sonata-form movements, but i s the type least relevant to this study, as I am mainly interested i n expositions and recapitu-l a t i o n s . This r e t r a n s i t i o n type i s most often not a d i s t i n c t small section but rather the f i n a l part of the development section. I t i s normally recognizable by the use of a dominant pedal (although Mozart often substitutes a dominant pedal of the submediant, bringing i n the primary dominant at the l a s t instant before the rec a p i t u l a t i o n ) , and by a fragmentation and l i q u i d a t i o n of motives into grouplets. See example 2, mm. 122-129; and example 1, mm. 73-89. For further discussion of r e t r a n s i t i o n s , see F a i r l e i g h , "Transition and r e t r a n s i -t i o n i n Mozart's sonata-type movements;" and Shamgar, "On locating the r e t r a n s i -t i o n i n c l a s s i c sonata form." 33 Codettas are added to themes as expansions of the thematic area. For example, i f a theme i s eight bars long, the addition of a codetta lengthens what would otherwise be a short small section. Codettas may be added for rea-sons of tonal balance. If a main theme i s short, an immediate move to the dom-inant i n the t r a n s i t i o n might give the exposition too much emphasis on the dom-inant key area. The addition of a codetta to the main theme might a l l e v i a t e this problem. See, for example, the String Quartet i n B - f l a t Major, K. 589: the MT features some interesting expansions and the codetta i s i n part a response to these. 34 In these diagram summaries of closing sections the timespans are shown with the i r associated groups/phrases. Thus the f i r s t number i n diagram 6, "K. 388:", refers to the f i r s t 8-bar timespan of the closing section. This begins with the f i r s t beat of m. 66, i n i t i a t e d there primarily by v i r t u e of tonic a r r i v a l . The pattern of timespan i n i t i a t i o n by tonic a r r i v a l has been established by the subordinate theme, which features 6-bar timespans (mm. 42-47, 48-53, 54-59, and 60-65). Group £ begins just before the end of the f i r s t bar of the f i r s t timespan of the CS, i . e . , with the upbeat to m. 67. 35 In part, t h i s use of codas may be due to the fact that Mozart was strongly influenced by Haydn i n his quartet w r i t i n g , especially with regard to the s i x opus 10 quartets dedicated to Haydn. These were written from 1782 to 1785, and i t was Haydn's opus 33 quartets, written i n 1781, that were of some influence on Mozart. In Haydn's opus 33, half have codas (nos. 3, 4, and 6), and i n Mozart's opus 10, half also have codas.(nos. 2, 3, and 6). 36 Omitting the repeat of the development-recapitulation i n t h i s sonata w i l l obviously change the relationship of the coda to the rest of the movement. 229 Doing so w i l l give the coda greater s t r u c t u r a l weight, thereby making the whole work more l i k e Beethoven's and l a t e r composers' sonata forms. To p i a n i s t s who perform more romantic than c l a s s i c piano music, omitting t h i s repeat may seem l i k e the natural thing to do because i t w i l l make the movement more romantic. 37 In example 8, from the Piano Sonata K. 309, the two forms of the c l o s i n g section are shown. The r e c a p i t u l a t i o n form (within the repeat signs, of course), i s three bars longer than the exposition form. This new material includes a reference to the opening main theme motive i n mm. 152-153(3) and concludes with common cadential material. The extension gives the c l o s i n g section more s i g n i f i c a n c e than i t had i n the exposition, thereby making i t more of a d i s t i n c t small section than i t was i n the exposition. In example 1 the c l o s i n g section i n the r e c a p i t u l a t i o n i s extended by about ten bars as compared to i t s exposition form (as discussed e a r l i e r i n chapter 2). There i s not a separate coda here: the material i n mm. 135-159 forms one small section. The new codetta material grows out of the o l d , with no s i g n i f i c a n t separation between the two, s t a r t i n g with the sequence i n mm. 147(3)-148(2). For f u r t h e r discussion of codas, see, f o r example, Smyth, "Codas i n c l a s s i c a l form: aspects of large-scale rhythm and pattern completion." 38 In example 1, although there are no overt motivic references between th i s introduction and the r e s t of the movement, there are many features i n common between the introduction and the c l o s i n g section, e.g., the use of grouplets and groups as opposed to motivic segments and phrases. In a d d i t i o n , the c l o s i n g model may be seen to apply to mm. 5-13, and mm. 9-13 may be heard as a codetta. (Another way to hear the introduction i s as a large sentence, i n which the o v e r a l l tonic-dominant motion overshadows the PAC i n mm. 8-9. A t h i r d i n t e r p r e t a t i o n would hear mm. 1-9 as a sentence, with mm. 9-13 as a codetta.) 39 There are no works invo l v i n g a t o t a l lack of a p p l i c a b i l i t y of the exposition model (excepting, of course, those few f i r s t movements not i n sonata form, such as that of the Piano Sonata i n A Major, K. 331). This i s so i f only because every work i n sonata form must begin with a theme, or theme-like s t a t e -ment (except f o r works beginning with an introduction, which postpone the theme), Obviously, a movement cannot begin with a t r a n s i t i o n or with a c l o s i n g s e c t i o n . 40 Returning to the analogy with house construction mentioned m note 20, such larger, double function small sections could be compared to larger rooms that function as combinations of normal si n g l e function rooms, such as l i v i n g -dining rooms. 41 This i s unlike the t y p i c a l meaning of "monothematic" i n Haydn's works, where a motive w i l l be common to the two themes, but w i l l not be used through-out, other motives being used i n addition (e.g., the Piano Sonata i n E - f l a t Major, H. XIV: 49, f i r s t movement). In the Haffner Symphony, by comparison, a s i n g l e motive i s used almost constantly, and there i s no r e a l ST. 42 In the analogy with house construction, the exposition of the Ju p i t e r Symphony i s s i m i l a r to a f l o o r i n which a l l the rooms have windows on every 230 w a l l , permitting one to see into adjacent rooms. The Haffner Symphony, being even more continuous, i s l i k e a f l o o r which i s one large multi-function room. 43 For discussion of the change i n sonata forms, see, f o r example, Newman, The Sonata i n the C l a s s i c Era, chapter 6; and Rosen, Sonata Forms, chapter 7. For examples of sonatas s i m i l a r to K. 545 i n form, see, f o r example, those Haydn was w r i t i n g i n the 1760s (e.g., the Piano Sonata i n C Major, H. XIV: 10, f i r s t movement). 44 . A b r i e f summary of development section structure may be included here. Many developments have a short introduction leading to a larger c e n t r a l section, which functions as the main area of contrast and development. This leads into the r e t r a n s i t i o n , which prepares f o r the r e c a p i t u l a t i o n . The harmonic contrast c h a r a c t e r i s t i c of developments comes about not through the use of a standard non-tonic k e y — a s i n the e x p o s i t i o n — b u t by the use of f l u c t u a t i n g t o n a l i t y . A v a r i e t y of keys w i l l be referred to i n the ce n t r a l section, leading to the dominant pedal of the r e t r a n s i t i o n . Melodic contrast i s generated by the use of remote motive-forms, sometimes to the extent of introducing a new theme. When exact transpositions of complete phrases from the exposition are used, they are often found i n d i f f e r e n t contexts, such as with a new accompaniment, or having a new continuation. However, sometimes a theme i s simply transposed i n the development. Rhythmic contrast i s formed by the use of a v a r i e t y of d i f f e r e n t length timespans over the course of the development, often by a pro-cess of shortening the lengths of the timespans. Further sources of contrast include those of t e x t u r e — f o r example by the use of i m i t a t i o n — a n d dynamics. The continuous nature of developments, which contrasts with the exposition, i s generated by the use of open-ended units on l e v e l s (b), ( c ) , and (d). Ex-amples of these features are found i n most developments. Some developments have as r e t r a n s i t i o n the end of the t r a n s i t i o n section from the exposition, transposed or otherwise a l t e r e d to end on the dominant. This i s done i n cases where the r e c a p i t u l a t i o n begins with the second theme, the main theme following l a t e r . For further discussion, see, for example, Bushier, "Harmonic structure i n Mozart's sonata-form developments;" Beach, "A recurring pattern i n Mozart's music;" Davis, "Harmonic rhythm i n Mozart's sonata form;" and Lowinsky, "On Mozart's rhythm." 45 Rosen r e f e r s to t h i s as the "secondary development" (Sonata Forms, 276-277). See also Brown, "Mozart's r e c a p i t u l a t i o n s : a point of s t y l e . " 46 In cases where the r e c a p i t u l a t i o n begins with the second theme, the t r a n s i t i o n section, a l t e r e d i f necessary to end on V, i s placed before the theme; i n t h i s p o s i t i o n i t acts as a r e t r a n s i t i o n within the development section: Development Recapitulation Model: ^ r e t r a n s i t i o n MT TR ST CS V a r i a t i o n : -^transition ST CS MT Examples include the Piano Sonata K. 311, and the V i o l i n Sonata K. 306. 47 For further discussion of r e c a p i t u l a t i o n s see, f o r example, Benjamin, "A theory of musical meter," 405-406 (quoted i n chapter 1, p. 11); and Rosen, 231 Sonata Forms, chapter 11. The exposition of example 2 was discussed i n connec-t i o n with Level (d): "Expositions" as to i t s p e r i o d i z a t i o n of lengths of groups, phrases,, and timespans. This process of p e r i o d i z a t i o n i s important to the r e c a p i t u l a t i o n of t h i s Serenade as w e l l , despite the f a c t that considerable rewriting takes place. The main theme i s the same as i n the exposition. The t r a n s i t i o n begins as i n the exposition but becomes greatly changed; i t s timespan and grouplet structure i s (2 x 4) + (2 x 3) + (2 x 2) + (2 x 4), i . e . , a series of 2-bar units grouped i n d i f f e r e n t ways. The r e c a p i t u l a t e d second theme i s very i n t e r e s t i n g : i t i s m o t i v i c a l l y d i f f e r e n t from the second theme i n the exposition, yet i t maintains exactly the same timespan structure, i . e . , ( 6 x 4 ) . The c l o s i n g section i s lengthened s l i g h t l y , but i s otherwise the same as i n the exposition. 48 . . For discussion of b i p a r t i t e and t r i p a r t i t e approaches, see, for ex-ample, Newman, The Sonata i n the C l a s s i c Era, 143-147. Examples w i l l be seen i n subsequent chapters. 49 . . . . . For d e t a i l e d s t a t i s t i c s on proportions i n t h i s music, see, f o r ex-ample, William Abbott, "Certain aspects of the sonata-allegro form i n piano sonatas of the 18th and 19th centuries," (Ph.D. d i s s . , Indiana Univ., 1956); and Hans Engel, "Haydn, Mozart und die K l a s s i k , " Mozart-Jahrbuch, 1959, 46-79. 232 Notes to Chapter 3 (The Closing Model) The (1 x 4) + (4 x 1) rhythmic pattern i s not s t r i c t l y a thematic model, as i t i s seen i n other than thematic sections. It may form part of a theme or section as opposed to the thematic models which usually account f o r a l l of a theme. At any r a t e , i t i s not seen frequently i n these works. (This pattern was drawn to my a t t e n t i o n by Dr. William E. Benjamin.) This theme i s unique i n my d e f i n i t i o n of "unique theme" but not i n the broader meaning of the term. 2 This explanation of the coda was suggested to me by Dr. William E. Benjamin. 233 Notes to Chapter 4 (The Closing Codetta) That c l o s i n g sections function to prolong the tonic f o r a length of time i s suggested by Kramer i n "Beginnings and endings i n Western a r t music;" e.g., "A tonal composition reaches i t s g o a l — t h e return of the tonic as s t a b l e — before the actual close. The tonic must then be extended, or prolonged, f o r a s u f f i c i e n t amount of time f o r i t s s t a b i l i t y to be f e l t f u l l y and f o r the mom-entum that brought the music to that goal to be d i s s i p a t e d " (p. 3). 2 I have suggested a tonic ending f o r t h i s theme i n the example below, i . e . , to replace mm. 30-33(1). (Tonic endings s i m i l a r to t h i s are found, i n f a c t , i n mm. 74-75, repeated i n 76-77, of the development section.) #— 12 5 f t J # J * \ * T —f-—--J-4—I—£—f—t- H 7 f 7 1 A major: I - i i - V I- I That many developments prolong IV i s suggested by Bushier i n "Harmonic structure i n Mozart's sonata-form developments." One of the two development section progressions he posit s has the subdominant as i t s goal. 4 Schenker's a t t i t u d e towards formal analysis i s shown, for example, by the following quote: "I . . . r e j e c t those explanations which are based upon phrases, phrase-groups, periods, double periods, themes, antecedents, and consequents." Free Composition (Per f r e i e Satz), 131. I t should be noted that I am not implying that diagrams 38 and 39 are Schenkerian analyses; instead, I w i l l say that they are influenced by Schenkerian techniques. See chapter 5, "Form," of Free Composition, f o r Schenker's approach to sonata form a n a l y s i s . (See also pp. 27-29 above.) He maintains that a l l sonata form music must be analysed as in t e r r u p t i o n s : i n the present work t h i s would l i k e l y mean a de-emphasis of the extreme s i m i l a r i t y between the- outer large sections. 234 The o v e r a l l form of t h i s movement has been described as ABCBA or mirror form ( i . e . , o v e r s i m p l i f i e d , A = MT, B_ = ST area, and £ = development). See, fo r example, Newman, The Sonata i n the C l a s s i c Era, 146. 6 The Piano Sonata K. 333 i s discussed on pp. 44, 47, 50, 52, 63, 83, 87. 7 The r e c a p i t u l a t i o n of K, 545 begins i n m. 42 i n the subdominant key. A possible explanation f o r t h i s unusual tonal beginning i s that, since the movement i s so short, a l i t e r a l repeat of mm. 1-12 so soon a f t e r they were heard i n the exposition would be uninteresting. (See Rosen, The C l a s s i c a l Style, 152, f o r other views on the non-tonic beginning of the r e c a p i t u l a t i o n . ) In addition, the rewritten main theme d i f f e r e n t i a t e s the r e c a p i t u l a t i o n from the exposition, the two sections being almost i d e n t i c a l except for t h i s and the usual change of key i n the subordinate theme area. An a d d i t i o n a l 4-bar unit i s included i n the main theme, i n part prompted by the use of the subdominant ( i . e . , mm. 42-49 are a transposition of mm. 1-8 to F major, mm. 50-53 are a v a r i a t i o n of mm. 5-8 i n C major, and mm. 54-57 repeat mm- 9-12). The subordinate theme area i s unchanged except f o r the key and a rewritten form of mm. 67-69 compared with mm. 22-24. The t o n i c i z a t i o n of V here strengthens the cadence, and the use of a main theme motive i n m. 69 i s an a d d i t i o n a l connection between the two themes. It i s i n t e r e s t i n g to compare the timespan organization of t h i s movement with other movements and to see how these other timespan arrangements r e l a t e to t h e i r thematic structures. For example, Haydn's Piano Sonata i n D Major, H. XIV: 14, f i r s t movement, exposition, i s comprised of a s t r i n g of equal length time-spans: (4 + 4) + (4 + 4) + (4 + 4 + 4) + (4 + 4). In t h i s movement the small sections are undistinguished; i . e . , i d e n t i f y i n g the themes, transition,, and c l o -sing section i s very d i f f i c u l t . This i s p a r t l y due to the extreme consistency of timespan lengths. (Another reason here i s that there i s frequent use of se-quence, both within and between 4-bar units.) g Both themes i n K. 570 can be analysed as sentence variants with codettas, and both share the same opening t r i a d i c motive. Of course, there are a number of differences between the two themes, i n p a r t i c u l a r i n the r e l a t i o n the codettas have to t h e i r respective themes. In the main theme codetta (mm. 12[2]-20), the codetta i s d i s t i n c t from the theme (by v i r t u e of i t s d i f f e r e n t motives, e t c . ) . On the other hand, the subordinate theme codetta (mm. 57[2]-69[l]) i s based d i r -e c t l y on the second, h a l f of the theme (mm. 49-56). In other words, the ST and i t s codetta form a more cohesive u n i t , despite t h e i r greater combined length, than do the MT and i t s codetta. The t r a n s i t i o n i s i n t e r e s t i n g f o r i t s 2-bar introduction i n mm. 21-22 that abruptly leaves both the tonic key and main theme material; a theme-like statement then follows beginning i n the subdominant key. A curious and unusual connection i s formed between the c l o s i n g section and the t r a n s i t i o n when, a f t e r the repeat of the exposition, the development i s begun. The l a s t bar of the c l o s i n g section and the f i r s t bar of the devel-opment resemble the f i r s t two bars of the t r a n s i t i o n , and i n f a c t the develop-ment then continues with the t r a n s i t i o n "theme" as well as with the f i r s t part of the subordinate theme transposed to new keys (one of which, G minor, i s the one implied by the f i r s t two bars of the t r a n s i t i o n [mm. 21-22] although t h i s key i s a t r i t o n e d i s t a n t from that implied by mm. 79-80). The r e c a p i t u l a t i o n begins i n m.> 133 with the main them