Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Interactions of conventional and nonconventional tonal determinants in the string quartets of Béla Bartók Morrison, Charles Douglas 1987

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1987_A1 M66.pdf [ 16.34MB ]
Metadata
JSON: 831-1.0097482.json
JSON-LD: 831-1.0097482-ld.json
RDF/XML (Pretty): 831-1.0097482-rdf.xml
RDF/JSON: 831-1.0097482-rdf.json
Turtle: 831-1.0097482-turtle.txt
N-Triples: 831-1.0097482-rdf-ntriples.txt
Original Record: 831-1.0097482-source.json
Full Text
831-1.0097482-fulltext.txt
Citation
831-1.0097482.ris

Full Text

INTERACTIONS OF CONVENTIONAL AND NONCONVENTIONAL TONAL DETERMINANTS IN THE STRING QUARTETS OF BELA BARTOK by CHARLES DOUGLAS MORRISON B.Mus., The U n i v e r s i t y of Manitoba, 1981 M.A., The U n i v e r s i t y of B r i t i s h Columbia, 1983 A T H E S I S S U B M I T T E D IN P A R T I A L F U I J F I L L M E N T OF THE R E Q U I R E M E N T S FOR THE D E G R E E OF D O C T O R OF P H I L O S O P H Y i n THE F A C U L T Y OF G R A D U A T E S T U D I E S (School of Music) We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA August 1987 © Charles Douglas Morrison , 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I 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 M u s i c  The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 D a t e August 20, 1987 DE-6(3/81) ABSTRACT Although t h e r e e x i s t s s u b s t a n t i a l l i t e r a t u r e on B e l a Bartok's music, few sources address h i s t o n a l language i n a p e n e t r a t i n g , a n a l y t i -c a l way. Analyses o f t e n l a c k p r e c i s i o n i n demonstrating adaptations o f conve n t i o n a l p r i n c i p l e s of t o n a l o r i e n t a t i o n i n the o f t e n n o n t r a d i t i o n a l contexts o f Bartok's music, and a r e g e n e r a l l y i n c o n c l u s i v e i n e x p l a i n i n g the p a r t i c u l a r s o f i n t e r a c t i o n between c o n v e n t i o n a l and nonconventional t o n a l determinants. The present study seeks t o demonstrate adaptations and i n t e r a c t i o n s o f s p e c i f i c c o n v e n t i o n a l and n o n c o n v e n t i o n a l t o n a l determinants, t a k i n g these shortcomings i n t o account. I n C h a p t e r I , a b r i e f b u t c r i t i c a l s u r v e y o f app r o a c h e s t o t o n a l i t y i n B a r t o k i s f o l l o w e d by a r e d e f i n i t i o n o f t o n a l i t y , w h i c h embodies both c o n v e n t i o n a l and nonconventional determinants o f c e n t r i c o r i e n t a t i o n , many o f the l a t t e r being analogues o f the former. Progres-s i o n and p r o l o n g a t i o n are c i t e d as two fundamental processes by which t o n a l o r i e n t a t i o n i s e f f e c t e d . Because Bartok's s t r i n g q u a r t e t s span h i s compositional c a r e e r , r e f l e c t i n g g l o b a l changes i n h i s m u s i c a l language, they are p a r t i c u l a r l y convenient f o r study. Chapter I I i n t r o d u c e s f o u r c a t e g o r i e s o f progres-s i o n r e l e v a n t t o Bartok's q u a r t e t s : c o n v e n t i o n a l l y f u n c t i o n a l progres-s i o n s , nonconventional t o n i c i z i n g p r o g r e s s i o n s , f i f t h p r o g r e s s i o n s , and l i n e a r progressions. Each i s f u r t h e r subdivided, w i t h d i s c u s s i o n o f the t h e o r e t i c a l p r i n c i p l e s o f c l a s s i f i c a t i o n , examination of the e x i s t i n g i i l i t e r a t u r e where r e l e v a n t , and i l l u s t r a t i o n o f the element of' progres-s i o n i n q u e s t i o n , u s u a l l y by excerpt from the q u a r t e t s . Chapter I I I takes H e i n r i c h Schenker's theory o f p r o l o n g a t i o n as a departure p o i n t f o r the study of nonconventional but analogous proce-d u r e s i n Bartok's q u a r t e t s . P r o l o n g a t i o n o v e r f o r e g r o u n d , m i d - l e v e l , and l a r g e - s c a l e spans i s s t u d i e d , and subcategories of m i d - l e v e l p r o l o n -g a t i o n i n p a r t i c u l a r are d i s c u s s e d i n r e l a t i o n t o commentary by Wallace B e r r y , C r a i g A y r e y , and A r n o l d W h i t t a l l on t h i s v i t a l b u t p r o b l e m a t i c concept. Each p r o l o n g a t i o n a l d e t e r m i n a n t i s e x e m p l i f i e d i n p a s s a g e s from the q u a r t e t s . The focus of Chapter IV i s the f i n a l movement o f Bartdk's s i x t h q u a r t e t , t h e a n a l y s i s o f w h i c h i l l u m i n a t e s d e t a i l s o f i n t e r a c t i o n between c o n v e n t i o n a l and n o n c o n v e n t i o n a l t o n a l d e t e r m i n a n t s — s u c h i n t e r a c t i o n being c r u c i a l i n understanding Bartdk's t o n a l i t y as a u n i -f i e d system of f u n c t i o n a l l y i n t e r r e l a t e d p r i n c i p l e s o f c e n t r i c o r i e n t a -t i o n and s t r u c t u r a l coherence. Chapter V summarizes the f i n d i n g s o f the analyses i n Chapters II-TV. i i i TABLE OF CONTENTS VOLUME 1 ABSTRACT i i L I S T OF EXAMPLES v i AC^C&KJEDGMENTS x EDITORIAL NOTES x i CHAPTER I . INTRODUCTION 1 I I . PROGRESSION IN BARTOK'S STRING QUARTETS 24 I n t r o d u c t i o n 24 Co n v e n t i o n a l l y F u n c t i o n a l P r o g r e s s i o n s 25 F u n c t i o n a l progressions i n t e r t i a n contexts 25 S i n g l e c o n v e n t i o n a l t o n i c i z i n g p r o g r e s s i o n s i n n o n t r a d i t i o n a l contexts 36 T o n i c i z i n g p rogressions c o n c l u d i n g formal s e c t i o n s . . 37 T o n i c i z i n g p r o g r e s s i o n s i n i t i a t i n g formal s e c t i o n s . . 39 M i d - l e v e l f u n c t i o n a l p r o g r e s s i o n s 41 Nonconventional T o n i c i z i n g Progressions 44 Contextual t o n i c i z i n g agents 44 D i s p o s i t i o n note and d i s p o s i t i o n dominant 47 O b l i q u e l y r e s o l v i n g t r i t o n e 52 F i f t h P r o g r e s s i o n s 58 Descending f i f t h s l i n k i n g t e r t i a n harmonies 60 F i f t h p r o g r e s s i o n s l i n k i n g nonconventional v e r t i c a l i t i e s and n o n s i m u l t a n e i t i e s . . . 65 F i f t h r e l a t i o n s between thematic t r a n s p o s i t i o n s . . . . 72 L i n e a r P r o g r e s s i o n s 78 I n h e r e n t l y d i r e c t e d l i n e a r p r ogressions 83 C o n t e x t u a l l y d i r e c t e d l i n e a r p r o g r e s s i o n s 87 M o t i v i c a l l y d e r i v e d l i n e a r p r ogressions 98 I I I . PROLONGATION IN BARTOK'S STRING QUARTETS 109 I n t r o d u c t i o n 109 Foreground P r o l o n g a t i o n 112 i v Mid-Level Prolongation 116 Prolongation through conventionally functional harmonic progressions 119 Prolongation through linear progression . . 121 Prolongation through surface-exposed octave progression 121 Prolongation through motivically derived octave progression 123 Prolongation through linear unfolding 124 Prolongation through o s c i l l a t i o n and/or reiteration 130 Oscillation of conventional dominant and tonic . . . . 133 Oscillation of elaborative and referential elements . 135 Oscillation of disposition and referential elements . 139 Simultaneous prolongation of more than one referential element 153 Large-Scale Prolongation 162 IV. PROGRESSION AND PROLONGATION IN THE FINAL MOVEMENT OF BARTOK'S SIXTH QUARTET 169 V. CONCLUSION 192 GLOSSARY 201 SELECTED BIBLIOGRAPHY 204 v LIST OF EXAMPLES 2.1. Quartet No. 1, I, mm. 1-8 217* 2.2. Quartet No. 1, I, mm. 8-16 218 2.3. Quartet No. 1, I, nm. 23-32 219 2.4. Quartet No. 1, I, mm. 65-71 220 2.5a. Quartet No. 5, III, mm. 3-9 221 2.5b. Quartet No. 5, III, mm. 92-93 221 2.6a. Quartet No. 2, I, mm. 171-180 222 2.6b. Quartet No. 2, II, mm. 6-9, 14-16 222 2.7a. Quartet No. 6, II, mm. 17-19 223 2.7b. Quartet No. 6, II, mm. 122-123 223 2.8. Quartet No. 1, III, mm. 156-160 224 2.9. Quartet No. 1, III, mm. 1-14 225 2.10. Quartet No. 5, II, mm. 1-4 . 226 2.11. Quartet No. 4, V, mm. 295-367 227 2.12. Quartet No. 5, II, mm. 6-7, 9-10, 19-22, 45-46, 54-56 . . . 228 2.13. Quartet No. 1, III, mm. 368-372 229 2.14. Interval structure of the lydian and phrygian octave patterns 230 2.15. Quartet No. 6, IV, mm. 12-13 231 2.16. Quartet No. 5, I, mm. 23-25 231 2.17. Quartet No. 2, I, mm. 31-32 231 A l l page numbers refer to Volume 2. v i 2.18a. Quartet No. 6, I, mm. 52-53 232 2.18b. Quartet No. 6, I, mm. 59-60 232 2.19. Quartet No. 6, I, mm. 80-82 232 2.20. Derivation of obliquely resolving tritones i n the lydian and phrygian octave patterns 233 2.21. Quartet No. 2, II, mm. 1-7 234 2.22a. Quartet No. 4, V, mm. 14-18 235 2.22b. Quartet No. 4, V, mm. 391-392 235 2.23. Quartet No. 3, Seconda parte, mm. 56-61 236 2.24. Quartet No. 6, I, mm. 81-99 237 2.25. Quartet No. 6, I, mm. 312-332 238 2.26. Quartet No. 6, I, mm. 342-354 239 2.27. Quartet No. 3, Prima parte, mm. 65-72 240 2.28. Quartet No. 5, III, mm. 39-53 241 2.29. Quartet No. 4, V, mm. 156-182 242 2.30a. Quartet No. 4, III, mm. 1-13 243 2.30b. Quartet No. 4, III, mm. 64-71 243 2.31. Quartet No. 4, II, mm. 1-12 244 2.32a. Quartet No. 4, IV, mm. 6-14 245 2.32b. Quartet No. 4, IV, mm. 35-37 245 2.33. Quartet No. 3, Seconda parte, mm. 103-149 246 2.34. Quartet No. 5, I, mm. 6-13 247 2.35. Quartet No. 5, I, mm. 11-25 248 2.36. Quartet No. 5, II, mm. 39-46 249 2.37. Quartet No. 4, V, mm. 102-143 250 2.38. Quartet No. 4, V, mm. 236-297 251 v i i 2.39. Quartet No. 1, III, mm. 115-122 252 2.40. Quartet No. 6, I, mm. 126-143 253 2.41. Quartet No. 5, III, mm. 1-39 254 2.42. Quartet No. 4, V, mm. 183-195 255 3.1. Quartet No. 6, I, mm. 60-82 256 3.2. Quartet No. 1, III, mm. 107-112 257 3.3. Quartet No. 6, I, mm. 1-13 258 3.4. Quartet No. 4, V, mm. 374-385 259 3.5. Quartet No. 5, I, mm. 44-58 260 3.6. Quartet No. 6, I, mm. 141-157 261 3.7. Quartet No. 5, II, mm. 26-29 262 3.8. Quartet No. 3, Prima parte, mm. 76-83 263 3.9. Quartet No. 4, V, mm. 196-213 264 3.10. Quartet No. 2, III, mm. 47-55 265 3.11. Quartet No. 2, I, mm. 60-69 266 3.12. Quartet No. 5, I, mm. 23-29 267 3.13. Quartet No. 4, V, mm. 214-237 268 3.14. Quartet No. 6, I, mm. 352-390 269 3.15. Quartet No. 4, V, mm. 1-5, 11-18, 23-26, 29-34, 37-45 . . . 270 3.16. Quartet No. 4, V, mm. 47-49, 52-53, 56-61, 63-75 271 3.17. Quartet No. 4, V, mm. 75-79, 81-87, 89-92, 97-104 272 3.18. Quartet No. 4, V, mm. 320-332 273 3.19. Quartet No. 2, I, mm. 14-32 274 3.20. Quartet No. 1, I, mm. 33-53 275 3.21. Quartet No. 3, Prima parte, mm. 27-33 276 3.22. Quartet No. 3, Prima parte, mm. 35-43 277 v i i i 3.23. Quartet No. 3 f Prima parte, mm. 53-64 278 3.24. Quartet No. 6, I, mm. 31-60 279 3.25. Quartet No. 5, I, mm. 1-2, 8, 24-25, 44-45, 59-60, 126-127, 132-133, 146-148, 159-160, 167-168 280 4.1. Quartet No. 6, IV, mm. 78-86 281 4.2. Quartet No. 6, IV, mm. 1-13 282 4.3. Quartet No. 6, IV, nm. 1-13 . 283 4.4. Quartet No. 6, IV, mm. 13-22 284 4.5. Quartet No. 6, IV, mm. 22-39 285 4.6. Quartet No. 6, IV, mm. 40-54 286 4.7. Quartet No. 6, IV, mm. 55-63 287 4.8. Quartet No. 6, IV, mm. 62-72 288 4.9. Quartet No. 6, IV, mm. 72-79 289 4.10. Quartet No. 6, IV, mm. 1-86 290 i x A<^<mEDQyiENTS I would l i k e t o express my utmost g r a t i t u d e t o Dr. Wallace Berry f o r h i s many i n v a l u a b l e suggestions as s u p e r v i s o r of t h i s d i s s e r t a t i o n , and e s p e c i a l l y f o r h i s unceasing commitment t o the p r o j e c t . H i s uncom-pr o m i s i n g a t t e n t i o n t o d e t a i l has t r u l y been a constant source of i n s p i -r a t i o n . I a l s o w i s h t o thank Dr. W i l l i a m Benjamin f o r h i s involvement t h r o u g h o u t t h e d u r a t i o n o f t h e p r o j e c t and f o r h i s numerous h e l p f u l annotations. To Dr. Eugene Wi l s o n , f o r h i s r e a d i n g o f the paper and f o r h i s thought-provoking d i s c u s s i o n s and comments, I o f f e r my a p p r e c i a t i o n . I would l i k e t o acknowledge generous f i n a n c i a l support from the S o c i a l Sciences and Humanities Research C o u n c i l o f Canada, the U n i v e r -s i t y o f B r i t i s h Columbia, and the Izaak Walton K i l l a m Memorial Fund. For p e r m i s s i o n t o use c o p y r i g h t e d m a t e r i a l s , the f o l l o w i n g pub-l i s h e r s are g r a t e f u l l y acknowledged: European American Music D i s t r i b u -t o r s , s o l e C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n ( P h i l h a r m o n a ) ; and Boosey and Hawkes (Canada) L t d . My most s i n c e r e thanks go t o my w i f e , Brenda, f o r her constant encouragement and p a r t i c u l a r l y f o r her t i r e l e s s p a tience throughout the c o u r s e o f t h e p r o j e c t , and t o my son, C h r i s t o p h e r , whose b i r t h i n 1986 gave s p e c i a l meaning t o the paper's completion. T h i s d i s s e r t a t i o n i s d e d i c a t e d t o my mother, and t o the memory of my f a t h e r . x EDITORIAL NOTES Certain notational and editorial practices i n this paper require preliminary comment. Upper-case l e t t e r s which denote conventional keys represent those of the major mode, while lower-case letters refer to minor keys. At times the qu a l i f i e r major or minor w i l l be given, i n which case the tonic of the key w i l l be upper-case f o r both major and minor (thus, F major or F minor). Roman numerals representing harmonic function are s i m i l a r l y grouped. Major and augmented chords are indicated with upper-case roman numerals, and minor and diminished chords with lower-case roman numerals. Depending on the mode of a designated key, some scale degrees have two inflections, each supporting a harmony of a different quality. In this paper, harmonies from the major and minor modes are designated as follows: Major: I i i i i i IV V v i v i i Minor: i i i b i l l i v v bVI bVEI Roman numerals enclosed i n quotation marks denote nontertian or nontraditional v e r t i c a l i t i e s whose inferred roots function analogously to those of their conventional counterparts i n the major-minor system. Pi t c h - c l a s s i s abbreviated PC and i n t e r v a l - c l a s s IC. P i t c h -classes are denoted by upper-case l e t t e r s (context w i l l determine the d i s t i n c t i o n between PC and key). R e g i s t r a l l y s p e c i f i c pitches are designated a c c o r d i n g t o the f o l l o w i n g octave c l a s s i f i c a t i o n s : C l C 2 C 3 c 4 c 5 c 6 c 7 Often, a PC i n the music i s b e t t e r understood as i t s enharmonic e q u i v a l e n t , p a r t i c u l a r l y i n l i n e a r step and PC-step successions; where t h i s o c c u r s , t h e PC l e t t e r w h i c h b e s t d e n o t e s f u n c t i o n i s g i v e n f i r s t and i s f o l l o w e d i n p a r e n t h e s e s by t h e PC w h i c h a p p e a r s i n t h e m u s i c [thus, Eb(=D#) denotes a D# i n the music, which f u n c t i o n s as Eb]. Many d e t a i l s i n the music examples are i d e n t i f i e d w i t h a r e f e r -ence number housed i n the f o l l o w i n g enclosure: These numbers c o r r e -spond t o s i m i l a r l y denoted t e x t u a l r e ferences. x i i CHAPTER I INTRODUCTION A complete l i s t of sources dealing with Bela Bartdk's music would indeed be extensive. If, from such a l i s t , sources dealing in some detailed-, analytical way with his music were extracted, the result would be a considerably shorter body of literature. And, although i t is widely acknowledged that Bartdk's music is "tonal" in some sense, few of the published analyses focus on aspects of tonality, so that a collec-tion of sources dealing with the latter would be even more diminutive. Yet, with so few penetrating discussions of tonality in Bartdk's music, there is l i t t l e unanimity as to the means by which asserted tonal orien-tation is effected. For example, tonality in Bartdk is at times repre-sented by the adaptation of only certain general principles of the major-minor system, while at other times i t i s demonstrated through application of specific determinants associated with Heinrich Schenker. Moreover, tonality is often said to include nontraditional principles of PC-centricity along with those of the major-minor system. Analysis of tonality in Bartdk's music (and that of other twentieth-century com-posers) i s often imprecise in i t s details of affirmed adaptations of traditional principles, and inadequate in its explanation of particulars of interaction between conventional and nonconventional determinants. The issue of tonality in this music is thus challenging and intricate, 1 i f not perplexing and enigmatic. The concept of "key," as a ref lect ion of tonality i n music of the major-minor system, is often problematic when applied to twentieth-century music. For example, David Gow claims that Bartok's second quartet contains a classical key-relationship between the three movements: the outer movements are in A minor with the central movement in the subdominant . . . . What can "in the key of A minor" possibly mean in this context? Gow goes on to acknowledge that the "final tonal centre is not stated at the beginning" and that "it is the way in which Bartok arrives at this final tonality which is so intriguing."^ He further explains that i t isn't as though Bartok begins in one key and ends in another but, rather, that he deliberately obscures not only the ultimate goal, but any clear tonal centre at the beginning . . . allowing the tonality to emerge gradually as the quartet unfolds—we might c a l l this process emergent tonality. It becomes clear from Gow's analysis that what he rea l ly means by "tonality" and "in the key of" pertain to brief and periodic—often only final—statements of a re lat ive ly exposed tertian harmony or diatonic collection. He notes, for example, that there are only four moments in the whole [opening] section where the lower parts remain stat ic long enough for the ear to hear them as clearly defined chords. •^David Gow, "Tonality and Structure i n Bartok's F i r s t Two String Quartets," The Music Review 34/3-4 (1973): 259. 2 Ibid. 3 Ibid. 4 Ib id . , p. 260. 2 And, although he states that events leading to such points of unequivo-cal conventionality are vital to the notion of emergent tonality, there i s l i t t l e deta i l in his analysis to suggest how such tonally unstable events—however vague because of the constant rhythmic shift ing of chord-tones—are related to the ultimate goal. And i t is precisely such relationships—not merely the presence of a "tonic" triad—which are fundamental to the establishment of tonal structure in major-minor music and in twentieth-century music asserted to be "tonal." Colin Mason makes s imi lar statements of conventional key-relations in his analysis of Bartok's fourth quartet: The main key of the work, i n the two outer movements, i s C. The second movement is in E, and the fourth is in A flat, respectively a major third above and below the main key of the work.^  Here, again, tonality and key are associated with a main PC or harmony exposed at structural junctures. Relationships between such focal points and their surrounding pitch events are, however, rarely identi-fiable with the degree of precision possible in the major-minor system. Thus, while the characteristic.of centricity is apparent in Bartok's music, not a l l processes and relations common to the major-minor system are operable i n Bartrik, and the assertion of "key" i s accordingly suspect. Halsey Stevens is somewhat more careful in his characterization of tonal centers and keys. He notes in connection with the f irs t quar-tet that its Col in Mason, "Tonality, Symmetry and Latent Serialism i n Bartok's Fourth String Quartet," The Music Review 18 (1957): 189. 3 tonalities . . . are handled so freely that one is justified only in saying that they are "on"—not "in" this or that tonality. . . . By this i t i s understood that [these] keynotes serve as orientation points: that the music is organized around them, modally or chroma-tically, freely fluctuating, using the keynotes as points of depar-ture and points of repose, affecting modulation from and back to them.6 Stevens thus acknowledges the restricted role of "key" in these contexts by suggesting that music between points of tonal orientation is, even in the quasi-conventional f i r s t quartet, not clearly representative of a particular key in the s t r i c t sense. Stevens, however, continues his analysis without substantial reference to the particulars of pitch organization in passages between flashes of unequivocal conventionality. In the opening remarks to his analysis of the fi r s t movement of Bartok s fourth quartet, Leo Treitler asserts that, although the PC-dyad C-E occurs at many structural points in the movement, neither the note C nor the C-E dyad i s "a tonality." 7 He claims, rather, that i t i s "an arbitrarily chosen, static 'tonal center' which is not involved in any scheme for generating secondary tonal areas," and goes on to suggest that the dyad is a static "point of reference" to which other sections Q may be related. Treitler, l i k e Stevens, i s thus cautious in his assertion of tonality, acknowledging the limited extent to which tonal procedures are relevant in this context. And, although he notes that focusing on the "maintaining of a pitch or pitches as a point of refer-^Halsey Stevens, The Life and Music of BeLa Bartok (New York: Oxford University Press, 1964), pp. 171-172. 7 Leo Treitler, "Harmonic Procedure i n the Fourth Quartet of Bartok," Journal of Music Theory 3/2. (1959): 294. 8Ibid. 4 ence" d e f i n e s one v i a b l e approach t o the work, he chooses t o examine the m a n i p u l a t i o n o f t h r e e f o u r - n o t e c e l l s , o f w h i c h two were o r i g i n a l l y -i d e n t i f i e d by George P e r l e . ^  One p r o b l e m i n d e a l i n g w i t h t r a d i t i o n a l t o n a l i t y i n Bartok's m u s i c , r e v e a l e d i n t h e q u o t a t i o n s c i t e d above, c o n c e r n s t h e e x t e n t t o which p r i n c i p l e s o f t r a d i t i o n a l t o n a l i t y are a s s e r t e d t o operate. While c e r t a i n of those p r i n c i p l e s are indeed r e l e v a n t , a l l u s i o n s t o the major-minor system are most o f t e n s p o r a d i c and c o m p l i c a t e d by the n o n t r a d i -t i o n a l c o n t e x t s i n w h i c h t h e y o c c u r . Because o f t h i s i n t e r a c t i o n o f d i s p a r a t e f a c t o r s o f t o n a l o r g a n i z a t i o n , the a d a p t a t i o n o f t r a d i t i o n a l elements must be s y s t e m a t i c a l l y documented. For example, a f t e r sugges-t i n g t h a t t h e f i n a l movement o f Bartok's second q u a r t e t i s one whose "approaches t o t o n a l s t r u c t u r e a r e s t r i n g e n t and d e f i n i t e , " W a l l a c e B e r r y s t i p u l a t e s and demonstrates t h r e e fundamental techniques of t r a d i -t i o n a l t o n a l o r i e n t a t i o n r e l e v a n t t o the work: . . . emphasis upon the t o n a l c e n t e r and i t s s u p p o r t i v e f u n c t i o n s by i t e r a t i o n , p r o l o n g a t i o n , s t r e s s , e t c . ; a f f i r m a t i o n by q u a s i - f u n c -t i o n a l harmonic and melodic elements resembling conventions of the t o n a l p e r i o d (the quasi-dominant a c t i o n c o n t i n u e s t o r e l y h e a v i l y upon the concept o f leading-tone tendency and accustomed r o o t move-ment); and [by] l i n e a r d i r e c t i o n t o w a r d and i n d i r e c t o r d i r e c t e n c i r c l e m e n t of the t o n i c PC, e s p e c i a l l y a t p o i n t s of f o r m a l punctu-a t i o n . 0 I n s h o w i n g " q u a s i - f u n c t i o n a l " h a r m o n i c and l i n e a r approaches t o , and The two four-note c e l l s a t t r i b u t e d t o P e r l e are, i n i n t e g e r n o t a t i o n , 0,1,2,3 ( P e r l e ' s c e l l "X") and 0,2,4,6 ( P e r l e ' s c e l l "Y"). F o r t h e d e r i v a t i o n o f t h e s e see George P e r l e , " S y m m e t r i c a l F o r m a t i o n s i n t h e S t r i n g Q u a r t e t s o f BeLa Bartok," The M u s i c R e v i e w 16 (1955): 3 1 0 f f . T r e i t l e r l a b e l s a t h i r d c e l l , 0,1,5,6 i n i n t e g e r n o t a t i o n , as c e l l "Z". • ^ W a l l a c e B e r r y , S t r u c t u r a l F u n c t i o n s i n M u s i c (Englewood C l i f f s : P r e n t i c e - H a l l , Inc., 1976), p. 148. 5 organization around, primary PCs, Berry demonstrates processes by which the movement's tonality i s established and maintained—factors of struc-ture indeed more far-reaching than mere sporadic points of r e l a t i v e tonal c l a r i t y . While other means of p i t c h organization may we l l be identified i n the movement, this analysis focuses on identifiable fac-tors of conventional tonal structure, e s t a b l i s h i n g a v i t a l s t r u c t u r a l frame which may be heard to i n t e r a c t with and complement other, less traditional interpretations. Sources c i t e d above have i n some way approached t o n a l i t y i n Bartok's music through generally acknowledged factors of the major-minor system. Roy Travis has analyzed the opening movement of Bartok's fourth quartet with techniques sp e c i f i c a l l y associated with Heinrich Schenker's systematic theory of t r a d i t i o n a l tonal ity. ^ Through extensive quasi-Schenkerian graphic representations, Travis's analysis reveals many interesting structural relationships i n the movement. The analysis i s not, however, without major theoretical problems, two of which I suggest here. F i r s t , i n h i s attempt t o adapt Schenker's n o t i o n of a "fundamental l i n e " (i.e., U r l i n i e ) ^ to the piece, Travis d i s t o r t s the o r i g i n a l concept of that construct, while adding l i t t l e to our under-standing of the movement's large-scale structure. He posits a funda-mental l i n e spanning an F#-C t r i t o n e , the outer i n t e r v a l of a primary Roy Travis, "Tonal Coherence i n the F i r s t Movement of Bartok's Fourth String Quartet," The Music Forum 2 (1970): 298-371. Heinrich Schenker, Der f r e i e Satz, trans, and ed. Ernst Oster (New York: Longman, Inc., 1979), p. 4. 6 whole-tone c e l l i n the movement. The fundamental l i n e as conceived by Schenker, however, i s a l i n e a r i z a t i o n o f the t o n i c t r i a d (or a p o r t i o n of the l a t t e r i n the case of a 3-1 descent), the c o n s t i t u e n t members of which are f u n c t i o n a l l y d i r e c t e d by v i r t u e o f r o o t r e l a t i o n s i n h e r e n t i n t h e m a j o r - m i n o r system. A l t h o u g h t h e l i n e a r i z e d g r o up o f PCs i n T r a v i s ' s U r l i n i e d e f i n e s a p r i m a r y , r e c u r r e n t " c e l l " i n t h e movement, t h a t c e l l i s n o t t h e o v e r a l l r e f e r e n t i a l g o a l o f t h e work, w h i c h i s , r a t h e r , a C-major t r i a d . The F# a t t h e head o f T r a v i s ' s U r l i n i e , i n f a c t , r e s o l v e s t o G, the f i f t h o f the c a d e n t i a l t r i a d , as I w i l l show i n t h e n e x t c h a p t e r . What T r a v i s i d e n t i f i e s as a f u n d a m e n t a l l i n e — a c o n s t r u c t which, i n t r a d i t i o n a l terms, l i n e a r i z e s a consonant e v e n t — i s , i n f a c t , a v e r y mobile, u n s t a b l e event, and one which I w i l l demonstrate l a t e r t o have a p a r t i c u l a r type of t o n i c i z i n g f u n c t i o n . Were the p i e c e t o end on t h e w h o l e - t o n e c e l l d e l i n e a t e d by t h e o s t e n s i b l e s t r u c t u r a l d e s c e n t F# t o C, t h e a n a l o g y o f t h e l a t t e r t o a c o n v e n t i o n a l U r l i n i e would be more accurate. As i t stands, however, Schenker's concept of a fundamental l i n e i s somewhat misrepresented by T r a v i s . The second problem concerns t h e l a r g e - s c a l e "harmonic" s t r u c -t u r e , a s s e r t e d t o a r t i c u l a t e the movement's sonata form. T r a v i s notes t h a t the movement has been recognized " i m p l i c i t l y " as i n sonata form but t h a t t h e " r e l a t i o n s h i p — e s s e n t i a l t o any sonata a l l e g r o d e s i g n — w h i c h The p r i m a r y w h o l e - t o n e c e l l h e r e i s P e r l e ' s c e l l "Y" (note 9), h e r e c o m p r i s e d o f PCs F#, E, D, and C. T r a v i s shows t h i s h o r i z o n t a l i z a t i o n i n i t s most c o n c i s e f o r m i n Ex. 1 and i n more e l a b o r a t e s e t t i n g s i n subsequent examples. 7 obtains between tonal and formal a r t i c u l a t i o n " has not yet been ex-plained. 1 4 Yet he proceeds to p o s i t exposition, development, and r e c a p i t u l a t i o n sections which prolong the dissonant tonic sonority.-^ Although one might well not expect to find i n this piece a conventional tonic-dominant " p o l a r i t y " expressed at various levels of tonal struc-ture, some form of harmonic departure i n the exposition, and especially in the development, i s surely v i t a l to the notion of sonata. Moreover, such a harmonic departure would need to be tie d to a system of hierar-c h i c a l r e l a t i o n s h i p s , however contrived, i n order to simulate corre-sponding relations i n traditional sonata structure. What Travis posits, however, i s a prolonged "tonic" throughout the e n t i r e work, u n t i l the f i n a l 28 bars, where a tenuous IV i s said to oc c u r . ^ Although Travis i d e n t i f i e s passages of prolonged "secondary" c e l l s , these are not accorded s i g n i f i c a n c e as form-defining tonal departures, analogous to large-scale harmonic motions i n the major-minor system. Furthermore, the asserted large-scale "I-IV-V-I" progression i s , i n t r a d i t i o n a l l y tonal music, significant at higher levels because i t i s comprised of the most fundamental of harmonies i n the major-minor system, and because i t i s applicable at the most foreground l e v e l s to e f f e c t palpable tonal orientation. This "nesting" process—whereby an acknowledged functional progression at the surface i s heard to operate at in c r e a s i n g l y higher Travis, "Tonal Coherence," p. 301. 'See, f o r instance, h i s Exx. 2a and 2b, Ex. 3, and Ex. 6. 'Travis, "Tonal Coherence," p. 300 (Exx. 2a and 2b) and p. 308 (Ex. 3). 8 levels of s t r u c t u r e — i s clearly not a factor i n this piece; the claimed large-scale "I-IV-V-I" progression i n t h i s context thus has l i t t l e meaning. I t was suggested at the opening of the chapter that nontradi-t i o n a l determinants of c e n t r i c o r i e n t a t i o n are often ascribed tonal significance i n Bartok's musical language. Symmetry may be cited as one such determinant. E l l i o t t Antokoletz has written extensively about that property as i t r e l a t e s to Bartok's music.^ Antokoletz acknowledges conventional means of tonal orientation i n Bartok, but advances the view that, where a p a r t i c u l a r PC i s established as the "primary tone of a 1 ft t r a d i t i o n a l mode," the term "tonal center" i s inaccurate. He notes further that the term tonal center i s more ideally suited to the "estab-lishment of a given sonic area by symmetrical organization of a conglom-erate of pitches around an axis of s y m m e t r y . A n t o k o l e t z seeks to show how t r a d i t i o n a l and nontraditional (i.e., symmetrical) means of tonal establishment are "integrated by means of special interactions and on transformations." E l l i o t t Antokoletz, The Music of Bela Bartok (Berkeley: University of California Press, 1984); "The Musical Language of Bartok's 14 Bagatelles for Piano," Tempo 137 (June, 1981): 8-16; "Principles of Pitch Organiza-tion i n Bartok's Fourth String Quartet," In Theory Only 3/6 (September, 1977): 3-22. 1 8Antokoletz, Music of Bartok, p. 138. 1 9 I b i d . 2 0 I b i d . 9 Antokoletz s assertions of conventionality are based on factors discussed already: fragments of diatonic collections, functional t o n i c i -zing progressions, and leading-tone relationships. There i s , however, a tendency i n some of his analyses to regard b r i e f l y established tertian harmonies as dist i n c t tonal areas, rather than integrating them into a single, underlying conceptual frame within which the established harmo-nies are functional components i n a broader harmonic progression. I t i s Antokoletz's documentation of symmetrical structures, which are said to express referential tonal centers, which I w i l l focus on here. After establishing a theoretical basis for symmetrical struc-tures based on i n t e r v a l cycles, i n t e r v a l couples, J and sum couples, 2 4 the author proceeds to i l l u s t r a t e progressions of three four-note c e l l s which establish and maintain a particular axis of symmetry. J Isolating progressions of transpositionally equivalent c e l l s , i n which a r e f e r e n t i a l l y primary t r a n s p o s i t i o n i s e n c i r c l e d symmetrically, and demonstrating contiguous and noncontiguous recurrences of c e l l s 91 • See, for instance, Ex. 166 (Music of Bartok), i n which F minor may be heard u l t i m a t e l y as a large-scale bvi i n A major; Ex. 170, i n which Antokoletz's A major and C# minor may be heard as Db aeolian (natural minor) and Db phrygian (with the Ebb), corroborating the Db which he notes i s e x p l i c i t at one bar before rehearsal 7; and Ex. 172, where the C# minor may be heard at a higher l e v e l to be i i i i n A, the t r a d i -tionally tonicized goal of the opening phrase. 2 2Antokoletz, Music of Bartok, p. 68. 2 3 I b i d . , p. 69. 2 4 I b i d . , p. 70. The three c e l l s (referred to i n note 9) are, i n integer notation, 0,1,2,3; 0,2,4,6; and 0,1,5,6. 10 having the same symmetrical center indeed reveals aspects of p i t c h organization. In many cases, however, one i s not convinced that the symmetrical center i s perceived i n t u i t i v e l y as referential ly primary. One of the most s t r i k i n g of such misinterpretations concerns Antokoletz's analysis of Debussy's "Voiles" (Preludes, v o l . I ) . 2 ^ Antokoletz posits D (and the tritone D-G#) as the tonal center based on the symmetrically central position of D i n the cadential C-E dyad i n m. 5 and at the end of the piece. He further states that the middle section has G#—the tritone counterpart of D—as i t s axis because of the central position of that PC i n the pentatonic collection, Eb-Gb-Ab-Bb-Db, on which that section concentrates. The asserted D axis i n the outer sections i s problematic because i t involves focal significance for a PC that i s never exposed cadentially, as opposed to a dyad (C-E) which i s given much greater prominence and would more l i k e l y be i n t u i t i v e l y grasped as the primary element i n the essentially whole-tone construc-tion. The problems with interpreting the middle section around G# are twofold: f i r s t , Eb (with Gb) i s , l i k e C-E i n the outer sections, more obviously exposed as primary (through neighbour-note elaboration and durational emphasis i n mm. 45-47); and second, the assertion that a l l three sections of an ABA form are centered around a single t r i t o n a l axis 27 f a i l s to account for any true sense of harmonic departure. 2 bAntokoletz, Music of Bartok, pp. 6-8. 2 7He comes to the same conclusions with respect to the third movement of Bartok's fourth quartet (Music of Bartok, pp. 166-172). The outer sec-tions of the movement are clearly based on the PC D. The middle section i s c l e a r l y oriented to a C-E dyad, the C of which i s durational l y 11 Where the symmetrically central element i s perceived as focal, i t i s more often through surface factors of expression than symmetrical placement, although the latter may be heard as an element of corrobora-t i o n . 0 For example, i n the c e l l G#-C#-D-G, i d e n t i f i a b l e i n much of Bartok's music, each of four orderings of these same four PCs y i e l d s a d i f f e r e n t semitonally r e l a t e d p a i r of PCs as i t s axis of symmetry. In the sum-3 ordering given above, the C#-D dyad i s a x i a l . 2 9 If rotated to D-G-G#-C#, the a x i a l dyad i s G-G#—a t r i t o n e from that of the f i r s t . The remaining two "rotationally related" orderings—C#-D-G-G# and G-G#-C#-D—have axial dyads E-F and Bb-B respectively. 3 0 The potential prob-lem i n a s c r i b i n g r e f e r e n t i a l s i g n i f i c a n c e based s o l e l y on symmetry should i n t h i s case be obvious: four orderings of the same four PCs provide eight of the possible twelve PCs with p o t e n t i a l primacy. Without a d d i t i o n a l surface i n d i c a t o r s of emphasis and o r i e n t a t i o n , a p a r t i c u l a r r e f e r e n t i a l PC would thus be d i f f i c u l t to apprehend. A l -exposed i n mm. 47-49, and, with E, durationally exposed and elaborated i n mm. 51-54; m. 55 concludes the middle section with the sole C-E dyad. And yet, he once again posits D as the central PC, denying any sense of harmonic departure i n the three-part form. Paul Wilson, i n his review of Antokoletz's Music of Bartok [Journal of Music Theory 30/1 (Spring, 1986): 113-121] makes a similar claim: "In the majority of pieces, whatever audible structural tonality i s present depends on the use of more traditional and familiar devices, ranging from the perfect f i f t h a t a cadence to an extended or repeated bass pedal. This i s true even where whatever symmetries are present reinforce the audible tonality." (p. 120) TO ^ T h e sum-3 de r i v a t i o n of the c e l l G#-C#-D-G (integers 8,1,2,7) i s as follows: 8 + 7 = 15 (=3 mod 12) and 1 + 2 = 3; an odd sum has two notes a semitone apart as i t s axis, here 1 and 2 or C# and D. 3 0These rotations and orderings are shown i n Antokoletz, Music of  Bartok, p. 72 (Ex. 75). 12 though symmetrically central position may be said to reinforce orienta-tion i n relation to a given PC or PC collection already rendered focal through palpable exposure, i t i s problematic as a p r i n c i p a l means of referentiality. Problems i n adapting t r a d i t i o n a l tonal p r i n c i p l e s to Bartdk's music, some of which are r a i s e d i n the foregoing paragraphs, apply to much music of the twentieth century. Many factors of tonal expression relevant to music of the common-practice period i n general, and certain of those a r t i c u l a t e d by Schenker i n p a r t i c u l a r , are simply not a p p l i -cable to newer contexts. Other factors, however, are indeed relevant to our cognition of music subsequent to the common-practice period. Some principles—"particularized" within the conventional system—are often assumed to be applicable only to music of the eighteenth and ninteenth centuries or directly applied to newer contexts without adequate speci-f i c a t i o n of the t h e o r e t i c a l bases on which such applications rest. T o n i c i z a t i o n through semitonal and descending-fifth motions are two determinants of the major-minor system i n general which may be heard to function i n the most nontraditional of contexts. Furthermore, "prolon-gation" and "s t r u c t u r a l l e v e l s " are two p r i n c i p l e s associated with Schenker which, conceived as general concepts, are subject to adaptation to (and p a r t i c u l a r i z a t i o n in) newer contexts. The ce n t r a l i s s u e — whether i n connection with a generally acknowledged factor of conven-ti o n a l i t y or a specific principle associated with Schenker—is precision of documentation of the means by which individual, potentially appli-cable principles are adapted to new contexts. 13 In addition to—perhaps at times in response to—the existent, large body of theoretical literature in which aspects of conventional tonality are problematically applied to twentieth-century contexts (and not just to the music of Bartok) is a growing list of sources addressing such problems. Travis's pioneering work in the late 1950s and early 60s on the application of Schenker's theory to twentieth-century music elicited immediate response. Ernst Oster wrote, with regard to Travis's notion of a "dissonant tonic sonority," that Schenker's basic idea is the projection in time of the triad as given by nature. Mutilate this idea and substitute for triad va particular tone, interval, or chord' (no matter how dissonant or far-fetched), and an vexplanation' for virtually anything can be devised. Edward Laufer, writing much more recently, suggests, in connection with the adaptation of Schenkerian principles to newer contexts, that There is no triad to be prolonged: thus, some contextually derived associative sonority must take its place. The concepts of conso-nance and dissonance, as technically defined, therefore cannot exist, nor can, strictly speaking, the notions of passing and neigh-bour notes where these were dissonant events. Their attendant constraints, which provided motion and delays, must be compensated for by other kinds of embellishing and traversing motions. 2 It would sem from these two coments that the problem with the concept of a nontraditional "tonic" harmony lies not so much in its interval structure—for any such element, with enough exposure in the capacity of an elaborated, focal element, may be perceived as contex-tually primary—but, rather, in the specification of new procedures, or J i : E;rnst O s t e r , "Re: A New Concept o f T o n a l i t y ( ? ) , " J o u r n a l o f M u s i c Theory 4 (1960): 96. - l 2Edward L a u f e r , r e v i e w o f Der f r e i e S a t z , by H e i n r i c h S chenker, i n Music Theory Spectrum 3 (1981): 161. 14 means o f a d a p t i n g c o n v e n t i o n a l p r o c e d u r e s , i n t h e p r o j e c t i o n o f t h a t n o n t r a d i t i o n a l t o n i c over t i m e — " p r o l o n g a t i o n " i n conventional terms, a necessary c o n d i t i o n f o r the est a b l i s h m e n t and p e r c e p t i o n o f l a r g e - s c a l e t o n a l coherence. W i t h q u e s t i o n s o f a p p l i c a b l e p r o l o n g a t i o n a l techniques momen-t a r i l y a s i d e , James Baker's comments w i t h r e s p e c t t o S a l z e r ' s work i n tw e n t i e t h - c e n t u r y t o n a l s t r u c t u r e s , and A r n o l d W h i t t a l l ' s d i s c o u r s e on d i s s o n a n c e i n S t r a v i n s k y ' s R i t e o f S p r i n g w o u l d seem t o s u p p o r t t h e n o t i o n o f a ( n o n c o n v e n t i o n a l ) r e f e r e n t i a l t o n i c . B a k e r c r i t i c i z e s S a l z e r f o r e x t r a c t i n g n o n t r i a d i c members from o t h e r w i s e t r i a d i c c o l l e c -t i o n s and c o n s e q u e n t l y e l i m i n a t i n g t h e p o s s i b i l i t y t h a t t h e o r i g i n a l c o l l e c t i o n s "might t h e m s e l v e s c o n s t i t u t e b a s i c components o f a non-t r i a d i c s t r u c t u r e . " ^ W h i t t a l l contends t h a t "the 'norm' f o r the work as a whole [the R i t e o f Spring] i s dissonant, not consonant" but t h a t we hear t h a t norm as an e n t i t y o f f u n d a m e n t a l s t r u c t u r a l s i g n i f i c a n c e , r a t h e r t h a n s o m e t h i n g — c a l l e d a d i s s o n a n c e — w h i c h n e v e r t h e l e s s does not f u n c t i o n as a dissonance f u n c t i o n s i n t o n a l music. . . . The "norm' o f Le S a c r e i s n o t one i n w h i c h p r e d o m i n a n t dissonances i m p l y unheard consonant r e s o l u t i o n s — a n d i t f o l l o w s t h a t such * imagined' r e s o l u t i o n s a r e unnecessary. 4 The p r o b l e m , t h e n , l i e s n o t i n t h e p o t e n t i a l f o r a n o n t r a d i -t i o n a l t o n i c t o be s t r u c t u r a l l y f o c a l b u t , as a l l u d e d t o above, i n t h e James Baker, "Schenkerian A n a l y s i s and Post-Tonal Music," i n Aspects  o f S c h e n k e r i a n A n a l y s i s , ed. D a v i d Beach (New Haven: Y a l e U n i v e r s i t y P r e s s , 1983), p. 156. ^ 4 A r n o l d W h i t t a l l , " M u s i c A n a l y s i s as Human S c i e n c e ? Le S a c r e du  Printemps i n Theory an P r a c t i c e , " Music A n a l y s i s 1/1 (March, 1982), p. 45. 15 p r o j e c t i o n o f a t h a t t o n i c — h e r e a f t e r , r e f e r e n t i a l element - 3 — i n what-e v e r f o r e g r o u n d f o r m i t t a k e s . B a k e r s a y s o f T r a v i s ' s a n a l y s i s o f Bartok's f o u r t h s t r i n g q u a r t e t t h a t . . . the f a c t t h a t o s t e n s i b l y opposing systems are seen t o operate a t d i f f e r e n t l e v e l s o f s t r u c t u r e i n these analyses i s a t odds w i t h t h e v e r y c o n c e p t o f s t r u c t u r a l c o h e r e n c e a s e s t a b l i s h e d by s t r u c -t u r a l i s t s ( i n c l u d i n g S c h e n k e r ) . . . . T r a v i s [does n o t e x p l a i n ] t h e r e l a t i o n s h i p between t h e s e s y s t e m s — i f a n y — n o r [does he] s p e c i f y t h e o p e r a t i o n s whereby a s t r u c t u r a l b a l a n c e between them i s achieved. 6 C r a i g Ayrey has expressed s i m i l a r concern w i t h regard t o the r e l a t i o n between d i s s o n a n t r e f e r e n t i a l t o n i c s (my " r e f e r e n t i a l elements") and the processes by which they are p r o j e c t e d : . . . no a t t e m p t has been made t o d e s c r i b e t h e s p e c i f i c t e c h n i q u e s t h a t prolong a d i s s o n a n t s o n o r i t y o r produce a fundamental l i n e , so t h a t t h e r e has a l w a y s been a c e r t a i n d i s c o n t i n u i t y between t h e n a t u r e o f background a s s e r t e d and t h e means by w h i c h i t i s achieved. ' The term " r e f e r e n t i a l element" i s used throughout t h i s study t o r e p r e -sent the analogue o f a co n v e n t i o n a l t o n i c t r i a d . " R e f e r e n t i a l " denotes t h e f u n c t i o n o f s u c h a s o n o r i t y as t h e t o n a l " p o i n t o f r e f e r e n c e " t o which other p i t c h events are r e l a t e d as subordinate i n some c o n t e x t u a l l y d e f i n e d manner (explained i n each case). "Element" suggests the v a r i e t y o f "sonorous q u a l i t i e s " which the re f e r e n c e may take. For example, the terms " r e f e r e n t i a l v e r t i c a l i t y " and " r e f e r e n t i a l PC" w i l l be used where f u r t h e r d i s t i n c t i o n o r p r e c i s i o n i s r e q u i r e d i n s p e c i f y i n g the form o f t h e r e f e r e n t i a l e l e m e n t . The f i r s t o f t h e s e t e r m s r e f e r s t o a v e r t i -c a l i t y heard as f o c a l , w h i l e the second denotes the s i n g l e most funda-mental and f o c a l PC i n a g i v e n context. " R e f e r e n t i a l element" i s thus a g l o b a l term i n c l u d i n g both s p e c i f i c types d e s c r i b e d above. And, w h i l e a c o n v e n t i o n a l t o n i c t r i a d i s an example o f a r e f e r e n t i a l e l e m e n t , t h e l a t t e r t e r m i s r e s e r v e d f o r t h o s e o f a n o n t r i a d i c s t r u c t u r e , o r o f a t r i a d i c s t r u c t u r e o f a nonconventional b a s i s . "Tonic t r i a d " w i l l thus be r e t a i n e d f o r examples d e a l i n g w i t h c o n v e n t i o n a l l y t r i a d i c t e x t u r e s . 3 6James Baker, "Schenkerian A n a l y s i s , " p. 158. 3 7 C r a i g Ayrey, "Berg's "Scheideweg': A n a l y t i c a l Issues," Music A n a l y s i s 1/2 (July,1982) : 195-96. 16 The employment o f d i s p a r a t e means o f t o n a l o r i e n t a t i o n i s a v i t a l f e a t u r e o f much t w e n t i e t h - c e n t u r y music. Many composers i n the t w e n t i e t h c e n t u r y — p a r t i c u l a r l y i t s f i r s t h a l f — u s e d patent f a c t o r s o f t r a d i t i o n a l t o n a l i t y as a means o f p r o v i d i n g r e c o g n i z a b l e p o i n t s o f o r i e n t a t i o n between which newer techniques of p r o g r e s s i o n and prolonga-t i o n were employed. Edward Cone says of the p e r s i s t e n c e of conventional p a t t e r n s i n music t h a t " i n an a r t both a b s t r a c t and temporal they [con-v e n t i o n a l p a t t e r n s ] f u r n i s h s i g n p o s t s t o a i d t h e l i s t e n e r , who c a n n e i t h e r t u r n back nor pause t o look around him." J O I t seems t o me t h a t the key t o understanding t h i s music l i e s i n the study of ways i n which d i s p a r a t e p r i n c i p l e s o f o r i e n t a t i o n c o e x i s t and i n t e r a c t , n o t i n t h e e x c l u s i o n of t r a d i t i o n a l elements because of t h e i r o s t e n s i b l e "incompa-t i b i l i t y " w i t h n o n t r a d i t i o n a l s o n o r i t i e s and processes. The d e t a i l s o f i n t e r a c t i o n between con v e n t i o n a l and nonconventional p r i n c i p l e s a r e i n f a c t i n t e g r a l t o t h e e s t a b l i s h m e n t o f s t r u c t u r a l c o h e r e n c e i n t h i s music. C o n c e r n i n g Ayrey's comments, t h e n e c e s s i t y f o r p r i n c i p l e s by which dis s o n a n t s o n o r i t i e s (i.e., nonconventional r e f e r e n t i a l elements) a r e p r o l o n g e d i s i n d e e d c r u c i a l ; t h e g e n e r a t i o n o f a f u n d a m e n t a l l i n e seems t o me t o be l e s s i m p o r t a n t f o r t h i s m u s i c , as i t i s a c o n s t r u c t having l i t t l e r e l a t i o n t o the o f t e n h i g h l y v a r i a b l e i n t e r v a l l i e s t r u c -t u r e o f a p r i m a r y r e f e r e n t i a l e l e m e n t i n any g i v e n p i e c e . A t t i m e s a s i n g l e PC i s r e f e r e n t i a l and i s r e p r e s e n t e d i n a s i n g l e p i e c e by more Edward Cone, "The Uses of Convention: S t r a v i n s k y and H i s Models," i n S t r a v i n s k y : A New A p p r a i s a l of His Work, ed. Paul Henry Lang (New York: W. W. N o r t o n & Company, Inc., 1963), p. 21. 17 than one i n t e r v a l l i e s t r u c t u r e ; a t o t h e r t i m e s a p a r t i c u l a r i n t e r v a l l i c s t r u c t u r e i s i n i t s e n t i r e t y r e f e r e n t i a l throughout a piece. I n e i t h e r c a s e , because o f t h e n o n t r a d i t i o n a l s t r u c t u r e o f t h e r e f e r e n t i a l e l e -ment, and e s p e c i a l l y because o f t h e g e n e r a t i v e means by w h i c h i t i s e l a b o r a t e d , t h e c o n v e n t i o n a l c o n c e p t o f f u n d a m e n t a l l i n e has l i t t l e s i g n i f i c a n c e . T h i s i s not t o say t h a t n o n t r a d i t i o n a l t w e n t i e t h - c e n t u r y music i s w i t h o u t some form o f "background" s t r u c t u r e , and Ayrey s com-ments r e g a r d i n g d i s c o n t i n u i t y between s t r u c t u r a l l e v e l s a r e I t h i n k v a l i d . B u t , a g a i n , i t i s i n t h e d e t a i l s o f i n t e r a c t i o n between d i s -parate p r i n c i p l e s of p i t c h o r g a n i z a t i o n t h a t the r i c h n e s s of much music of t h i s century may be found. Even i n c o n s i d e r a t i o n o f t h i s b r i e f s u r v e y o f approaches t o t o n a l i t y i n Bartok, i t i s abundantly c l e a r t h a t a fundamental problem i n t h e a n a l y s i s o f t w e n t i e t h - c e n t u r y m u s i c f r o m t h e p o i n t o f v i e w o f " t o n a l i t y " i s t h a t o f a r e q u i s i t e r e d e f i n i t i o n and r e e v a l u a t i o n o f " t o n a l " p r i n c i p l e s as a p p l i e d c o n v e n t i o n a l l y , and a s o p e r a t i v e i n a giv e n n o n t r a d i t i o n a l i d i o m i n general o r i n a s p e c i f i c corpus i n p a r t i c -u l a r ( i n t h i s case the s t r i n g q u a r t e t s o f Be l a B a r t o k ) . A c c o r d i n g l y , I would propose t h a t t o n a l i t y be viewed as any p r i n c i p l e o r s e t o f p r i n -c i p l e s b y w h i c h a p a r t i c u l a r PC o r PC c o m p l e x ( i . e . , a r e f e r e n t i a l element) i s e s t a b l i s h e d as primary i n a g i v e n context and whose primacy i s m a i n t a i n e d a t a p a r t i c u l a r l e v e l o f s t r u c t u r e . T h i s d e f i n i t i o n recognizes c e n t r i c i t y as a fundamental c o n d i t i o n f o r t o n a l i t y , w i t h the p r i n c i p l e s o f e s t a b l i s h i n g s u c h c e n t r i c i t y as t h e d i f f e r e n t i a t i n g f e a t u r e s f o r v a r i o u s t o n a l i t i e s . C o n v e n t i o n a l t o n a l i t y , f o r example, would thus be thought of as embodying one s e t of p r i n c i p l e s a c c o r d i n g t o 18 which c e n t r i c i t y i s achieved, while the means of c e n t r i c o r i e n t a t i o n i n a piece by Bartok might consist of nonconventional determinants and conventional analogues (i.e., p r i n c i p l e s which are i n some sense analogous to c e r t a i n conventional procedures), as well as c e r t a i n devices directly associated with the major-minor system. In l i e u of a s t r i c t l y segmented historical perspective of t o n a l i t y , t h i s broadened concept recognizes various t o n a l i t i e s , each characterized by a d i f -ferent, although not necessarily exclusive, set of interacting p r i n c i -ples of p i t c h - c l a s s c e n t r i c i t y . Each t o n a l i t y i s thus conceptually d i s t i n c t by v i r t u e of factor s of tonal expression not found i n the other. Tonality, as conventionally understood and as broadly defined above, may be understood to embody two general and often interrelated processes, identified i n this study by the terms progression and prolon-gation. The f i r s t involves principles which direct the listener from one event to another related, but d i f f e r e n t , event; and the second consists of principles which orient a l l events i n a given context to a single event, thereby extending the temporal span over which the latter i s heard as primary. These two general processes define broad cate-gories of functional activity, each process being achieved i n a variety of ways. One of the main tasks i n a r r i v i n g at an understanding of Bartok's tonal language i s the precise s p e c i f i c a t i o n of the means— conventional and otherwise—by which progression and prolongation are effected. The second and t h i r d chapters of the present study w i l l , 19 a c c o r d i n g l y , be devoted t o the d e f i n i t i o n and demonstration o f r e l e v a n t p r i n c i p l e s o f p r o g r e s s i o n and p r o l o n g a t i o n i n t h e q u a r t e t s t h r o u g h e x c e r p t s f r o m t h e l a t t e r . The f i n a l c a t e g o r y o f t h e t h i r d c h a p t e r examines passages where two o r more r e f e r e n t i a l elements a r e prolonged s i m u l t a n e o u s l y , a p r o c e s s o f t e n r e f e r r e d t o as " b i t o n a l i t y . " Many f a c t o r s o f p r o g r e s s i o n and p r o l o n g a t i o n d i s c u s s e d i n t h e s e c o n d and t h i r d c h a p t e r s w i l l be i d e n t i f i e d i n t h e s e e x c e r p t s as i n t e r a c t i n g processes. E x e m p l i f i c a t i o n o f the ways i n which c o n v e n t i o n a l and nonconven-t i o n a l p rogressions and p r o l o n g a t i o n s i n t e r a c t as determinants o f t o n a l s t r u c t u r e — b e i t i n a cont e x t o f a s i n g l e r e f e r e n t i a l element o r one o f s e v e r a l — m u s t s u r e l y be considered fundamental t o the understanding o f Bartok's music as demonstrative of a " u n i f i e d " t o n a l system. E x p l i c a -t i o n o f such modes of i n t e r a c t i o n occurs throughout Chapters I I and I I I , p a r t i c u l a r l y i n the l a r g e r examples, and i s one of the c h i e f f u n c t i o n s of Chapter IV, the d e t a i l e d a n a l y s i s of the s i x t h quartet's f i n a l move-ment. T h i s p a r t i c u l a r movement w i l l be exam i n e d p h r a s e by p h r a s e , f a c i l i t a t i n g the view o f each as a dynamic i n t e r a c t i o n o f s e v e r a l s p e c i -f i c determinants of t o n a l o r i e n t a t i o n . A n a l y s i s o f a complete movement such as t h i s a f f o r d s t h e o p p o r t u n i t y t o s t u d y Bartok's t r e a t m e n t o f t o n a l c o h e r e n c e as t h e co m p r e h e n s i v e r e l a t i o n s h i p b etween s u r f a c e d e t a i l , m i d - l e v e l p r o c e s s e s , and l a r g e - s c a l e a c t i v i t i e s , t h e r e b y r e v e a l i n g the i n t e r a c t i v e f u n c t i o n s of o s t e n s i b l y opposing p r i n c i p l e s o f t o n a l o r g a n i z a t i o n a t d i f f e r e n t l e v e l s o f s t r u c t u r e . P r i o r t o t h e c a t e g o r i z a t i o n and e x e m p l i f i c a t i o n o f a s p e c t s o f p r o g r e s s i o n and p r o l o n g a t i o n i n Bartok's q u a r t e t s i n Chapters I I , I I I , 20 and IV, i t i s important to note that, in the absence of a consistent underlying triadic basis and system of conventionally functional rela-tions, there may be considerable diversity, within a single movement, in the intervallic composition of the referential element. According to Jim Samson, Bartok demonstrated that "a tonal argument need not be dependent upon triadic harmonies" and that, as a result, major composers in this century "did not equate tonality with major-minor keys or for that matter with the triad."^ I would go so far as to suggest that the tonal reference in Bartok's music is often a single pitch or PC. To quote Bartok, "Hungarian art music is always based on a single fundamen-tal tone, in i t s sections as well as i n i t s whole."4^ But although a single PC is often referentially focal, the v e r t i c a l i t i e s and collec-tions associated with or representative of such structural PCs are, as indicated earlier, richly diversified. Although this diversity will be demonstrated in the next three chapters, i t might be said here that purely conventional, t r i a d i c expressions of the referential element define one end of the spectrum. Additional referential elements associated with the major-minor system, accorded significance in Bartok's Quartets, include major-third and minor-third dyads, and extended triads. The latter, although heard as dissonant (i.e., unstable) structures in the major-minor system (because Jim Samson, Music in Transition (New York: W. W. Norton & Company, Inc., 1977), p. 33. 4 0Bela Bartok, "The Relation Between Folk Music and Art Music," Bel a Bartrik Essays, ed. Benjamin Suchoff (London: Faber & Faber, 1976), p. 371. 21 o f t h e i n c l u s i o n o f s e v e n t h s , e t c . ) , a r e i n t h e s e i n s t a n c e s o f t e n p e r -c e i v e d as c o n t e x t u a l l y s t a b l e r e l a t i v e t o surrounding, o f t e n n o n t r i a d i c events. A t t h e o t h e r end o f t h e s p e c t r u m a r e n o n t e r t i a n v e r t i c a l i t i e s f u n c t i o n i n g as r e f e r e n t i a l elements. One p a r t i c u l a r v e r t i c a l i t y f r e -q u e n t l y accorded p r i m a r y s i g n i f i c a n c e as an element o f c o n t e x t u a l s t a -b i l i t y i s t h e p e r f e c t f i f t h . The l o w e r n o t e o f t h e f i f t h r e t a i n s i t s c o n v e n t i o n a l c a p a c i t y as " r o o t " and t h e f i f t h may, i n most c a s e s , be represented by i t s i n v e r s i o n , the f o u r t h ( i n which case t he upper note f u n c t i o n s as r o o t ) . The i n t e r v a l l i e s u p e r i o r i t y o f the p e r f e c t f i f t h i n the conventional major-minor s y s t e m — a s the out e r , s t a b l e i n t e r v a l o f the t r i a d — m a y thus be considered a p p l i c a b l e t o much of Bartok's music. O c c a s i o n a l l y , t h e p e r f e c t f i f t h i s , as w i l l be shown, t h e i n t e r v a l l i c u n i t f o r v e r t i c a l i t i e s o f t h r e e o r more members, analogous t o the t h i r d i n c o n v e n t i o n a l t r i a d i c s t r u c t u r e s (e.g., C-G-D as a v e r t i c a l i t y ) . V e r t i c a l i t i e s of conse c u t i v e whole-tones o r semitones may s i m i l a r l y be a c c o r d e d c o n t e x t u a l s t a b i l i t y . T h i s p a r t i c u l a r t y p e o f s t r u c t u r e i s termed homointervallic. 4-'-One f i n a l b a s i s f o r the r e p r e s e n t a t i o n of r e f e r e n t i a l elements, r e l e v a n t t o Bartok's q u a r t e t s , should be i d e n t i f i e d . In t h i s case the r e f e r e n t i a l element i s not a v e r t i c a l i t y , nor i s i t considered a h o r i -z o n t a l i z a t i o n o f a v e r t i c a l i t y . Rather, i t i s a s c a l a r p a t t e r n o f which ^ A " h o m o i n t e r v a l l i c " v e r t i c a l i t y o r c o l l e c t i o n i s one whose c o n -s t i t u e n t s , when e x p r e s s e d as PCs, may be a r r a n g e d s u c h t h a t t h e y a r e s e p a r a t e d by t h e same i n t e r v a l ; i n su c h a r r a n g e m e n t s , t h e l o w e s t PC ( i . e . , t h e " P C - l o w e s t " c o n s t i t u e n t ) i s d e s i g n a t e d as " r o o t " f o r t h e purposes o f d e f i n i n g "root r e l a t i o n s " i n s t r u c t u r a l p r o g r e s s i o n s . 22 the lydian and phrygian orderings of the diatonic collection, the penta-tonic scale, and the major scale i t s e l f are examples. The middle movement of the fourth quartet w i l l be shown to manifest this type of referential element—an element which i s established over time and accordingly involves different criteria for the inference of progression and prolongation of such elements. A consequence of such a diversity in structure of the referen-t i a l element is that in some pieces a particular structure may be accor-ded primacy over others by virtue of factors of contextual stability and may be heard to evolve as such gradually from earlier forms. In other pieces, different intervallie structures in the capacity of referential element are difficult to hierarchize in any systematic way, such variety being heard as a fundamental means of harmonic diversity. At times, such diversity in the intervallic structure of the referential element will even be shown to replace the conventional function of tonal depar-ture. Extreme diversity in structure of the referential element is thus integral to Bartok's musical language in general and his tonal system in particular, and i t is a characteristic which will be manifest constantly as principles of progression and prolongation are examined in the next three chapters. 23 CHAPTER I I PROGRESSION IN BARTOK'S STRING QUARTETS I n t r o d u c t i o n In the opening chapter, I suggested t h a t a p a r t i c u l a r t o n a l i t y i s c h a r a c t e r i z e d by v a r i o u s i n t e r a c t i n g p r i n c i p l e s a c c o r d i n g t o which a percei v e d sense of PC c e n t r i c i t y i s achieved, and t h a t the two processes w h i c h g e n e r a t e t o n a l s t r u c t u r e a r e p r o g r e s s i o n and p r o l o n g a t i o n , each a c h i e v e d i n d i f f e r e n t ways d e p e n d i n g on p a r t i c u l a r i t i e s o f c o n t e x t . T h i s chapter d e a l s w i t h f o u r s p e c i f i c types o f p r o g r e s s i o n , the f i r s t o f these fundamental processes. Each type i s f u r t h e r d i v i d e d i n t o subcate-g o r i e s , w i t h d i s c u s s i o n of the r e q u i s i t e t h e o r e t i c a l p r i n c i p l e s by which the c l a s s i f i c a t i o n i s determined, c r i t i c a l examination' o f the e x i s t i n g l i t e r a t u r e where r e l e v a n t , and i l l u s t r a t i o n o f t h e p r i n c i p l e i n ques-t i o n , u s u a l l y by excerpt from Bartok's q u a r t e t s . I do not w i s h t o imply t h a t the l i s t i s exh a u s t i v e and t h a t other means of connecting d i f f e r e n t b u t r e l a t e d e v e n t s a r e n o t r e l e v a n t ; t h e c o n s i d e r a t i o n o f o t h e r p r i n -c i p l e s , a l t h o u g h s u r e l y v i t a l t o a c o m p l e t e u n d e r s t a n d i n g o f Bartok's m u s i c a l language i n g e n e r a l and h i s t o n a l s y s t e m i n p a r t i c u l a r , i s s i m p l y beyond t h e scope o f t h e p r e s e n t s t u d y . The f o u r c a t e g o r i e s o f pr o g r e s s i o n t o which I focus a t t e n t i o n a r e as f o l l o w s : c o n v e n t i o n a l l y f u n c t i o n a l p r o g r e s s i o n s ( i n c l u d i n g c o n v e n t i o n a l t o n i c i z i n g p r o g r e s -s i o n s ) , nonconventional t o n i c i z i n g p r ogressions, f i f t h p r o g r e s s i o n s , and 24 l i n e a r p r o g r e s s i o n s . C o n v e n t i o n a l l y F u n c t i o n a l Progressions I t i s important both s t y l i s t i c a l l y and t o n a l l y t h a t the m u s i c a l language which c h a r a c t e r i z e s Bartok's f i r s t and l a s t q u a r t e t s m a n i f e s t s a marked d e g r e e o f a l l e g i a n c e t o t h e c o n v e n t i o n a l ( a l b e i t expanded) m a j o r - m i n o r t o n a l s y s t e m . The t r a d i t i o n a l p r i n c i p l e o f f u n c t i o n a l l y r e l a t e d ^ t e r t i a n s t r u c t u r e s i s one which "frames" h i s t o t a l composi-t i o n a l o u t p u t , s u g g e s t i n g , o v e r t h e b r o a d e s t span, a m a n i f e s t a t i o n o f f o r m used a t a l l l e v e l s o f s t r u c t u r e and i n a l l c o m p o s i t i o n a l phases: the "arch." The r e t u r n t o r e l a t i v e l y e x p l i c i t t r a d i t i o n a l elements i n the f i n a l q u a r t e t , however, c a r r i e s w i t h i t the experience and accumula-t i o n of techniques used i n the middle phases of development. Bartok's f i n a l w o r k s , t h u s , come " f u l l c i r c l e , " and r e p r e s e n t m e t i c u l o u s refinement of c o m p o s i t i o n a l processes used throughout h i s l i f e , as w i l l be demonstrated i n Chapter IV through a n a l y s i s o f the f i n a l movement o f the s i x t h q u a r t e t . F u n c t i o n a l p r o g r e s s i o n s i n  t e r t i a n contexts To i l l u s t r a t e c o n v e n t i o n a l l y f u n c t i o n a l p r o g r e s s i o n s and t o n i c i -In t h i s study, f u n c t i o n a l l y r e l a t e d and f u n c t i o n a l l y d i r e c t e d harmonies are those whose r o o t r e l a t i o n s e f f e c t o r i e n t a t i o n t o a p a r t i c u l a r t o n i c i n the conv e n t i o n a l major-minor system. The term " f u n c t i o n a l " w i t h o u t any f u r t h e r q u a l i f i c a t i o n t h u s means c o n v e n t i o n a l l y f u n c t i o n a l . I f elements i n a c o n t r i v e d system o f p i t c h r e l a t i o n s serve i n c a p a c i t i e s analogous t o c o n v e n t i o n a l l y f u n t i o n a l harmonies, they w i l l be r e f e r r e d t o as c o n t e x t u a l l y f u n c t i o n a l . 2 5 zation patterns in the present chapter, I begin with four excerpts from the opening movement of the f i r s t quartet, a movement which perhaps best i l l u s t r a t e s Bartok's allegiance to the tonal style of the late nineteenth century. Indeed, i t is a movement which reveals a consistent tertian harmonic framework—beneath the surface polyphonic texture of ostensibly "independent" linear instrumental parts—characterized by functional relations and traditional means of tonicization. Among the characteristics of this movement which may be associated with nineteenth-century practice—particularly that of Liszt, Strauss, and Wagner—are: (1) the appoggiatura approach to chord-tones; (2) irregular resolutions (in which notes of a dominant resolve one semitone too high or too low, thus yielding a tertian harmony different from that implied); (3) continuous tonal fluctuation; (4) multiple tonal implica-tion; (5) tonal ambiguity; (6) major-minor mixture; and (7) harmonic substitution of constituents of functional progressions. As w i l l be shown, these characteristics are integral to the tonal workings of the f i r s t movement and w i l l be discussed in conjunction with aspects of progression and tonicization. The specific excerpts from the f i r s t quartet s opening movement to which I w i l l direct attention are mm. 1-8, 8-16, 23-32, and 65-end (Exx. 2.1-2.4). A general characteristic which will be demonstrated in these examples is the tertian harmonic framework which underlies the polyphonic texture. Although nonharmonic notes frequently mask that underlying t r i a d i c makeup, the latter i s nonetheless apprehensible because of the frequent confluence of linear independent parts on con-ventionally tonicized consonant triads, which are most often further 26 emphasized by r e g i s t r a l exposure, m e t r i c p u n c t u a t i o n and dynamic i n t e n -s i t y . To expose and i d e n t i f y t e r t i a n s t r u c t u r e s , not always i m m e d i a t e l y obvious i n the movement s t e x t u r e s , system (a) i n each o f these examples i n d i c a t e s members of a l l t e r t i a n harmonies w i t h open notes and "nonhar-monic" ( i . e . , n o n t e r t i a n ) n o t e s w i t h f i l l e d - i n note-heads. [At h i g h e r l e v e l s o f s t r u c t u r e o n l y t o n i c i z e d h a r m o n i e s w i l l be d e s i g n a t e d w i t h open notes, t o symbolize s t r u c t u r a l s u p e r i o r i t y . ] A l s o apparent from t h i s mode of r e p r e s e n t a t i o n i s the prevalence o f t h e a f o r e m e n t i o n e d r h y t h m i c d i s p l a c e m e n t of harmonic c o n s t i t u e n t s through appoggiaturas, suspensions, and a n t i c i p a t i o n s . I n Ex. 2.1, the most s t r i k i n g o f such rhythmic s h i f t s i n v o l v e the t r i t o n e s i n mm. 2, 3, and 6, the t r i t o n e and i t s conventional r e s o l u t i o n b e i n g a potent t o n i -c i z i n g d evice i n the major-minor system, p a r t i c u l a r l y i n i t s a b i l i t y t o e f f e c t t o n a l o r i e n t a t i o n i n a s i m p l e t w o - p a r t t e x t u r e , as i n t h i s e x c e r p t . The t r i t o n e s i n q u e s t i o n a r e c i r c l e d on t h e s c o r e and, w i t h t h e i r r e s o l u t i o n s , a r e i d e n t i f i e d w i t h d o u b l e a r r o w s , |/L, a t N j , \2\, and £3J. As i n d i c a t e d , the r e s o l u t i o n s occur i n r h y t h m i c a l l y and met-r i c a l l y weak p o s i t i o n s , t h e f i r s t two a t t h e end o f b e a t f o u r , and t h e t h i r d one a t t h e end o f b e a t two. These t r i t o n e r e s o l u t i o n s , and t h e i n f e r r e d f u n c t i o n a l h a r m o n i e s a p p r o a c h i n g them, a r e v e r t i c a l i z e d on s y s t e m (b), where t h e y a r e a l s o compressed i n t o one o c t a v e t o e x p r e s s more s i m p l y the i n f e r r e d u n d e r l y i n g v o i c e l e a d i n g . ^The chord p o s i t i o n s i n d i c a t e d on systems (b) and (c) a r e o f course not t r u e t o the a c t u a l music. I n compressing the harmonies f o r the purposes i n d i c a t e d , t h e r e g i s t r a l p o s i t i o n s a r e a d a p t e d i n o r d e r t o c l a r i f y i m p l i e d v o i c e l e a d i n g . 27 The weak r h y t h m i c - m e t r i c placement o f these t r i t o n e r e s o l u t i o n s r e s u l t s i n nonclosure and forward momentum: m e t r i c and t o n a l c l o s u r e a r e a t odds, c r e a t i n g a s t a t e o f c o n t i n u o u s f l u x . Two f a c t o r s t e n d t o weaken f u r t h e r the unaccented t r i t o n e r e s o l u t i o n s i n t h i s passage. One i s t h e m o t i v i c d e s c e n d i n g l e a p s , F#-B and Eb-Ab on t h e f i r s t b e a t s o f mm. 3 and 4, f o l l o w i n g t h e f i r s t two t r i t o n e r e s o l u t i o n s (see (T) and These d e s c e n d i n g l e a p s i m i t a t e t h e o p e n i n g t h e m a t i c d e s c e n d i n g s i x t h , F-Ab ((6))/ and u l t i m a t e l y a t t r a c t a t t e n t i o n over the immediately preceding t r i t o n e r e s o l u t i o n i n each case. The o t h e r a t t e n u a t i n g f a c t o r concerns the t h i r d t r i t o n e r e s o l u t i o n , i n m. 6. The second beat o f t h a t measure, d u r i n g which the r e s o l u t i o n occurs, i s s u b d i v i d e d i n t o a d o t t e d e i g h t h - n o t e and s i x t e e n t h , a p a t t e r n w h i c h t e n d s t o d r i v e t o t h e n e x t beat. The G-Bb dyad on t h e t h i r d b e a t o f m. 6 i s t h e f i r s t m e t r i c a l l y s t r o n g c o n f l u e n c e o f s i m u l t a n e o u s a r t i c u l a t i o n s on a c o n v e n t i o n a l l y consonant major o r minor t h i r d thus f a r i n the movement, as a suspension occurs i n one of the p a r t s on a l l p revious f i r s t and t h i r d beats. A l s o , t h i s G-Bb dyad comes a t t h e end o f a l o n g s t e p d e s c e n t i n t h e second v i o l i n ( ( j ) ) bypassing by one step the A of the t o n i c i z e d F-A dyad. The G-Bb dyad i s t r a n s f o r m e d i n t h e e n s u i n g a s c e n d i n g a r p e g g i a t i o n (m. 6) i n t o an augmented t r i a d which may be heard t o f u n c t i o n as a dominant o f Ab minor (^))r i t s r e s o l u t i o n represented by the v e r t i c a l l y a l i g n e d Ab-Cb t h i r d on t h e r h y t h m i c a l l y weak f i n a l s i x t e e n t h - n o t e o f m. 6 ((^)) — the same rhythmic placement, i n f a c t , as the r e s o l u t i o n t o F d u r i n g the second b e a t o f t h a t same bar. The F m a j o r - m i n o r t r i a d , t o n i c i z e d 28 r e p e a t e d l y f r o m t h e b e g i n n i n g o f t h e movement, i s t h u s subsumed, as V l / v i (see e d i t o r i a l n o t e s ) , w i t h i n Ab, and i s d i r e c t e d t o t h e r h y t h m i c a l l y more emphatic dominant of Ab on beat t h r e e of m. 6. T h i s m i d - l e v e l p r o g r e s s i o n - 3 i s summarized on the top s t a f f o f system (c). The lower s t a f f o f system (c) r e v e a l s a m i d - l e v e l p r o g r e s s i o n o f s l i g h t l y b r o a d e r p r o p o r t i o n s , i t s g o a l harmony, p u n c t u a t e d more d e c i s i v e l y than the preceding r h y t h m i c a l l y weak Ab c h o r d , d e l i n e a t i n g t h e end o f t h e o p e n i n g p h r a s e . I n t h i s p r o g r e s s i o n , t h e r e c u r r e n t F major-minor t r i a d f u n c t i o n s as bVI/bvi i n A major-minor, the dominant of the l a t t e r a r t i c u l a t e d a t the end of an ascending a r p e g g i a t i o n i n i t i a t e d by the G-Bb dyad i n m. 6. N o t i c e t h a t the Ab-Cb dyad, i n t e r p r e t e d above as r e p r e s e n t i n g an Ab-minor t r i a d , i s here e n h a r m o n i c a l l y i n t e r p r e t e d as t h e t h i r d and f i f t h o f t h e d o m i n a n t o f A ((io}). T o n i c i z a t i o n o f A i n m. 7 o c c u r s most i m m e d i a t e l y t h r o u g h a c o n v e n t i o n a l t r i t o n e ((n) ), whose r e s o l u t i o n i s l e s s persuasive as i t o m i t s the r o o t i n f a v o r o f the f i f t h . The s e m i t o n a l d u a l i t y between Ab and A — e a c h t h i r d - r e l a t e d t o t h e o p e n i n g and r e c u r r e n t F m a j o r - m i n o r — e s t a b l i s h e d i n t h i s o p e n i n g phrase i s a r e l a t i o n s h i p which w i l l be shown t o m a n i f e s t i t s e l f t o the very end of the movement. A l s o r e l e v a n t t o the r e s t o f the A s e c t i o n i s t o n i c i z a t i o n t h r o u g h t h e d o m i n a n t p r e f i x 4 - dominant - t o n i c p a t t e r n ^In t h i s study, m i d - l e v e l r e f e r s t o progressions and p r o l o n g a t i o n s whose c o n s t i t u e n t s are noncontiguous and f r e q u e n t l y e l a b o r a t e d by i n t e r v e n i n g p i t c h and PC e v e n t s . M i d - l e v e l p r o g r e s s i o n s and p r o l o n g a t i o n s o c c u r over b r i e f segments as w e l l as passages of a much broader temporal span. 4 D o m i n a n t p r e f i x r e f e r s t o h a rmonies ( o t h e r t h a n t h e t o n i c ) w h i c h p r e c e d e t h e d o m i n a n t i n a f u n c t i o n a l p r o g r e s s i o n . They a r e most 29 shown in this opening phrase to effect tonal orientation to D ((l2j), Ab ((13) ), and A ( (14) ). The second excerpt begins in m. 8, immediately after the cadence on A. At this point the other two voices enter and repeat the imitative thematic content of the opening in a four-voice texture whose harmonic content is richer and, at times, different from that of the opening in tonal implications. Measures 8-10 (Ex. 2.2) correspond thematically and, in part, tonally to the opening three bars. The rhythmically delayed tonicization of F at the end of m. 2 is repeated at the end of m. 9 by way of a harmony which is in a sense a "fusion" of the dominants of F in mm. 2 and 6, this fusion fa c i l i t a t e d by the four-part texture: that i s , the dominant at m. 9 (£l)) employs the conventional tritone, E and Bb, common to both precedent dominants, as well as the Db of the former and Gb of the latter. The implication of D at the end of m. 3, indicated on the lower staff of system (b) of Ex. 2.1, does not occur in the analogous place in m. 10. In light of the Bb and Ab (m. 10), contributed by the two "nonthematic" voices (violins I and II), the functions of D and Gb(=F#) in the thematic parts are reinterpreted as scale degrees 7 and #2 in Eb [i.e., the third and raised f i f t h in the dominant of Eb ( f2j in Ex. commonly related to the dominant by whole-tone (e.g., IV/iv and Vl/vi), by semitone (e.g., bVI, v i i of V, augmented sixth), or by descending f i f t h (e.g., i i , V of V). Most phrases of music i n the major-minor system can be heard to articulate a pattern of tonic-dominant prefix-dominant-tonic; frequently (especially in the nineteenth century) either or both tonics may be absent, the dominant prefix - dominant progression being sufficient to imply a particular tonic. 30 2.2)]. Eb, were i t to appear i n m. 11, would be the f i r s t conven-tionally tonicized t r i a d on a strong beat. As indicated at (3), however, E occurs in place of Eb, effecting a type of deceptive resolu-tion and resultant sense of mobility in the realm of tonal structure. ^ This deceptive re s o l u t i o n — i n which the leading-note of Eb resolves one semitone too high—effects a harmony with an entirely different implication. In fact, i t i s a V of F, as indicated at £4) in Ex. 2.2, and further initiates a progression along the descending circle of f i f t h s , culminating on an explicit resolution to Db i n m. 12 ((5)). Although aspects of prolongation are dealt with extensively in Chapter III, I acknowledge a particularly lucid instance of conventional har-monic prolongation in the present context. I am referring to the pro-longation of C#—enharmonically equivalent to Db just arrived a t — i n mm. 12-16, which concludes with a V 4, implying a return to Db. The func-tionally related harmonies which generate this prolongation are given below the bottom system of Ex. 2.2. In this reading, the A-major triad in m. 15 forms, with the conventional dominant seventh of C# which precedes i t , an unequivocal traditional deceptive cadence ((s))-^ Notice also the use of consecutive applied dominants in the connection ^It is interesting and I think significant that at the analogous point in the opening, m. 4, Eb does occur although i t i s not tonicized. Remember that a sense of resolution to D occurred just prior to the Eb at the end of m. 3, the Eb being absorbed into a nontonic tertian harmony out of which the motivic descending leap emerges [see the lower two staves of system (b) i n Ex. 2.1]. ^The importance of this shift to C# w i l l be f u l l y realized in Chapter III, where the middle section of the movement is discussed in terms of prolongation of more than one referential element. 31 of VI to V ((7) ). Measures 23-32 (Ex. 2.3) comprise a tonally symmetrical, but conventionally functional, drive to the movement's B section. This passage is symmetrical because the mid-level progression articulated by the tonicized triads ((T)) ascends by minor thirds, the final component of the progression initiating the opening of the B section. The conven-tionally functional quality of the passage i s demonstrated at a more foreground level, at which each tonicized triad in the minor-third cycle i s approached through traditional, functionally directed harmonies. Although many chord-tones are rhythmically shifted through appoggiaturas and suspensions (as in the two previous excerpts), the mid-level toni-cized harmonies occur on the downbeats of measures, creating a more distinct broadly spaced harmonic progression. Moreover, each tonicized harmony is f i r s t a major triad, f o l -lowed immediately by a version featuring the minor third (in addition to other "nonharmonic" notes). This is an example of major-minor mixture common to the nineteenth century, but i s also, I think, a modulatory device. That i s , the minor form of each tonicized major triad i s pivotal: the Eb-minor harmony i n m. 25 i s an enharmonic v i to the next mid-level referential triad, F# ((2)), the minor form of which (m. 27) is vi of the ensuing tonicized A-major triad ((3)). The minor triad, v i, in these two instances thus functions as the dominant prefix in the conventional, three-element tonicizing progression alluded to earlier. The pattern ends here, however, as a recurrence of Eb (m. 30) precedes the final component of the minor-third cycle, C. Another characteristic of nineteenth-century music is apparent 32 i n the t o n i c i z a t i o n o f these m i d - l e v e l r e f e r e n t i a l t r i a d s : the m u l t i p l e t o n a l i m p l i c a t i o n of the diminished-seventh chord. T h i s harmony may, of c o u r s e , r e f e r v a r i o u s l y t o e a c h o f f o u r k e y s a m i n o r t h i r d a p a r t , p r e c i s e l y the i n t e r v a l l i e r e l a t i o n o f the m i d - l e v e l t o n i c i z e d t r i a d s i n t h i s excerpt. I n f a c t , recurrence of the same c o l l e c t i o n , f u n c t i o n i n g as the dominant of Eb and F#, s e t s up an e x p e c t a t i o n i n the p r o g r e s s i o n t o A. The " e x p e c t e d " e n h a r m o n i c e q u i v a l e n t i s , however, a v o i d e d as a r e s u l t of an " i r r e g u l a r " v o i c e exchange between Bb and G#, both of which pass through A: Bb moves one semitone too f a r , t o G, and G# one semitone t o o f a r , t o B ( ^ ) . A l t h o u g h B i s , i n f a c t , r e q u i r e d f o r an e x a c t enharmonic e q u i v a l e n t of the dominant of Eb and F#, a r r i v a l on G i n l i e u o f G# c a n c e l s t h e l e a d i n g - t o n e , t h e r e b y r e n d e r i n g t h e c o l l e c t i o n l e s s f u n c t i o n a l . I t i s s i g n i f i c a n t t h a t , i n l i g h t of t h i s i r r e g u l a r exchange, the harmony preceding A i s not a dominant o r dominant v a r i a n t of A a t a l l , but a t r a d i t i o n a l dominant seventh o f C — t h e r o o t o f the open f i f t h and subsequent m i n o r t r i a d (mm. 3 2 f f . ) w h i c h i s t h e u l t i m a t e g o a l o f t h e m i n o r - t h i r d c y c l e as a whole and the i n i t i a l harmony i n the B s e c t i o n . Although c h a r a c t e r i z a t i o n of the p r o g r e s s i o n as d e c e p t i v e l y r e f e r e n t t o C would be dubious, i t i s perhaps not c o i n c i d e n t a l t h a t the e x p l i c i t A-major t r i a d i n m. 15 was shown t o f u n c t i o n u n e q u i v o c a l l y i n a d e c e p t i v e p r o g r e s s i o n ( t h e r e as bVI i n Db) r a t h e r t h a n as t h e g o a l o f a conven-t i o n a l t o n i c i z i n g p r o g r e s s i o n . 7 A r t i c u l a t i o n o f C a t t h e end o f t h e 7 I w i l l show i n the next example t h a t Bartok " p l a y s " w i t h t h i s t e n t a t i v e exposure of A r i g h t t o the very end of the movement. 33 opening section, m. 32, occurs through independent l i n e a r semitonal motion to members of the C t r i a d , rather than through a recognizable conventional dominant, and thus represents a harbinger of what w i l l become a prominent means of t o n i c i z a t i o n i n the l a t e r quartets. This technique w i l l be discussed l a t e r i n t h i s chapter i n the category of linear progressions. The fourth and f i n a l excerpt from the opening movement of the f i r s t quartet, Ex. 2.4, consists of the c l o s i n g seven measures. The two-measure approach to the (French) augmented-sixth chord i n m. 67, although tri a d i c , i s clearly nonfunctional i n a conventional sense. The approach does, however, exhibit a device to be more f u l l y examined later in the chapter: the contextually directed linear progression. In brief, t h i s type of progression i s comprised of step-related members, the connection of which i s not governed by, or even necessarily reinforced by, any inherent functional implications i n the underlying harmony, but i s , rather, understood retrospectively—i.e., through realization of the contextual goal of motion, the latter exposed through patent factors of arrival such as agogic emphasis and rhythmic caesura. Here, the paral-l e l t h i r d s i n the outer voices (the top voice i n v o l v i n g o s c i l l a t i o n between the f i r s t and second v i o l i n s ) s y s t e m a t i c a l l y lead to the augmented-sixth chord, the a r r i v a l of which i s further confirmed by rhythmic relaxation and resultant relative agogic emphasis. The f i n a l cadence (mm. 67-71), expressing an Ab-minor t r i a d through the conventional augmented s i x t h - cadential 4 - dominant -tonic progression, i s unequivocal [system (b) of Ex. 2.4]. The paren-34 t h e t i c a l i n t r u s i o n of A major a t [l)t and i t s r e l a t i o n t o the c a d e n t i a l -l y confirmed Ab minor, however, deserve comment as t h e r e i s not unanimi-t y o f i n t e r p r e t a t i o n i n t h e l i t e r a t u r e . D a v i d Gow, i n h i s v i e w o f t h e t o n a l i t y o f the movement and of the q u a r t e t as "emergent," a s s e r t s t h a t The t h i r d s e c t i o n — a m o d i f i e d repeat of the opening canon—ends on an o l d - f a s h i o n e d h a l f - c l o s e i n A m i n o r . . . even i f Bartok's somewhat obscure n o t a t i o n o f the f i n a l two bars would t r y t o suggest otherwise! T h i s key i s s a i d t o be r e i n f o r c e d by t h e r e g i s t r a l l y and d u r a t i o n a l l y e m p h a s i z e d A m a j o r - m i n o r t r i a d s i n mm. 15 and 29, t h e a p p e a r a n c e o f which e s t a b l i s h e s a "b a s i c dichotomy between two keys [F and A] a major t h i r d a p a r t — s o m e t h i n g w h i c h w i l l d o m i n a t e t h e w h o l e c o u r s e o f t h e q u a r t e t . " 9 I have noted above the absence of e x p l i c i t t o n i c i z a t i o n o f t h e s e e a r l i e r A t r i a d s and have o f f e r e d f u n c t i o n a l a n a l y s e s i n w h i c h they are regarded as dec e p t i v e r e s o l u t i o n s ; I i n t e r p r e t A a t the f i n a l cadence as deceptive i n t h a t i t e n t e r s p r e c i s e l y a t the p o i n t o f r e s o l u -t i o n o f Ab:V, " t a i n t i n g " the f i n a l i t y o f A b ^ Fu r t h e r , I have sugges-t e d t h a t a c o n f l i c t o c c u r s a l r e a d y a t t h e end o f t h e movement's f i r s t phrase, but t h a t the c o n f l i c t i s between Ab and A, i n which the F major-m i n o r harmony f u n c t i o n s as V l / v i and b V I / b v i respectively."' -''" The ^David Gow, " T o n a l i t y and S t r u c t u r e i n Bartok's F i r s t Two S t r i n g Quar-t e t s , " The Music Review 34/3-4 (1973): 260. 9 I b i d . •^Janos K a r p a t i , on page 179 of h i s Bartok's S t r i n g Quartets (Budapest: Corvina Press, 1975), r e c o g n i z e s the s t r u c t u r a l motion t o the Ab-minor t r i a d here. •'•"'"Of A major and Ab m i n o r — t h e two t r i a d s a s s e r t e d here t o be i n o p p o s i -t i o n a t t h e end o f t h e f i r s t p h r a s e and a g a i n a t t h e end o f t h e m o v e m e n t — t h e l a t t e r i s o f c o u r s e more r e l a t e d c o n v e n t i o n a l l y t o t h e 35 d u a l i t y between Ab and A i s shown i n Ex. 2.4 t o m a n i f e s t i t s e l f a g a i n a t t h e movement's c l o s e . The q u a r t e t as a w h ole i n d e e d ends on A, b u t f a c t o r s which obscure o r i e n t a t i o n t o t h a t r e f e r e n t i a l PC e a r l i e r i n the work a r e v i t a l t o an u n d e r s t a n d i n g o f t h e c o n c e p t o f "emerging" t o n a l i t y . I n t h e f o u r e x c e r p t s j u s t examined, t h e c o n v e n t i o n a l l y f u n c -t i o n a l t e r t i a n framework i s r e l a t i v e l y c o n s i s t e n t and, thus, r e p r e s e n t s a s i g n i f i c a n t l i n k w i t h nineteenth-century t r a d i t i o n . The most impor-t a n t of f u n c t i o n a l p r o g r e s s i o n s i s , of course, t h a t between the dominant and t o n i c , the b a s i c t o n i c i z i n g progression. Because t h i s p r o g r e s s i o n i s t h e most d i r e c t means o f t o n a l o r i e n t a t i o n , i t o c c u r s o f t e n as a r e c o g n i z a b l e p a t t e r n o f t o n a l - c a d e n t i a l p u n c t u a t i o n i n c o n t e x t s n o t otherwise as e x p l i c i t l y c onventional. Temporally spaced p o i n t s o f t o n a l o r i e n t a t i o n , each a r t i c u l a t e d by t h i s p a l p a b l e c a d e n t i a l p a t t e r n , provide the l i s t e n e r w i t h a s t r u c t u r a l frame o f r e c o g n i z a b l e departure and a r r i v a l p o i n t s f o r l e s s t r a d i t i o n a l l y ordered m u s i c a l m a t e r i a l , and may be heard t o a s s i s t i n a s c r i b i n g c o n t e x t u a l f u n c t i o n a l i t y t o i n t e r -vening n o n t r a d i t i o n a l elements. S i n g l e conventional t o n i c i z i n g progressions  i n n o n t r a d i t i o n a l contexts I n a d d i t i o n t o e s t a b l i s h i n g a b r o a d l y s p a c e d , c o n v e n t i o n a l l y a r t i c u l a t e d h a r m o n i c framework, a g a i n s t w h i c h o t h e r e v e n t s may be o p e n i n g F m i n o r (as t h e p a r a l l e l m i n o r o f t h e r e l a t i v e m a j o r ) . The s t r e n g t h o f t h i s r e l a t i o n s h i p — i n f a v o r o f Ab m i n o r r a t h e r t h a n A m a j o r — a t t h i s p o i n t i n the q u a r t e t i s , I t h i n k , an important d e t a i l i n the "emerging" t o n a l s t r u c t u r e of the work as a whole. K a r p a t i o f f e r s c o r r o b o r a t i o n of t h i s view (Bartok's S t r i n g Quartets, p. 179). 36 under stood, the conventional tonicizing progression of dominant to tonic may conclude or even i n i t i a t e a movement or section which i s otherwise nontraditional. T o n i c i z i n g progressions concluding formal sections. The f i f t h quartet's middle movement—a scherzo and t r i o which i s e s s e n t i a l l y nontraditional i n i t s d e t a i l s of tonal s t r u c t u r e — c o n c l u d e s with a conventional cadence formula which provides a recognizable point of traditional tonal punctuation [system (a) of Ex. 2.5]. Although conven-tionally functional progressions of tertian harmonies of the type found here are uncommon earli e r i n the movement, the structure of the dominant used i n this f i n a l cadence i s , i n one way, consistent with the interval structure of v e r t i c a l i t i e s used i n the scherzo. The primary theme of the scherzo, mm. 3-9, for example, i s a succession of three arpeggiated, overlapping t e r t i a n c o l l e c t i o n s which, when con-sidered together, express, i n the form of an extended v e r t i c a l i t y of thirds ((%))r the seven-note diatonic collection of C# minor, the tonic t r i a d of which concludes the movement. The concept of extended tertian structure at the opening may be said to account for the specific type of dominant used i n the f i n a l cadence, which, as indicated at (6) i n Ex. 2.5b, includes a seventh, ninth and thirteenth. The tonicizing progression which concludes the opening movement of the second quartet has a basis i n nineteenth-century tonality i n the f a m i l i a r augmented-sixth chord as a t r i t o n e dominant substitute. 1 2The referential C# minor i s further reinforced i n this opening through the mid-level arpeggiation, C#-E-G#, each note of which i s articulated as the f i r s t note of a lower-level arpeggiated t r i a d i n mm. 3-8 (LjpK 37 However, Ex. 2.6a reveals that, i n this particular excerpt, resolution of the augmented s i x t h to the root of the to n i c t r i a d ((T) ) i s not accompanied by resolutions of other chord members associated with the various, traditional augmented-sixth harmonies; rather, the augmented sixth occurs with "anticipations" of two members of one version of the tonic ( @ ) . The tonic harmony articulated i n the upper three parts at this f i r s t resolution of the augmented sixth i s an augmented t r i a d b u i l t on A, as indicated by the open notes at (3) on systems (a) and (b). The c e l l o begins i n mm. 170-171 to arpeggiate the same augmented t r i a d ( ( T ) ) , but immediately s h i f t s to a minor t r i a d on the same root, A ((5)). This arpeggiation occurs i n i t s own tex t u r a l stratum but may be heard as an underlying, c o n c u r r e n t — i f " d i s p l a c e d " — r e s o l u t i o n of the aforementioned augmented sixth i n the violins. In m. 176, the augmented si x t h occurs i n the c e l l o , the major t h i r d and augmented f i f t h of the tonic i n the v i o l a , and the arpeggiated minor t o n i c t r i a d i n the v i o -l i n s . Measures 177 to the end repeat the instrumental d i s p o s i t i o n of mm. 174-175. The textural-instrumental separation and exchange of the two qualities of tonic harmony i n this excerpt, and the tonicization of the common root of both versions through the augmented sixth are summa-rized on system (b) of the example. I would suggest that, i n the c l o s i n g measures analyzed above, each triad version—the minor and the augmented—has a d i s t i n c t function 3The dual modality of the referential tonic appearing here i s sugges-tive of a similar point of major-minor mixture i n mm. 28-29 of the same movement (see score), this being another aspect of tonal practice common to the nineteenth century. 38 over and above mere modal inflection of a single tonic harmony, and that those functions are indicative of nineteenth-century practice. The more consonant minor triad, for example, better represents a stable tonal conclusion to this opening movement, while the augmented version may be heard to represent a dominant of the referential PC, D, of the second movement, as summarized in Ex. 2.6b.^ Tonicizing progressions i n i t i a t i n g formal sections. I have chosen four examples to illustrate different contexts in which a conven-tional tonicizing progression initiates less conventional content, the f i r s t of which comes from the opening of the Marcia i n the sixth quartet (Ex. 2.7a). It is a simple progression which implies in a very general but direct way a tonal and rhythmic anacrusis into the movement's opening on B major, the latter explicitly represented here by the root, doubled at the octave in the f i r s t violin, with the third and f i f t h implicit i n the inner-voice arpeggiation ( Q ) ) - The dominant-tonic, arsis-thesis, progression also initiates the A' section in mm. 122-123 (Ex. 2.7b), where each member of the arpeggiated dominant is the root of a distinct harmony ((2))- The referential tonic to which the dominant resolves in m. 123 is also of a fuller texture than that of the i 4 I n Bartok's String Quartets, Karpati does not identify a distinct function to the two t r i a d i c structures; rather, he suggests that the augmented triad provides support for the "A tonality" through its A and C# and that F "has only a colouring function" with respect to the f i f t h (E) of the tonic triad, (p. 190) He states further that "the augmented triad in the upper voices is coloured into A tonality by the l i t t l e melody in the cello. The notes A and E dominate, and they are given colour by C, C sharp, and F without any feeling of the tonality disintegrating." (pp. 190-191) 39 beginning, as here the third and f i f t h of the B-major triad are sus-tained with the root (CD)-The second example, mm. 159-160 of the f i r s t quartet's f i n a l movement, initiates a scherzo-like section (Ex. 2.8). In scope, this example is not unlike the previous one: the dominant-tonic progression provides a conventional point of tonal orientation after which develop-ment of thematic and motivic content involves less traditional harmonic content. One detail of interest in these two bars concerns the relation between the melodic component in the viola [on staff (i) of the reduc-tion] and the harmonic "accompaniment" in the cello [staff (ii)]. The progression Ab-Db in the viola ( ( T ) and (2)) occurs over a V-I progres-sion i n both Db ((3) ) and A In the f i r s t instance, Ab-Db represents the root motion of the progression, scale degrees 5 to 1 ( ( T ) ) , and i n the second, those same PCs (enharmonically spelled) represent 7 (the leading-tone in the dominant) and 3 ( ( T | ) . a conventional dominant-tonic cadence comes at the end of an expanded harmonic progression from i i i (the details of expansion are to be dis-cussed under prolongational techniques in the next chapter). The pro-gression serves in a larger context to establish a point of familiar tonal punctuation as a basis for subsequent, less traditional directed motions (as i n the beginning of the scherzo section in the same movement, just discussed). As indicated by the roman-numeral analysis below system (b), the tonicizing progression i s expanded to dominant prefix - dominant - tonic, a pattern cited above, particularly in connection with the opening movement of the fi r s t quartet. In the opening fourteen measures of the same movement (Ex. 2.9), 40 And finally, the opening four bars of the second movement of the fif t h quartet illustrate a conventional I-V-I progression before less conventional material enters (Ex. 2.10). The referential element estab-lished in this tonicizing progression i s not primary for the movement but is, rather, an auxiliary to the primary referential element, as will be discussed later. The progression i s straightforward: each of the implied tertian structures i s arpeggiated, and the voice leading involves PC-step connections, registrally compressed on system (b) and further summarized on system (c). Mid-level functional progressions In concluding this study of conventionally functional progres-sions, I draw attention to two large excerpts, each of which articulates a basic, tonality-defining I-IV-V-I root progression of broad mid-level proportions at the end of a movement. One of these comprises mm. 354-390 of the opening movement of the sixth quartet, a passage which will receive further attention in the chapter on prolongational devices. For present purposes, see system (b) of Ex. 3.14, where constituents of the broadly articulated functional progression are indicated. The second i s of comparable length and occurs in an analogous position in the final movement of the fourth quartet. The progression in question occurs in mm. 299-367, its constituents indicated by roman numerals below system (a) in Ex. 2.11. It will be noted that, although the root relations of the progression are conventional, the structures of the individual verticalities associated with the inferred roots are less traditional (unlike the tertian structure of constituents in the 41 broadly articulated progression cited in the foregoing paragraph). One such structure features the perfect f i f t h as the basic interval for homointervallic v e r t i c a l i t i e s (hence the enclosure of roman-numeral indications in quotation marks). In mm. 296-299, for example, a reiter-ated v e r t i c a l i t y of f i f t h s based on C occurs ((£))• This marks the end of a mid-level linear progression (to be examined later i n this chapter), which i n turn marks the structural return to C, the primary referential PC of the movement. The structural "IV" is similarly con-structed in vertical f i f t h s (^p). Its connection to the preceding "I" and prolongation in mm. 323-332 also involve the perfect f i f t h as a primary referential harmonic interval and as an interval of root pro-gression, but entail concepts to be dealt with later in the chapter and in the next chapter. I therefore reserve comment on those details until relevant theoretical concepts have been specified, at which point I return to this example. In the connection of "IV" to "V", the latter also represented by an embellishing pattern 1 3 involving motion to the A-E f i f t h in m. 357 after which a PC-step descent to G-D in the second v i o l i n of m. 363 ((?)) completes the "IV-V" progression. The G-D f i f t h ("V") i s 3An embellishing pattern is a succession of at least four notes which, when expressed as PCs, can be shown to begin and end with the same note (prolongational), or begin and end with notes which are PC-step-related (progressive). Motion between endpoints of the pattern is as follows: a leap from the f i r s t note, followed by step or PC-step motion to the final note; step or PC-step motion away from the f i r s t note, followed by a leap to the fi n a l note; or step or PC-step motion away from the opening note and back to the final note. 42 subsequently sustained i n the second v i o l i n unt i l m. 367, where the resolution to "I" takes place. The tetrachord G-A-B-C, the upper fourth of the C-major scale, bridges mm. 366 and 367 {(7)), and serves to connect l inearly (and diatonically) the roots of "V" and "I" (the tetrachord extending the thematic element in an ascending direct ion after the characteristic F#-G motion). The conventional tonicizing root progression i s further punctuated by the fact that the sustained G-D f i f t h ("V") breaks off precisely at the arr iva l and subsequent sus-taining of C ("I") in the aforementioned tetrachord ((8})- The referen-t ia l tonic is also represented by a fifth, the details of i ts inference involving theoretical concepts to be developed in the next section of this chapter. For present purposes the establishment of C as the primary referential PC through a most conventional large-scale func-tional root progression should be reasonably clear. In the examples offered above, I have demonstrated conventional functionality in the relation of constituent harmonies in progressions of various spans, at various levels of structure, and i n various contexts. With regard to the last two excerpts, i t might be argued that large-scale functional progressions are inferred merely by isolating certain pitch events which, given the nonconventional structure of intervening content, cannot be said to function as comparable events might in a traditionally tonal setting. Yet, such broadly articulated fundamental progressions at strategic formal junctures are, in light of their palpable association with conventional t e r t i a n contexts , appreciable as examples of Bartok's continued allegiance to tradition, 43 m a n i f e s t i n a v a r i e t y o f contexts throughout h i s c o m p o s i t i o n a l output, as we s h a l l continue t o see i n the ensuing chapters o f t h i s study. Nonconventional T o n i c i z i n g Progressions W i t h i n a more e n c o m p a s s i n g c o n c e p t o f t o n a l i t y , i n w h i c h t h e d i v e r s i t y o f i n t e r v a l l i e s t r u c t u r e o f t h e r e f e r e n t i a l e l e m e n t i s exten s i v e , the component f u n c t i o n i n g i n the c a p a c i t y o f the d o m i n a n t — t o be d e f i n e d as a c o n t e x t u a l t o n i c i z i n g a g e n t — i s a l s o , o f n e c e s s i t y , t o be c o n s t r u e d more b r o a d l y . B e f o r e s p e c i f i c t o n i c i z i n g a g e n t s can be i d e n t i f i e d , however, i t must be noted t h a t the two p r i m a r y r o l e s o f the conventional dominant i n the major-minor system are c a d e n t i a l and pro-l o n g a t i o n a l , e a ch i n v o l v i n g a s s o c i a t i o n w i t h a r e f e r e n t i a l t o n i c . F u n c t i o n a l r e l a t i o n s i n h e r e n t i n the major-minor system i m p l y t h e t o n i c a t t h e sound o f t h e d o m i n a n t ( t o such a d e g r e e , i n f a c t , t h a t i n n i n e t e e n t h - c e n t u r y m u s i c t h e t o n i c may n e v e r sound, a l t h o u g h i t s i d e n t i t y i s unequivocal). I n the absence o f the s y n t a c t i c r e l a t i o n s o f major-minor t o n a l i t y , however, the p o t e n t i a l f o r a comparable degree o f i m p l i c a t i o n i n a n o n t r a d i t i o n a l d o m i n a n t a n a l o g u e i s s i g n i f i c a n t l y compromised. I w i l l show i n t h e f o l l o w i n g e x a m p l e s t h a t , a l t h o u g h c o n c l u s i v e c a d e n t i a l p u n c t u a t i o n t h r o u g h a f u n c t i o n a l c h o r d - p a i r analogous t o the dominant-tonic p r o g r e s s i o n i s r a r e i n u n c o n v e n t i o n a l c o n t e x t s , t o n i c i z i n g p r o g r e s s i o n s a n a l o g o u s t o c o n v e n t i o n a l e l i d e d cadences a r e frequent. Contextual t o n i c i z i n g agents A c o n t e x t u a l t o n i c i z i n g agent i s a PC, v e r t i c a l i t y , o r c o l l e c -44 t i o n o f PCs, which i m m e d i a t e l y precedes, and i s subsequently a s s o c i a t e d w i t h , an i d e n t i f i a b l e r e f e r e n t i a l element. C l a r i t y o f exposure o f the r e f e r e n t i a l element t o which such an agent i s s a i d t o r e l a t e — t h r o u g h d ynamic, m e t r i c , r e g i s t r a l , and/or a r t i c u l a t i v e e m p h a s i s — i s a v i t a l f a c t o r i n t h e p e r c e p t i o n o f a c o n t e x t u a l t o n i c i z i n g agent. A n o t h e r c o n d i t i o n concerns the degree o f dissonance o f the c o n t e x t u a l t o n i c i z i n g agent r e l a t i v e t o the r e f e r e n t i a l element, p a r t i c u l a r l y when the l a t t e r i s c o n v e n t i o n a l l y t e r t i a n , t h e r e b y p r o v i d i n g a p a l p a b l e b a s i s f o r consonance-dissonance e v a l u a t i o n . Apart from these s u r f a c e f a c t o r s o f exp r e s s i o n , two i n t e r r e l a t e d c o n c e p t s f i g u r e i m p o r t a n t l y i n a s c r i b i n g t h e f u n c t i o n o f t o n i c i z i n g agent t o a p a r t i c u l a r element: r e t r o s p e c t i o n and frequency o f a s s o c i a -t i o n . R e t r o s p e c t i o n p e r t a i n s e s p e c i a l l y t o the r e c o g n i t i o n o f a p a r t i -c u l a r c o n t e x t u a l t o n i c i z i n g agent when the l a t t e r occurs o n l y once i n a movement, a s i t u a t i o n which occurs i n Bartok's music, where p r i n c i p l e s o f p i t c h o r g a n i z a t i o n o f t e n v a r y s i g n i f i c a n t l y f r o m p h r a s e t o p h r a s e . There are two s c e n a r i o s i n which r e t r o s p e c t i o n i s l e s s c r i t i c a l t o the i n f e r e n c e o f a c o n t e x t u a l t o n i c i z i n g a gent, b o t h o f w h i c h i n v o l v e t h e n o t i o n o f f r e q u e n c y o f a s s o c i a t i o n . I n one s i t u a t i o n , t h e t o n i c i z i n g agent and r e f e r e n t i a l element may be engaged i n an o s c i l l a t i o n p a t t e r n . I n such cases, frequency o f a s s o c i a t i o n i s immediate and d i r e c t , but i s a l s o a p r o l o n g a t i o n a l determinant and w i l l a c c o r d i n g l y be d i s c u s s e d i n t h e n e x t c h a p t e r . I n t h e o t h e r s e t t i n g , t h e p a i r e d components, t o n i c i z i n g agent and r e f e r e n t i a l element, occur a t more than one cadence o r e l i d e d cadence. Here, i t i s f r e q u e n c y o f a s s o c i a t i o n o f t h e c h o r d -p a i r , t e m p o r a l l y d i s t r i b u t e d throughout a s e c t i o n , t h a t i s s u f f i c i e n t t o 45 generate expectation of the referential element at the occurrence of the contextual tonicizing agent. It i s this latter type I wish to exemplify now i n the second movement of the f i f t h quartet. The progression from contextual tonicizing agent to referential element occurs at f i v e points i n t h i s movement (Ex. 2.12). At each recurrence, the harmonic construction of the tonicizing agent i s d i f f e r -ent from the preceding version; the referential element undergoes simi-lar transformation as the movement unfolds. In the f i r s t instance, mm. 6-7, each constituent of the contextual t o n i c i z i n g progression i s a t h i r d : the contextual t o n i c i z i n g agent, at ( T ) , i s C-E (although E i n the v i o l a i s not v e r t i c a l l y aligned with C i n the c e l l o ) , and the referential element i s D-F ((2}). In mm. 9-10 the tonicizing agent i s a C major-seventh chord [(2)) and the r e f e r e n t i a l element, s t i l l a two-note v e r t i c a l i t y , i s the open f i f t h , D-A ((4)). The end of a ten-measure prolongation of the tonicizing agent i s marked by the v e r t i -c a l i t y i n m. 19, C-E-G-B (($)), which resolves i n m. 20 to a new version of the r e f e r e n t i a l element: the D-major t r i a d ((3))- This version of the tonicization progression i s repeated i n mm. 21-22 ((j))-The fourth instance occurs at the end of the middle section, and i C ,Although prolongation i s the subject of Chapter III, I w i l l describe br i e f l y the details of the prolongation referred to here. The C-G f i f t h i s prolonged through motion to the G-D f i f t h i n m. 13, the l a t t e r repeated i n m. 19 before returning to C-G (see the score). Its prolon-gation i s thus conventional—through an upper f i f t h , analogous to a traditional I-V-I motion. The G-D f i f t h , however, i s i t s e l f prolonged through an encirclement pattern (i.e., a double neighbour motion): G-D to i t s upper nieighbour A-E i n m. 15, A-E to F-C (the lower neighbour of G-D) i n m. 17, and from the lower neighbour F-C back to G-D i n m. 19. 46 e l i d e s with the beginning of the A' section i n m. 46. As indi c a t e d at (8), the tonicizing agent i s comprised of C-Eb-G-Bb, a new configuration although s t i l l rooted on C. The referential element ((jfy), on the other hand, i s not new, but i s , rather, a D-A f i f t h , heard a t the analogous place i n the opening A section. The f i n a l c onfiguration of the t o n i c i z i n g agent ( ^ 5 ) ) i s arpeggiated over mm. 54-55 and, i n i t s C-E-G-Bb structure, i s i n a sense an amalgamation of previous versions. Coincident with this four-note version i s a drastic reduction i n com-plexity of the referential element which, i n i t s f i n a l form, i s the sole PC D, a r t i c u l a t e d at the end of a quasi glissando ( ( ^ ) - Each version of the contextual t o n i c i z i n g agent i n the movement, then, i s t r a d i -tionally "rooted" on C, while each version of the referential element i s on D, as summarized on system (b). The presence of these two PCs fa c i l i t a t e s a perceived frequency of association such that, by the end of the movement, the expectation that C w i l l ascend to D i s f i r m l y established as the primary tonicizing motion.-'-7 Disposition note and disposition dominant A s p e c i a l form of contextual t o n i c i z i n g agent ap p l i c a b l e to Bartok i s one I refer to as a disposition dominant—a construct made up 7Salzer interprets the tonal structure of the movement differently; for him, the opening C#, prolonged through upper and lower neighbours (amal-gamated i n my Ex. 2.10 in t o a single V) i s the tonic, and the D element a "contrapuntal s t r u c t u r a l chord." In hi s reading, the recurrent C-D motions are lower-level, lower-neighbour motions to D, i t s e l f a struc-t u r a l upper neighbour to the primary C#. See S t r u c t u r a l Hearing, 2 vols. (New York: Dover Publications, Inc., 1952), v o l . 2, pp. 209-213. On the other hand, i n Bartok's String Quartets, Karpati asserts that the movement's t o n a l i t y " s o l i d i f i e s only i n the f i f t h bar on the basis of the cello's held D." (p. 231) 47 of disposition notes. 1 0 The latter are PCs which are semitonally related to constituents of a referential element (from above or below). At the end of the third movement of Bartok's f i r s t string quartet (Ex. 2.13), for example, a whole-tone succession beginning on Bb3 ascends through two octaves and an augmented sixth, whereupon G#6 ascends by semitone to Ag and Bb-j descends to A^ . Here, the notes which break the succession of whole-tones through semitonal resolution, A in both cases, are perceived as arrival points, presumably as a consequence of inter-ruption and relative proximity, fortified in this case through associa-tion with the conventional resolution of the augmented sixth. The tendency for disposition notes to resolve semitonally may be said to be reinforced i f they replicate certain conventional tonicizing motions, such as the augmented sixth just noted, or i f they are asso-ciated with unstable degrees of a lydian or phrygian ordering of the diatonic collection, two constructs frequently used by Bartok as bases for linear motion. When applied to these particular diatonic orderings, the criterion of semitonal interruption of a whole-tone succession—in which the second tone of the linear semitone i s sensed as focal (as demonstrated in Ex. 2.13)—provides the potential for semitonal tonici-zation of the f i r s t and f i f t h scale degrees from both above and i aThe term disposition note i s a derivative of William Benjamin's "disposition-pair," originated in connection with the music of Debussy. See his "pour les Sixtes: An Analysis," Journal of Music Theory 22/2 (1978): 261. 48 below. In the ascending lydian ordering, for example, the pattern of whole-tones is broken after three and the semitone which follows empha-sizes step 5 of the ordering. Similarly, in the ascent from 5 to 8 the pattern i s broken after two whole-tones, simulating the conventional resolution of the leading-tone. The descending phrygian ordering reveals similar tendencies to degrees 1 and 5 but from above. That is, in the descent from 8 to 5 the whole-tone succession is broken after two and in the descent from 5 to 1, after three. The l i n e a r properties of these two particular diatonic orderings, as defined above, are indicated on systems (a) and (b) in Ex. 2.14. The complete "encirclement" of scale degrees 1 and 5 resulting from the composite of these two patterns i s apparent on system (c) of the example. Specific disposition notes provided by these two diatonic orderings are b2 and b6 from the phrygian ordering and #4 and 7 from the lydian ordering, of which b2 and #4 are particularly important as they are not available from the major and minor scales. Bartok's idiomatic use of these particular diatonic orderings thus provides an important link with convention, and a new, but analogous basis from which linear tonicization progressions—disposition-note resolutions—may be per-ceived. Disposition notes, in particular, are most characteristically employed as tonicizing agents in a prolongational capacity, as will be demonstrated in the next chapter. Disposition dominants, although simi-This i s particularly relevant because the perfect f i f t h often func-tions as a primary referential element in Bartok's music. 49 l a r l y employed, are also used at conclusive and elided cadences. A cadential disposition dominant tonicizes the referential t r i a d at the end of the f i r s t phrase of the sixth quartet's f i n a l movement (Ex. 2.15) . Although the lydian and phrygian patterns from which these disposition resolutions may be said to derive are not e x p l i c i t here, they occur later in the movement, providing a basis for resolution of #4 and b2 in particular. I have chosen four examples to i l l u s t r a t e various contexts in which the disposition dominant occurs in an elided cadence. In these examples, only the immediate tonicizing progression wil l be illustrated, although each comes at the end of a phrase-level progression or prolon-gation and w i l l be reexamined later in this chapter or i n the next in connection with other aspects of those processes. The f i r s t example occurs in the f i r s t movement of the f i f t h quartet. Measures 23-25 (Ex. 2.16) define the end of the transition from the f i r s t theme and i t s connection' to the second theme. As indicated on system (b), each note of the reiterated disposition dominant resolves by semitone to a member of the referential element of the second theme. The arrival on the C#-D disposition pair will be examined later in the chapter. The disposition dominant which resolves into the beginning of the second theme in the opening movement of the second quartet (mm. 31-32) is indicated in Ex. 2.17. This dominant i s like that demonstrated in Ex. 2.15 (the end of the f i r s t phrase of the sixth quartet's fourth movement) in that i t embodies the fi n a l note of each polyphonic line just prior to the beginning of the second theme. Again, the larger context in which this tonicization progression occurs will be studied 50 later. The f i n a l three examples of disposition dominants i n elided cadences, Exx. 2.18a, 2.18b, and 2.19, are from the opening movement of the sixth quartet. The f i r s t two of these correspond to elided cadences at mm. 52-53 and 59-60, respectively, the larger context in which these occur being the focus of a more detailed study in the next chapter. Although a rest occurs between the two components of the cadential progression in Ex. 2.18b, the semitonal relation between those compo-nents clearly identifies the v e r t i c a l i t y arrived at i n bar 59 as a tonicizing agent and i t s resolution to the v e r t i c a l i t y at m. 60 as a point of elision. The scale-degree analysis below system (b) (in Exx. 2.18a and 2.18b) reveals the similarity in structure of the two disposi-tion dominants: the f i r s t progresses to a triad with a minor (as well as a major) third, with scale-degree progression 2 to 1^ 3, while the second moves to a triad with a major third, with #2 progressing to #3. In the third example, mm. 80-81, the resolution passes through a more conventional dominant before arriving on the tonic (Ex. 2.19). Both the passage preceding this excerpt and that which follows i t will be studied further in this chapter and the next; suffice i t to say at this point that the measures preceding bar 80 point to the primary referential PC of the movement, D, while the disposition dominant artic-ulated at the very end of m. 80 implies a sudden turn of events. As indicated at (T) , the disposition dominant f i r s t resolves into a more conventional V of F, the movement's secondary referential PC. Although scale degrees b6 and #4 resolve to 5, that note i s at f i r s t the root of 51 the aforementioned conventional dominant. The leading-tone (scale degree 7, articulated in the cello, m. 80) does not resolve until m. 82, and then only implicitly through PC-step motion to F in the f irst vio-l i n , as suggested at The disposition dominant i n this instance, thus, not only l inks two phrases—through i t s elided resolution—but also effects tonal orientation to a secondary referential element. Obliquely resolving tritone The position and resolution of the tritone in the phrygian and lydian diatonic patterns is different from that of the major scale. The tritone s conventional resolution, of course, involves contrary motion: the semitone resolution of the leading-tone (as the third of the domi-nant) to the root of the tonic, most often accompanied by the descending resolution of the fourth scale degree (as the seventh of the dominant chord) to the third of the tonic. In the lydian ordering, however, the tritone i s delineated by scale degrees 1 and #4, and in the phrygian ordering by scale degrees b2 and 5, these particular tritones implying resolution to the perfect f i f t h defined by scale degrees 1 and 5, of which one member i s already present i n the tritone. Thus, in the unfolding of the lydian f i f t h , the disposition note #4 breaks the ascending whole-tone succession by resolving to 5, while scale degree 1 is common [system (a) of Ex. 2.20]; and in the unfolding of the phrygian f i f t h , the disposit ion note b2 breaks the descending succession of whole-tones by resolving to 1, while scale degree 5 i s common [system (b) of 2.20]. Thus, rather than resolving i n contrary motion, as i n 52 conventional procedure, the tritone resolves obliquely. The term oblique tritone resolution (or obliquely resolving tritone) is used in this paper to refer to these processes. While obliquely resolving tritones frequently occur without explicit statement of the lydian and Phrygian orderings to which I relate them, these particular diatonic orderings are prevalent enough in Bartok's music that they may be under-stood to function as an underlying idiomatic basis which often motivates surface events, not unlike the major or minor scales in conventionally tonal music. As with other types of disposition dominants, the obliquely resolving tritone may occur at both conclusive and elided cadences. An example of the former is found at the beginning of the second movement of the second quartet (Ex. 2.21). In fact, the opening six bars feature semitonally related tritones, the final b2-5 tritone of which resolves to a D-A f i f t h on the downbeat of bar 7. This type of cadential punc-tuation is repeated in mm. 48, 75, and 111-112. The last of these i s particularly interesting because each of the two tertian components comprising the composite verticality in m. 112 (Eb major and G minor) is tonicized through an obliquely resolving tritone. The primary theme and final cadence of the fourth quartet's last movement are particularly interesting from the point of view of disposition-note resolutions in general and the obliquely resolving tritone i n particular. The two excerpts are, i n fact, intimately related, as I will show. The final cadence is also a summing up of many relationships of significance earlier i n the movement—relationships which will be evident in discussion of the derivation and resolution of 53 the t r i t o n e , our p r i n c i p a l concern here. The thematic and accompanimental elements o f the opening o f the movement a r e s u m m a r i z e d on s t a v e s ( i ) and ( i i ) r e s p e c t i v e l y i n Ex. 2.22a. The r e i t e r a t i v e and a c o u s t i c a l p r o m i n e n c e o f t h e open f i f t h , apparent i n the accompanimental v i o l a , e s t a b l i s h e s t h a t i n t e r v a l as the c o n t e x t u a l l y s t a b l e e x p r e s s i o n of the r e f e r e n t i a l l y p r i m a r y PC C, and f u r t h e r s e r v e s t o c o n f e r f u n c t i o n a l s i g n i f i c a n c e on t h e s e m i t o n a l l y r e l a t e d PCs, Db, F#, and Ab, h e a r d i n t h e v i o l a and c e l l o and d e p i c t e d 70 on the bottom s t a f f o f system (a). T h i s i s a case where, as suggested above, p h r y g i a n and l y d i a n p a t t e r n s , a l t h o u g h n o t e x p l i c i t , may be u n d e r s t o o d t o g e n e r a t e t h e t o n i c i z a t i o n p o t e n t i a l o f s u c h e l e m e n t s — p a r t i c u l a r l y degrees b2 and #4—when they are e l a b o r a t i v e o f the r e f e r -e n t i a l p e r f e c t f i f t h . As i n d i c a t e d on s t a f f ( i ) , t h e theme i n c l u d e s t h e t w o most p r o m i n e n t d i s p o s i t i o n n o t e s h e a r d i n t h e accompaniment, b2 and #4, o f which the l a t t e r i s shown a t t o r e s o l v e t o 5 e x p l i c i t l y w i t h i n the theme. The r e s o l u t i o n o f b2, on t h e o t h e r hand i s o n l y i m p l i e d i n t h e theme ( ( ^ ) ) , a l t h o u g h t h i s b2 i s a s s o c i a t e d w i t h t h a t o f t h e accompa-nimental instruments, i n which i t does r e s o l v e e x p l i c i t l y . The theme i s t h u s h e a r d as i n c o r p o r a t i n g members o f b o t h t h e t o n i c i z i n g a g e n t and ^ A l t h o u g h the f u n c t i o n o f D# i n the theme i s not im m e d i a t e l y c l e a r a t t h e b e g i n n i n g , i t w i l l be shown i n t h e n e x t c h a p t e r t o have a "modulatory" d i s p o s i t i o n - n o t e f u n c t i o n i n the opening s e c t i o n . Over a b r o a d e r span t h e D# r e t a i n s i t s d i s p o s i t i o n - n o t e f u n c t i o n b u t i n a d i f f e r e n t r e l a t i o n t o i t s note of r e s o l u t i o n , as w i l l be exp l a i n e d . 54 referential element, and derives its quality of mobility in part from this blend of contextually conflicting elements. Although the potential for an obliquely resolving tritone is present in the theme—because i t includes both b2 and 5—the absence of explicit resolution of b2 in the theme, as noted above, undermines the perception of b2-5 as a distinct element. The potential of the theme to generate such a construct, however, is exploited at the end of the movement, as wil l be revealed. Before examining the fi n a l cadence and i t s relation to the opening theme, I re c a l l Ex. 2.11, i n which resolution to the fi n a l "I" of the "I-IV-V-I" progression may now be more fully comprehended. The return to "I" in m. 367 (Ex. 2.11) i s preceded in m. 365 by a return to the primary theme at i t s original pitch level (see f i r s t v i o l i n and viola). And, as indicated above, although the theme does not express the referential C-G f i f t h explicitly, i t at least implies that element through the express resolution of #4 to 5. The implied resolution of b2 to 1 is explicit in the arrival of C through the diatonic ascent in mm. 366-367 Ex. 2.11), coincident with the underlying motion from the G-D f i f t h in the second v i o l i n to C i n the f i r s t v i o l i n and cello ((IT) in Ex. 2.11). This f i f t h relationship will be shown to establish a precedent for the inference of a comparable conventional progression in the final cadence. Reference [3) in Exx. 2.22a and 2.22b indicates that the tonicizing agent at the final cadence includes the exact PC content of the opening primary theme. D# i s shown at (4) to resolve as scale degree #2 to 3 (E in the f i n a l referential element). Because of the vertical configuration of the tonicizing agent at this f i n a l cadence, 55 the disposition note #4 and its resolution note 5 are vertically aligned ((^)). The resolution of #4 i s also linearly expressed i n the motion from F# to G from the tonicizing agent to the final referential element ((^) . Scale degree 5, in the tonicizing agent, may be heard to provide the potential for inference of a traditional descending-fifth motion, characteristic of the V-I progression, the precedent for this aspect of conventionality established in mm. 366-367 (the close of the large-scale traditional "I-IV-V-I" progression), recalled above. The b2-5 tritone i s more e x p l i c i t l y expressed at the f i n a l cadence than in the earlier theme, for here i t is a vertical construct generated ((7)) and resolved ((1p) after the upper third (E-G) of the referential element has sounded in m. 392. Although the theme and final cadence corroborate the primary referential f i f t h and tonicizing agent, each reveals different details of resolution of the tonicizing agent: #4 resolves explicitly within the theme, while b2 resolves implicitly, and in the tonicizing agent at the final cadence, #4 resolves explicitly to the f i n a l referential element, and b2 resolves e x p l i c i t l y within the referential element. Before leaving this excerpt for now, a f i n a l comment i s warranted, concerning the isolation of b2 and 5 as a vertical construct in the final cadence discussed above. The b2-5 and l-#4 tritones were said to derive from phrygian and lydian bases, frequent in Bartok, and were said to impart directive, contextual functionality regardless of whether or not those scalar references were explicit in the music. But what of the b2-5 tritone in this final cadence? Why draw attention to 56 that construct as a distinct element in lie u of simply asserting the instability of b2 in relation to 1? The isolation of the b2-5 tritone as a construct to be resolved has, in this instance, to do with i t s emergence and prolongation leading into the f i n a l cadence. In that prolongation is the subject of the next chapter, I will postpone further discussion of this example until then, at which point I wi l l reinforce the assertion of an obliquely resolving tritone. To conclude this classification of contextual tonicizing agents, I cite mm. 56-60 of the third quartet's Seconda parte (Ex. 2.23) as an example of an obliquely resolving tritone in an elided cadence. Here the tritone and its explicit resolution occur after the linear-thematic element of the next phrase enters. Note, for example, the initiation of the theme in the viola in the score and on system (a)], beneath which the tritone i s reiterated [(2) in the score and on system (a)]. Only after the two thematic voices occur in contrary motion, mm. 58-59, does the vertical tritone resolve to a vertical D-A f i f t h ( (^ ) ). Although the tritone might here be interpreted as a quasi-stable event— Eb reinforcing the theme in the viola at and transferring to the Eb-theme at m. 58 i n the f i r s t v i o l i n , and the A of the tritone anticipating the upper note of the D-A f i f t h at m. 60 ((5})—the linear-registral continuity of the tritone to the D-A f i f t h , preserved on system (b), supports interpretation of the tritone as a tonicizing agent resolving to the D-A f i f t h at (5). Additional examples of obliquely resolving tritones at conclusive and elided cadences w i l l be demon-strated in the analysis in Chapter IV. 57 F i f t h Progressions The fundamental importance of the perfect f i f t h i n the overtone series i s probably one important factor contributing to the tonicization potential of that interval when stated as the descending root relation of two adjacent triads. It i s indeed a factor which was recognized long before the common-practice period and may be assumed relevant after that period. I t i s also s i g n i f i c a n t that the perfect f i f t h occurs as a stable v e r t i c a l i n t e r v a l a r t i c u l a t i n g the root and f i f t h of the t o n i c triad, the primary harmonic unit of the major-minor system. It might be said that, i n the dominant-tonic progression, the f i f t h s cale degree seeks to a l i g n i t s e l f v e r t i c a l l y with the root of the tonic. In a general, but significant, way, the descending f i f t h may, i n i t s e l f , be said to express a "dominant effect" which—as supported by the aforemen-tioned f a c t o r s — s u r e l y accounts to a great extent f o r the primacy of progressions along the descending c i r c l e of f i f t h s as the ultimate i n directed harmonic motion to the tonic. Each descending f i f t h , regardless of i t s distance from I, imitates, i n a palpable way, the potent V-I root progression, "on i t s way" back to I. Given the s t r u c -tural function and recognizable quality of the f i f t h as an interval of d i r e c t i v e s i g n i f i c a n c e i n the major-minor system, i t i s indeed a suitable element of conventionality for extrapolation to nontraditional contexts. Bartrik never r e a l l y severed his t i e s with conventionality e n t i r e l y and i t i s i n part h i s use of the perfect f i f t h as an i n t e r v a l of functional "root" r e l a t i o n i n numerous contexts and a p p l i c a t i o n s which reflects his manifest allegiance to tradition. 58 In t h i s section I demonstrate three important categories of f i f t h progression and f i f t h relation through ten excerpts, the variety of which i l l u s t r a t e s the breadth of a p p l i c a t i o n of t h i s p a r t i c u l a r aspect of conventionality. The f i r s t of the three categories to be examined i s progression along the t r a d i t i o n a l descending c i r c l e of f i f t h s , the components of which are conventional tertian harmonies. In the three excerpts i l l u s t r a t i n g t h i s f i r s t category, a l l e g i a n c e to tradition i s twofold: i n the use of tri a d i c harmonies, and i n the afore-mentioned dominant e f f e c t of the descending-fifth root r e l a t i o n i n a fu n c t i o n a l l y d i r e c t i v e process. Two of the three excerpts i n t h i s category also reveal a significant aspect of interaction of great rele-vance to Bartok's tonal language: the root r e l a t i o n of a f i f t h — b o t h ascending and descending—between adjacent v e r t i c a l i t i e s , and the linear d i r e c t e d motion connecting those roots. As w i l l be shown, the contextual f u n c t i o n a l i t y of the phrygian and lydian orderings of the diatonic collection i s of utmost importance here. The second category, r e l a t e d to the f i r s t , i s that of f i f t h progression between nonconventional v e r t i c a l i t i e s and nonsimultaneities. In these examples the concept of root requires qualification. Many such elements i n Bartok's music are homointervallic i n structure, the interval between constituents being the perfect f i f t h . Here, then, are elements composed of f i f t h s moving by fi f t h s . As indicated earlier, i n such homointervallic collections the PC-lowest member, i n an ordering based on d u p l i c a t i o n of the referent i n t e r v a l , i s asserted to be root for the purpose of measuring i n t e r v a l s of pr o g r e s s i o n — a n a s s e r t i o n which has some acoustical justification i n that the lowest member of the 59 f i f t h i s r e i n f o r c e d by the upper note. When e x t r a p o l a t e d t o more than one f i f t h i n a v e r t i c a l s t r u c t u r e , t h e l o w e s t n o t e o f t h e P C - l o w e s t f i f t h would assume the f u n c t i o n o f root. Where n o n t e r t i a n v e r t i c a l i t i e s o r n o n s i m u l t a n e i t i e s a r e heard t o be r e l a t e d by the i n t e r v a l of a f i f t h , as o u t l i n e d above, d e s c e n d i n g - f i f t h r e l a t i o n s might be s a i d t o i m i t a t e t h e d o m i n a n t e f f e c t i n a d i r e c t e d t e n d e n c y t o w a r d a r e f e r e n t i a l g o a l , w h i l e ascending f i f t h s may be heard t o represent motion away from such a refer e n c e p o i n t o r a t l e a s t negate any dominant e f f e c t . The t h i r d c a t e g o r y i s t h a t o f t h e f i f t h a s t h e i n t e r v a l o f t r a n s p o s i t i o n between them a t i c elements. I n the second category, non-s i m u l t a n e i t i e s a r e g e n e r a l l y p e r c e i v e d as "arpeggiated" v e r t i c a l i t i e s , whereas t h e n o n s i m u l t a n e o u s c o l l e c t i o n s i n t h i s t h i r d c a t e g o r y a r e thematic statements not n e c e s s a r i l y t o be p e r c e i v e d as l i n e a r expres-s i o n s of u n d e r l y i n g v e r t i c a l i t i e s . T his type o f f i f t h p r o g r e s s i o n — w h e r e the i n t e r v a l o f t r a n s p o s i t i o n i s a f i f t h — i s analogous t o co n v e n t i o n a l i m i t a t i v e c o u n t e r p o i n t i n which "thematic" m a t e r i a l o f t e n answers a t the f i f t h . I n one o f t h e e x c e r p t s t o be d i s c u s s e d i n t h i s c a t e g o r y , t h e con t e x t u a l f u n c t i o n a l i t y o f the phrygian and l y d i a n d i a t o n i c o r d e r i n g s w i l l be seen t o have s i g n i f i c a n c e . Descending f i f t h s l i n k i n g t e r t i a n harmonies The t h r e e e x c e r p t s i l l u s t r a t i n g t h i s f i r s t c ategory are, approp-r i a t e l y , from t he f i r s t movement o f the s i x t h q u a r t e t , a movement which w i l l be shown here and elsewhere t o embody notable p r o p e r t i e s o f conven-t i o n a l t o n a l o r i e n t a t i o n . Measures 80-81 of t h i s movement were r e f e r r e d t o e a r l i e r as an e l i d e d cadence i n which the d i s p o s i t i o n dominant e f f e c -60 tively reoriented motion from the movement's primary referential element on D, to the movement's secondary element on F. Measures 81-94 of Ex. 2.24 indicate oscillation between the F triad and its dominant, a device which will be examined more extensively in the next chapter. Measures 93-99 illustrate a progression of triads along the descending circle of f i f t h s , which, after the V-I progression in F at (T), begins at a rate of one harmony per bar (summarized in the roman-numeral analysis at (^). As denoted by the large f l a t and sharp symbols [mm. 93-99 of system (a)], the interval of root relation i s f i l l e d linearly with a descending phrygian f i f t h or an ascending fourth (identical to the upper fourth of the lydian ordering and the major scale), providing a secondary factor of directed motion to that of the functional root motion of descending fifths. These linear components are a continuation from the i n i t i a l measures of the excerpt (mm. 81ff.), discussed in the next chapter. One final detail concerning mm. 93-99 i s noteworthy: the departure and arrival points of the cycli c progression are F and F#, respectively, and represent a large-scale III and #111 with respect to the primary referential t r i a d of the movement, as indicated at (3). Elsewhere i t w i l l be noted that the referential D triad, takes both a major and minor third, at times simultaneously and at other times in close proximity; the cyclic progression noted here articulates the major and minor third of D on a much grander scale. Measures 312-332 of the same movement, Ex. 2.25, encompass the analogous passage in the A' section, where the descending-fifth cycle is more complex. Example 2.25 begins (as did Ex. 2.24) with an oscillation 61 between dominant and tonic, in this case i n F#, also to be studied i n the next chapter. The conclusion of this oscillation does not reinforce the referential triad, here F#, through a "fin a l " V-I progression (as did the oscillation in Ex. 2.24); rather, as indicated at (T) , the final progression in F# i s from I to V. There i s , however, at least a tenta-tive suggestion of resolution to the tonic of F# in mm. 319-320. Here, the violins unfold a phrygian descent from F to Bb ((2)), representing a descending-fifth tonicization of Bb. This linear passage may also be interpreted enharmonically in F# as a descent from the third of the dominant, E#(=F), through the root and seventh, C#(=Db) and B(=Cb), to A#(=Bb), the third of F# on the downbeat of m. 321. The linear motion in mm. 319-321, thus, looks both ways: back to F# and ahead to Bb. The root representation of the harmonies in the descending-fifth cycle, given on the top staff of system (c), indicates that the components are, at times, out of sequence, arrows above and below the staff denoting this. [Refer also to the roman-numeral analysis below system (b).] As already noted, the f i r s t tonicized constituent of the cycle, F#, i s followed by an ascending f i f t h back to i t s dominant. Although a descending-fifth motion from F-Bb was noted in the violins, mm. 320-321, Bb is also followed by an ascending f i f t h to i t s dominant, the tonicization pattern once again left "open" ((3})- Furthermore, Bb and F# are not adjacent in a descending cycle, the details of this It is the earlier analogous descending-fifth cycle, where the constit-uents are in order, which sets the precedent for this cycle, estab-lishing a basis on which i t s constituents may be judged to be out of order. 62 reordering and others to be discussed. The tonicization of D which follows includes both an ascending f i f t h from I to V and a descending f i f t h back to I, and from here the descending cycle i s uninterrupted until the very close of the excerpt, where Eb i s expected, though denied, at the beginning of the next phrase (m. 332). With respect to anomalies in this phrase, I f i r s t direct atten-tion to the bottom staff of system (c), which portrays an uninterrupted descending-fifth cycle from the opening tonicization of F# to the con-cluding, implied tonicization of Eb. In comparing the two staves of system (c)—the actual temporal order of the fifths in the music, and an uninterrupted "model"—it becomes obvious where "adjustments" occur. First, the B-E fifth which would connect F# to A ((4)) i s missing. This particular f i f t h w i l l be shown in the next example to occur shortly after the excerpt i n question, where i t functions i n an ex p l i c i t descending-fifth progression back to the movement's primary D. Second, the F-Bb fifth—which occurs temporally reversed in mm. 321-322—does not f i t at this point in the cycle but, rather, should come in mm. 328-329 ({^)- Third, concerning the F-Bb progression i n mm. 328-329, the tertian structure rooted on F i s merely implied in m. 328 through the preceding V 4. The root i s denied in the cello in favor of Gb (^)), although resolution of the dominant seventh i s e x p l i c i t in the f i r s t v i o l i n ((j)). In fact, this tentative resolution to an F tri a d i s analogous in approach to that of the tentative, final resolution to F# noted in mm. 320-321 (Q)). The fourth and final detail concerns the descending-fifth motion to the cycle's concluding, implied Eb. Eb, in fact, occurs in the 63 cello already in m. 329—beneath an arpeggiated Bb triad in the violins ( ). The dominant and tonic of Eb are thus a r t i c u l a t e d simultaneously—telescoped into the same temporal span (£9)). There occurs, however, a palpable motion through the dominant seventh implying resolution to Eb in m. 332 ((U?)). Rather than realizing this implica-tion, the elided resolution into m. 332 is to A, a tritone away from the implied Eb. This is achieved quite simply through an enharmonic inter-pretation of the tritone which occurs in the dominant seventh of Eb. That i s , D and Ab—scale degrees 7 and 4 in Eb—are also 4 and 7 in A, and i t is their resolution to scale degrees 1 and 3 in A which links the two phrases ((H) ). It i s interesting to speculate about the large-scale tonal implication of such an abrupt shift. The analogous passage in the A section moves from F to F#, III and #111 i n D, while the passage discussed above moves from F# to A, or #111 to V. As w i l l be demonstrated in the next example, V returns within another descending-fif t h cycle and this time resolves to D:I, articulating the beginning of the final section of the movement. The f i n a l excerpt to be discussed here as i l l u s t r a t i v e of a descending-fifth cycle of conventionally tertian harmonies is mm. 342-354 of the same movement (Ex. 2.26). The example is uncomplicated and extremely apprehensible: the opening Bb-Eb-Ab progression is repeated up one semitone ("TIC+1" denotes "transposition by interval-class plus 1"), arriving in m. 351 on A, the dominant of D. Through one f i n a l descending fifth, this dominant resolves to D, the movement's primary referential tonic. Arrival on D i s indeed structural as i t in i t i a t e s 64 the large-scale, functional I-IV-V-I progression which concludes the movement, as discussed earlier in this chapter. Fifth progressions linking nonconventional  verticalities and nonsimultaneities Four examples wil l be used to illustrate the second category of f i f t h progression, the f i r s t of which i s mm. 64-72 of the third quar-tet's Prima parte (Ex. 2.27). This particular excerpt i s i l l u s t r a t i v e of a technique which wil l be shown in Chapter III to figure prominently elsewhere in the same movement, but in a context where two referential PCs are simultaneously prolonged. The technique is one in which homo-int e r v a l l i c elements constructed of f i f t h s move by the interval of a fi f t h to generate s t i l l larger elements of fifths. In this excerpt, the progression i s one of ascending f i f t h s (expressed i n the music as descending fourths), effectively avoiding the dominant effect so readily 77 associated with the descending fifth.^ Also, the three-note components of the fifth cycle are arpeggiated, thereby generating lower-level fi f t h progressions of single pitches. On system (a) of the example, the aforementioned arpeggiated components are verticalized and the fifth relation (TIC-5) linking each pair i s indicated. The goal of the foreground f i f t h cycle of arpeg-giated components i s the v e r t i c a l i t y rooted on F# i n m. 69 (F#-C#-G#). The ultimate goal of the cycle, however, is the verticality on C# in m. 71, related to the foreground F# goal by TIC-5, as indicated at (T). 2 2This circumvention of dominant effect is particularly appropriate for this movement, which represents Bartok's most extensive departure from tradition. 65 Although F# and C# are not the lowest sounding pitches i n these two verticalities, each is the PC-lowest in its homointervallic f i f t h struc-ture and is therefore asserted to be the "root." The latter function is reinforced in the f i r s t verticality by the motion from F# to A# in the cello ((2)), imbuing the sonority with a tertian quality. The analogous progression, C#-E#, and resultant effect occur i n the second v e r t i -cality, as indicated at (3). System (b) portrays a descending-fourth cycle from the PC-highest member of the cycle, Eb (also the highest sounding pitch), to the PC-lowest member of the cycle, D#. The dotted slur at indicates that this D# closes the twelve-note aggregate arpeggiated in the cycle. The second example in this category also features the generation of large homointervallic structures through the accumulation of indepen-dently elaborated fifths. The excerpt in question is mm. 39-53 of the trio section of the f i f t h quartet's middle movement, represented schema-t i c a l l y in Ex. 2.28. The eighth-note thematic element in the f i r s t v i o l i n , m. 39, spans a perfect f i f t h , A to E. This interval i s articu-lated at the beginning of the theme with the root (lowest member of the fifth) followed by its upper semitonal auxiliary and the upper member of the f i f t h preceded by i t s lower semitonal auxiliary, as indicated at . This pattern i s then repeated in the three upper instruments at TIC+5 (expressed as descending fi f t h s ) , noted at f^ }. The cello, not partaking in the thematic unfolding, will be discussed shortly. System (b) summarizes the accumulation and progression of fifths defined by the various transpositions of the thematic element. It i s 66 revealed on this system that by m. 44 a four-note homointervallic col-lection of f i f t h s has accumulated, the whole of which descends by a f i f t h in m. 49 through the addition of the C-G f i f t h to the bottom and elimination of the A-E f i f t h from the top. The process occurs once again in m. 50, at which point the bottom f i f t h i s F-C. From m. 50 to m. 53 the top fifths are dropped until only the F-C f i f t h remains. The significance of this arrival, although not indicated in this example, w i l l be treated in the next section, on linear progressions. For our purposes here, i t i s sufficient to note the means by which Bart5k achieves the effect of a mid-level progression of descending fifths. The arpeggiated D-F-A triad in the cello of m. 53 ([2) ) initiates a rhythmically augmented version of the primary theme of the large formal sections which frame the t r i o from which this excerpt comes. This augmented version may be said to be represented by the f i f t h D-A. As indicated on the bottom staff of system (a), C# and Bb are reiterated i n the cello part in mm. 40-51 and represent the "opposite" semitonal auxiliaries to those employed i n the thematic 91 fifths in the upper parts. Their resolution to the D-A f i f t h in m. 53 is shown at ( T ) on systems (a) and (b). The middle section of the fourth quartet's final movement begins with a mid-level progression of open perfect fifths, their roots related by an ascending f i f t h . As noted elsewhere i n this chapter, any given Z JThat i s , C# approaches the lower note of the D-A f i f t h from below while Bb approaches the upper note from above. Earlier, the lower note of each f i f t h was approached from above and its upper note from below in a configuration referred to as a b2-#4 disposition pair. 67 phrase or segment in a work by Bartnk wi l l generally involve an inter-action of principles of organization, and this particular excerpt, mm. 156-196, i s no exception. Although the overall progression i s one of ascending fifths, there are important details of disposition-note reso-lution, linear progression through motivic transposition, and prolonga-tion through linear octave unfolding. Some of these details are acces-sible in l ight of previous discussion i n this chapter and w i l l be addressed in conjunction with the fifth progression, while other details wil l come into clearer focus later in this chapter and in the next. The excerpt i n question encompasses mm. 156-182, given i n Ex. 2.29. The three constituents of the mid-level f i f th progression—D-A, A-E, and E-B—are beamed at (l) on system (c). Also noted on that system i s that each i s preceded by a lower semitonal auxi l iary f i f t h (^2)), which is prolonged through a descending octave (l^))- Details of the octave transfers are given on system (a): each member of the auxil-iary fifth, and of the goal f ifth which generates the large-scale pro-gression, is prolonged independently in a thematic element in either one of the violins or the viola. Three additional details in this excerpt are of interest. The in i t ia l constituent of the large-scale fifth progression, the open fifth D-A, is approached through the lower semitonal auxiliary f i f th C#-G#, which is employed i n a dual role. For example, at the end of the A section, a Db-Ab f i f t h was heard to function as an upper semitonal auxiliary to the primary referential C-G fifth. Here, the same auxil-iary, enharmonically spelled, functions to elaborate a referential f i fth a semitone above, art iculat ing the beginning of a contrasting formal 68 section through a type of "modulation" away from the primary referential fi f t h of the movement. In that the C#-G# fi f t h serves a functional role of elaborating both the larger primary C-G fi f t h and the more local D-A fifth, i t f u l f i l l s a "pivot" function in the aforementioned modulation. Moreover, each semitonal auxiliary fifth (except the first) also relates to the primary f i f t h which precedes i t i n a parallel manner. For example, G#-D#, the auxiliary f i f t h which precedes the second primary f i f t h , and to which i t ascends by semitone, relates enharmonically as Eb-G#, to the primary D-A f i f t h which precedes i t ((4^); the same relation holds between the A-E fi f t h in m. 172 and the lower auxiliary fi f t h to the subsequent E-B fif t h ((5) ). This manner of tonicization— through b2 and #4—is precisely that which is employed from the outset of the movement, as noted in Ex. 2.22 and w i l l be noted again later in this chapter and in the next. System (d) of the example w i l l also be dealt with later in this chapter. It is also significant that, concurrent with the mid-level f i f t h progression, discussed above, i s an element of stasis provided by the sustained G of the second v i o l i n (mm. 156-173) and f i r s t v i o l i n (mm. 174-182), the sustained A of the cello (mm. 156-171 and 176-182), and the briefly sustained A-E fi f t h in mm. 172-175 of the viola. Examina-tion of the score reveals that A and G i n particular are approached through "grace-note" fifth-arpeggiations which, taken together, supply a l l but one member of the white-note diatonic collection (perhaps an expression of C, the referential PC of the opening section, which just ended). After the excerpt given in this example, an A-E f i f t h i s sus-69 tained (mm. 182-186), following which an E-B f i f t h occurs (mm. 196-200), the latter providing B, the PC which was missing in the aforementioned white-note collection. In m. 206, B i s absorbed into the thematic fabric. As the sustained PCs change throughout this section, they generate a broadly articulated progression. Motion from the sustained A-E f i f t h to the sustained E-B f i f t h i s particularly relevent as i t projects over a broader span the progression between those two fifths in the thematic voices of mm. 166-182, discussed in Ex. 2.29. The opening thirteen bars of the middle movement of the fourth quartet, given in Ex. 2.30, represent a carefully crafted "root" pro-gression of a fifth. The root of each constituent in the progression is an inferred "tonic" in a diatonic ordering, as will be explained. Bars 1-5 introduce and sustain six PCs ( ) which, when added to D— emphasized through recurrent durational exposure in the cello of mm. 6-9 ( f ^ ) ) —articulate a diatonic collection ( ( ^ ). Although this collec-tion i s , conventionally speaking, that of an A-major scale, the PC A does not figure prominently in these bars. Rather, D i s the PC which completes the seven-note aggregate and i s consistently elaborated through neighbour-related PCs in mm. 6-11 of the rhythmically active cello part. I would assert on this basis that D i s the referential PC in these measures, the diatonic pattern being that of a lydian ordering. (Additional c r i t e r i a i n support of D as the primary referential PC of the movement will be given.) In m. 12, a shift of emphasis effects a change of implied tonic, particularly in light of the referential status ascribed to the lydian ordering of the diatonic collection. Specifically, m. 12 sees emphasis 70 on D# ( ^ ) , the latter superseding D and creating, with the same six PCs in the upper three parts ((B}), a lydian ordering with A as its root ((§)). This shift to A as primary is corroborated by i t s conventional root status in the cello's A-E f i f t h of m. 13. The single semitonal motion from D to D# ((^)) thus represents an implied root motion of a f i f t h : from D lydian to A lydian ((1p).24 This may be construed as analogous to the motion from tonic to dominant which characterizes the first mid-level harmonic progression in many conventional formal units. A comparable descending-fifth progression may be heard i n the final eight bars of the movement to "balance" the opening ascending f i f t h discussed above. In bar 64, six of the seven notes of the D-lydian ordering return and are sustained ((9) in Ex. 2.30b). Although absent at f i r s t , the tonic, D, arrives in m. 67 i n the rhythmically active f i r s t violin ((H))) and completes the seven-note D-lydian refer-ential ordering ((£l)). Within the D-lydian pattern, the c e l l o arpeg-giates E and A through two octaves, mm. 64-68 ((12)), representing the outer f i f t h of the dominant of D, the same representation of the domi-nant which occurred i n the cello of m. 13 ((l3) in Ex. 2.30a), where i t reinforced the motion to A lydian. D continues to be the focal point of the active f i r s t v i o l i n and i s the f i n a l sounding PC of the movement. The implicit f i f t h motion from D lydian to A lydian at the opening i s thus effectively balanced at the end with the partial arpeggiation of 2 4The lydian pattern itself has been shown to be a construct which tends toward its fi f t h scale degree. Here, that relation i s manifest over a broader span—in the motion from D lydian to A lydian—and w i l l be revealed as significant in other excerpts. 71 the dominant of D within the D-lydian ordering. Fifth relations between  thematic transpositions Two of the three examples chosen to i l l u s t r a t e this f i n a l category of f i f t h progression are from the fourth quartet—one from the second movement and one from the fourth^ J—and the third i s from the Seconda parte of the third quartet. The opening sixteen measures of the fourth quartet's second movement, of which mm. 1-12 are shown in Ex. 2.31, comprise two statements of an arch-like scalar theme, the f i r s t in the viola and cello to m. 10 and the second in the two violins beginning in m. 10. The arch pattern of the theme consists of an uninterrupted ascending fi f t h f i l l e d in semitonally (Q))f followed by a more broadly spaced descent back to the i n i t i a l pitch, the details of which will be discussed following explanation of the mid-level f i f t h relation perti-nent to this category. The highpoint of the f i r s t theme is the top note of the f i f t h i t traverses. This in turn becomes the departure pitch for the second statement—the bottom note of i t s f i f t h . Although the descending portion of the arch w i l l be shown to return to the opening pitch by the time the second statement begins, the two violins articu-late a rhythmically augmented version of the ascending fifth, spanning mm. 1-9 ((T)). Completion of the rhythmically extended version °The second and fourth movements of this quartet are related in thema-tic structure, this aspect of symmetry being relevant to the f i r s t and last movements as well. The middle movement is itself ternary in form. The whole thereby illus t r a t e s the utmost in symmetrical design on a broad level. 72 coincides with the beginning of the transposed statement in the violins, m. 10 ((3)). Before leaving this excerpt, I will comment on the descent back to the lower note (i.e., "root") of the theme and a complementary inter-pretation of the opening ascent. Constituents of the mid-level descend-ing f i f t h of the arch-theme ((^)) are pitches which initiate lower-level descents in the second half of the theme (i.e., they mark changes of direction in the "wavering" theme, these points indicated with arrows below the score). The arrival of the root, E, in m. 7 is followed by an oscillation between i t and two inflections of the note above i t — F and F# (^)). At I have suggested that the beginning of a mid-level Phrygian descent to E, generated through the aforementioned criterion of direction change, i s construed as completed through interpretation of the E# in m. 6 as F ((7^), the F# which immediately precedes the goal E being an "escape tone." The progression of the upper semitone to the tonic is then reinforced by those oscillations in mm. 7-10 indicated at (^). A complementary, ascending lydian fifth, may be inferred from the chromatic surface in mm. 1-3 ((§)) by ascribing an appoggiatura function to the PCs F, G, and A, based on their rhythmic position. That i s , the omission of a downbeat in m. 1 points to the pitch on the second eighth-note, repeated on the third, as primary. If the second and third eighth-notes of subsequent patterns are similarly accorded significance, the rhythmically superior f i r s t and fourth eighth-notes assume the function of appoggiaturas and the lydian ascent at i s discernible within the semitonal construct. This inference of alternating struc-tural and elaborative elements within an essentially undifferentiated 73 chromatic resource is advanced solely as an alternate interpretation, to complement the mid-level phrygian descent discussed above-One final comment concerns the upper whole-tone auxiliary to the root E. The configurations in brackets at (10) and their reduction on the lower staff of system (b) reveal that, through consideration of appoggiaturas elaborating the lower points of direction change in mm. 4 and 6, F# i s a broadly articulated upper neighbour to the root E, this relation reiterated at (Tl) . The duality between F and F#—the former completing a phrygian descent and the latter a mid-level upper auxiliary to E — i s expressed at the surface in mm. 7-10, where the two alternate as upper auxiliaries to E, as already noted at QT). The opening of the fourth movement has been referred to as a diatonic version of that of the semitonal second movement.26 The rela-tion between the two becomes apparent upon comparison of Ex. 2.31, just examined, with Ex. 2.32, the top staff of which shows a reduction of the thematic element heard in the viola, mm. 6-13. Although the theme here spans an octave (as distinct from the boundary f i f t h of the theme in the second movement), there is strong centrality of the f i f t h because of the explic i t lydian ascent to scale degree 5 (as distinct from the lydian structure inferred from the chromatic surface in the earlier movement). The boundary interval of an octave is indicated at (T), and the lydian f i f t h at ^2). Once again the theme is in the shape of an arch and, as in the earlier instance, the i n i t i a l ascent i s unembellished while the ^DHalsey Stevens, The Life and Music of Bela Bartok (Oxford: Oxford Uni-versity Press, 1953), p. 189. 74 subsequent descent to the opening pitch i s interrupted by changes of direction, the return thus more broadly art iculated, as w i l l be d i s -cussed. F i r s t , i t must be said that i t is the lydian structure of the lower fifth of the octave, with i ts #4-5 motion interrupting the whole-tone pattern (as noted in the preceding section of this chapter), which emphasizes the f i f t h . The local orientation to scale degree 5 at the outset of the theme, i s projected over a broader span as transposition of the next thematic entry ( ( 3 } at m. 13) i s at the f i f t h above (Eb) and, following that (u) in m. 20), at the next f i f t h above (Bb). The descent back to the i n i t i a l tonic of the scalar theme (Qp) i s again comprised of pitches selected from the rhythmically active surface, here according to metric placement and position in the linear configuration of the theme. For example, D i n m. 8 occurs on the downbeat of the bar and is followed by a leap, marking i t as a local arr iva l point of a descending-step pattern; C in m. 9 i s s imi lar ly placed as the end of a descending-step succession, although not metri-ca l ly punctuated. In bar 10, the metrically emphasized pitch i s Bb, which is prolonged through the brief embellishing pattern before resol-ving down to Ab. The Gb on the downbeat of m. 9, though not part of the descending f i f t h from Eb, has a structural function which i s better understood i f considered an octave lower than in its sounding register. As indicated at i t may be heard as the lower member of a whole-tone encirclement pattern around Ab, a pattern which is immediately repeated at the surface ((^)). Although the inferred descending f i f t h i s not phrygian in composition, a descending phrygian f ifth is employed in mm. 7 5 35-37 (Ex. 2.32b) to return to Ab after the aforementioned thematic transpositions (Hp). The final example of fifth-related thematic transpositions, the roots or tonics of which articulate a broad fi f t h progression, consists of mm. 103-125 of the third quartet's Seconda parte (Ex. 2.33). (The score fragment given in this example continues to m. 149 for reasons to be explained.) In this example, each subsequent transposition of the theme i s at the f i f t h below the preceding one, contrary to the two examples just noted. Staff (a) shows the descending-fifth relation between the tonics of adjacent transpositions (the tonic enclosed in parentheses where its registral placement in the score is different from that required to i l l u s t r a t e the inferred descending-fifth relation). The cycle spans four fifths from E to C, the last of these initiating a bitonal interaction, as w i l l be explained. It i s interesting that, because each thematic entry is imitated in a second part at a temporal interval of exactly one bar, the repeated arrival on C in the second imitative voice—mm. 136, 140, and 143—is accompanied by E in the primary part (summarized at Q)), thus placing the tonic of the i n i t i a l pitch level of the theme in vertical alignment with the tonic of the final transposition. As regards the structure of the theme and the linear connection between transpositions, the former i s consistently lydian, perhaps suggesting broad relations at an ascending f i f t h as in the earlier examples, while the connection, at least in the case of the progression from E to A, involves the phrygian fifth, a construct defined earlier as one with a descending tendency, particularly suitable for linking a 76 theme to i t s transposition a f i f t h below. The phrygian descent i n question begins with the tonic of the fi r s t theme, E, and arrives on A, the tonic of the f i r s t transposition ((2)). The progression to A i s further strengthened through resolution of the diminished seventh in the cello of m. I l l (£3)). Subsequent transpositions are not so systemati-cally connected. In fact, and (5) point out unequivocal toniciza-tion of the "relative minor" key of two of the transpositions, producing a "counterpoint" of referential tonics. One detail of particular interest concerns the way in which the texture, originally supportive of a single referential tonic at any one time (apart from brief sections of overlap due to the imitative expres-sion of the thematic material and the two "relative minor" relationships noted above), comes to support the bitonal section beginning in m. 136. The transformation starts in m. 129, where the C-D-E-F# portion of the C-rooted lydian theme in the upper parts is altered to F#-E-D-C# ((6))-The fragment noted at ( 7 ) continues to retain elements of both C and C#: note the G-F# (scale degrees 5-#4 in C) but also the D#-C#-B# (degrees 2-1-7 in C#). Suggestion of the semitonally related referential ele-ments i s maintained i n mm. 136-145: as sumarized at (IT), below the reiterated C-E third alluded to earlier, the C#-E# third passes through D#-F# i n m. 140 to E#-G# i n m. 143 i n the manner of a f i l l e d - i n arpeg-giation of a C#-major triad; the E#-G# upper third is reiterated i n m. 145, where the C-E third i s superseded by E-G (a direct arpeggiation within the C-major triad). The semitonal duality i s at this point replaced by a whole-tone duality of referential tonics (Hp). 77 Linear Progressions Step r e l a t i o n s are fundamental to musical coherence. Linear constructs are relevant to, and apprehensible at, diverse l e v e l s of structure and i n both conventional and nonconventional contexts. This, however, i s not to say that a l l such events are generated by the same underlying principles. In the major-minor system, for example, linear progressions are v i t a l components possessing an important q u a l i t y of directedness as a result of functional r e l a t i o n s governing the under-l y i n g harmonic progressions which support such l i n e a r events. That linear and harmonic function are intimately related i n the major-minor system i s an important r e a l i z a t i o n , p a r t i c u l a r l y when i t comes to ascribing function to ostensibly comparable linear constructs i n nontra-d i t i o n a l contexts. Wallace Berry, for example, states that l i n e a r function and tonal function "do not reflect, as i s sometimes supposed, mutually contradictory or exclusive concepts." And further that except i n r e l a t i v e l y rare t o n a l l y "nonfunctional" elaborations, tonal function i s of significance and i n evidence (and an experien-t i a l r e a l i t y ) i n foreground, immediate contexts a t the same time that the s e r i e s of harmonies may be of s i g n i f i c a n c e as a "space-f i l l i n g linear stream" of passing or neighbour auxiliaries. . . . linear and tonal functions nearly always appear i n complemen- tary conjunction i n tonal music.27 Later, i n connection with a passage from Beethoven's Symphony No. 3 i n which linear elaboration i s i n evidence, he underscores the inextricable relation between linear and tonal functions: ^'Wallace Berry, Structural Functions i n Music (Englewood C l i f f s , N.J.: Prentice-Hall, Inc., 1976), p. 30. (Berry's emphasis.) 78 . . . purely l inear factors are obvious and extremely persuasive (and they are accounted for); but tonal function is in no sense  superseded by linear function, and tonal function is strongly felt, even very locally, in expansion of the tonal-harmonic resources of PC [pitch-class] content. 8 At the beginning of this chapter, in connection with conven-tionally functional harmonic progressions, I noted that inherent direc-tedness results in the listener's being able to relate particular func-t ional ly subordinate harmonic events to the underlying tonic of a passage. In that linear function is bound up with harmonic function, as I have suggested above, a comparable inherent directedness may be ascribed to l inear events. We perceive each element i n a l inear construct as a member in , or d irect ly associated with, an underlying, often only implied, harmony, the functional relat ion of the latter to the tonic dictating a comparable functional position of the linear event i t supports. Linear progressions in nontraditional contexts, however, rarely enjoy the quality of inherent directedness described above. In certain contexts, contrived systems of relations may be said to account for functional attributes comparable, i f not analogous, to those of the major-minor system. Where such systems are relevant and appreciable, the l istener can conceivably relate elaborative (i.e., contextually subordinate) events to some referential element, analogous to that process in the major-minor system. And, in l ight of such a system, aspects of contextual expectation and deception could be inferred. There are, for example, instances where Bartok employs the part icular °Ib id , pp. 34-35. (Berry's emphasis.) 79 i n t e r v a l l i e p a t t e r n s o f the phrygian and l y d i a n o r d e r i n g s as r e f e r e n t i a l b a s es i n w h i c h l i n e a r d i r e c t e d n e s s and s e m i t o n a l e l a b o r a t i o n c a n be understood as i n h e r e n t f u n c t i o n a l a t t r i b u t e s . N o n t r a d i t i o n a l o r d e r i n g s o f t h e d i a t o n i c c o l l e c t i o n , u sed i n t h i s way, may be s a i d t o be t o n a l analogues. In a d d i t i o n t o the a l t e r n a t e means of c o n t e x t u a l f u n c t i o n a l i t y d e s c r i b e d above, v a r i o u s systems o f o r g a n i z a t i o n , some v e r y e l a b o r a t e , may be c o n c e i v e d t o a c c o u n t f o r r e l a t i o n s i n n o n t r a d i t i o n a l c o n t e x t s . Such s y s t e m s embody f u n c t i o n a l e l e m e n t s — o t h e r t h a n a r e f e r e n t i a l e l e m e n t ( i . e . , t o n i c a n a l o g u e ) and a t o n i c i z i n g a g e n t ( i . e . , d o m i n a n t a n a l o g u e ) — w h i c h are h i e r a r c h i c a l l y r e l a t e d t o the r e f e r e n t i a l element t h r o u g h s t a t e d c r i t e r i a . That i s , t h e y g e n e r a t e e v e n t s w h i c h a r e n e i t h e r t o n i c a n a l o g u e s n o r d o m i n a n t a n a l o g u e s b u t a r e u n d e r s t o o d as f u r t h e r subordinated i n the same way t h a t I I , IV, and VI (and a l l t h e i r chromatic v a r i a n t s ) are i n the major-minor system, the l a t t e r f u n c t i o n a l h a r m o n i e s and l i n e a r e l e m e n t s t h e y s u p p o r t a c c o u n t a b l e as t o t h e i r p r e c i s e r e l a t i o n s h i p t o the r e f e r e n t i a l element. I t i s , however, pe r h a p s more o f t e n t h e c a s e t h a n n o t t h a t s u c h analogues o f dominant p r e f i x e s are not g e n e r a l l y i d e n t i f i a b l e i n no n t r a -d i t i o n a l contexts. That i s , t h e r e may w e l l be r e c o g n i z a b l e t o n i c i z i n g agents and r e f e r e n t i a l elements, but events l e a d i n g t o those f u n c t i o n a l e l e m e n t s — a l t h o u g h f r e q u e n t l y " s y s t e m a t i c a l l y " a r t i c u l a t e d i n terms o f p a r t i c u l a r c o n t e x t s , as w i l l be e x p l a i n e d — a r e u s u a l l y not capable o f being h i e r a r c h i c a l l y r e l a t e d t o the go a l o f the pr o g r e s s i o n . Although i t i s t r u e t h a t t h e e a r w i l l n a t u r a l l y t e n d t o f o l l o w a p i t c h - s t e p o r 80 PC-step succession, w i t h o u t the syntax o f the co n v e n t i o n a l t o n a l system, t h e r e i s no way o f t e l l i n g how a p a r t i c u l a r c o n s t i t u e n t o f a l i n e a r p r o g r e s s i o n i s r e l a t e d t o t h e u l t i m a t e g o a l o r , f o r t h a t m a t t e r , what t h a t g o a l i s . When t h e s u c c e s s i o n ends, t h e r e i s o f t e n l i t t l e t o s u g -gest t h a t i t c o u l d not have continued f u r t h e r . In s h o r t , the c o n c l u s i o n of many such successions i s marked by s u r f a c e i n d i c a t o r s such as r e g i s -t r a l exposure, agogic emphasis, and rhythmic caesura, r a t h e r than e x p l i -c i t o r i m p l i c i t f u n c t i o n a l r e l a t i o n s . Only a f t e r the endpoints o f these s u c c e s s i o n s a r e exposed a s p r i m a r y through the aforementioned f a c t o r s can a q u a l i t y o f f u n c t i o n a l d i r e c t e d n e s s be a t t r i b u t e d t o t h e s u c c e s -s i o n s t h e m s e l v e s . T h e i r d i r e c t e d n e s s i s , t h u s , p u r e l y c o n t e x t u a l and r e t r o s p e c t i v e l y r e a l i z e d . I r e f e r t o l i n e a r c o n s t r u c t s o f t h e t y p e j u s t d e s c r i b e d as c o n t e x t u a l l y d i r e c t e d l i n e a r p r o g r e s s i o n s — s u c c e s s i o n s o f s t e p - o r PC-s t e p - r e l a t e d p i t c h e s and/or PCs which a r e comprehended as t o d i r e c t i v e p o t e n t i a l o n l y a f t e r t h e i r e n d p o i n t s a r e o t h e r w i s e p u n c t u a t e d as p r i m a r y . I f u r t h e r advance t h e v i e w t h a t s u c h p r o g r e s s i o n s a r e v i t a l and r e c u r r e n t c o n s t r u c t s i n Bartok's m u s i c and i n d e e d , i n much tw e n t i e t h - c e n t u r y music. The absence o f s y s t e m a t i c a l l y o r a n a l o g i c a l l y f u n c t i o n a l r e l a t i o n s i n such p r o g r e s s i o n s — r e l a t i o n s a c c o r d i n g t o which one might h i e r a r c h i z e subordinate events i n l i g h t o f a p a r t i c u l a r g o a l or even p r e d i c t what the g o a l w i l l b e — i s not merely a r b i t r a r y ; r a t h e r , i t f r e q u e n t l y e f f e c t s a v i t a l sense o f t e n s i o n , i n s t a b i l i t y , and, U l t i -mo ^They w i l l a l s o be shown i n t h e n e x t c h a p t e r t o s e r v e i n a p r o l o n g a -t i o n a l c a p a c i t y as, f o r example, when they span an octave o r u n f o l d an i n t e r v a l l a t e r v e r t i c a l i z e d i n a harmonic pro g r e s s i o n . 81 m a t e l y , m o b i l i t y t o a p o i n t p e r c e i v e d t h r o u g h o t h e r f a c t o r s a s an i n t e r i m s t r u c t u r a l g o a l . The v a r i e t y i n make-up o f l i n e a r p r o g r e s s i o n s i s , as w o u l d be expected, e x t e n s i v e i n Bartok's s t r i n g q u a r t e t s . C o n s t i t u e n t s o f pro-g r e s s i o n s c o n s i s t i n g o f s c a l a r p a t t e r n s , f o r example, a r e n o t n e c e s -s a r i l y "harmonized" a t a l l , b u t d i r e c t l y and s i m p l y a r t i c u l a t e d and p e r c e i v e d . I n m i d - l e v e l , c o n t e x t u a l l y d i r e c t e d l i n e a r p r o g r e s s i o n s , c r i t e r i a a c cording t o which p i t c h e s are s e l e c t e d from the o v e r a l l t e x -t u r e and assigned membership i n a l i n e a r c o n s t r u c t o f t e n v a r y w i t h each c o n t e x t . One f r e q u e n t l y employed t e x t u r a l c o n f i g u r a t i o n f r o m w h i c h pa l p a b l e m i d - l e v e l l i n e a r p r ogressions may be i n f e r r e d i s the s u c c e s s i v e l i n k i n g o f s t e p - o r P C - s t e p - r e l a t e d t r a n s p o s i t i o n s o f a p a r t i c u l a r m o t i v i c p a t t e r n . Here, a r e f e r e n t i a l member of one motive i s heard t o connect by step o r PC-step t o the analogous member i n the next tra n s p o -s i t i o n and an extended, m i d - l e v e l l i n e a r p r o g r e s s i o n r e s u l t s , as o f t e n i n s e q u e n t i a l p a s s a g e s i n t r a d i t i o n a l m u s i c . 3 0 T h i s t y p e o f l i n e a r p r o g r e s s i o n — d e r i v e d from s u c c e s s i v e t r a n s p o s i t i o n s o f an i d e n t i f i a b l e motive o r t h e m e — i s what I a l l u d e d t o e a r l i e r as b e i n g " s y s t e m a t i c a l l y a r t i c u l a t e d . " There a r e o f c o u r s e o c c a s i o n s i n w h i c h o t h e r , l e s s s y s t e m a t i c f a c t o r s expose p i t c h and PC events i n such a way as t o f a c i l i t a t e s t e p c o n n e c t i o n t o c o m p a r a b l y exposed e v e n t s which a r e t e m p o r a l l y removed 3 0 I n t r a d i t i o n a l sequences, f o r example, the endpoints a r e f u n c t i o n a l l y r e l a t e d , but the connecting h a r m o n i e s — t h o s e e f f e c t i n g t h e s e q u e n t i a l m o t i o n — a r e f r e q u e n t l y n o n f u n c t i o n a l , s e r v i n g s o l e l y t o connect the end-p o i n t s l i n e a r l y and s y s t e m a t i c a l l y . 82 (i.e., noncontiguous). R e g i s t r a i placement as the lowest or highest sounding p i t c h , f o r example, i s often such a f a c t o r i n music of a l l ages. Dynamic intensity, durational emphasis, and tirnbral quality are other such factors which may interact to expose and connect constituents of an appreciable mid-level linear succession. As already suggested, the po s s i b i l i t i e s are many, and c r i t e r i a w i l l have to be considered for each particular situation. Three broad classifications of linear progression w i l l be dealt with here: those derived from d i a t o n i c octave patterns analogous to the major and minor scales (inherently directed), those consisting of exposed pitches and whose directive properties are retro-spectively realized (contextually directed), and those which are contex-tually directed but whose constituents are inferred through successive transpositions of motivic material (motivically derived). Inherently directed linear progressions The lydian and phrygian orderings of the d i a t o n i c c o l l e c t i o n were discussed ear l i e r as referential bases i n which disposition notes to scale degrees 1 and 5 are deemed to have functional, directive s i g -nificance. Semitonal intrusion into a whole-tone succession was sugges-ted as the c r i t e r i o n according to which such t o n i c i z i n g p o t e n t i a l i s inferred. Thus, i n the context of these two p a r t i c u l a r patterns, a sense of inherent directedness may by ascribed to d e r i v a t i v e l i n e a r progressions. Examples of this type of lydian-phrygian directed motion have already been noted as i n t e r a c t i n g elements of f u n c t i o n a l i t y i n conventional harmonic progressions. In Exx. 2.24 and 2.25, f o r instance, passages from the opening movement of the sixth quartet were 83 shown to comprise an os c i l l a t i o n between a particular tonic and i t s dominant, followed by a progression along the descending c i r c l e of fi f t h s i n which the direction of the root motion i s corroborated by lydian and phrygian linear f i f t h s . And in Ex. 2.32, from the fourth movement of the fourth quartet, the lower f i f t h of the scalar theme was shown to comprise an ascending lydian pattern, a directed motion whose tonicization of the fi f t h scale degree was said to strengthen the root relationship of the theme and its subsequent transposition at the fi f t h above. Moreover, i t was noted that the phrygian f i f t h provided an inherently directed linear connection back to the original pitch level after several transpositions. I cite at this point a primary theme whose basic structure i s arguably that of an ascending lydian octave pattern followed by an incomplete descending phrygian pattern, and whose directive and implica-tive properties derive to a great extent from those particular diatonic orderings. The theme i s that of the opening of the f i r s t movement of the f i f t h quartet, mm. 6-13 of which are given on the top staff of system (a) in Ex. 2.34. The bottom staff of that system offers a partial reduction of the theme, in which elements exposed through metric, durational, articulative, and or dynamic means are connected by slurs. The bottom staff of system (a) reveals a broad ascent through an octave connecting Bb^ i n m. 6 to Bb^ in m. 12. But on what basis can the motion connecting the two occurrences of Bb, separated by an octave, be heard as directed from one to the other—i.e., as oriented to the PC 84 Bb? Staves (b) and (c) offer different mid-level step progressions—a whole-tone and lydian scale, respectively—which may be inferred from the "exposed" pitches on the lower staff of system (a). It w i l l be noted that mm. 6-10 articulate a mid-level whole-tone ascent, Bb-C-D-E, which is common to both patterns. Bb is exposed through reiteration, C and D through strong rhythmic position relative to surrounding semi-tonally related pitches, and E through reiteration. As indicated on staff (b), a continuation of the whole-tone ascent, through Gb^  to Ab^ , is inferrable in mm. 10-11 and again in m. 11 implying that completion of a whole-tone scale is imminent. And, such a whole-tone octave com-pletion may be heard as confirmed by the Bb 5 of m. 12 ((^ T) ), the criterion being the registral exposure of that event and the associated Ab^ of m. 11. It could, however, also be argued that, in light of the weak rhythmic position of Bb in m. 12, relative to the Ab which follows, octave completion through whole-tone ascent is in effect denied. The Ab[j in m. 11 may thus be heard as connected to that of m. 12, the latter construed as the extent of the whole-tone ascent, as suggested at {2). tone scale or not, the homointervallic structure of that linear construct is problematic as each note is the same interval l i e distance from i t s predecessor and successor; i.e., no constituent of the scale can be assigned primacy on the basis of its semitonal approach relative to surrounding whole-tone motion. The sense of expectancy of the Bb which completes the scale is contextual: based on the reiterative empha-sis of Bb^ at the beginning and the subsequent whole-tone ascent from that pitch, expectation of Bbc is heightened as the intervallie distance Whether Bb^ in m. 12 is heard to complete the ascending whole-85 to the octave decreases. Staff (c) offers a further interpretation of implied octave completion from the E5 in m. 10 with reassessment of the quintuplet in m. 11. The rhythmically strong F5 (m. 11, third beat) represents an i n f i l t r a t i o n into the whole-tone pattern and may be heard to define a #4-5 resolution within the lydian ordering (^)). Octave completion through a lydian ascent is thus suggested by this unfolding of its lower f i f t h and is realized through the final ascent to Bb 5 in m. 12 (Q))r even i f closure of the octave i s tentative, as the Bb^ i n m. 12 i s rhythmically weak. Tonal and rhythmic-metric factors are, as often i n conven-tionally tonal music, at odds at this point and i t i s the absence of coincident closure in the domains of pitch content and rhythmic position which, in part, effects a sense of continuation. Furthermore, the articulation of Bb^ is immediately followed by an incomplete phrygian descent to m. 13 ( (| ) ) , constituents of the descent occurring in succes-sion, without lower-level elaboration. This demonstrates Bartok's technique of pairing descending phrygian and ascending lydian -5-1 ^ A Karpati cites the prominent Bb-E tritone in the opening theme as an example of a "mistuned fifth," suggesting i t may have been transformed from a perfect f i f t h , the l a t t e r too " f l a t and uninteresting" (Bartok's String Quartets, pp. 143-144). In such a reading, the tritone assumes a contextually stable quality. I regard this particular tritone as unstable, implying an oblique resolution to a perfect fift h ; in this interpretation, the tritone retains qualities of tension and mobility comparable to those attached to the tritone in the major-minor system. While i t is true that the tritone receives much more emphasis than its resolution (here and in other instances in BartDk), i t nonetheless must be acknowledged that i t does often resolve (conventionally or obliquely) and is therefore not to be viewed as stable in and of itself. 86 constructs, presumably because of the interval l i e disposition of those orderings, as discussed elsewhere i n this chapter. The progression of Cb(=B)^ to A 4 rather than to the contextually expected Bb 4 ( (6^ h however, represents a departure from the phrygian descent, resulting i n a denial of closure on Bb^—a d e t a i l which s i g n i f i e s the beginning of the t r a n s i t i o n i n t o the second theme. Both the ascending l y d i a n (and whole-tone) scales and descending phrygian scale thus retain a degree of openness, the former i n terms of rhythmic structure and the l a t t e r i n terms of PC content. In s p i t e of r e l a t i v e openness, however, both diatonic orderings—lydian and phrygian—imply s p e c i f i c goals through t h e i r i n t e r v a l l i e structures, and e s t a b l i s h expectations i n l i g h t of which departures and deceptions are understood. Contextually directed linear progressions As i n the foregoing analysis of inherently d i r e c t e d l i n e a r progression, factors of contextually d i r e c t e d l i n e a r progression have been alluded to i n discussion of other aspects of progression. In Ex. 2.31, for instance, the opening theme of the fourth quartet's second movement was shown to comprise an arch pattern of semitonal motion spanning a perfect f i f t h . And this interval l i e boundary was said to be enhanced through a rhythmically augmented ascending-fifth progression i n the two violins, the conclusion of which coincides with the beginning of the transposition of the theme at a f i f t h above. Here the rhythmically augmented ascent of a f i f t h i s chromatic, i t s constituents punctuated through a r t i c u l a t i v e and rhythmic exposure: they occur as contiguous events, separated by rests, which further emphasizes them. As the 87 progression i s not constructed of a pattern with inherent directive properties, i t acquires contextual directedness retrospectively, in light of i t s elided conclusion at the start of the next theme, and associatively, in light of the more rhythmically active version of that fif t h in the theme itself. As suggested in connection with Ex. 2.34, the point of departure from the inferred phrygian descent initiates a transitional section leading to the second theme. In those transitional measures, 12-25, the cello in particular may be heard to define a mid-level, contextual ly directed linear progression to the root (C) of the tertian referential element on which the second theme i s based (fT) i n Ex. 2.35). Cr i t e r i a for the inference of constituents in the progression are basic: regis-t r a l exposure (as the lowest sounding voice), and durational emphasis relative to surrounding pitches. The upper parts i n these measures, at least u n t i l m. 21, are developmental and tonally unstable owing to their transitional function. Measures 24-25 were cited earlier as an example of an elided resolution of a disposition dominant, and i t i s i n the measures directly approaching the dominant that the upper parts assume correspondingly directed linear organization in counterpoint to the cello. In the f i r s t violin, for example, the linear progression from Eb^ in m. 21 arrives in m. 23 on Dg (^ p)f which, at (expressed as D 4 ) becomes one of the two disposition notes which make up the tonicizing agent of the second theme's referential C minor. Its PC-step resolution i s to Eb^, as indicated at extending the Eb-D progression (^2)) to an octave (f^ J). The other member of the disposition dominant, C#, is the penul-88 timate constituent of the cello's broadly spaced linear progression ((T)). More immediately, the cello's C#2 of m. 23 is , like i t s counter-part D in the v i o l i n , the goal of a progression spanning a major seventh, here from C4 in m. 21 (^). The resolution to C2 i n the cello of m. 25 ((^) thus completes the aforementioned broader linear progres-sion spanning the transition as well as the more immediate octave descent from m. 21 ((&)). The second movement of the same quartet offers a contextually directed linear progression consisting of both pitch-step and PC-step connections, the constituents of which are exposed in a variety of ways. In Ex. 2.36, mm. 39-46 represent the approach to the movement's A' section, the cello part again providing a governing linear cohesiveness. And, as in the preceding example, registral placement and durational emphasis are two factors of exposure by which constituents of the mid-level PC ascent are articulated; these factors are supported here by dynamic intensities and, in the case of D#, elaboration over an octave transfer (£l)). One might be tempted to interpret the progression as one of a PC-step octave from D2 i n m. 39 to D2 i n m. 46: D i s , after a l l , the referential PC of the movement and is tonicized i n a variety of ways (Ex. 2.12). However, the progression actually begins with C#2, which is in a sense superseded by C 2 immediately before arrival on D i n m. 46. There are several details which support such a view. Fi r s t , C i s the acknowledged root of the contextual tonicizing agent employed throughout the movement (again, Ex. 2.12). Second, the dual inflection (C, C#) of 89 the lower neighbour to D is manifest at other points in the music. The opening four bars, for instance, were shown in Ex. 2.10 to articulate a conventional I-V-I progression in C#, the tonic of which immediately and directly resolves to D in bar 4. Following this, the various forms of the C-rooted contextual tonicizing agent, cited above, further elaborate D. And immediately after the arrival on D i n m. 46, an ascending succession of triads occurs, beginning on C and moving through E, G#, B, to C#, the last of these sustained i n mm. 48-52 (see the score). Although C is here momentarily displaced by C#, a descending arpeggiated version of the tonicizing agent occurs i n mm. 54-55; C# i s , thus, once again superseded by C. These instances are cited as support for the interpretation of the linear progression in mm. 40-46 as a connection of C# to C ( ( ^ ) , of which C i s consistently employed as the primary tonicizing agent. The final two examples of contextually directed linear progres-sion to be illustrated in this category come from the final movement of the fourth quartet. Each spans a descending tritone and serves to direct motion back to the referential tonic of the movement at a junc-ture i n the formal scheme; the second progression i s accordingly analogous to the f i r s t in both structure and function. The f i r s t excerpt i s mm. 102-143, represented in Ex. 2.37. Although the context from which this progression emerges will be dealt with in considerable detail in the next chapter, i t may be said at this point that an F#-C# f i f t h i s reached i n m. 76, where i t i s in a contextually functional interlocking relationship with the primary C-G f i f t h established at the beginning of the movement. The F#-C# f i f t h , then, represents the 90 maximum degree of tonal departure in the movement, and i t i s from this point of optimum tonal opposition that the linear progression under -59 discussion departs in m. 102. Measures 102-143 represent the closing bars of the f i r s t A section of a large ABA form; the arrival on the open f i f t h rooted on the movement's primary referential PC, C, in m. 143 is analogous to the tonic cadence at the end of the f i r s t section of a conventional ternary design. Appropriately, since harmonic expression here involves the open perfect fifth, each constituent of the tritone progression occurring in the cello, as well as those of other, less exposed linear progressions in the cello and viola, assumes that i n t e r v a l l i c basis. The less exposed progressions derive from the registral disposition of elements in the patterns identified at (l) and (^) in the score. That i s , the f i r s t and third constituents of the pattern are either the same ((T}), fortifying a particular PC through reiteration, or they are step-related (f^ ) ), defining motion i n one linear stratum. The middle element i s always exposed in a higher register and i s therefore step-related to analogous members of adjacent patterns, effecting a second linear stratum. The cello similarly defines two strata of linear activity, the lowest of which is the primary tritone progression. Reference [2j in Ex. 2.37 identifies the structural tritone progression, the details of which w i l l be discussed with those of the aforementioned interacting progressions. The cello's F#-C# f i f t h that 32 The connection of F# in m. 76 to that in m. 102 w i l l be discussed in Chapter III. 91 initiates the progression moves to and from the lower auxiliary fifth, E#-B#, in mm. 105 and 106, after which an upper embellishing pattern {(5)) advances the progression to F-C in m. 109. The v io la reinforces the F#-C# fifth through reiteration ((%)), the progression from the E#-B# lower auxi l iary f i f t h to the F#-C# f i f t h at (5) insuring that the aforementioned osc i l l a t ing pattern in the cel lo i s not construed as a structural descent of a semitone in the progression. Art iculat ion of the E-B and Eb-Bb fifths—the third and fourth members of the broadly articulated tritone progression—involves a shift in interpretation of the basic pattern to one which is end-oriented, contrary to the opening motion which, for reasons already stated, focuses on the pattern s f irs t element. In m. 112, for example, the F-C fifth becomes upper auxiliary to E-B in m. 113 and E-B at the end of that bar i n turn becomes upper auxi l iary to Eb-Bb i n m. 114. The absence of a "returning motion," analogous to the progression from the E#-B# fifth to the F#-C# f i f th in the v io la of m. 107, fac i l i ta tes perception of the f ina l f i f t h i n each pattern as an element advancing the large-scale linear progression. It is with respect to the next member of the tritone progression that the function and relationship of the subordinate progressions, occurring alongside the primary one, take on special meaning. The upper stratum of the viola consists of an embellishing pattern in which a D-A fifth leaps to F-C before moving down by PC-step to C-G in m. 117 ( (£ ) ) • The opening of the lower stratum of the viola has already been referred to; i t s continuation in mm. 112-113, £T) , suggests a potential chromatic embellishing pattern returning to F#-C#, and in mm. 117 (f8)), 92 118, and 119, a truncated version could s t i l l be considered to imply a complete return to F#-C#, although that member of the progression has long been superseded. And, the upper stratum of the cello consists of a pattern not unlike the embellishing pattern in the top stratum of the viola: i t , too, arrives on a C-G f i f t h , but i n m. 114 Thus, we have two linear events which, by m. 120, conclude on a C-G f i f t h and one which articulates a motion between A-E and G-D. Before explaining the relationship of these culmination points to the penultimate constituent of the tritone progression, I consider the relation between the verticality, Db-Ab-Eb, repeated in the upper three parts in mm. 121-136 in rhythmic counterpoint with the cello's D-A-E verticality. In that each is step-related to the ultimate C-G goal, the former by semitone and the latter by whole-tone, each could be ascribed membership in the linear tritone progression as the second-last constituent. Or, both could be considered to f i l l that function, the oscillation between the two construed as changes of "inflection" rather than motion between opposing elements. The notation of Db-Ab-Eb in parentheses on the lower staff at (10) , and the dual stem to the large beam of the tritone progression at ^ ) , suggest this twofold inflec-tion of the penultimate constituent—an interpretation which i s rein-forced by juxtaposition of D and Db at the very close of the section ((12)). Another factor of corroboration for this dual inflection i s found in the independent encirclement and resultant elaboration of the Db-rooted and D-rooted verticalities, noted at (13). If a single constituent i s to be heard as primary over the 93 other, however, i t would undoubtedly be the D-rooted v e r t i c a l i t y : as suggested at (l4), the Db-Ab-Eb verticality of fifths in the upper three instruments might be construed as a lower auxiliary to the D-rooted complex, and the Ab-Eb portion, enharmonically Eb-G#, as an interlocking f i f t h to the D-A portion of the main constituent of the progression. And, although i t could be suggested that the reverse relation—in which the D is perceived as upper auxiliary to Db—would preclude hierarchiza-tion of the two, registral exposure of the D-rooted v e r t i c a l i t y , and dynamic and durational amplification of the PC D in mm. 140-142, justify a view of the D-rooted verticality as primary. Regardless of how the relation between the D- and Db-rooted verticalities in mm. 121-136 is interpreted, the goals of the secondary progressions in mm. 102-120 may be perceived as related to the two v e r t i c a l i t i e s in an auxiliary sense. The C-G f i f t h i n the viola in m. 117, repeated until m. 120, and in the cello in m. 114, repeated until m. 119, is best not considered an anticipation of the goal of the large-scale tritone progression, for this would contradict the effect of the intense exchange in mm. 121-136 leading into the unison arrival on C at the end of the section (m. 143). Rather, the C-G f i f t h might be construed as a lower auxiliary to the Db-rooted v e r t i c a l i t y ( (^ } ). Both elements of the progression from A-E to G-D in the viola (^p) may function as comparable semitonal auxiliaries to the Ab-Eb upper portion of the Db-rooted verticality ( ^ 6) ). This encirclement of Ab through A and G is precisely the pattern of elaboration in the top voice in m. 133 94 In this mid-level linear tritone progression, then, concurrent, ostensibly tonally independent progressions are seen to contribute to the primary progression through auxiliary elaborations, and demonstrable ambivalences of associative relations, enhancing the sense of resolution fe l t in m. 143. It must be restated, however, that the progression, however systematic in i ts organization and articulation, is nonetheless accorded directive significance in retrospect. It is in the context of conclusive arr iva l on the C-G f i f t h i n m. 143 that previous events are ascribed commensurate function; the progression, in and of i t s e l f , i s not inherently directed. An analogous tritone progression occurs in mm. 242-281 ((T) in Ex. 2.38). As in the previous excerpt, many interactive elements are relevant, although this context i s much more of a s t ra t i f i ed texture. The progression spans the bulk of the A' section (its goal, C, leading into the final coda), and features juxtaposition of elements in several strata—a technique of intense recapitulation of preceding material. Essentially, the tritone progression occurs in only one of the strata, but certain of the events in the other two are at times related, as I wi l l show. The stratum comprising the tritone progression is characterized by reiterated verticalities of predominantly homointervallic construc-tion, the perfect f i f t h once again being the component interval . One detail common to the Gb-, F- , and Eb-rooted constituents of the progres-sion i s the inclusion of the lower semitonal auxi l iary to the highest pitch of the v e r t i c a l i t y , as noted at (^), and f^. The penul-timate ver t i ca l i t y of the progression i s not homointervallic but, 95 rather, an octave C# i n mm. 280-281. The aforementioned semitonal auxiliary relation—the auxiliary and its principal note sounding simul-taneously in the f i r s t three instances—is a factor relating the last two elements of the tritone progression. Here, C# functions both as a lower auxiliary to D, which sounds at the top of the C-rooted v e r t i -c a l i t y and (enharmonically) to i t s root ((^})- The reiterated C--rooted v e r t i c a l i t y returns in mm. 296-299, initiating the large-scale "I-IV-V-I" progression illustrated in Ex. 2.11. The construction here is different from that at mm. 281-284 i n that the highest pitch is Eg ((?)); the preceding D#4 imitates once more the precedent of PC-semi-tonal elaboration. The D#2~C2 resolution at (d), enharmonically spelled, recalls the minor-third motive at the end of the B section ( ) , which carries over to effect one of the aforementioned strata in the A' section. The continuity within this particular stratum is indicated by the beamed elements at (H)) . Following reiteration of the Gb-rooted i n i t i a l element of the tritone progression, the fi r s t repetition of the motive at (9) occurs and i s here untransposed ((H) )• As noted at (l2), the top note of the motivic minor third, Eb 4, relates back to the top note of the Gb-rooted vert i c a l i t y , while the bottom note of the third, C 4, looks ahead to the top note of the Gb-rooted verticality repeated in mm. 256-260 ( (T3) ). Although subsequent transpositions of the minor-third motive are not so systematically related to constituents of the tritone progression, the continuity of descending minor thirds (C, A, F#), stemmed and beamed at U-Oj, articulates the root progression found in 96 the opening A section, as will be discussed in the next chapter. Thus, distinct strata in this closing section are at times interrelated and at other times related to primary materials found earlier in the work. I now draw attention to the opening constituent in this progres-sion, the Gb-rooted verticality in mm. 242-248. As in the duality noted at the penultimate element (mm. 121-142) in the tritone progression in Ex. 2.37, the upper three instruments are here separated from the cello's Gb-rooted v e r t i c a l i t y through a lack of continuity in f i f t h -construction. That is, the top note of the Gb verticality i s Eb and the bottom of the upper collection, F; the absence of Bb interrupts the principle of homointervallic construction at this point. The rhythmic exchange between the two also emphasizes their independence (as compared to subsequent verticalities in the progression). The semitonal relation between their PC-lowest members—their roots—suggests a circular pattern of elaboration: F as lower auxiliary to Gb ( (14))* and Gb as upper auxiliary to F ((l5)). Four factors of support for the Gb v e r t i -cality as hierarchically superior might be cited: f i r s t , as earlier, the Gb v e r t i c a l i t y i s exposed as the lowest registrally; second, the Gb-rooted verticality recurs in mm. 256-260 without the opposing F; third, the thematic element in the f i r s t violin in mm. 238-255 linearizes a Db-Gb(=C#-F#) fourth (the G of the theme being an upper auxiliary to the oo root Gb) and fourth, association with the tritone progression at the analogous place i n the opening A section suggests a parallelism, 3 3This theme—with its potential for, and realization of, multiple tonal implications—will be the focus of extensive study in Chapter III. 97 favoring Gb as the i n i t i a l constituent in the final mid-level descending progression. Motivically derived linear progressions This particular technique of effecting a sense of linear organi-zation is used throughout Bartok's quartets but with varying degrees of strictness. Much of the f i r s t quartet, particularly its f i r s t movement, has already been shown to involve conventional procedures of tonal orientation and pitch organization. Even in this early work, however, we may note the seeds of what was to become a clearly defined and frequently employed principle of linear connection. Measures 115-122 of the final movement of the f i r s t quartet (Ex. 2.39) will serve to i l l u s -trate one manifestation of a motivically derived linear progression. The function of the progression is one of climactic intensifica-tion in part attributable to ascending motion. Here, the increase of tension resulting from the ascent i s supplemented by crescendo and accelerando. The motivic transpositions effect palpable step connec-tions between noncontiguous pitches, although the overall progression is not without shifts in orientation. In mm. 115-116, for example, i t is the lowest note of each arpeggiated triad which is deemed to constitute the progression. The f i n a l triad i n m. 116, however, i s not step-related to i t s predecessor in this way; rather, i t s lower note i s the upper octave of the opening pitch of the progression. This particular triad thus serves two functions: first, to articulate the upper octave of the opening referential PC, as just noted, thereby prolonging that PC for the purpose of engaging i n subsequent progressions (to be 98 explained), and second, to effect a shift of emphasis whereby the ascending progression initiated by the lower notes of previous ascending triadic arpeggiations i s continued by the upper notes of subsequent descending tri a d i c arpeggiations. This shift commences i n m. 117, at which point ascending and descending arpeggios alternate until m. 119. Reference (T) shows that D#6—the top note of the descending arpeggios, and the octave-displaced continuation of the ascending progression—is prolonged, the upper note of each ascending arpeggio functioning as a lower auxiliary. The lower note of each ascending arpeggio, the octave-displaced F arrived at in m. 116 (where the pattern of step connections was broken) i s shown at (2) to be prolonged, the lower note of each descending arpeggio functioning as an upper auxiliary. With regard to the referential PC i n m. 121 (i.e., invoking the notion of retrospection), the beginning of the recapitulation, the two PCs prolonged i n mm. 116-118 may be heard as upper and lower auxil-iaries. Commencing with m. 119, the alternation between descending and ascending arpeggios ceases and a reiterated descending arpeggio sounds until the end of m. 120. This particular arpeggio represents a resolu-tion of one of the aforementioned, retrospectively characterized auxil-iaries: the top note, E, i s heard locally as a resolution of the D# prolonged i n the preceding descending arpeggios, and, over a broader span, as the culmination of the step ascent from the beginning of this passage. The bottom note of the reiterated arpeggio, however, does not resolve the other prolonged auxiliary; rather, i t moves a semitone in the opposite direction. Thus we have partial resolution, with F super-seded by F# before resolving to E in m. 121, a move which temporarily 99 contradicts the implied resolution of the augmented sixth, F-D#. Refer-ence (T) illustrates this implied resolution of auxiliaries prolonged in mm. 116-118, and summarizes what happens in the music: resolution of D# with an "escape tone" between F and its note of resolution. The opening movement of the sixth quartet contains numerous passages in which motivically derived linear progressions occur simul-taneously i n more than one strand of a polyphonic texture. Some of these examples will be cited in the next chapter, on prolongation, but for present purposes, I draw attention to mm. 126-143, represented in Ex. 2.40. Unlike i n ostensibly comparable textures i n music of the major-minor system—where an underlying functional harmonic unity is most often clearly discernible in spite of the rhythmic independence of individual p a r t s — l i n e a r constituents in a contrapuntal context i n Bartok's music tend to be truly independent, both rhythmically and tonally. Only at points of vertical alignment—junctures which mark phrase beginnings and/or endings through surface indicators such as rhythmic caesura, tempo change, dynamic change, etc.—are the multiple streams of linear a c t i v i t y heard to define appreciable, unified, functional verticalities. In the excerpt in question, the verticality at the beginning of m. 137 represents the confluence of a l l but the lowest linear progres-sion, eliding with the beginning of a new thematic section (the lowest progression, overlapping those thematic boundaries, concludes in m. 142, as wil l be discussed). The main criterion by which pitches are assigned significance i n the linear progressions in mm. 127-136 i s motivic articulation. The motive consists of two segments—e.g., i n the 100 violins, mm. 127 and 128, respectively—which alternate until m. 132. The f i r s t note of each marks the interval of transposition, IC 1 or 2, defining mid-level linear step progressions. For the most part, up to m. 132, the second v i o l i n doubles the f i r s t and the viola doubles the cello. After m. 132 there is some voice crossing (as far as the linear successions are concerned) and the inner parts progress independently of the outer parts with which they were in i t i a l l y associated. The linear progressions are stemmed and beamed on system (a), and the aforemen-tioned crossings are indicated on system (a) by the crossed beams. System (b) offers a reduction of the linear progressions indicated on (a). Although these progressions have been shown to be systematically articulated, their respective goals are not preestablished and are accordingly not "foreseeable." The significance of these contextually directed progressions is appreciated retrospectively, upon the awareness of arrival points i n m. 137 as significant at some level of tonal structure and formal delineation. For example, the v e r t i c a l i t y at m. 137—the alignment of endpoints of the preceding independent linear progressions—also initiates a brief progression along the descending circle of fifths, of which the constituents are conventionally tertian ((T)). The root of the i n i t i a l harmony, D, recalls the primary referen-t i a l PC of the movement while that of the f i n a l triad in the cycle, F, articulates the movement s secondary PC, this progression being signifi-cant at this point in the movement (near the close of the A section), as will be explained in the next chapter. The criterion for inference of the linear progression in the 101 lower line of the cello i s the same as that i n the upper voices. Factors governing i t s extension over the thematic boundary include pattern interruption, octave completion, and functional harmonic arrival. The continuity of step successions in the lower line of the cello part is interrupted after arrival on Bb2 in bar 135 [system (a)]. As i t turns out, the octave completion of the upper line in the c e l l o — the Eb3 cf m. 137—is also the i n i t i a l event in a descending line which, traversing the aforementioned descending c i r c l e - o f - f i f t h s progression (at (T)), arrives on C3 in m. 142 ((2)). This C may also be perceived as a continuation of the lower line in the cello (from Bb2 i n m. 135) and an octave completion of that line in bar 127 ((3)). The octave completion of the extended cello line thus coincides with the arrival of the F-major triad as the goal of the circle of fifths, this coincidence being one factor marking the F triad as a juncture of significance. While the implication of F major i s considerable, given i t s function as goal in two streams of activity outlined above, the sta b i l i t y of the F triad i s compromised in the interest of ongoing continuity. One important event precluding stability i s the avoidance of resolution of the leading-tone in the f i r s t v i o l i n in m. 142 ((£})• Two additional circumstances are the second-inversion at this point—a decisive consideration in the often functionally tertian context of this movement—and the arrival of F in the middle of a thematic statement. Although these factors undermine any sense of structural finality, the status of the triad as a goal in two linear progressions and a 102 descending-fifth cycle suggests its broad importance. 4 In Ex. 2.28, the trio of the fif t h quartet's middle movement was studied for its organization of fifth-chords progressing by the interval of a f i f t h , and the A-E f i f t h , arrived at i n m. 39, was shown to in i t i a t e a descending-fifth cycle. The approach to that i n i t i a l con-stituent of the cycle, on which I w i l l now focus attention, i s a lucid example of a mid-level, contextually directed linear progression gener-ated by step-related transpositions of a particular, identifiable motive or theme. Here, the motive i s unfolded in the f i r s t v i o l i n in m. 1 of the trio {(l) in Ex. 2.41). The remainder of staff (a) shows subsequent transformations and transpositions of the motive to m. 39. As shown at (2), the primary form of the motive traverses a f i f t h , alternately diminished, the latter representing secondary constituents in the pro-gression. The primary and secondary intervals are verticalized on staff (c) and one member of each tritone i s indicated by a black, note-head denoting its passing function, while the other is notated open, reflec-ting i t s membership in either the primary f i f t h which precedes the tritone or that which follows. Of the four stemmed, perfect fifths on staff (c)—F-C, G-D, Ab-Eb, and A-E—the Ab-Eb f i f t h i s for two reasons an anomaly in this progression. First, the whole-tone relation between the i n i t i a l two fifths is violated and, second, without consideration of As I w i l l show in the next chapter, subsequent measures, leading to the close of the A section, reveal an unequivocal prolongation of, and ultimate arrival on, a root-position F-major triad, the movement's secondary referential triad. 103 the Ab-Eb fifth, the three remaining fifths, when concatenated, would yield a six-note, homointervallic collection, F-C-G-D-A-E, consistent with the type of f i f t h "accumulation" shown earlier to occur subsequent to m. 39 (see Ex. 2.28). I w i l l return to this latter detail. Staff (d) offers an interpretation in which the Ab-Eb f i f t h i s not deemed primary at a l l , but is, rather, a vertical coincidence of two passing notes, suspended from or in anticipation of one note of a secon-dary tritone. As indicated at (^), the lower note of the Ab-Eb f i f t h , notated as G#, i s a suspension from the preceding tritone and passing tone between G and A, the roots of two primary fifths. And ^} reveals a reverse procedure with respect to the top note of the Ab-Eb f i f t h , here notated as D#: D# is an anticipation and passing tone with respect to the A-D# tritone connection of G-D to A-E. The interpretation outlined above yields three f i f t h s i n the progression—F-C, G-D, and A-E—which, when vertically aligned, as at (^), yields the aforementioned six-note homointervallic collection. A synopsis of the descending-fifth progression and accumulation which occurs in mm. 39-65 (detailed in Ex. 2.28) is shown between the brackets at revealing that the top fi f t h of the six-note fifth-collection at f^ 5) is that which initiates the fifth progression (f^ 7)), while the lower fifth is that which concludes the trio ((j) ). This relation between the step progression of the opening 39 measures and the balance of the trio, organized i n f i f t h progressions, corroborates the interpretation on staff (d) of the Ab-Eb f i f t h as subordinate to the other three whole-tone-related fifths. The beginning of the middle section in the final movement of the 104 fourth quartet was cited earlier (Ex. 2.29) as an example of mid-level progression by f i f t h . At the arrival of each constituent of the temporally spaced progression, but prior to approach to the next consti-tuent, a brief contrasting thematic element emerges in the cello (Ex. 2.29). This gesture represents the primary thematic material of the B section, contrasting with that of the A section not only i n general contour and intervallie structure, but also in the means of tonal orien-tation, which i s , here, one of linear connection achieved i n part through motivic transposition. Before examining the linear progressions indicated on staff (d) of Ex. 2.29 and their continuation in Ex. 2.42, i t i s necessary to note three aspects of the motive: first, i t is comprised of four semitonally adjacent PCs (e.g., Eb, E, F and Gb in the f i r s t instance, mm. 162-164 of Ex. 2.29); second, the transpositions are not stated in the complete rhythmic configuration of the i n i t i a l statement (mm. 162-164) and do not include a l l four PCs (in which case the rhythmic disposition of those PCs which are stated w i l l provide the referential PC for determining transposition); and third, the motive, as f i r s t established in mm. 163-164, is end-oriented, a characterization based in part on its occurrence at the final cadence of this movement and the first, where i t is expli-citly end-oriented, and in part on its recurrences, in which its rhyth-mically distinct end fragment represents a particular transposition of the entire motive. The final member (not necessarily the PC-lowest) is, in these recurrent—if incomplete—statements, thus sensed as focal, and may be heard to engage in higher-level (i.e., more broadly spaced) 105 linear step connections. 3 At in Ex. 2.29 the fi r s t mid-level step connection is noted: Eb-D, the i n i t i a l E notated with a flag to represent i t s subordinate, anacrustic status. Each of the two constituents in this linear progres-sion corresponds to a statement of the motive, the second of which i s complete in PC content but lacking the anacrusis. At (T) the progres-sion is repeated but carried one step further to include a third state-ment of the motive, which i s further truncated to include only the motive's fi n a l three-note fragment. The three constituents of this second linear progression correspond to the f i n a l notes of the three motivic statements. Although significance of the specific PCs involved in the progression i s perhaps not so clear at this early stage in the middle section, examination of the B section's f i n a l cadence, m. 237, reveals that the ultimate referential element of this middle portion is the PC C associated with i t s minor third, Eb. In this sense the ultimate referential PC in both the A and B sections i s C although the intervallic structures in which i t is expressed vary significantly as do the principles of orientation toward those structures. The progression from Eb to C, in i t i a t e d i n mm. 162-165 and completed in 172-175, then, is a linear expression of the in t e r v a l l i c structure with which the •^In his analysis of the fi r s t movement of Bartdk's fourth quartet, Roy Travis interprets a derivative of the motive cited here as end-oriented and identifies a linear progression (in mm. 43-46) based on the f i n a l notes of subsequent transpositions of the motive, not unlike the linear progressions exhibited here. See "Tonal Coherence in the First Movement of Bartdk's Fourth String Quartet," The Music Forum 2 (1970): 303, 329-330. Karpati similarly reveals linear continuities constructed of the final notes of end-oriented motives in the f i r s t and last movements of the f i f t h quartet. See p. 241 (Ex. 224) in Bartdk's String Quartets. 106 primary PC C is ultimately associated at the end of the B section (and i t is a structure which becomes "inflected" in the final cadence, as was shown in Ex. 2.22). Development of the B section s primary motive does not, however, end with the completed traversal from Eb to C. At the a r r i v a l of the third constituent of the broad f i f t h progression i n m. 182, motivic material emerges in a l l parts (Ex. 2.42). System (a) of Ex. 2.42 denotes the final pitches of a l l motivic transpositions with a stem and the anacrustic beginning pitches with a stem and flag. Qn system (b), only the focal pitches of the transpositions are indicated and are here stemmed to adjacent transpositions showing the brief mid-level linear progressions. The f i r s t linear connection after the Eb-C progression discussed above occurs at (T), also taking off from Eb, here as D#. In this succession, however, the second statement of the motive ((Q) i s inverted; i t arrives on F and produces a mid-level ascent of a second, D#(=Eb)-F. In the second group of mid-level dyads, mm. 188-192, the second v i o l i n articulates a descending linear connection between endpoints of the two adjacent transpositions, again with D# as i t s starting point ( ( ^ ) . Each of the remaining instruments completes its mid-level dyad before the f i r s t violin articulates a major third (rather than a second) between endpoints of the two adjacent transpositions. The top PC i s the new arrival point of the previous linear dyad, F, and the bottom is the PC which will become the arrival point of the second violin s step descent, C#. The i n i t i a l Eb-C progression in the measures preceding this excerpt and a summary of the linear fragments of this 107 section are given at (4}. The two primary motions in mm. 183-195—i.e., after the Eb-C progression—are D#-F and D#-C#, of which F and C# are prolonged into the next section, as w i l l be ill u s t r a t e d i n the next chapter. It will suffice to note here that F is extensively elaborated in the ensuing measures, after which i t is the i n i t i a l member of a broad descent of a third back to D, which in turn descends to C at the f i n a l cadence of the B section. C# does not eventually resolve to C as might be expected, but i s rather superseded by the aforementioned D before resolving to C. The motivically derived linear progressions outlined in this example are essentially no different from those discussed earlier; what they lack i n extent they make up i n emphasis through intense rhythmic vitality, repetition, and superposition. See, for example, mm. 222ff. of Ex. 3.13, where D becomes the focal PC of reiterated motivic, mid-level dyads, and is treated as scale degree 2 at the final cadence of the section. 108 CHAPTER III PROLONGATION IN BARTOK'S STRING QUARTETS Introduction Music i s a temporal art. Tonal music i s a s p e c i a l kind of temporal a r t whose coherence r e l i e s to a great extent on p a r t i c u l a r r e l a t i o n s h i p s between contiguous and noncontiguous points of tonal import. The complex functional r e l a t i o n s of the major-minor system f a c i l i t a t e varying degrees of perceptual orientation—at various levels of structure, over a v a r i e t y of temporal s p a n s — t o a s i n g l e t o n i c harmony. Principles according to which such tonal orientation may be understood were sy s t e m a t i c a l l y illuminated and explicated by Heinrich Schenker, whose concept of prolongation was advanced as a fundamental process, operative at a l l l e v e l s of tonal structure i n music of the common-practice period. Schenker's prolongation—Auskomponierung or composing-out—has as i t s goal the horizontalization of an interval or chord, ultimately, though by no means e x c l u s i v e l y , the to n i c t r i a d of a given piece. Already i n his Harmony Schenker wrote that "The harmonic element . . . has to be pursued i n both d i r e c t i o n s , the hor i z o n t a l as w e l l as the vertical."-'" The basic process by which t h i s h o r i z o n t a l i z a t i o n of a •'-Heinrich Schenker, Harmony, ed. Oswald Jonas, trans. E l i s a b e t h Mann 109 (tertian) harmony may occur is arpeggiation/ the "filling-in" of which defines the concept of linear progression.3 These two related prolonga-tional processes are united i n Schenker's contrapuntal "fundamental structure," which defines the "background" of a traditionally tonal piece and represents the latter's broadest of prolongations.4 Schenker writes: Fundamental line is the name which I have given to the upper voice of the fundamental structure. It unfolds a chord horizontally while the counterpointing lower voj.ce effects an arpeggiation of this chord through the upper fifth. While this ultimate structure is the most skeletal representation of a piece's tonal scheme, Schenker notes that The l i f e of the fundamental line and the bass arpeggiation manifests i t s e l f not only in the f i r s t [i.e., background] horizontal succes-sion and i n the f i r s t arpeggiation; i t also expands through the middleground, through what I have called the voice-leading transfor-mation levels, prolongations, elaborations, and similar means, in to the foreground. Components of the fundamental structure thus serve as the basis for lower level imitations—mid-level and surface-level prolongations— Borgese (Chicago: University of Chicago Press, 1954; paperback edition, Boston: M.I.T. Press, 1973), p. 134. Heinrich Schenker, Free Composition, trans, and ed. Ernst Oster (New York: Longman, Inc., 1979), p. 10. Also, Oswald Jonas, Introduction  to the Theory of Heinrich Schenker, trans, and ed. John Rothgeb (New York: Longman, Inc., 1982), p. 37. Schenker, Free Composition, p. 44. Also, Jonas, Introduction to  Schenker, pp. 51, 62. 4Schenker, Free Composition, p. 4. 5 -Ibid. (Schenker s emphasis.) 6Ibid., pp. 4-5. (Schenker's emphasis.) 110 which, in their duplication of background structural events, create the ultimate in organic coherence. Examination of conventional prolongation s essential properties, as they operate at various levels of structure, must surely be regarded as the f i r s t step i n any meaningful extrapolation of the concept of prolongation to less t r a d i t i o n a l contexts, i f , i n f a c t , such extrapolation is just i f ied . As a point of departure I c i t e a concise, i f more general, interpretation of Schenker's concept of prolongation, given by Al len Forte and Steven Gilbert i n a pedagogical book on Schenker's system of tonal analysis. It is a definition which is appli-cable to a l l levels of structure and i t illuminates a quality which is implicit in Schenker's principle of composing-out. They define prolon-gation as the ways in which a musical component—a note (melodic prolongation) or a chord (harmonic prolongation)—remains in effect without being l i t e r a l l y represented at every moment. . . . a given harmony i s prolonged so long as we feel i t to be in control over a'particular passage. Whether linear or harmonic, immediate or of deeper implications, prolon-gation embodies according to this particular definition the implication of a primary event over a particular temporal span without l i teral and recurrent statement of that event. In the discussion which follows, I wil l suggest that, even in traditionally tonal music, the perceptibility of implication of an event without i t s l i t e r a l restatement i n fact varies over different temporal spans, and that this has important rami-7 Allen Forte and Steven E. Gilbert, Introduction to Schenkerian Analysis (New York: W. W. Norton & Company, Inc., 1982), p. 142. I l l f i c a t i o n s f o r t h e i n f e r e n c e o f p r o l o n g a t i o n a l s t r u c t u r e s i n n o n t r a d i -t i o n a l contexts. As I w i l l show, i f we can speak of p r o l o n g a t i o n a t a l l i n l e s s c o n v e n t i o n a l c o n t e x t s , i t w i l l have t o be w i t h a c e r t a i n degree of l a t i t u d e w i t h r e s p e c t t o t h i s p r o p e r t y of c o n v e n t i o n a l t o n a l i t y . Foreground P r o l o n g a t i o n P r o l o n g a t i o n a t l o c a l l e v e l s i s l e a s t p r o b l e m a t i c , f o r reasons w h i c h w i l l be s t a t e d , and t h e r e f o r e s e r v e s as a c o n v e n i e n t s t a r t i n g p o i n t . One m a n i f e s t a t i o n o f c o n v e n t i o n a l p r o l o n g a t i o n w h i c h p r o l i f -e r a t e s o v e r t h e s u r f a c e o f most m u s i c o f t h e m a j o r - m i n o r s y s t e m i s l i n e a r m o t i o n " w i t h i n " a t r i a d — i . e . , f r o m one o f i t s c o n s t i t u e n t s t o a n o t h e r — r e s u l t i n g i n a h o r i z o n t a l i z a t i o n o f the t r i a d i c s t r u c t u r e . I n a p a s s i n g m o t i o n between t h e r o o t and t h i r d o f a t r i a d , f o r example, q u a l i t i e s o f t e n d e n c y and i m p l i c a t i o n i n the i n t e r v e n i n g p a s s i n g note may be accounted f o r w i t h extreme p r e c i s i o n by i n v o k i n g s t r i c t r u l e s o f c o n v e n t i o n a l d i s s o n a n c e t r e a t m e n t . R e c o g n i z i n g the dissonance o f the second o r n i n t h , a g a i n s t the u n d e r l y i n g r o o t , the l i s t e n e r expects the nonharmonic note t o e i t h e r continue t o the next t r i a d m ember—in which case the i n t e r v e n i n g note would be c h a r a c t e r i z e d as a p a s s i n g t o n e — o r t o r e t u r n t o the chord t o n e — i n which case i t would be understood as a neighbour note. I n e i t h e r case the process i s , a t the foreground, over °The r e s o l u t i o n can, o f c o u r s e , c o i n c i d e w i t h a new harmony, b u t t h i s would not y i e l d a foreground prolongation. Should the harmonic motion c o n t i n u e i n a f u n c t i o n a l manner, a h i g h e r - l e v e l p r o l o n g a t i o n c o u l d r e s u l t , as w i l l be e x p l a i n e d l a t e r i n t h i s c h a p t e r . 112 in such a short time that the listener i s not oriented away from the triad, and a sense of local prolongation may be said to be based purely on proximity. While this is true, prolongation is here underscored by rules of dissonance treatment which govern the motion of the intervening element—rules which generate a sense of implication even in this local event. As demonstrated in Chapter II, many referential elements encoun-tered in Bartok's music are tertian in structure and occur i n contexts which are conventionally functional. In such instances foreground pro-longations through passing and neighbour motions of the conventional type described above are relevant. In that this particular prolonga-tional technique is basic and easily apprehended, illustration may be kept to a minimum. In Exx. 2.2 and 2.3 instances of foreground prolon-gational motion within a triad are bracketed in the score. The conso-nant tertian harmonic framework in these excerpts provides a basis for the inference of nonharmonic elaborative notes which, in accordance with rules of dissonance treatment, imply resolution in specific ways. In Ex. 3.1, motion within a chord over a slightly broader span i s shown at Cp. Here, a tertian basis i s suggested by the ex p l i c i t D-major triad on the downbeat of measure 60, its root, sustained in the cello, provid-ing a constant reference for the linear motions. Foreground prolongation in the excerpts just noted is unproblem-atic because of the unequivocal tertian basis of the music; but what of prolongation over comparable spans in contexts more readily associated with Bartok's music—and that of other twentieth-century composers— 113 where referential elements are nontertian? Edward Laufer, commenting on the application of conventional prolongational procedures to nontertian contexts in general, asserts that The concepts of consonance and dissonance, as technically de-fined, . . . cannot e x i s t , nor can, s t r i c t l y speaking, the notions of passing and neighbour notes where these were dissonant events. Their attendant constraints, which provided motion and delays, must be compensated f o r by other kinds of embellishing and t r a v e r s i n g motions. 9 S t r i c t rules of dissonance treatment associated with the major-minor system are indeed less applicable to nontertian contexts; however, unless a nonconventional r e f e r e n t i a l element i s comprised entirely of semitonally adjacent PCs, i t i s i n principle possible to connect certain of i t s members by (PC-)step (i.e., "passing") motion. Arnold Whittall, for example, claims that, ". . . dissonances lack the capacity f o r substantial vprolongation', since their possible functional significance within a f u l l y layered harmonic hierarchy i s so d i f f i c u l t to define[,]" but l a t e r acknowledges that, although extension of dissonant (i.e., nontertian) structures most readily occurs through textural and rhythmic factors, ". . . occasional h o r i z o n t a l i z a t i o n and neighbour-note motion . . . may suggest connections with t r a d i t i o n a l tonal tech-niques."^ 0 In such nontraditional contexts, of course, "nonharmonic" notes are not governed by any p a r t i c u l a r rules of dissonance treatment and, ^Edward Laufer, review of Free Composition, by Heinrich Schenker, translated and edited by Ernst Oster, i n Music Theory Spectrum, 3 (1981): 161. •^Arnold W h i t t a l l , "Music Analysis as Human Science?," Music Analysis 1/1 (March, 1982): 44. 114 consequently, are not bound to resolve i n any p a r t i c u l a r way. Such elements are thus devoid of inherent i m p l i c a t i o n , analogous to that generated i n the major-minor system, and cannot be s a i d to generate conventional prolongations. In that constituents of an i d e n t i f i a b l e referential element are horizontalized and connected linearly, however, the process achieves the same end result as conventional prolongation, namely, extension of the span over which a particular element i s heard to prevail. For this reason I think i t appropriate to understand such a process as prolongational, i f only "contextually" so (i.e., determined by context rather than by underlying conventional relations). In s u r f a c e - l e v e l (contextual) prolongations, the intervening, subordinate event i s , by definition, neither inherently implicative of, nor i n e v i t a b l y d i r e c t e d to, a member of the r e f e r e n t i a l element i t expands. Rather, i t may be understood more generally as a "departure" from an unequivocally identifiable primary element. Arrival on a member of the r e f e r e n t i a l element would, i n turn, be understood, not as a resolution i n the conventional sense, but as "return" i n a more general sense. I w i l l put forward the view that, i n order f o r a p a r t i c u l a r departure-return pattern to generate prolongations at higher levels of structure i t must f i r s t be articulated at a level where the association i s perceptibly appreciated. Paul Wilson o f f e r s corroboration of t h i s view. He find s , i n Bartok's Op. 20 piano pieces, a "basic structural model" in "the estab-lishment of a primary chord, a departure from that chord, and a return to i t , " and characterizes such a model of departure and return as an 115 "inherent hierarchical resource" which, when reiterated over different spans, may be said to generate "nested prolongational structures."-'-^ Two important points are advanced here. The f irst , having relevance to the present discussion, concerns the characterization of a basic model of departure and return without any strict notions of dissonance treat-ment as demonstrative of a prolongational structure. The second con-cerns the concept of nested structures at various levels, a concept which is dealt with later. Bartok's quartets offer many examples of foreground prolonga-tional patterns of departure and return. But because these patterns are more often reiterated in succession—defining a specific type of mid-level prolongation discussed later in the chapter, in connection with Exx. 3.8-3.19—I postpone the discussion of examples until then. Mid-Level Prolongation It is at higher levels of structure, beginning with that of the phrase and comparable spans, that the criterion of implication without l i t e r a l and constant restatement—the essence of the def ini t ion of conventional prolongation given earlier—assumes greater significance because of the increased temporal distances between explicit articula-tions of the element being prolonged. In traditionally tonal music, the functionality of the major-minor system becomes all-important in mid-Paul Wilson, "Concepts of Prolongation and Bartok's Opus 20," Music  Theory Spectrum 6 (1984): 88. 116 l e v e l p r o l o n g a t i o n s , w h i l e i n m u s i c n o t b a s e d e n t i r e l y on t h e m a j o r -m i n o r s y s t e m , c o m p a r a b l e p r o c e s s e s f o r m a i n t a i n i n g t h e v a l i d i t y o f a r e f e r e n t i a l element a r e c r i t i c a l . W ith r e s p e c t t o m i d - l e v e l harmonic p r o l o n g a t i o n i n the major-m i n o r system, f o r a harmony t o be " i n e f f e c t " o v e r o r " i n c o n t r o l " o f a p a r t i c u l a r span, we must hear a l l o t h e r h a r m o n i e s as s u b o r d i n a t e b u t f u n c t i o n a l l y r e l a t e d t o the c o n t r o l l i n g harmony. I n a p r o g r e s s i o n along the descending c i r c l e o f f i f t h s , f o r example, the f u n c t i o n o f nontonic harmonies and t h e i r r e l a t i o n t o the prolonged harmony can be d i s c e r n e d w i t h p r e c i s i o n , p a r t i c u l a r l y as we n e a r e x p l i c i t s t a t e m e n t o f t h a t p r i m a r y e v e nt. Thus, i n t h e m i d - l e v e l p r o g r e s s i o n I - I I I - V I - I I - V - I — r e g a r d l e s s o f t h e t e x t u r a l c o n f i g u r a t i o n i n w h i c h t h e p r o g r e s s i o n i s expressed—we can i n f e r the primacy o f I throughout because we under-stand t h a t I I I , VT, I I , and V r e l a t e t o the i n i t i a t i n g and c o n c l u d i n g I i n v a r y i n g degrees o f p r o x i m i t y along the f u n c t i o n a l c i r c l e o f descen-d i n g f i f t h s . I i s t h e r e f e r e n c e t o w h i c h t h e o t h e r h a r m o n i e s a r e r e l a t e d and, i n s o f a r as i t " c o n t r o l s " the span over which the s i x - c h o r d p r o g r e s s i o n occurs, i t i s s a i d t o be prolonged. T h i s p a r t i c u l a r mode o f p r o l o n g a t i o n r e v e a l s an important aspect o f i n t e r a c t i o n i n the major-minor system: f u n c t i o n a l p r o g r e s s i o n s — t h e b a s i c means of connecting one s t r u c t u r a l h a r m o n i c e v e n t t o a n o t h e r — a r e , by d e f i n i t i o n , d i r e c t e d t o w a r d , and t h e r e f o r e i m p l i c a t i v e o f , a p a r t i c u l a r t o n i c g o a l , and i n t h i s sense may be s a i d t o pro l o n g t h a t goal. F u n c t i o n a l harmonic p r o -g r e s s i o n and harmonic p r o l o n g a t i o n are thus i n e x t r i c a b l y a l l i e d i n the major-minor system. F u n c t i o n a l harmonic p r o g r e s s i o n may a l s o be understood t o pro-117 v i d e a b a s i s on w h i c h l i n e a r p r o l o n g a t i o n i s p e r c e i v e d . T h at i s , a l t h o u g h l i n e a r c o n s t r u c t s may be h e a r d t o d e r i v e i n h e r e n t d i r e c t e d tendency from the s c a l a r resource of which they are p a r t , t h e i r poten-t i a l d i r e c t e d n e s s i s r e a l i z e d e x p l i c i t l y when they a r e heard a g a i n s t an u n d e r l y i n g f u n c t i o n a l h a r m o n i c framework. C o n s t i t u e n t s o f a l i n e a r p r o g r e s s i o n are l i n k e d t o t h e i r corresponding harmonies, the r e l a t i o n -s h i p o f t h e l a t t e r t o t h e t o n i c s e r v i n g t o i m p a r t f u n c t i o n a l s i g n i f i -cance t o t h e f o r m e r . R e c a l l t h e q u o t a t i o n f r o m B e r r y ' s S t r u c t u r a l  F u n c t i o n s c i t e d i n C h a p t e r I I , i n w h i c h he s u g g e s t s t h a t l i n e a r and t o n a l f u n c t i o n are not " m u t u a l l y c o n t r a d i c t o r y o r e x c l u s i v e c o n c e p t s " b u t , r a t h e r , t h a t t h e y "nearly always appear i n complementary conjunc-1 9 t i o n i n t o n a l music. The degree of separate i d e n t i t y o f l i n e a r and harmonic pro g r e s -s i o n and of f u n c t i o n a l p r o g r e s s i o n and p r o l o n g a t i o n i n major-minor t o n a l m u s i c i s t h u s n o t so g r e a t as i t i s sometimes t h o u g h t t o be. I n l e s s conventional contexts, however, such d i s t i n c t i o n s a r e o f t e n v e r y r e a l . In Chapter I I , I c h a r a c t e r i z e d l i n e a r p r o g r e s s i o n i n Bartok's q u a r t e t s as a s e p a r a t e o r g a n i z a t i o n a l d e t e r m i n a n t and n o t e d t h a t , o f t e n i n t w e n t i e t h - c e n t u r y music, t h e r e are analogues of the dominant and t o n i c components o f t h e m a j o r - m i n o r s y s t e m b u t n o t o f i n t e r v e n i n g , f u n c -t i o n a l l y r e l a t e d , d o m i n a n t - p r e f i x components ( i n the major-minor system, those harmonies which a r e f u n c t i o n a l l y d i r e c t e d t o w a r d t h e d o m i n a n t -t o n i c p r o g r e s s i o n ) . T h i s has i m p o r t a n t r a m i f i c a t i o n s f o r m i d - l e v e l I T Wallace B e r r y , S t r u c t u r a l F u n c tions, p. 30. (Berry's emphasis.) 118 p r o l o n g a t i o n a l s t r u c t u r e s i n Bartok's musical language, as I w i l l demon-s t r a t e h e r e. Four c l a s s i f i c a t i o n s o f m i d - l e v e l t o n a l expansion a r e d i s c u s s e d i n t h i s s e c t i o n . The term p r o l o n g a t i o n denotes expansion i n which the i n t e r v e n i n g event i s sensed as d i r e c t e d toward, and t h e r e f o r e i m p l i c a -t i v e o f , i t s g o a l (understood as conventional p r o l o n g a t i o n ) , as w e l l as expansion i n which no such i n f e r e n c e of i m p l i c a t i o n i s j u s t i f i e d , and i n which constant recurrence o f the c o n t e x t u a l l y primary event i s a f a c t o r ( u n d e r s t o o d as c o n t e x t u a l p r o l o n g a t i o n ) . The c l a s s i f i c a t i o n s a r e a s f o l l o w s : (1) p r o l o n g a t i o n t h r o u g h c o n v e n t i o n a l l y f u n c t i o n a l h a r m o n i c p r o g r e s s i o n s , (2) p r o l o n g a t i o n t h r o u g h l i n e a r u n f o l d i n g , (3) prolonga-t i o n through o s c i l l a t i o n and/or r e i t e r a t i o n , and (4) simultaneous p r o -l o n g a t i o n o f more t h a n one r e f e r e n t i a l e l e m e n t ( t h r o u g h t h e f i r s t t hree p r i n c i p l e s ) . As t h e r e i s constant i n t e r p l a y between p r o g r e s s i o n and p r o l o n g a t i o n — e . g . , a p r o g r e s s i o n generating a broader p r o l o n g a t i o n w h i c h , i n t u r n , expands a component of a h i g h e r - l e v e l p r o g r e s s i o n — p r i n c i p l e s o f p r o g r e s s i o n d e a l t w i t h i n C h a p t e r I I w i l l a t t i m e s be reexamined here f o r t h e i r r o l e i n p r o l o n g a t i o n a l processes. P r o l o n g a t i o n through c o n v e n t i o n a l l y f u n c t i o n a l harmonic pr o g r e s s i o n s I t was s u g g e s t e d i n t h e o p e n i n g comments t o t h i s s e c t i o n t h a t c o n v e n t i o n a l l y f u n c t i o n a l progressions i n t r a d i t i o n a l l y t o n a l music, i n t h e i r d i r e c t e d a p p r o a c h t o and i m p l i c a t i o n o f a t o n i c g o a l , s e r v e t o prolong t h a t t o n i c between recurrences, o r even i n i t s absence. Indeed, i t i s a s i g n i f i c a n t f e a t u r e o f t h e m a j o r - m i n o r s y s t e m t h a t e n r i c h i n g d e t a i l s o f v o i c e l e a d i n g need n o t be i n v o k e d f o r t h e c o m p r e h e n s i o n o f 119 such prolongational effects, for the very presence of a palpable func-tional harmonic framework i s sufficient to evoke a strong sense of tonality. In Chapter II, excerpts from the f i r s t and last quartets served to demonstrate both the inference of tertian structures within a complex contrapuntal fabric, and the use of traditional root relations in effecting conventionally functional harmonic progression. Those same excerpts may be studied for their prolongational structures—structures arising largely from identifiable functional progressions, the two regarded as intimately related. Examples 2.1, 2.2, and 2.3 furnish numerous instances of pro-longation (in advance of explicit tonic arrival) through conventionally functional progressions. In Ex. 2.1, tonicizations of F ( (1^ 5) ), D ((^) ), Ab ((^) )i and A ( f^ ) ) involve basic, conventional harmonic progressions, usually consisting of a dominant prefix, dominant, and tonic. Because of the functionality of the progressions, the dominant-prefix harmonies, though subordinate, are understood in light of their goals and may be said in a general way to prolong them. In Ex. 2.2, harmonic prolongations of F, Eb, and Db occur through conventionally functional progressions involving dominant-prefix chords followed by traditional dominant-to-tonic progressions [refer to the roman-numeral analyses on system (b)]. Example 2.3 i s particularly i l l u s t r a t i v e of prolongation through patterns of functional harmonies beginning with a dominant-prefix harmony (rather than the prolonged harmony). The roman-numeral analyses below system (c) reveal a ii-V-I pattern in Eb, a v i -ii-V-I pattern in F#, and a vi-V-I pattern in A. In these progressions, conventional functionality accounts for mid-level prolongation of the 120 goal harmonies i n advance o f t h e i r a r r i v a l , i n s p i t e o f the b r i e f span o v e r w h i c h t h e y a r e f o c a l , and r e g a r d l e s s o f t h e b r o a d e r , f l u c t u a n t t o n a l scheme i n w h i c h t h e y p a r t i c i p a t e . I n t h e e x c e r p t s d i s c u s s e d above, then, c o n v e n t i o n a l l y f u n c t i o n a l r o o t r e l a t i o n s (both i m p l i c i t and e x p l i c i t ) p r o v ide the b a s i s f o r the i n f e r e n c e o f t o n a l o r i e n t a t i o n and attendant harmonic p r o l o n g a t i o n s . P r o l o n g a t i o n through l i n e a r p r o g r e s s i o n In Chapter I I , l i n e a r p r o g r e s s i o n was i d e n t i f i e d as an important means by which two d i s p a r a t e m u s i c a l s t r u c t u r e s (e.g., PCs, p i t c h e s , o r v e r t i c a l i t i e s ) a r e c o n n e c t e d . I n h e r e n t l y d i r e c t e d and c o n t e x t u a l l y d i r e c t e d were c i t e d as t h e two main t y p e s o f l i n e a r c o n s t r u c t , t h e i r c o n s t i t u e n t s s e l e c t e d f r o m t h e o v e r a l l t e x t u r e a c c o r d i n g t o v a r i o u s c r i t e r i a of s u r f a c e exposure—e.g., emphasis i n the realms o f dynamics, r e g i s t e r , and d u r a t i o n , among o t h e r s — o r through m o t i v i c t r a n s p o s i t i o n by step. These l i n e a r c o n s t r u c t s and c r i t e r i a f o r p i t c h s e l e c t i o n a l s o apply t o l i n e a r p r o g r e s s i o n s which may, i n t u r n , be heard t o d e f i n e mid-l e v e l p r o l o n g a t i o n . Two s i t u a t i o n s i n which a l i n e a r p r o g r e s s i o n may be heard a t a higher l e v e l t o d e f i n e a p r o l o n g a t i o n a r e r e l e v a n t t o Bartok: i n one o f t h e s e , e n d p o i n t s ( s i n g l e p i t c h e s o r v e r t i c a l i t i e s ) o f a p r o -g r e s s i o n a r e t h e same b u t s e p a r a t e d by one o r more o c t a v e s ( h e r e a f t e r r e f e r r e d t o as octave p r o g r e s s i o n s ) ; i n the oth e r , d i f f e r e n t endpoints f u n c t i o n as c o n s t i t u e n t s o f a s i n g l e v e r t i c a l i t y ( h e r e a f t e r r e f e r r e d t o as u n f o l d i n g and p r o l o n g a t i o n a l progression). P r o l o n g a t i o n through surface-exposed octave p r o g r e s s i o n . The 121 m i d - l e v e l f i f t h p r o g r e s s i o n w h i c h b e g i n s t h e B s e c t i o n o f t h e f o u r t h q u a r t e t s f i n a l movement i s noted a t (T) i n Ex. 2.29, and the s e m i t o n a l a u x i l i a r y w h i c h p r e c e d e s each c o n s t i t u e n t of the f i f t h p r o g r e s s i o n i s marked (2). Each of these a u x i l i a r i e s i s prolonged a t a lower l e v e l o f s t r u c t u r e t h r o u g h a l i n e a r o c t a v e p r o g r e s s i o n ( ( J ) ) . T here i s l i t t l e e f f o r t r e q u i r e d f o r i n f e r e n c e o f t h e d e s c e n d i n g l i n e b ecause most p i t c h e s t a k e p a r t i n t h e s t e p s u c c e s s i o n , and t h o s e t h a t do n o t a r e e a s i l y i n t e r p r e t e d as l o c a l e l a b o r a t i o n s (e.g., n e i g h b o u r and p a s s i n g notes), as demonstrated on system (a). As i n d i c a t e d a t QT), each l i n e a r p r o g r e s s i o n c o n t i n u e s p a s t completion of the o c t a v e — t h e p o i n t where the p r o l o n g a t i o n i s r e a l i z e d — t o a r r i v e on t h e " o p p o s i t e " ( i . e . , n o n - s e m i t o n a l l y r e l a t e d ) member o f t h e c o n s t i t u e n t i n t h e l a r g e f i f t h p r o g r e s s i o n . I n mm. 1 6 0 - 1 6 2 , f o r example, the prolonged a u x i l i a r y i s the C#-G# f i f t h and the c o n s t i t u e n t of the l a r g e r f i f t h p r o g r e s s i o n t o which i t r e s o l v e s by semitone ( i n PC t erms) i s t h e D-A f i f t h ; t h r o u g h l i n e a r e x t e n s i o n beyond t h e o c t a v e , however, C# r e s o l v e s t o A ( r a t h e r t h a n by s e m i t o n e t o D) and G# t o D ( r a t h e r then by semitone t o A). Another i n s t a n c e o f p r o l o n g a t i o n through surface-exposed octave p r o g r e s s i o n may be n o t e d i n Ex. 2.35. Here, a s i n t h e e x c e r p t j u s t c i t e d , t h e r e i s l i t t l e d i f f i c u l t y i n s e l e c t i n g c o n s t i t u e n t s o f t h e l i n e a r c o n s t r u c t from the t e x t u r e because the octave p r o g r e s s i o n s ( ( 5 ^ and (^}) occur a t the s u r f a c e of the music, uncomplicated by l o w e r - l e v e l e l a b o r a t i o n (apart from the r e i t e r a t i v e p r o l o n g a t i o n o f the C#-D dyad i n mm. 2 3 - 2 4 ) . I t w i l l be n o t e d i n t h i s example t h a t t h e p r o l o n g a t i o n s c r o s s f o r m a l boundaries: the octave progressions begin i n the t r a n s i t i o n 122 to the second theme, and the point of octave completion—i.e., the point at which the prolongation i s realized—coincides, or elides, with the start of the second theme. Expectation of octave completion increases as the octave i s approached, and that keener sense of expectation, i n turn, f o r t i f i e s the quality of i n s t a b i l i t y ascribed to the C#-D dyad i n mm. 23-24, increasing the tendency of the latter to resolve. Prolongation through motivically derived octave progression. Two clear instances of motivically derived octave progressions which prolong t h e i r endpoints are indicated at £5} and (6) i n Ex. 2.40. As noted i n Chapter II, the two-bar motivic pattern i s i n two parts, each contribu-t i n g pitches to a d i s t i n c t l i n e a r progression. As i n the previous example, the significance of prolongation through octave progression i n t h i s excerpt l i e s i n the res u l t a n t overlap of formal d i v i s i o n s . That i s , a c l e a r change of texture and tempo occurs i n m. 137, the l i n e a r progressions i n the upper three parts culminating i n that bar. The upper l i n e of the c e l l o part concludes on Eb-j a t t h i s same point, completing the octave from m. 126 ( ( 5 ) ) - i s subsequently prolonged through a foreground lower-neighbour pattern u n t i l m. 139, where i t i n i t i a t e s a descent to C3 (^)), t h i s p i t c h completing a l i n e a r i z e d octave i n the lower line of the cello ((^ p). It i s this octave progres-sion from C2 to C3 which provides thematic o v e r l a p — a n event a l l the more significant because of the large-scale prolongational unfolding initiated by the cello's C3 i n m. 142, to be dealt with later. The excerpt given i n Ex. 3.2, from the t h i r d movement of the f i r s t quartet, i l l u s t r a t e s prolongation through an octave progression 123 which involves both motivic transposition and factors of surface expo-sure. The opening ascending third in m. 108, C#-D#-E, is interrupted by the leap up to G#, after which an embellishing pattern connects F# at the end of the measure to that on the downbeat of bar 109. This locally prolonged F# is thus perceived as the continuation of the opening third-ascent. F# i s subsequently further prolonged through upper and lower embellishing patterns in m. 109, i t s metrically strong arr iva l on the downbeat of m. 110 i n i t i a t i n g a varied transposition of the two-part motive in mm. 108-109. Measure 110 i s a variat ion of m. 108: an i n i t i a l ascent of a third—here F#-G#-A—is interrupted by a leap, after which B, the pitch which continues the i n i t i a l ascent, is elaborated through an embel-lishing pattern leading to the downbeat of the next bar (compare and (2}). Measure 111 corresponds to m. 109 in i t s upper and lower embel-lishing patterns (compare (3) and (T)) with one important change. This transposition of the last part of the motive is temporally extended—the meter now 3/2 rather than 2/2—and thereby facilitates inclusion of a passing tone (B#) after the embellishing pattern completes i ts surface prolongation of B ((5))- r^ne result is that, unlike mm. 109-110—where the embellished pitch in m. 109 is repeated on the downbeat of m. 110— the embellished pitch in m. I l l , B, passes through B# to arrive on C# on the downbeat of m. 112. C# i s the opening PC of the passage, which, through varied motivic transposition and surface exposed pitch events, has been prolonged through an ascending octave progression (f^)). Prolongation through linear unfolding. Conventional mid-level 124 l i n e a r unfolding, as operative i n music of the major-minor system, occurs when two members of a single harmony are temporally separated and connected linearly, as i n foreground motion within a chord, described earlier. In foreground unfoldings, however, passing notes are usually unharmonized, while, i n mid-level unfoldings, they are often supported by harmonies of subordinate function relative to the prolonged harmony. The linearization of vertical interval structures over mid-level spans occurs often i n Bartok's music but, because the texture i s so often polyphonic—in which parts are r e l a t i v e l y autonomous rhythmically and tonally-'- 3—mid-level unfoldings are rarely harmonized as such. They are more often set i n counterpoint to other, t o n a l l y autonomous l i n e a r unfoldings. As regards c r i t e r i a f o r identifying potential members of such linear unfoldings, surface exposure and motivic transposition are fundamental, often interactive, factors of articulation. Although examples of l i n e a r unfolding i n complex polyphonic textures w i l l be cited, the viola solo which appears at the opening of the s i x t h quartet's f i r s t movement i l l u s t r a t e s the concept of l i n e a r unfolding i n an uncomplicated texture and i s thus a s u i t a b l e f i r s t example of t h i s type of l i n e a r prolongation. The theme, given i n Ex. 3.3, twice unfolds the b2-#4 disposition pair to the movement's referen-i JBy "tonally autonomous" I suggest that each line of the overall con-trapuntal f a b r i c i s oriented to a p a r t i c u l a r r e f e r e n t i a l PC, the con-fluence of these lines at cadences and comparable structural junctures articulating unified v e r t i c a l i t i e s of i n d i v i d u a l l y prolonged elements. This i s in marked contrast to conventionally tonal polyphony, where the i n d i v i d u a l l i n e s , although rhythmically autonomous, are nonetheless fused into a single tonal implication. 125 t i a l f i f t h , D-A and (^). 1 4 In the opening unfolding (mm. 1-8), connection of A# to C# (mm. 2-4) occurs through a descending sixth ((3)) rather than a more direct ascending third: the descending sixth "repre-sents" the PC "ascent" of a third In fact, both unfoldings employ PC-step connections for the realization of linear constructs, as demonstrated in the registral compaction employed on staff (b). The dotted slurs at (^ ) and identify the overall prolongation of Eb and G# as b2 and #4 with respect to the movement's primary D-A f i f t h ((^}), which enters later. With reference to Ex. 2.22, I suggested that the inference of an obliquely resolving b2-5 tritone in the final cadence (mm. 391-392) was based on the prolongation of that tritone in the immediate approach to the f i n a l cadence. Example 3.4 illustrates the details of that pro-longed tritone. In mm. 374-385 the viola doubles the fi r s t violin and the cello doubles the second v i o l i n , yielding a two-part imitative texture, indicated on system (a). Each of these two parts unfolds, and thereby prolongs, the b2-5 tritone ((T) and (^)) through a contextually directed linear progression ( (p and f^j) generated by the concatena-tion of two alternating motives ((5) and The f i r s t and last pitches of each of the two motives (in each of the two essential parts) are stemmed on system (a) as they are the pitches, selected from the overall texture, which make up the descending linear unfoldings of the tritone. The criterion for selection of these pitches from the overall Janos Karpati notes the semitonal expansion of the opening theme's Eb-Ab to the primary D-A f i f t h of the movement; see Bartdk's String  Quartets (Budapest: Corvina Press, 1975), p. 250. 126 texture i s simply t h e i r p o s i t i o n as extremities of the motives. Each motive functions to effect a descending step, the linking of transposed descending steps generating a descending linear continuity. System (d) shows the "inversion" of the prolonged t r i t o n e , r e s u l t i n g from the simultaneous unfoldings. Example 2.22 may be reexamined for the posi-t i o n of the prolonged t r i t o n e i n the f i n a l cadence and i t s oblique resolution i n the f i n a l referential element. Example 2.9 was cited e a r l i e r as an instance of a conventional tonicization pattern which serves to establish a referential t r i a d i n a d i r e c t and appreciable way, before less t r a d i t i o n a l means of tonal orientation become focal. In this particular excerpt, mm. 1-14 of the f i r s t quartet's t h i r d movement, the i n i t i a l chord of the progression, the I I I 7 , i s prolonged through simultaneous l i n e a r unfoldings of i t s chord-tones. The upper two unfoldings—from the third up to the f i f t h ((T)) and the t h i r d down to the root ((2))—are d i r e c t , t h e i r c o n s t i t -uents reiterated without lower-level elaboration. The unfolding of the seventh down to the f i f t h {($)) i s more complicated as i t occurs within a more elaborate surface texture. The motive i n mm. 5-6, for example, involves PC-step motion i n r e a l i z i n g the o v e r a l l accented, lower-neighbour motion B-A-B ((4}). Because r e p e t i t i o n of the motive i n mm. 7-8 i s followed by r e i t e r a t i v e prolongation of G ((5)), A i n m. 8 ((&)) assumes a passing function (as compared to i t s accented, lower-neighbour role i n the i n i t i a l statement of the motive). G eventually relates to the goal of the unfolding (G#) as a semitonal lower neighbour ((^)), and the A of m. 8 may be heard to function as a passing tone over a broader 127 span ([8J). In this excerpt, then, thematic gestures (in the v io la and cello) and accompanimental elements (in the two viol ins) are unified through their common function of unfolding intervals of the f i rs t con-stituent in the three-chord tonicizing progression. Measures 44-58 of f ifth quartet's opening movement are the focus of Ex. 3.5, which i l lus trates a mid-level unfolding of the outer f i f t h of the referential element, and one of comparable temporal dimension of the root to th ird of that same referential element. Foreground unfoldings are also an important feature of these measures as they contribute components of the aforementioned mid-level third-unfolding. The referential f i f t h of this thematic section, D-A, i s art iculated immediately and d irect ly through foreground l inear unfoldings at(T} (violins I and II). The f ina l descending portions of these i n i t i a l motives (^ 2)) arrive on Bb, the second constituent in the mid-level A-D ascent ((^)). In the f i r s t repetit ion of the theme i n the two v io l ins (£4)), the f i r s t note (Eb=D#) of the ascent to A functions within the mid-level unfolding of D-F (summarized at and the last note of the descent from A (i.e., B) functions in the mid-level prolongational progression from A to D (^}). The third thematic statement in the two vio l ins ((7}) begins with F (or E#), which contributes to the D-F unfolding. The second viol in's descent ends on C#—the penultimate constituent in the mid-level A-D unfolding—and the f i r s t v io l in 's descent provides the culminating D of that same mid-level event. Fore-ground unfoldings are also heard in the viola and cello and, like those of the violins, contribute to the mid-level prolongational progressions of D to F and A to D, as shown at (8) and f^ T). 128 Although constituents of the mid-level prolongational progres-sion of A to D ((3^) are rei n f o r c e d by the foreground unfoldings d i s -cussed above, those constituents are more simply articulated as r e i t e r -ated and sustained pitches i n the v i o l a and c e l l o i n mm. 45-55. The r e f e r e n t i a l D-A f i f t h , l i n e a r i z e d at the foreground i n the opening measures of the excerpt, i s projected as an ascending A-D fourth over the span of the entire third-theme section, thereby imparting coherence to that section. At the goal of the mid-level A-D unfolding, m. 55, the original D-A f i f t h i s once again prolonged through reiterated foreground unfoldings ( ( ^ ) ) , here against an underlying b2-#4 d i s p o s i t i o n p a i r , prolonged through the same reiterative means ((^) ). The dual prolonga-tion, summarized at (^), provides a degree of tension i n advance of the "development" section, which commences i n m. 59. In the f i n a l example of mid-level l i n e a r unfolding (as i n the one just examined), the unfolded interval does not subsequently resolve to a more structural element; i t i s , rather, i t s e l f a structural event— specifically, the outer interval of the referential element of the large A section i n the sixth quartet's opening movement. The unfolded f i f t h , between scale degrees 5 and 1, i s indicated at (T) i n Ex. 3.6. Although, at the surface, the f i f t h i s f i l l e d i n chromatically, metric placement and durational emphasis invite reference to the stemmed pitches as more structural within the overall texture. The unfolded f i f t h i s shown at (^ ) i n i t s most skeletal form which, as suggested by the symbol at (S), i s phrygian in structure—a feature which promotes descending motion. In that phrygian (and lydian) constructs are here conceived as inher-129 e n t l y d i r e c t e d , t h i s p a r t i c u l a r p r o l o n g a t i o n a l p r o g r e s s i o n i s analogous t o t r a d i t i o n a l u n f o l d i n g s , i n which i n h e r e n t d i r e c t e d n e s s d e r i v e s from the major and minor s c a l e s . T h i s m i d - l e v e l phrygian f i f t h i s d u p l i c a t e d e l s e w h e r e a t t h e f o r e g r o u n d , a s a l l u d e d t o i n C h a p t e r I I (see, f o r i n s t a n c e , Exx. 2.24 and 2.25) and as w i l l be f u r t h e r documented i n t h e p r e s e n t c h a p t e r , a l o n g w i t h d e t a i l s o f t h e u p p e r p a r t s i n t h i s e x c e r p t . ^ P r o l o n g a t i o n through o s c i l l a t i o n  and/or r e i t e r a t i o n Many passages i n Bartok's music f e a t u r e constant recurrence o f a p a r t i c u l a r r e f e r e n t i a l element, e i t h e r through s i m p l e r e i t e r a t i o n o r i n o s c i l l a t i o n w i t h a n o t h e r , s u b o r d i n a t e , e l e ment. I t was n o t e d a t t h e b e g i n n i n g o f t h e c h a p t e r t h a t f o r e g r o u n d p a t t e r n s o f d e p a r t u r e and r e t u r n occur more o f t e n i n suc c e s s i o n than s i n g l y . I n f a c t , when con-catenated, these foreground p a t t e r n s y i e l d a l a r g e r p a t t e r n o f o s c i l l a -t i o n . When, f o r example, the p a t t e r n X-Y-X ove r l a p s w i t h another such p a t t e r n and t h i s process i s continued, an o s c i l l a t i o n occurs: X-Y-X + X-Y-X + X-Y-X = X-Y-X-Y-X-Y-X O s c i l l a t i o n i s s i m u l a t e d where a c o n t r a s t i n g d e p a r t u r e e l e m e n t i s p e r i o d i c a l l y a r t i c u l a t e d o v e r a s t e a d y , r e i t e r a t e d e l e m e n t . The •^These l o w e r - l e v e l , p h r y g i a n - f i f t h progressions a r e heard over r e s t r i c -t e d spans which enhance t h e i r d i r e c t i v e q u a l i t y , and t h i s i n t u r n e s t a b -l i s h e s a "pr e c e d e n t " f o r s u c h p a t t e r n s o f i n h e r e n t l y d i r e c t e d m o t i o n o v e r b r o a d e r l e v e l s . T h i s n o t i o n o f f o r e g r o u n d p r e c e d e n t and l a r g e -s c a l e d u p l i c a t i o n w i l l be d e a l t w i t h i n the t h i r d major s e c t i o n o f t h i s chapter, on l a r g e - s c a l e p r o l o n g a t i o n . 130 departure-return pattern, although i r r e g u l a r , i s nontheless i d e n t i -fiable : X-X-X-X-X-X-X-X-X-X-X-X-X-X + Y Y Y Y = X-X-X-Y-X-X-X-Y-X-Y-X-X-Y-X The condition of " i m p l i c a t i o n without l i t e r a l presence"—a primary criterion for conventionally defined p r o l o n g a t i o n — i s obviously inap-p l i c a b l e i n these processes. And, yet, the o v e r a l l e f f e c t of t r a d i -t i o n a l p r o l o n g a t i o n — t h e extension of a span over which a p a r t i c u l a r element i s sensed as f o c a l — i s achieved, a l b e i t through less conven-t i o n a l means. In l i g h t of t h i s circumstance, can the processes of oscillation and reiteration be properly regarded as prolongational? Craig Ayrey s comments on Roy Travis's attempt to elucidate the means of prolonging a "dissonant tonic sonority" i n Stravinsky's Rite of  Spring address the v a l i d i t y of ascribing prolongational significance to similar basic processes i n general. Ayrey asserts that . . . i t [the dissonant tonic sonority] can be effectively prolonged o n l y by the most elementary t e c h n i q u e s — u s u a l l y a complete neighbouring-note progression or a passing note between two forms of the dissonant " tonic' which must also redefine i t s e l f perpetually by saturating the texture with i t s particular sound. If this i s the case, then (as f o r t o n a l i t y which i s not determined only by the omnipresence of t r i a d i c forms) an identification of prolongational techniques i s required, and although the Schenkerian concepts of prolongation and structural repetition remain, the techniques need not resemble Schenkerian models. Arnold Whittall expresses a similar view in connection with prolongation of "dissonant" structures: "Craig Ayrey, "Berg's "Scheideweg': Analytical Issues," Music Analysis 1/2 (July, 1982): 196. 131 ". . . s t r u c t u r a l d i f f e r e n t i a t i o n of dissonance i n the absence of consonance may only be possible i f degrees of prominence are very strongly asserted by contrasts between the repetition or sustaining  of certain chords and their s ornamental' extension."17 Each author identifies constant, l i t e r a l restatement of a non-traditional element as perhaps the only means of extending the span over which such an element i s to be heard as contextually primary, p a r t i c -ularly i n the absence of dissonance c r i t e r i a associated with the major-minor system. The processes of r e i t e r a t i o n and o s c i l l a t i o n , while indeed basic, are considered i n this study to be v i t a l factors of mid-level prolongation i n Bartok's musical language. Often, for example, a stream of activity, consisting of immediately apprehensible patterns of reiteration and o s c i l l a t i o n involving a particular referential element, provides a degree of c e n t r i c orientation--a sense of contextual "stability." Over this clearly established stratum, a second stream of a c t i v i t y may emerge as supportive of the r e f e r e n t i a l element i n the underlying stratum or i n contrast to i t . * 8 This second stratum may i t s e l f take the form of an o s c i l l a t i o n or reiteration pattern, i n which case the overall texture w i l l consist of two contrasting, but hierarchi-cally equal components; or, i t may take the form of a thematic gesture, i n which case the o v e r a l l texture may be characterized as a theme and (oscillatory) accompaniment. I t was explained e a r l i e r that mid-level o s c i l l a t i o n may be Arnold W h i t t a l l , "Music Analysis as Human Science?," Music Analysis 1/1 (March, 1982): 44. (Emphasis mine.) 1 Q This, i n fact, i s the tonal-textural configuration which, i n Bartok's music i s often cited as an expression of bitonality. 132 achieved through the concatenation of foreground departure-return pat-terns. The departure element i n these foreground patterns may or may not be inherently implicative of the primary element which frames i t . Implication i s , for example, e x p l i c i t and the prolongation reinforced where the subordinate component i s a conventional dominant structure. Moreover, I r e f e r r e d i n Chapter II to Bartok's l y d i a n and phrygian orderings of the diatonic collection as "tonal analogues." Where those patterns are heard as a basis for l i n e a r organization, r e s o l u t i o n s of scale degrees #4 to 5 and b2 to 1 were said to be inherently directed, their tonicizing potential deriving from the semitonal departure from a whole-tone succession. If the departure element comprises such "active" degrees, i t may be said to be inherently directed toward, and implica-tive of, the element comprised of notes of resolution. Prolongation i s thus effected by a degree of contextual f u n c t i o n a l i t y d i f f e r e n t from, but analogous to, the characterization of dissonance treatment i n the major-minor system. Even i n those patterns where the departure element lacks the a n a l o g i c a l l y d i r e c t i v e q u a l i t y , discussed above, a sense of contextual implication i s generated through successive statements of the pattern. The categories of oscillatory prolongation given below include patterns with inherently implicative departure components and those of nonimplicative status. O s c i l l a t i o n of conventional dominant and tonic. Examples 2.24 and 2.25 present analogous passages from the A and A' sections of the sixth quartet's f i r s t movement. Each passage opens with a referential triad, prolonged through o s c i l l a t i o n with i t s conventional dominant. In 133 Ex. 2.24, the oscillatory prolongation spans mm. 81-94, at which point a descending c i r c l e of f i f t h s begins (as explained i n Chapter II). Until the f i n a l r e s o l u t i o n to I (m. 94), scale degree 5 i s held as a pedal i n the bass, tonic elements i n the o s c i l l a t i o n occurring i n second inver-sion, preventing a sense of f i n a l i t y . The large sharp and f l a t signs i n d i c a t e connection of dominant and t o n i c roots through lydian and Phrygian directed linear motion. As the reduction and verticalization of functional harmonies on system (b) reveal, the o s c i l l a t i o n begins at a rhythm of one harmony per bar. Measures 85-89 consist of a prolonga-tion of V, and mm. 90-92 an extended tonic, thereby slowing the o s c i l l a -t i o n pattern. The o r i g i n a l harmonic rhythm of one per bar returns at the end of the oscillatory prolongation as a f i n a l V-I occupies mm. 93-94, the descending phrygian f i f t h once again connecting the root of V to that of I. Variation i n harmonic rhythm within the o s c i l l a t i o n i s thus one important element of contrast i n t h i s otherwise straightforward prolongation; subtle changes i n i n t e r v a l l i c composition and i n upper-voice configuration of the tonic and dominant components are other such elements. The o s c i l l a t o r y prolongation i n Ex. 2.25 occurs i n mm. 312-320 and features a more consistent harmonic rhythm (one harmony per bar) than i t s corresponding passage i n the A section. It also involves more root progressions, the dominant pedal sustained for only the f i r s t five of i t s nine bars. This s h i f t midway through the prolongation—from o s c i l l a t i o n above a pedal to root-position o s c i l l a t i o n — i s a factor of contrast, given the unyielding harmonic rhythm, cited above. Interest 134 in this basic osc i l la tory prolongation i s further achieved through changing intervallic composition of tonic and dominant elements and the outer-part contrary motion beginning in m. 314. With respect to this contrary motion, note in particular the one-bar lydian connections of the roots of V and I in the cel lo of mm. 316-320 ((l2) ) in counterpoint with the single, rhythmically elongated, descending phrygian f i f th in the f irst viol in of mm. 316-319 ((^ }). This rhythmic counterpoint is a third element of mobility in what would otherwise be a simple and static alternation of harmonic events. A final example of conventional dominant and tonic harmonies in osc i l l a t ion is taken from the second movement of the f i f t h quartet, spec i f ica l ly mm. 26-29. Here the conventional harmonies are more implicit than in the previous two excerpts, but the characterization of their conventional function is , I think, justified in the analysis. The excerpt in question is given i n Ex. 3.7, where system (a) identif ies •7 unfoldings of V' and I, and system (b) verticalizes them. Oscillation of elaborative and referential elements. In this classification of oscillatory prolongation, the departure element of the foreground pattern is not inherently implicative, although i t acquires contextual implication through frequency of association with the refer-ential element as the oscillation continues. In the f irst excerpt, mm. 76-83 of the th ird quartet's Prima parte, the recurrent elaborative element is a verticality of four PCs, stemmed upward and beamed at (T) in Ex. 3.8. The referential element prolonged through the oscillation is stemmed downward and beamed at f^). References f^ ) and fT) indicate 135 lower-level prolongations of the elaborative element, the f i r s t through a voice exchange, and the second through an embellishing pattern.^ 9 The oscillatory prolongation i n mm. 196-213 of the fourth quar-tet s f i n a l movement (Ex. 3.9) takes place i n the context of a thematic element, f i r s t heard i n the second v i o l i n (mm. 196ff.), then an octave higher i n the f i r s t v i o l i n (mm. 202ff.), and, f i n a l l y , transposed i n the cello (mm. 206ff.). The thematic structure supports a prolonged F-minor t r i a d i n i t s f i r s t two statements ((£)) and an Ab-minor t r i a d i n i t s t h i r d statement ((2)), the o s c i l l a t o r y elaboration comprised of upper and lower neighbour notes, u l t i m a t e l y providing encirclement of the triads' lower thirds. References (3) and identify the f i r s t elabo-rative neighbour notes i n the second violin's oscillatory prolongation; each of the other thematic statements begins i n the same way. Three details i n this excerpt deserve comment. Fi r s t , a lower-level prolongation of a G-minor t r i a d at Qp functions as a large-scale upper neighbour to the mid-level prolonged F-minor triad, projecting one component of the foreground encirclement pattern over a broader span. Second, the s i g n i f i c a n c e of the unfolded Ab-Eb f i f t h (G#-D# i n the score), r e i t e r a t e d at (1p and (T), l i e s i n i t s foreshadowing of the oscillatory, elaborative prolongation of the Ab-minor tr i a d i n the cello beginning i n m. 206, this relationship indicated by the dotted beam at (Q, which l i n k s these two events. And t h i r d , the sustained B i n the cello (mm. 196-205) and viola (mm. 196-201) i s another element of fore-shadowing: that PC (enharmonically spelled) becomes i n mm. 206ff. the 19 See Glossary for definition of embellishing pattern. 136 on third of the prolonged Ab-minor triad. In mm. 47-55 of the second quartet's f i n a l movement, the upper and lower fourths of a four-note, homointervallic v e r t i c a l i t y are pro-longed independently through o s c i l l a t i o n with elaborative components which, at a broader l e v e l , y i e l d embellishing patterns i n contrary motion and linear unfoldings of the two fourth-components of the pas-sage's r e f e r e n t i a l element. References (T) and (2) i n Ex. 3.10 beam recurrences of the two fourths of the referential verticality. Refer-ence i d e n t i f i e s elaborative departure components c o n s i s t i n g of a single v e r t i c a l i t y , ^ points out a double-neighbour encirclement, and f^ ) identifies those departure elements which may be characterized as lower-level embellishing patterns. The oscillatory prolongation i n this excerpt thus sustains v i t a l i t y through v a r i e t y i n the structure and position of the departure element. Because of the immediacy of o s c i l l a t i o n , foreground departure elements may be heard as adjacencies at a higher level and, because they constantly change position, two larger patterns are created i n the upper tonal-textural stratum (in the violins) and two comparable patterns i n the lower stratum (the v i o l a and c e l l o ) . These are represented on system (b) of Ex. 3.10. The f i r s t pattern i n each stratum i s the ^•UA1 though B i s , from the outset of t h i s excerpt, supported by E — suggesting o r i e n t a t i o n to E — t h i s f i f t h marks the completion of the "white-note" d i a t o n i c c o l l e c t i o n i n i t i a t e d by sustained pitches i n m. 151. This d e t a i l was discussed i n connection with Ex. 2.29, at which point i t was noted that the f i n a l PC required to complete the diatonic c o l l e c t i o n i s B. In the excerpt under discussion (Ex. 3.9), B i s the f i n a l PC of that collection to remain sustained, u n t i l , as noted, i t i s absorbed into the elaborated Ab-minor triad. 137 larger-level embellishing pattern alluded to above; this pattern ((&)) occurs in contrary motion in the the upper and lower strata. The larger patterns at (7} are the aforementioned mid-level linear unfoldings, also composed of foreground departure patterns considered as higher-level adjacencies. In the f ina l example of this c lass i f i cat ion of osc i l la tory prolongation, the elaborative departure element is once again an embel-l ishing pattern, reiterated to effect a mid-level prolongation. The excerpt in question (Ex. 3.11) i s mm. 60-69 of the second quartet's opening movement. Although the concept of embellishing pattern i s itself straightforward, in this particular excerpt i t appears in a more complex, but typ ica l ly Bartdkian, guise: i t appears in each strand of the polyphonic fabric , embellishing a different member of a single referential element. In this way, a foreground, elaborative figure generates a texture which i s more complex rhythmically, but unified tonally (because each prolonged PC i s a member of the single, t r iad ic referential element). The F# major-minor triad at the beginning of m. 61 is the refer-ent ial element whose root and f i f t h are subsequently prolonged as a vertical f i fth (as at (T) ); the fifth is also prolonged independently as at f^ 2). System (b) exhibits the higher-level arpeggiations of the referential triad which result from the independent foreground prolonga-tions. References (3), and ^ expose relations in each instrumental part between the referential triad as expressed vertically in m. 61 and as articulated independently at the end of the prolongation 138 (m.. 69). The f i r s t violin's C#, for example, undergoes octave transfer and, through large-scale arpeggiation, returns to the original octave level in m. 69 ((^))/ before descending through a foreground arpeggia-tion of the referential triad. The second violin's opening A# is super-seded by A at the end of the prolongation, articulating a large-scale inflection of the triad's third from major to minor ((^)). The v e r t i -cally expressed minor triad in the viola of m. 61 is arpeggiated in that instrument in m. 69 (($)), and the root of the triad, occurring i n the cello of m. 61, is shifted down an octave in m. 63, where i t remains for the balance of the prolongation ([6}). ted in Chapter II, disposition elements may occur in a variety of forms, from single PCs to more extensive v e r t i c a l i t i e s , the common property being semitonal relation to the referential element or to one of i t s constituents. If there is a substantial underlying diatonic basis, such disposition elements may have an inherent tendency of resolution, analo-gous to that which characterizes certain elements in the major-minor system (e.g., the leading-tone and fourth scale degree when the latter i s heard as the seventh over the dominant). Where no such underlying basis may be inferred, disposition elements are accorded such tendency retrospectively by virtue of semitonal proximity to a referential element. Both properties are found in the reiteration of foreground Retrospection and disposition-note resolutions were discussed i n Chapter II under "Contextual tonicizing agents" in the section on Non-conventional Tonicizing Progressions. Oscillation of disposition and referential elements. As sugges-139 oscillatory departure-return patterns i n the following excerpts. The f i r s t i s a simple example from the opening movement of the f i f t h quartet. Each note of a C minor-seventh chord i s prolonged inde-pendently i n mm. 24-29 (Ex. 3.12) through o s c i l l a t i o n with at least one disposition note. Scale-degree indications are given at the beginning of each prolonged chord-tone (see beamed segments i n the example). Reference collects a l l disposition notes into a single six-PC v e r t i -c a l i t y , showing the r e s o l u t i o n of each member to a component of the referential chord. [Note that B functions as scale degree 7 r i s i n g to C and as b l (Cb) descending to Bb, the seventh of the r e f e r e n t i a l chord; context demonstrates t h i s dual function.] While there i s no e x p l i c i t scalar reference according to which d i s p o s i t i o n notes i n t h i s excerpt may be ascribed inherent tendency to resolve the way they do, the ter-tian structure of the referential element i s a suitable, indeed recog-nizable, basis against which "nonharmonic" notes may be inferred. In mm. 65-80 of the sixth quartet's opening movement, as i n the excerpt just studied, oscillatory prolongation of a referential element occurs by way of rhythmically independent prolongations of i t s individ-ual components (see Ex. 3.1). Prolonged PCs are stemmed and connected with dotted beams on system (a): f o r example, C# and A i n the f i r s t v i o l i n , A i n the second v i o l i n , A and E i n the c e l l o , and C# and A i n the v i o l a from m. 75. The departure element i n each case i s a d i s p o s i -tion note but, as i n the previous excerpt, beyond interval l i e proximity, there i s no inherent basis for "expecting" i t s semitonal resolution. As the o s c i l l a t i o n proceeds, each w i l l , of course, accrue a sense of con-textual tendency and association through frequency of occurrence. 140 T h i s movement's primary r e f e r e n t i a l t o n i c i s D (major-minor) and i t s secondary r e f e r e n t i a l t o n i c F (major). The independently prolonged PCs i n t h i s passage are c o n s t i t u e n t s of an u n d e r l y i n g dominant t r i a d i n D, as suggested by the roman-numeral a n a l y s i s below system (b) and the v e r t i c a l i z e d harmony a t p^. Through enharmonic r e i n t e r p r e t a t i o n o f C# ( s c a l e d e gree 7 i n D) as Db (b6 i n F ) , and t h r o u g h a r t i c u l a t i o n o f B i n t h e c e l l o a t m. 80, t h e r e s o l u t i o n o f D:V i s d e n i e d and t o n a l m o t i o n r e o r i e n t e d t o F ( ( 3 } h I n t h i s example, t h e n , t h e e l e m e n t p r o l o n g e d through o s c i l l a t i o n i s i t s e l f subordinate t o a more pr i m a r y r e f e r e n t i a l e l e m e n t , whose e x p l i c i t a r r i v a l i s , as n o t e d above, d e n i e d a t t h i s j u n c t u r e . The c l o s i n g measures o f t h e B s e c t i o n i n t h e f o u r t h q u a r t e t ' s f i n a l movement (Ex. 3.13) demonstrate a s i m i l a r s i t u a t i o n — o n e i n which c e r t a i n of the prolonged components are themselves subordinate t o a more s t r u c t u r a l element, t o which they l a t e r r e s o l v e . I n a d d i t i o n t o these p r o l o n g e d s u b o r d i n a t e e l e m e n t s , t h e p r i m a r y r e f e r e n t i a l PC i s i t s e l f prolonged, as w i l l be explained. The e x c e r p t i n q u e s t i o n , mm. 214-237, f e a t u r e s t e c h n i q u e s o f p r o l o n g a t i o n o t h e r t h a n t h e d i s p o s i t i o n - n o t e o s c i l l a t i o n under immediate d i s c u s s i o n ; these w i l l a l s o r e c e i v e b r i e f a t t e n t i o n . The m o t i v e a t (T) i s used i n mm. 183-195 o f t h e same movement (see Ex. 2.42). I t i s , i n f a c t , a c h a r a c t e r i s t i c f i g u r e i n t h e B s e c t i o n , i n c o n t r a s t t o the A section's o s c i l l a t i o n - r e i t e r a t i o n s t r u c -t u r e i n v o l v i n g t h e b2-#4 d i s p o s i t i o n p a i r , d i s c u s s e d l a t e r i n t h i s chapter. The motive d e f i n e s a descent of a minor second, suggested a t 141 Q) and (|) ( Ex. 3.13), of which the f i r s t note may be heard as an appoggiatura to the second. When the motive i s reiterated, an osci l la-t ion of a disposition note and a primary note results. In these instances, however, the primary note is subordinate at a higher level of structure, as i t ultimately resolves to the B section's primary referen-t i a l element. Thus, oscillations achieved through rei terat ion of the motive prolong scale degree 2 ((4 )^ with' respect to the referential G-Eb third in m. 237, and scale degree b6 ((5^). Two additional factors of prolongation in this excerpt are worthy of note. First , the thematic element, responsible for prolonged triads in the measures preceding this excerpt (Ex. 3.9), returns in the v io l ins in mm. 220-227 (Ex. 3.13). Here, the elaborated element i s a Bb-minor tr iad ((6}h the root and third of which function at a higher level as lower neighbours to the root and third of the C-minor triadic referential element of the entire B section, arr iv ing f i r s t in m. 227 ( (^ }). The second deta i l involves prolongation of the B section's primary referential element subsequent to its "early" arrival in m. 227 (early in the sense that, as explained above, disposition notes to that referential element undergo prolongation until m. 236, resolving only in m. 237). Prolongation of the primary C-Eb third in mm. 227-237 involves two elements: a simple but sporadically articulated scale-degree 7 ( f^) , and two successive mid-level embellishing patterns ( ^ ) and (H)) ). The s impl ic i ty of the technique of osc i l la t ion i s i n this excerpt offset by the rhythmic independence of individual prolongations and the tonal independence resulting from the simultaneous prolongation of tonicizing elements against that of the referential element itself. 142 Measures 141-157 of the s i x t h quartet's opening movement (Ex. 3.6) come at the end of the A section of the large ABA form and prolong, through mid-level unfolding and o s c i l l a t i o n of foreground disposition-note resolutions, an F-major triad, the movement's secondary referential tonic, which made i t s f i r s t appearance i n m. 81 (the end of Ex. 3.1). The mid-level phrygian unfolding of the outer f i f t h of the referential F-triad (£p i n Ex. 3.6, discussed earlier) may be understood to provide a functional d i a t o n i c basis f o r the inference of foreground d i r e c t e d resolutions of b6 to 5 and b2 to 1, while the foreground lydian ascent i n the v i o l i n s i n mm. 153-154 establishes a s i m i l a r basis f o r r e s o l u -ti o n s of 7 to 1 and #4 to 5. The f i n a l thirty-nine bars of the sixth quartet's f i r s t movement (Ex. 3.14) were re f e r r e d to i n Chapter II as to a large-scale, conven-tion a l l y functional I-IV-V-I progression. Here, the progression may be examined for techniques of prolongation of the main harmonic components of that broadly articulated progression. In mm. 355-362, for example, the two violins prolong the root and f i f t h of the tonic D t r i a d through o s c i l l a t i o n with p a r t i c u l a r d i s p o s i t i o n notes—scale degrees 7 and b2 t o n i c i z i n g the former {(l)) and #4 and b6 t o n i c i z i n g the l a t t e r (£2)). The minor and major third of the t r i a d are simply sustained i n the two lower instruments. Although the remaining harmonies i n the large-scale functional progression employ different means of prolongation, these principles are f a m i l i a r as they were discussed e a r l i e r ; i n order to understand t h i s closing section more f u l l y , the remainder of the progression, with i t s 143 individual means of prolongation, w i l l be discussed briefly. Apart from the sustaining of elements of IV i n the v i o l i n s and c e l l o , two simple factors of prolongation are relevant: the embellishing pattern at (T), and the foreground motion within a chord at (4} (the latter followed by a foreground arpeggiation of IV). The prolongation of V i s i n two parts, the f i r s t of which occupies mm. 375-381 with an o s c i l l a t i o n between a conventional, cadential tonic | [whose upper notes are i n d i -cated with a diagonal slash ((5))] and a root-position V; components of each of these two harmonies are not always i n ver t i c a l alignment. The second part spans mm. 382-388, i n which upper parts of a third-inversion dominant-seventh chord are prolonged through foreground unfoldings as indicated graphically on system (a). Reference (fp points out the domi-nant's change i n position resulting from these superimposed unfoldings. The f i r s t one hundred and four measures of the large A section i n the fourth quartet's f i n a l movement are the focus of the next three examples, which i l l u s t r a t e consistent use of prolongation through o s c i l -l a t i o n of d i s p o s i t i o n and r e f e r e n t i a l elements. The movement begins with an unsettled v e r t i c a l i t y consisting of a C-G f i f t h , complicated by the addition of Db and F# ((T) i n Ex. 3.15). Janos Karpati regards this type of structure as a "mistuned f i f t h , a characterization which, i n my view, f a i l s to account f o r the basis of i t s unstable q u a l i t y . As I w i l l demonstrate, this opening sets into immediate and harsh opposition Janos Karpati, Bartok's S t r i n g Quartets, (Budapest: Corvina Press, 1967), pp. 143ff. 144 (through superposition) two functionally distinct components: a referen-t i a l f i f t h (C-G) and an inherently directed disposition pair (Db-F#). This d i s t i n c t i o n begins to emerge a f t e r m. 11 and e s p e c i a l l y a f t e r m. 14. Beginning i n m. 12 the two components are separated i n timbre, the r e f e r e n t i a l f i f t h r e i t e r a t e d i n the v i o l a , i n occasional o s c i l l a t i o n with b6, another disposition note ((?))» and the disposition p a i r i n o s c i l l a t i o n with the r e f e r e n t i a l f i f t h i n the c e l l o (^3)). In spite of this instrumental division, the two components are at certain points v e r t i c a l l y aligned as they were i n the beginning (e.g., ( J } ) . The disposition-note r e l a t i o n of b2-#4 to 1-5 i s summarized a t f5 Continued interaction between these two components establishes a tonal-textural stratum over which a thematic element emerges i n the violins, beginning i n m. 15. As t h i s theme was the subject of Ex. 2.22 i n the previous chapter, i t need only be said that the theme i s supportive of the underlying tonal basis i n i t s implication of the referential f i f t h through linear articulation of the b2-#4 disposition pair (of which #4 i s heard to resolve e x p l i c i t l y i n the theme i t s e l f ) . Reference details the relation of the theme to the underlying reiterated referen-t i a l f i f t h and disposition pair. As noted above, i n the o s c i l l a t i o n - r e i t e r a t i o n stratum ( v i o l a and cello) articulation of the b2-#4 disposition pair always occurs i n rhythmic alignment with the C-G f i f t h i n the viola, obviating e x p l i c i t linear resolution of the former into the latter. This linear resolution i s , however, expressed unequivocally i n mm. 29 and 30, where the dispo-s i t i o n p a i r i s followed by the C-G f i f t h i n the same part (\^)). Com-parison of those junctures, marked with vertical arrows, with that at 145 f^ 4J reveals the eighth-note rest which accompanies the C-G fifth in the later occurrences, facilitating explicit and uncomplicated punctuation of the referential f i f t h before a variation of the v io l ins ' theme i s presented. It is interesting that tonal clarification in the oscillation-reiteration stratum, just referred to, initiates a tonally more explicit thematic variation, beginning in m. 31. This tonal decisiveness is due to the fact that, as indicated at (8), l inear resolutions of both b2-l and #4-5 are expl ic i t . The thematic version with part ia l resolution returns in m. 37, but comparison of i t s concluding pitch with that of the i n i t i a l statement of the theme in mm. 15-18 reveals a difference: spec i f ica l ly , the theme ends in m. 40 with D# instead of F#. Although apparently of only minor consequence, this turns out to have important tonal implications regarding the secondary referential element soon to emerge. F# was, of course, understood in the in i t ia l statement as #4, resolving to 5 of the C-G primary referential f i f t h . In this later statement, D# functions analogously as #4 i n A ((9^), and occurs in m. 44 with Bb (i.e., b2 in A), both of which are in vertical alignment with element, the A-E fifth, superimposed with i ts b2-#4 disposition pair, marks the secondary referential element of the A section. It w i l l be noted that a C-G f i f t h continues to be reiterated along with the A-E secondary referential f i f th but this wi l l be discussed in the context of prolongation in the measures following arr iva l of the A-E f i f t h , the subject of the next example. This transposed referential 146 Example 3.16 begins i n m. 47 and reveals a more complex st r u c -ture, incorporating two r e f e r e n t i a l elements. One i s the C-G f i f t h , which w i l l be shown to be subordinate i n these measures (although i t i s primary with respect to the movement as a whole). The other i s the A-E f i f t h , which i s superior i n these measures but hierarchically inferior i n terms of the large-scale tonal scheme. Bartok uses an i n t e r e s t i n g technique of prolongation to e s t a b l i s h the A-E f i f t h as contextually superior to the C-G f i f t h i n this section. F i r s t , the A-E f i f t h begins with i t s b2-#4 d i s p o s i t i o n p a i r (noted at (nj) i n Ex. 3.15) and, a l -though that t o n i c i z i n g agent i s not used i n o s c i l l a t i o n with the A-E f i f t h (as i t was with the C-G f i f t h at the outset), the b6 d i s p o s i t i o n note i s heard to o s c i l l a t e with scale degree 5 ((T) i n Ex. 3.16). This disposition-note t o n i c i z a t i o n of the A-E f i f t h projects i t as contex-tually primary for these measures. The C-G f i f t h , by comparison, occurs here i n o s c i l l a t i o n with the less implicative whole-tone upper-neighbour D-A f i f t h ( { ^ ) - The p a r a l l e l r e s o l u t i o n of D-A to C'-G, the less frequent reiteration of the C-G f i f t h as compared to the A-E f i f t h , and the lower r e g i s t r a l p o s i t i o n of the A-E f i f t h are a d d i t i o n a l f a c t o r s which tend to subordinate the C-G f i f t h . Not only i s the o s c i l l a t i o n stratum more complex after m. 47— through i t s independent prolongation of the A-E and C-G f i f t h s i n the cello and v i o l a — b u t the thematic element i n the vi o l i n s i s correspond-ingly more complex. Here, the linear structure of the theme i s extended so as to imply resolutions to three d i f f e r e n t f i f t h s , beamed at f3). These multiple implications are based on the pattern established by the i n i t i a l theme, mm. 15-16, where the C-G f i f t h was easily inferred from 147 t h e s u c c e s s i o n C#-D#-F#-G and r e i n f o r c e d by t h e o s c i l l a t i o n s t r a t u m . Here, t h e l o w e r f o u r n o t e s o f t h e e x t e n d e d theme a r e e x a c t l y t h o s e o f the o r i g i n a l and thus i m p l y a C-G f i f t h , r e i n f o r c e d here by t h e secon-d a r y C-G f i f t h r e i t e r a t e d i n t h e v i o l a . The upper f o u r n o t e s o f t h e ex t e n d e d theme G-A-B#-C# (the G i s " p i v o t a l " a s i t i s common t o b o t h t e t r a c h o r d s ) i s an e x a c t t r a n s p o s i t i o n o f t h e o r i g i n a l theme and t h u s i m p l i e s a c o r r e s p o n d i n g F#-C# f i f t h , t h e l a t t e r e x p l i c i t i n t h i s e n -l a r g e d theme because o f t h e o c c u r r e n c e o f F# i n t h e l o w e r p a r t o f t h e theme. I n t h a t t h e A-E f i f t h i s c o n t e x t u a l l y p rimary f o r t h i s segment, t h e A i n t h e e x t e n d e d theme i s p o t e n t i a l l y r e f e r e n t i a l . A l t h o u g h i t s f i f t h , E, i s n o t p r e s e n t i n t h a t theme, i t s l o w e r d i s p o s i t i o n n o t e D#(=#4) i s p r e s e n t and r e p r e s e n t s t h e r e v e r s e p a t t e r n o f t h e i n i t i a l theme. That i s , i n t h e o r i g i n a l , t h e f i f t h was p r e s e n t and t h e r o o t i m p l i e d by i t s upper d i s p o s i t i o n note; here, the r o o t i s present and the f i f t h i m p l i e d by i t s l o w e r d i s p o s i t i o n n o t e (hence t h e E i n s q u a r e b r a c k e t s a t (3}). I t i s s i g n i f i c a n t t h a t t h e A-E and C-G f i f t h s — e x p l i c i t i n the lower instruments as p r i m a r y and secondary elements i n t h i s s e g m e n t — a r e among t h e t h r e e i m p l i e d . I m p l i c a t i o n o f an F#-C# f i f t h i s i m p o r t a n t i n l i g h t o f l a t e r e v e n t s ( s p e c i f i c a l l y a t m. 76, a n a l y z e d i n Ex. 3.17). A f t e r the C-G f i f t h i s dropped from the o s c i l l a t i o n s t r a t u m (m. 56), the the A-E f i f t h i s e l a b o r a t e d i n the same way t h a t the C-G f i f t h was s u b o r d i n a t e d t o t h e A-E f i f t h i n mm. 4 3 f f . S p e c i f i c a l l y , m. 58 i n i t i a t e s an o s c i l l a t o r y p r o l o n g a t i o n o f t h e A-E f i f t h i n w h i c h t h e departure elements are not d i s p o s i t i o n notes but, r a t h e r , f o u r t h - r e l a t e d 148 f i f t h - c h o r d s 2 3 ((4}) and whole-tone neighbours ( ( ^ ) . Measures 68-75 comprise an octave transfer of the A-E f i f t h ((6)) and a f i n a l descend-ing motion back to the C-G f i f t h of the opening ((7))-The passage which begins with t h i s ostensible return to the primary C-G r e f e r e n t i a l f i f t h of the opening i s analyzed i n Ex. 3.17. As at the opening of the movement, the C-G f i f t h i s here r e i t e r a t e d i n the vio l a [fT) on systems (a) and (b)], with i t s b2-#4 disposition pair reiterated i n the cello. As noted, at (5), however,' the latter disposi-t i o n p a i r i s here notated as an F#-C# f i f t h . In fact , each f i f t h (C-G and F#-C#), when enharmonically spelled, may be heard to function as the other s b2-#4 disposition pair, as suggested at (5). E x p l i c i t articula-tion and continued prolongation of the F#-C# f i f t h i n mm. 75-102 confers meaning on the i m p l i c a t i o n of that f i f t h i n the expanded theme of mm. 56ff. (noted above i n Ex. 3.16) and confirms that f i f t h as a s t r u c t u r a l component i n the large-scale harmonic scheme of the A section, particu-l a r l y i n l i g h t of the s t r u c t u r a l l i n e a r progression back t o the C-G f i f t h i n i t i a t e d by the F#-C# f i f t h i n m. 102 (discussed i n connection with Ex. 2.37). Three additional details i n this excerpt are noteworthy. Fi r s t , while the A-E f i f t h i s connected linearly to the C-G f i f t h i n mm. 72-75 (f^ ) i n Ex. 3.16), i m p l i c a t i o n of the A-E f i f t h continues i n mm. 75-86 through recurrence of i t s b2-#4 disposition pair on systems (a) and (b)]. Second, beginning i n m. 81, the thematic component i s heard at 93 These are the v e r t i c a l i t i e s which function as whole-tone neighbours i n the prolongation of the C-G f i f t h i n i t s secondary capacity (i.e., as subordinate to the A-E f i f t h ) . 149 two d i f f e r e n t p i t c h l e v e l s i n the two v i o l i n s ( Q j h thus c o n t i n u i n g the i m p l i c a t i o n o f the C-G f i f t h , but adding comparable suggestion o f a G-D f i f t h and, thus of a l a r g e r h o m o i n t e r v a l l i c v e r t i c a l i t y , C-G-D. Such a view i s p a r t i c u l a r l y s i g n i f i c a n t i n l i g h t o f the extended h o m o i n t e r v a l -l i c f i f t h - v e r t i c a l i t i e s encountered a t the end of the movement, where t h e y a r t i c u l a t e a l a r g e - s c a l e " I - I V - V - I " p r o g r e s s i o n (as n o t e d i n Ex. 2.11, and as w i l l be d e m o n s t r a t e d i n Ex. 3.18 w i t h r e s p e c t t o t h e "IV" of t h i s p r o g r e s s i o n ) . And t h i r d , the f i n a l note o f themat i c statements has been shown t o have an important f u n c t i o n : i n the f i r s t statement the #4 o f the C-G f i f t h concluded the theme, and i n m. 40 the c o n c l u d i n g D# was s a i d t o be a "modulatory" d e v i c e , f u n c t i o n i n g as #4 t o the A-E f i f t h , which was t o a r r i v e some t h r e e bars l a t e r . C o n s i s t e n t l y a p p l i e d a n a l y t i c a l c r i t e r i a would thus i n t e r p r e t the E#-A# i n mm. 84 and 98 as F-A#, a b2-#4 d i s p o -s i t i o n p a i r t o an E-B f i f t h , the r e s o l u t i o n t o which i s o n l y i m p l i e d i n m. 84 ((6)), b u t e x p l i c i t i n mm. 98-101 (( ? ) ) . W i t h t h e b r i e f a r r i v a l o f t h e subdominant i n t h e o p e n i n g measures, and t h e E-B f i f t h j u s t n o t e d , a seven-note d i a t o n i c c i r c l e o f f i f t h s i s c o m p l e t e : F-C a t t h e b e g i n n i n g ; C-G, t h e p r i m a r y f i f t h ; G-D i m p l i e d w i t h C-G i n mm. 8 I f f . ; D-A used as an e l a b o r a t i v e element i n the p r o l o n g a t i o n o f both the C-G and A-E f i f t h s ; A-E as the c o n t e x t u a l l y p r i m a r y f i f t h i n mm. 43ff.; and f i n a l l y E-B j u s t p r i o r t o a r r i v a l on the F#-C# f i f t h t h a t i n i t i a t e s the t r i t o n e p r o g r e s s i o n back t o C-G t o c l o s e the A s e c t i o n . The r e l a t i o n -s h i p of the F#-C# f i f t h , w i t h i n t h i s " d i a t o n i c " s t r u c t u r e w i l l be com-mented on i n the s e c t i o n on l a r g e - s c a l e p r o l o n g a t i o n . 150 The n e x t e x c e r p t a l s o comes f r o m t h e f o u r t h q u a r t e t ' s f i n a l movement and i l l u s t r a t e s a t e c h n i q u e o f i m p l i c a t i o n f o u n d t o be o f s i g n i f i c a n c e e a r l i e r i n the movement: i m p l i c a t i o n o f the melodic i n t e r -v a l o f a p e r f e c t f i f t h t h r o u g h a b~2-#4 d i s p o s i t i o n p a i r , e x p r e s s e d l i n e a r l y i n the content of themat i c s t a t e m e n t . 2 4 Reference fT) i n Ex. 3.18 beams recurrences o f a h o m o i n t e r v a l l i c v e r t i c a l i t y o f f i f t h s , w i t h F as the l o w e s t p i t c h (the " r o o t " ) . 2 ^ Between those v e r t i c a l i t i e s a r e the m a t i c statements w h i c h — a c c o r d i n g t o the c r i t e r i a e s t a b l i s h e d a t the beginning o f the movement, i n connection w i t h the f i r s t t h e m a t i c e n t r y — i m p l y , through a b2-#4 d i s p o s i t i o n p a i r , v a r i o u s p e r f e c t f i f t h s . These i m p l i e d , l i n e a r i z e d f i f t h s a r e beamed on s y s t e m (a) and r e p r e s e n t e d v e r t i c a l l y and superimposed on system (b), each note t i e d t o one member of the r e c u r r e n t "TV". Thematic gestures i n the v i o l a and c e l l o o f mm. 324-327 are more complex as each i m p l i e s two f i f t h s (see £2) and fT)). O s c i l l a t o r y p r o l o n g a t i o n i n t h i s e x c e r p t , t h e n , i n v o l v e s a l t e r n a t i o n between h o m o i n t e r v a l l i c v e r t i c a l i t i e s — i m p l i e d through the s u p e r p o s i t i o n o f i m p l i c a t i v e t h e m a t i c s t a t e m e n t s — a n d h o m o i n t e r v a l l i c v e r t i c a l i t i e s w h i c h a r e e x p l i c i t and w h i c h c o n t a i n t h o s e e l e m e n t s i m p l i e d by t h e themati c gestures. I n t h e f i n a l example o f p r o l o n g a t i o n t h r o u g h o s c i l l a t i o n o f d i s p o s i t i o n and r e f e r e n t i a l elements, a l t e r n a t i o n i n any s i n g l e i n s t r u -2 4Examples 3.15, 3.16, and 3.17 r e v e a l e d t h i s type o f i m p l i c a t i o n over a s t r a t u m o f r e i t e r a t e d and e x p l i c i t d i s p o s i t i o n - n o t e r e s o l u t i o n s ; Ex. 3.17, i n p a r t i c u l a r , begins the s u p e r p o s i t i o n o f m u l t i p l e i m p l i c a t i o n s r e l e v a n t t o the measures under immediate d i s c u s s i o n . 2 5 T h i s F v e r t i c a l i t y i s t h e "IV" i n a l a r g e - s c a l e " I - I V - V - I " p r o g r e s -s i o n r e f e r r e d t o i n Ex 2.11. 151 mental part i s not extensive but, as the o s c i l l a t i o n pattern occurs i n i m i t a t i o n , prolongation i s effected. The excerpt i s mm. 14-32 of the second quartet's opening movement (Ex. 3.19) of which mm. 19-27 i l l u s -trate the aforementioned technique of osci l l a t i o n ; the remaining mea-sures serve to e s t a b l i s h the larger context i n which the o s c i l l a t o r y prolongation occurs. An i n t e r e s t i n g s h i f t of emphasis may be i n t e r -preted i n these measures as regards the d i s p o s i t i o n and prolonged elements. In mm. 19-23, for example, the following factors suggest the primacy of the B-F# f i f t h (and the subordinacy of the C-G f i f t h ) : the extensive arpeggiation of a B-major t r i a d i n mm. 14-18, culminating i n a durationally emphasized B i n the cello (^?)); the rhythmic emphasis of B as compared with the anacrustic C-G-C arpeggiation, which precedes each a r r i v a l of B ((?) and a l l subsequent analogous points); and the exten-sive lower-level prolongation of the B-F# f i f t h through foreground arpeggiation ((3}) and surfa c e - l e v e l motion within a chord ((J))- I n s p i t e of such support, however, the return to C at (5), (6), and espe-c i a l l y f?) suggests that mm. 19-23 prolong the C-G f i f t h as primary for the span. Reference to the score reveals that a r e s t follows these r e a r t i c u l a t i o n s of C, and that f?) and (?) mark the end of a phrase. The "cadential" C at (?) i s accompanied i n the v i o l a by a conventional 2-b3 appoggiatura resolution [Eb playing a dual role as the major third of B (i.e., D#) and as the minor t h i r d of C]. The new phrase, beginning i n mm. 23-24, opens i n the same way as the f i r s t . Here, however, prolongations of the B triad—through surface motion within the chord ((IT)) and r e i t e r a t i o n of chord-tones (£9))—are 152 more substantial and, more importantly, f a i l to return to elements of the C triad. Compare, for example, the concluding pitch of the motion at (4) with that at In mm. 23-27 the B triad takes precedence. As suggested at (H)), the B triad moves to a dominant of A, which resolves immediately (m. 28). The shift of emphasis between C and B i n the phrases of mm. 19-23 and 23-27 thus creates a large-scale PC-step motion C-B-A, the B serving at this level as a passing element ( ) • The large-scale motion of a th ird , between C and A, is replicated i n the progression from A to F# in mm. 28-32, the detai ls of which are straightforward. Simultaneous prolongation of more than one referential element Many passages in Bartok's music appear to support or articulate more than one referential element simultaneously, such passages often being characterized as "bitonal." Within a more encompassing view of tonality, the concept of bi tonal i ty i s not necessarily contradictory, for i t is conceivable that principles of tonicization and prolongation may be applied to two different referential elements at the same time. If a s t r i c t l y unified tonal structure i s to be posited, however, one reference would have to be shown to take precedence over the other. But i t i s often the case in Bartdk's music that there i s l i t t l e to suggest the primacy of one element, short of lower reg is tra l placement of one with respect to the other(s). It i s quite possible, however, that in such passages the composer i s using simultaneously prolonged referential elements in developmental, transi t ional , or episodic contexts, where hierarchization and simple perceptual separation are dubious and tonal 153 orientation ambiguous. In other passages, c r i t e r i a f o r asserting the importance of one element over the other(s) are demonstrable. The analysis of passages with simultaneously prolonged referential elements, then, involves three steps: (1) documentation of specific techniques by which m u l t i p l e r e f e r e n t i a l elements are established and prolonged, (2) explanation of the relationships between elements where a primary element i s not i d e n t i f i a b l e , and (3) s p e c i f i c a t i o n of h i e r a r c h i c a l p r i n c i p l e s where one element emerges as f o c a l . The examples which follow w i l l take these factors into account. Simultaneous o r i e n t a t i o n to several r e f e r e n t i a l elements i s apparent i n mm. 33-43 of the opening movement of the f i r s t quartet (Ex. 3.20). In one instance, b i t o n a l i t y i s i l l u s o r y , r e s u l t i n g from " r e s i -due" of one r e f e r e n t i a l element extending past the i n i t i a l stages of orientation to the next. In another instance, one of two simultaneously sounding referential elements alludes to an event which occurs later i n the piece. In each case h i e r a r c h i z a t i o n of apparently c o n f l i c t i n g referential elements i s reasonable and perceivable. C major-minor i s convincingly projected i n mm. 33-40 through a sustained and r e i t e r a t e d C-G f i f t h i n the c e l l o ( ( ^ ) and the r e i t e r -ated, unfolded f i f t h s i n the f i r s t v i o l i n (^^). A C#-minor t r i a d i s prolonged i n mm. 33-38 through successive l i n e a r connections of i t s chord-tones ( ^ ) . The roots of these two referential triads, C and C#, while suggesting a bitonal conflict, represent a point of overlap of two large-scale progressions. C i s the culmination of a mid-level progres-sion of ascending minor thirds, i l l u s t r a t e d i n Ex. 2.3, while C# i s the f i r s t harmony i n a cycle of descending f i f t h s that continues through F# 154 to B, as w i l l be explained. The issue of hierarchy does not arise, as one harmony marks the end of a formal section, the other defining the beginning of a new section, while the two overlap. Already in m. 38 the second viol in is beginning to assert an F#-major t r i a d ( ^ ) . In m. 39 the v io la joins the projection of that harmony through reiterated linear motions connecting chord-tones of the F# t r iad ((^), and in m. 40 the f i r s t v io l in's unfolded f i f ths may be heard as supportive of F# as well (^)). The ce l lo of mm. 40-41 ((?}) confirms an unequivocal orientation to F#. The function of the F# harmony is that of a conventional dominant of B, which arrives in m. 43 through the root-motion of an ascending fourth in the cello (£8)). Yet, B, as a referential harmony, is short-lived, in spite of i ts substantial approach: the next measure features an abrupt, though not completely unprepared, motion to Bb. Preparation comes from the unfolded fifths in the f irs t viol in of mm. 40-41 ((^), earlier interpreted enharmonically within the F# harmony. The beam at ^)) i l lus trates this connection, and continues at ^ p to reveal an explicit confirmation and prolonga-t ion of Bb just prior to the return of the A section. Devices of prolongation include the, by now common, unfolded fifths in the violin ( Q.2J ), foreground unfolded descending f i f ths i n the second v i o l i n ^Antokoletz views this C/C# duality as a reference to the A major-minor tonic t r iad he asserts to be primary i n the work. This assertion i s , like David Gow's, based on periodic points of vertically aligned articu-lations of the A major-minor triad and the half cadence in A which ends the movement. See his The Music of Bela Bartok (Berkeley: University of Cal i fornia Press, 1984), p. 145. Elsewhere in this paper I have given alternate interpretations of the function of the periodic A triads and the f inal cadence. See my Exx. 2.1-2.4 and 3.20. 155 (L13J ), and reiterated chord-tones in the ce l lo (|14J). One of the fundamental characteristics of the th ird quartet, from which the next three excerpts are taken, is i ts nearly consistent orientation to two referential elements. Some passages in the Prima parte feature simultaneous prolongation of two referential ele-ments in contexts where there is l i t t l e to suggest primacy of one over the other as, for example, mm. 27-32 (Ex 3.21). Allowing the root-function conferred on the PC-lowest member of a homointervallic f ifth collection, the cello reiterates a referential element whose root is G [(T) on systems (a) and (b)]. Applying the same criterion to the f irs t v i o l i n and v io la results i n interpretation of a prolonged F# [(2) on systems (a) and (b) ]. The inference here i s underscored by the "tonal answer" in the v i o l i n : the v io la r ises from C#^  to F#4 ((^)) and the v i o l i n rises from F#5 to C#g ((3))- A semitone root relat ion between two independently prolonged referential elements is thus established. The second v i o l i n wavers between G and Ab and, although this does not provide a direct l ink between the two referential roots, i t does so indirectly: G is , of course, one of the roots, and Ab (as G#), although not the root of the prolonged element in the f irst violin and viola, is the PC in the v i o l i n which i s most often metrically and agogically emphasized (C^ })* The passage ends with an inferred descending-fifth progression from G to C (£6)). Although the F# element i s temporarily absent, i t emerges immediately after the cadence in m. 33, as w i l l be discussed in the next example. In fact, the next phrase, mm. 35-43, begins with the dual refer-156 ent ia l elements, C and F#, prolonged i n the lower instruments through the same means employed in mm. 27-32. As indicated in Ex. 3.22, m. 40 is a point of harmonic change: the C-rooted referential element moves from the ce l lo to v io la ((?)) and the F#-rooted element in the v io la moves to C# i n the cel lo ((2)). The semitone relat ion in m. 27, F#-G, has thus been transposed a tritone to C-C# i n m. 40, the tritone r e l a -t ion in m. 33, C-F#, being a pivot (F# common to the f i r s t semitonal duality and C common to the second). The structure of the v i o l i n parts in mm. 36-42 and their r e l a -tionship to the underlying dual referential elements are not immediately apparent. As regards their structure, the reduction of these parts on system (b) reveals that each prolongs a single PC through a large-scale embellishing pattern, the detai ls of which are given on system (a). Comparison with the score w i l l show that durational emphasis i s the primary cr i ter ion for pitch selection in the analysis. Regarding the relationship of each viol in part to the prolonged referential elements in the lower parts, the f i r s t v iol in's prolonged A# is the PC-highest member of the C#-rooted col lect ion i n m. 40 ((2)) and the second v io -l in's A is the analogous member in the C-rooted col lect ion of m. 35 (f^) and the "missing" member of the C-rooted col lect ion at m. 40 (£5)). The individual PCs prolonged i n the two v io l ins thus relate to one or the other prolonged element i n the lower two instruments, providing tonal unification between two disparate textural strata. The main focus of Example 3.23, from the th ird quartet's Prima parte, is the explicit and simultaneous prolongation, in mm. 57-64, of a Db/C# homointervallic ver t i ca l i t y and a D-major t r i a d , C#-D 157 b e i n g the movement's most fundamental o f semitone r e l a t i o n s . 2 7 P r o l o n -g a t i o n o f Db/C# o c c u r s i n t h e v i o l a and c e l l o ((T)) and t h a t o f D i n t h e v i o l i n s (£2)). References (3} and (T) i n d i c a t e t h a t the f i r s t p r i n c i -p l e o f p r o l o n g a t i o n , i n e ach c a s e , i s t h a t o f an e m b e l l i s h i n g p a t t e r n . Db r e c u r s before D i n m. 59 and i s b r i e f l y prolonged through a neighbour t o i t s u pper f i f t h ( i . e . , t h e m o t i o n A-Ab a t (p) . T h i s m o t i o n , i n f a c t , becomes the o n l y f a c t o r o f p r o l o n g a t i o n w i t h r e s p e c t t o the Db/C# r e f e r e n t i a l element; recurrences o f t h i s motion are noted a t ((p. Pro-l o n g a t i o n o f the D-major t r i a d i s more ex t e n s i v e : a t ( 7 } ' f o r example, the f i n a l v e r t i c a l i t y i n the preceding e m b e l l i s h i n g p a t t e r n f u n c t i o n s as a t o n i c i z i n g a g e n t , and a t a d i f f e r e n t v e r t i c a l i t y s e r v e s i n t h a t c a p a c i t y . I n connection w i t h t h i s f i n a l t o n i c i z a t i o n o f D, o s c i l l a t i o n w i t h the r e f e r e n t i a l element strengthens t h e contextual-dominant f u n c -t i o n o f the t o n i c i z i n g agent. C o n s i d e r i n g t h e approach t o t h i s d u a l p r o l o n g a t i o n , t h e v e r t i -c a l i t y i n m. 56 may be pe r c e i v e d as the s u p e r p o s i t i o n o f a lower a u x i l -i a r y t o D (^p) and a p a r t i a l upper a u x i l i a r y t o Db. The l a t t e r i s p a r t i a l because the r o o t Db sounds i n a n t i c i p a t i o n ((w)), the a u x i l i a r y m o t i o n e l a b o r a t i n g o n l y t h e t w o upper n o t e s o f t h e Db r e f e r e n t i a l e l e m e n t ( ). W h i l e i t may seem odd t o r e g a r d a h o m o i n t e r v a l l i c v e r t i c a l i t y as s u p e r i o r t o t h e i n f e r r e d t r i a d i c a u x i l i a r y e l e m e n t — p a r t i c u l a r l y i n l i g h t o f t h e t r i a d i c s t r u c t u r e o f t h e r e f e r e n t i a l element i n the two v i o l i n s — s u b s e q u e n t p r o l o n g a t i o n of the h o m o i n t e r v a l -07 ^•'The movement b e g i n s w i t h a s u p e r p o s i t i o n o f C# and D and ends w i t h superimposed f i f t h s on the r o o t s C# and D. 158 l i e Db element corroborates such a view. In fact, this is an important factor of interpretation i n l ight of which the opening bars of this excerpt may be better understood. Without knowledge of the ensuing prolongation of Db and D, the opening four bars of the excerpt may be heard to prolong an F-major t r iad in the v io l ins ((12)) through neighbour encirclement, and an Eb-minor tr iad in the v io la and ce l lo ((0) ) through s imilar means. In l ight of the last eight bars of the excerpt, however, the f i r s t v e r t i -cality, in m. 53, may be reinterpreted as lower auxiliary to a prolonged G-major tr iad in the v io l ins ((^4))f superimposed over a part ia l upper auxi l iary to a Gb homointervallic v e r t i c a l i t y i n the v io la and cel lo ( (^p ) . The immediate approach to Gb and G and to Db and D are thus transpositionally related, and the former (i.e., Gb and G) are prolonged through embellishing patterns not unlike those used to prolong the latter at f^) and (T). Although the temporal order of events i s such that the prolongation of Db and D would be perceived as beginning with a transposition of the opening four bars, prolongation of Gb and G can only be fully appreciated after the more substantial and complete pro-longation of Db and D. At a higher level of structure the prolonged Gb and G are related to Db and D through the same interval of progression (IC 5) as indicated at ( (16)). The f ina l example of simultaneous prolongation of multiple referential elements, from the opening movement of the sixth quartet (Ex. 3.24), i s a convenient excerpt to end this section on mid-level prolongation because i t also demonstrates substantial and often complex 159 i n t e r a c t i o n o f many o f the techniques d i s c u s s e d above. The ex c e r p t i s o r i e n t e d t o three t r i a d i c r e f e r e n t i a l elements, c h a r a c t e r i s t i c s o f each b e i n g p r e s e n t f r o m t h e o u t s e t and a p p a r e n t even a t p o i n t s o f r e l a t i v e c l a r i t y w i t h r e s p e c t t o any s i n g l e r e f e r e n t i a l element. T h i s i s p a r t l y so because, as shown below, the th r e e r e f e r e n t i a l elements share common notes: G# B D# B - D/D# F# D F# A. T h i s scheme o f o v e r l a p p i n g t r i a d s represents the order i n which each emerges as f o c a l although, as suggested above, elements o f a t l e a s t two o f the t h r e e o f t e n emerge together. I n t e r a c t i o n between G# and B, f o r example, i s i m m e d i a t e l y a p p a r e n t . The l a r g e - s c a l e l i n e a r m o t i o n from D t o B a t ( l ) suggests primacy o f the B-minor t r i a d , as i t d e f i n e s an u n f o l d i n g o f t h e r o o t and t h i r d o f t h a t t r i a d ( ( ^ } ) , i t s r o o t r e i n -f o r c e d i n the c e l l o o f m. 32. Although B r e t u r n s i n the c e l l o i n m. 35, i t does so as t h e bas s o f a f i r s t - i n v e r s i o n G#-minor t r i a d (f^ ))» t h u s r e p r e s e n t i n g t h e f i r s t p o i n t o f t r i a d i c o v e r l a p . The end o f t h e D-B u n f o l d i n g a t (2) c a n be h e a r d t o p a r t i c i p a t e i n a v o i c e exchange w i t h the c e l l o ( @ ) r f u r t h e r i l l u m i n a t i n g the G# t r i a d through i t s r e s u l t a n t r o o t - p o s i t i o n a t ( 5 ^ . The second v i o l i n and c e l l o o f mm. 36-42 continue t o suggest the G# r e f e r e n t i a l t r i a d through t h e i r r h y t h m i c a l l y o f f s e t l i n e a r p rogres-s i o n s f r o m G# t o B, shown a t and d e n o t e d a t (T) as p r o l o n g a t i o n a l u n f o l d i n g s . The m i d - l e v e l p r o g r e s s i o n s are m o t i v i c a l l y d e r i v e d , as they r e s u l t from s u c c e s s i v e transpositions o f a m o t i v i c gesture s t a t e d i n the c e l l o and i n v e r t e d i n t h e second v i o l i n (£p). T h i s m o t i v e spans 160 a seventh i n the c e l l o i n mm. 36-38 and 38-40, the bottom note of the seventh p a r t i c i p a t i n g i n the larger step progression and res u l t a n t unfolding. However, i n the third statement of the cello motive, mm. 41-42, the i n t e r v a l traversed i s a s i x t h and i s , i t s e l f , a prolongational progression ( ( n j ) ) , a l b e i t one at a lower l e v e l . I t i s , i n f a c t , an important unfolding—one which serves to bridge the larger prolonga-t i o n a l progressions i n the c e l l o and second v i o l i n which, as already noted, are o f f s e t . The c e l l o a r r i v e s on B (m. 41) before the second v i o l i n (m. 42), and while the latter i s "catching up" the former engages in the aforementioned prolongational progression of a sixth. Arrival of B (with D#) i n the second v i o l i n (m. 42) thus coincides with completion of the foreground unfolding of B to G# i n the c e l l o ((^ p). As regards elements of the B major-minor r e f e r e n t i a l t r i a d during this expression of G# minor, the sustained B i n mm. 36-41 i n the f i r s t v i o l i n i s transferred to the second v i o l i n ' s B-D# t h i r d i n m. 42 ( ). Although t h i s supports the G# t r i a d , as noted above, i t could also be heard to r e l a t e to B, p a r t i c u l a r l y i n l i g h t of the b r i e f , mid-level unfolding of A# to F#—components i n the dominant of B — i n mm. 41-43 ( (^) ). In f a c t , i t i s i n mm. 41-44 that large-scale events i n support of B begin to emerge. While vestiges of the G#-minor element disappear after m. 42, elements of the D-major referential t r i a d begin to interact with the B major-minor element, as w i l l be explained. Measure 41 i n i t i a t e s two constructs relating to B: a mid-level unfolding of B to D i n the c e l l o ( ( ^ ) ) f and a large-scale unfolding of that same i n t e r v a l i n the f i r s t v i o l i n (fl5) ). The f i r s t of these i s 161 denoted with a dotted symbol because, as suggested by the slur at [16J, the motion from B to D may also represent a connection of r e f e r e n t i a l triads on those roots. The larger prolongational progression culminates on an elided cadence in m. 53, punctuating the B major-minor referential t r i a d , and occurs over lower-level events which suggest both B and D. For example, the f i r s t v i o l i n unfolds A to C# ( ) which, with the prolonged E i n the second v i o l i n , represents the dominant of D, a func-tion which i s further realized by the resolution of C# to D i n the f i r s t v i o l i n at the cadence i n mm. 52-53. Coincident with, but rhythmically independent of, t h i s prolonged dominant of D i s a comparably unfolded dominant of B ( ( ^ ) ) and, although the l a t t e r may be heard to resolve one bar ea r l y ( ( ^ ) ), i t s constituents are e i t h e r repeated or trans-fe r r e d to other parts f o r r e s o l u t i o n at the cadence i n m. 53 ( (^) ).. While satisfying the expectation of B, this cadence i s conventionally deceptive with respect to D, which i s not stated e x p l i c i t l y u n t i l m. 60 (as i n dicated i n Ex. 2.18b). The measures connecting the two cadences are uncomplicated and do not require comment. Large-Scale Prolongation The intimate bond between functional progression and prolonga-tion, referred to at the beginning of this chapter, i s further manifest i n the generation of large-scale tonal coherence. Consider, f o r example, two of the most common large-scale conventional tonal patterns as they occur i n numerous formal schemes: I-V-I and i - I I I - V - i . The tonally contrasting section frequently occurs i n the dominant, returning to the tonic at the return of the opening material. Sonata form i s 162 based on the tonic-dominant p o l a r i t y , although the development s e c t i o n , by d e f i n i t i o n , w i l l t o u c h , however, t e n t a t i v e l y , o n many r e f e r e n t i a l harmonies. I n minor, the middle s e c t i o n o f a t h r e e - p a r t form w i l l o f t e n a r t i c u l a t e motion from I I I t o V i n advance o f the t o n i c accompanying the r e t u r n o f o p e n i n g t h e m a t i c m a t e r i a l . The p o i n t h e r e i s t h a t t h e s e l a r g e - s c a l e t o n a l p a t t e r n s , i f heard as foreground pr o g r e s s i o n s , c l e a r l y p r o l o n g a s i n g l e t o n a l a r e a t h r o u g h f u n c t i o n a l r e l a t i o n s h i p s i n t h e major-minor system. Thus, t o n a l i t y - d e f i n i n g progressions which, a t the su r f a c e , d e f i n e p r o l o n g a t i o n s , are o f t e n p r o j e c t e d over an e n t i r e p i e c e , p r o v i d i n g t o n a l u n i t y through a l a r g e - s c a l e p r o l o n g a t i o n a l progression. S u r e l y t h e most a t t r a c t i v e a s p e c t o f t h e t y p e o f p r o l o n g a t i o n d i s c u s s e d a b o v e — a f e a t u r e w h i c h t r u l y s e p a r a t e s t r a d i t i o n a l l y t o n a l m u s i c f r o m t h a t w h i c h may be c h a r a c t e r i z e d as t o n a l i n some p u r e l y c o n t e x t u a l s e n s e — i s the degree of t o n a l o r i e n t a t i o n p o s s i b l e p r i o r t o e x p l i c i t o c c u r r e n c e o f t h e t o n i c r e f e r e n c e , even, i n f a c t , i n i t s absence. I f , f o r example, the l a r g e - s c a l e p l a n were v i - V - I o r I I I - V - i , the f a c t t h a t those p a t t e r n s are unequivocal, t o n a l - o r i e n t i n g progres-s i o n s a t l e v e l s where o r i e n t a t i o n i s most p a l p a b l e p r o v i d e s a f u n c t i o n a l b a s i s on w h i c h t o a s c r i b e t o n a l d i r e c t i o n , t o n i c e x p e c t a t i o n , and, u l t i m a t e l y , p r o l o n g a t i o n a l s i g n i f i c a n c e t o the br o a d l y a r t i c u l a t e d p a t -t e r n . I suggested a t the beginning o f t h i s chapter t h a t t h i s degree o f i m p l i c a t i o n and. e x p e c t a t i o n i n h e r e n t i n the major-minor system, w h i l e t h e o r e t i c a l l y r e l e v a n t a t many l e v e l s o f s t r u c t u r e , may not be e q u a l l y p e r c e p t i b l e over broader spans. F u n c t i o n a l progressions e f f e c t i n g p r o -163 l o n g a t i o n a t t h e p h r a s e l e v e l , f o r example, a r e i n d e e d p e r c e p t i b l e , w h i l e those over a broader span, although o f t e n f u n c t i o n a l i n the same sense as those w i t h i n phrases, are a p p r e c i a t e d "conceptually." That i s , because o f o u r knowledge o f f u n c t i o n a l r e l a t i o n s a c c o r d i n g t o w h i c h c o n s t i t u e n t s o f the l a r g e - s c a l e p r o g r e s s i o n are ordered, we "understand" s u c h a p r o g r e s s i o n t o be d i r e c t e d and i m p l i c a t i v e o f i t s l a r g e - s c a l e g o a l ; we do not,, however, n e c e s s a r i l y "hear" t h e p r o g r e s s i o n as an a r t i c u l a t e d s u c c e s s i o n o f adjacent, f u n c t i o n a l l y r e l a t e d events. There-f o r e , f u n c t i o n a l d i r e c t e d n e s s and r e s u l t a n t p r o l o n g a t i o n w i t h i n t h e p h r a s e a r e , i n t r a d i t i o n a l l y t o n a l m u s i c , q u i t e r e a l and p e r c e p t i b l e , w h i l e l a r g e - s c a l e f u n c t i o n a l progressions and attendant p r o l o n g a t i o n s , although grasped c o n c e p t u a l l y , are of u n c e r t a i n p e r c e p t u a l i d e n t i t y i n a c t u a l experience. The r a m i f i c a t i o n s o f t h i s s i t u a t i o n f o r l a r g e - s c a l e s t r u c t u r e i n n o n t r a d i t i o n a l contexts are i n d e e d f o r m i d a b l e . I f a l a r g e - s c a l e p r o -g r e s s i o n i n a conv e n t i o n a l context i s understood c o n c e p t u a l l y but i s not n e c e s s a r i l y p e r c e p t i b l e , then a comparable, s y s t e m a t i c a l l y a r t i c u l a t e d l a r g e - s c a l e p r o g r e s s i o n i n a n o n t r a d i t i o n a l context may be accorded some degree o f analogous s t r u c t u r a l s i g n i f i c a n c e . The c o n v e n t i o n a l l a r g e -s c a l e p r o g r e s s i o n i s a c c o r d e d p r o l o n g a t i o n a l s t a t u s because o f t h e p r e c e d e n t s e t a t f o r e g r o u n d and m i d d l e g r o u n d l e v e l s , where s i m i l a r p r o g r e s s i o n s y i e l d p a l p a b l e p r o l o n g a t i o n s . F o r a n o n t r a d i t i o n a l 28 Because o f our experience w i t h the major-minor system, t he p e r c e p t i b l e p r o l o n g a t i o n a l p r e c e d e n t need n o t even be a r e c u r r e n t f a c t o r i n t h e foreground harmonic s t r u c t u r e o f the p i e c e i n which i t i s s a i d t o e f f e c t l a r g e - s c a l e p r o l o n g a t i o n a l s i g n i f i c a n c e . T h a t i s , we c a n a s c r i b e meaning t o a l a r g e - s c a l e f u n c t i o n a l ( p r o l o n g a t i o n a l ) harmonic p a t t e r n 164 large-scale progression to acquire analogous prolongational s i g n i f i -cance, a comparable, perceptible foreground or mid-level precedent, linking progression and prolongation, must be apparent as an element of the tonal structure of the particular piece. 2 9 The large-scale tonal structure of much twentieth-century music, while systematic i n i t s organization, i s more problematic as to pro-longation. Recurrences of primary r e f e r e n t i a l elements over extreme temporal distances are often just that: recurrences. Recurrences of a tonic t r i a d over comparable spans i n major-minor music, on the other hand, are often achieved through broadly articulated functional patterns which, at perceptible l e v e l s , are prolongational. Two examples from Bartok's quartets w i l l serve to demonstrate large-scale structures which may be accorded prolongational significance by virtue of a perceivable prolongational precedent established at much lower levels. One occurs over a the f i r s t of three large formal sections and the other over an entire movement. The f i r s t example comes from the f i n a l movement of the fourth quartet, analyzed i n some detail i n this chapter and i n the preceding. Example 3.15 revealed prolongation of the primary referential C-G f i f t h based on the common usage of that pattern i n the major-minor system i n general. (Cf. note 29.) This i s consistent with Paul Wilson s concept of "nesting," mentioned in the quotation given earlier; refer to note 11. Compare this to note 28. In nontraditional contexts, the presence of a foreground precedent i s required for extrapolation of prolongational significance at higher levels, as we rarely have a clearly defined referential basis outside a given work on which large-scale contextual functionality and prolonga-tional v a l i d i t y can be ascribed. 165 through o s c i l l a t i o n with i t s b2-#4 disposition pair; Exx. 3.16 and 3.17 i l l u s t r a t e d motion to an i n t e r l o c k i n g of C-G and F#-C# f i f t h s , each f i f t h functioning as a b2-#4 disposition pair i n relation to the other; and Ex. 2.37 focused on a large-scale l i n e a r progression of a t r i t o n e , which links the F#-C# f i f t h of the aforementioned point of interlock to the primary C-G f i f t h which concludes the large A section. Large-scale prolongation i n this excerpt involves projection of the primary referential f i f t h , C-G, over the entire 148-measure A sec-t i o n . As noted above, the section begins and ends with the C-G f i f t h , but on what basis might the e n t i r e section be said to "prolong" that particular f i f t h ? The principle of large-scale articulation of a fore-ground or mid-level prolongation pattern concerns the b2-#4 disposition p a i r (i.e., Db-F#). This t o n i c i z i n g agent i s employed c o n s i s t e n t l y at the foreground i n mm. 1-42 to prolong the C-G f i f t h through oscillation, and emerges i n m. 75, enharmonically spelled, as a tonal event of struc-tural import. Although, as noted above, C-G and F#-C# interlock, F#-C# may be understood as the main event here, because i t i n i t i a t e s the aforementioned large-scale t r i t o n e progression back to the C-G f i f t h . As noted above, i n a conventionally tonal piece, the dominant serves to tonicize and prolong the tonic at the foreground but also over broader spans, as, for example, when functioning as a key-area i n the middle section of a ternary design. This movement i l l u s t r a t e s an analogous relationship within i t s A section: the Db-F# disposition pair prolongs the C-G f i f t h at foreground and. middleground levels, and acquires asso-ciative, prolongational significance at those levels. That disposition 166 p a i r i s s i m i l a r l y understood a t i t s s t r u c t u r a l a r r i v a l i n m. 75, where i t s e r v e s t o p r o l o n g t h e p r i m a r y C-G f i f t h a t a h i g h e r l e v e l o f s t r u c -t u r e . The s e c o n d example spans t h e o p e n i n g movement o f t h e f i f t h q u a r t e t . The l a r g e - s c a l e h a r m o n i c p l a n o f many c o n v e n t i o n a l l y t o n a l p i e c e s e v e n t u a l l y breaks down t o I-V-I and i t i s a v i t a l f e a t u r e of the major-minor system t h a t the p r o l o n g i n g component a t t h i s l e v e l i s p r e -c i s e l y t h a t w h i c h o c c u r s a t e v e r y l e v e l f r o m t h e i m m e d i a t e s u r f a c e upwards. T h i s " n e s t i n g " p r o c e s s i s s u r e l y one o f t h e most c o m p e l l i n g aspects of t o n a l u n i t y and coherence i n music o f the major-minor system. The components of the l a r g e - s c a l e s t r u c t u r e o f the movement i n q u e s t i o n f u n c t i o n w i t h i n a m i d - l e v e l c o n s t r u c t employed a t t h e b e g i n n i n g t o p r o l o n g the r e f e r e n t i a l PC o f the f i r s t theme ( a l s o t h a t o f the e n t i r e movement). As d i s c u s s e d i n c o n n e c t i o n w i t h Ex. 2.34, t h a t theme i s a m i d - l e v e l ascending s c a l a r c o n s t r u c t w i t h c h a r a c t e r i s t i c s o f a whole-t o n e s c a l e and a l y d i a n p a t t e r n r o o t e d on B b . 3 0 The theme, w i t h i t s octave completion, may thus be understood t o prolong Bb. L a r g e - s c a l e p r o l o n g a t i o n o f Bb i s generated through a key-scheme which p r o j e c t s the d u a l s c a l a r p a t t e r n over the whole movement. Example 3.25 shows the opening measures o f each of the t h r e e main themes as they occur i n the e x p o s i t i o n and r e c a p i t u l a t i o n s e c t i o n s . These t h r e e themes have a l r e a d y been examined i n v a r i o u s degrees o f d e t a i l and i t need o n l y be noted here t h a t , i n the r e c a p i t u l a t i o n , they occur i n r e v e r s e order 3 0 T h e a s s e r t i o n o f r o o t i n c o n n e c t i o n w i t h t h e w h o l e - t o n e s c a l e i s of c o u r s e based on c o n t e x t , as t h a t s u c c e s s i o n i s s y m m e t r i c a l and t h e r e -f o r e , i n and of i t s e l f , r o o t l e s s . 167 and are inverted—a detail which further enhances the symmetrical struc-ture of the movement. System (a) shows the referential PCs of the themes, which as indicated at f ^ , comprise the whole-tone structure of the opening theme ((2))* Dual emphasis of E and F at the end of the development section (mm. 126-127 in Ex. 3.25) may be heard to represent completion of a large-scale ascending lydian f i f t h ( ( ^ ) , also apparent in the structure of the f i r s t theme. A scalar pattern, which serves to prolong the movement's primary referential PC over a phrase-level span, is thus projected over the entire movement in large-scale prolongation of Bb. 168 CHAPTER IV PROGRESSION AND PROLONGATION IN THE FINAL MOVEMENT OF BARTOK'S SIXTH QUARTET As suggested by the f o r e g o i n g analyses, p a r t i c u l a r l y w i t h regard t o those e x c e r p t s used t o demonstrate more than one determinant o f t o n a l s t r u c t u r e , the m u s i c a l language o f Barto'k's q u a r t e t s f e a t u r e s complex i n t e r a c t i o n s between d i f f e r e n t t y p e s o f p r o g r e s s i o n and p r o l o n g a t i o n . And, as i n c o n v e n t i o n a l l y t o n a l music, components o f m i d - l e v e l progres-s i o n s a r e a t t i m e s prolonged a t a lower l e v e l , and a t other t i m e s mid-l e v e l p r o g r e s s i o n s themselves r e f l e c t h i g h e r - l e v e l p r o l o n g a t i o n s . Thus, t h e r e i s i n t e r a c t i o n between d e t e r m i n a n t s f u n c t i o n i n g w i t h i n phrases, b u t a l s o i m p o r t a n t r e l a t i o n s between e v e n t s o c c u r r i n g a t d i f f e r e n t l e v e l s o f s t r u c t u r e , o v e r v a r i o u s t e m p o r a l spans, b o t h c o n t i g u o u s and n o n c o n t i g u o u s . To f u l l y u n d e r s t a n d t h e r i c h n e s s o f Bartok's t o n a l language r e q u i r e s a view which takes i n t o account such complex i n t e r a c -t i o n s . A c c o r d i n g l y , the fundamental g o a l o f the present chapter i s t o i l l u m i n a t e i n t e r a c t i o n s between determinants o f t o n a l s t r u c t u r e w i t h i n p a r t i c u l a r phrases o r o t h e r segments, and t o e l u c i d a t e i n t e r a c t i o n s o f determinants a c r o s s the complete movement as they c o n t r i b u t e t o a sense of o v e r a l l t o n a l coherence and u n i t y . By way o f i n t r o d u c t i o n t o the a n a l y s i s , i t may be s a i d t h a t the f i n a l movement of the s i x t h q u a r t e t f e a t u r e s an amalgam of t o n a l d e t e r -169 minants, some associated dire c t l y with convention and others analogous to certain conventional procedures. One of the f i r s t general aspects of conventionality encountered i n the movement i s the abundant use of t e r t i a n harmonies, which often progress according to functional root relations associated with the major-minor system. Tonicization through the conventional dominant and a host of dominant substitutes well within the practice of the nineteenth century (e.g., diminished-seventh chords and harmonies akin to the augmented sixth) i s perhaps the most s i g n i f i -cant of functional progressions employed i n this music. One particular feature of this movement's tonal structure that has analogy i n conventional pr a c t i c e , p a r t i c u l a r l y of the nineteenth century, i s that of ambiguity of the overall tonality of the movement. In the s i x t h quartet's f i n a l movement, the primary, r e f e r e n t i a l t r i a d comes into focus only gradually as the piece unfolds. David Gow, i n his analysis of Bartok's f i r s t string quartet, has referred to this process as "emergent" to n a l i t y . ^ Inextricably t i e d to t h i s concept i s the condition of retrospection, discussed i n previous chapters. For example, the emergence and confirmation of the referential t r i a d at the end of the movement imparts functional s i g n i f i c a n c e to previous mid-level points of centric orientation. The primary referential t r i a d of the movement requires prelimi-nary explanation p r i o r to analysis. To be more exact, there are two referential triads i n the movement, although the problematic element of •'"David Gow, "Tonality and Structure i n Bartok's F i r s t Two String Quar-tets," The Music Review 34/3-4 (1973): 259. 170 c o n f l i c t a s s o c i a t e d w i t h " b i t o n a l i t y " i s not e v i d e n t here. Rather, the movements t o n a l d u a l i t y may be understood t o have a more conv e n t i o n a l precedent, namely the r e l a t i v e and p a r a l l e l major-minor r e l a t i o n s h i p s . The two r e f e r e n t i a l t r i a d s w i l l be shown t o be D m a j o r - m i n o r and F major; the p a r a l l e l r e l a t i o n h o lds between D major and D minor and the r e l a t i v e between D minor and F major. E x p l i c a t i o n o f how one r e f e r e n -t i a l t r i a d emerges as s t r u c t u r a l l y s u p e r i o r i s r e s e r v e d f o r the a n a l y s i s which f o l l o w s . In t h i s movement, conventional and nonconventional t o n a l d e t e r -minants o f t e n occur i n sharp j u x t a p o s i t i o n w i t h i n phrases and from one p h r a s e t o t h e n e x t , r e q u i r i n g t h e l i s t e n e r t o e v a l u a t e t h e s t r u c t u r e a c c o r d i n g t o d i f f e r e n t p r i n c i p l e s o f o r g a n i z a t i o n . A c c o r d i n g l y , t h e p h r a s e w i l l s e r v e as t h e a p p l i c a b l e f o r m a l u n i t f o r t h e s t u d y o f how these v a r i o u s t o n a l determinants ar e deployed throughout the movement. However, u n l i k e phrases i n c o n v e n t i o n a l l y t o n a l music, which most o f t e n c o n c l u d e w i t h a cadence o f some s o r t , p h r a s e s i n t h i s movement r a r e l y f e a t u r e s u c h t e r m i n a t i n g p a t t e r n s o f t o n a l punctuation. Some phrases have i n t e r n a l p o i n t s o f t o n a l o r i e n t a t i o n , and o t h e r s a r t i c u l a t e a p a r t i c u l a r nontonic harmony the f u n c t i o n o f which i s t h a t o f a component i n m i d - l e v e l f u n c t i o n a l h a r m o n i c p r o g r e s s i o n ( i . e . , a t a l e v e l beyond t h a t o f the phrase). Phrase d e l i n e a t i o n i s most o f t e n e f f e c t e d through s u r f a c e changes i n t e x t u r e , tempo, and dynamics, as w e l l as i n t e r v e n i n g r e s t s and rhythmic c a e s u r a s — f a c t o r s which, i n much t w e n t i e t h - c e n t u r y music not r e l i a n t on the syntax o f major-minor t o n a l i t y , assume v i t a l s t r u c t u r a l s i g n i f i c a n c e . In l i g h t o f emergent t o n a l i t y and r e t r o s p e c t i o n , d i s c u s s e d above 171 and i n previous chapters, b r i e f examination o f the end o f the movement w i l l a f f o r d a p e r s p e c t i v e i n which t o understand p h r a s e - l e v e l r e f e r e n -t i a l elements encountered from the outset. Upon g a i n i n g such an under-standing, we can a p p r e c i a t e t h e t o n a l a m b i g u i t i e s e x p r e s s i v e l y i n t e g r a l t o t h e music as i t u n f o l d s i n i t s proper temporal order w h i l e r e t a i n i n g a sense of heightened, o f t e n c o n t e x t u a l , e x p e c t a t i o n i n v o l v i n g l a r g e -s c a l e r e l a t i o n s d i s c l o s e d i n a n a l y s i s . Progressions and p r o l o n g a t i o n s t h r o u g h o u t t h e movement w i l l t h u s be e v a l u a t e d on t h e b a s i s o f t h e i r c o n t r i b u t i o n t o d e l i b e r a t e t o n a l ambiguity o r the process o f emergent t o n a l c l a r i f i c a t i o n , two v a l i d s t r u c t u r a l e l e m e n t s i n t h e movement's t o n a l i t y . I t i s a p p a r e n t f r o m Ex. 4.1 t h a t t h e f i n a l measures o f t h e movement u l t i m a t e l y focus on the aforementioned t o n a l d u a l i t y between D major-minor and F major, these two r e f e r e n t i a l t r i a d s exposed and pro-longed through r e c u r r e n t d i s p o s i t i o n - n o t e e l a b o r a t i o n o f t h e i r i n d i v i -dual chord-tones. The a n a l y s i s of s c a l e degrees, as represented below s y s t e m s (a) and (b), r e v e a l s c o n s i s t e n c y i n t h e use o f b2, #4, b6, and 7. A l s o apparent i s the o b l i q u e r e s o l u t i o n o f the b2-5 t r i t o n e i n the f i n a l a r t i c u l a t i o n o f D i n t h e two v i o l i n s ( ). These p a r t i c u l a r d i s p o s i t i o n n o t e s and t h e o b l i q u e l y r e s o l v i n g t r i t o n e were shown i n p r e v i o u s c h a p t e r s t o a c q u i r e d i r e c t i v e p o t e n t i a l f r o m t h e l y d i a n and Phrygian o r d e r i n g s o f the d i a t o n i c c o l l e c t i o n which, although not s t a t e d e x p l i c i t l y here, w i l l be shown t o occur e x p l i c i t l y e a r l i e r i n the piece. In the process o f examining i n t e r a c t i o n s o f v a r i o u s t o n a l d e t e r -m i n a n t s f r o m t h e b e g i n n i n g o f t h e movement, a l l u s i o n s t o , and d i r e c t 172 expressions o f , elements i n the t o n a l d u a l i t y by which t he movement i s f i n a l l y u n d e r s t o o d w i l l be d i s c l o s e d . Example 4.2 r e v e a l s t h a t t h e r e i s , i n f a c t , no s u g g e s t i o n o f F and an o n l y t e n t a t i v e i m p l i c a t i o n o f D i n the opening phrase o f the movement. The phrase begins w i t h a concen-t r a t i o n on A, by way o f a s u c c e s s i o n o f f u n c t i o n a l p r o g r e s s i o n s employing harmonies from both major and minor modes, and i t e n d s — w i t h one of the few d e f i n i t i v e cadences i n the movement—on a C-minor t r i a d , e xposed t h r o u g h f a c t o r s w h i c h w i l l be summarized. C o n c e r n i n g t h e opening i m p l i c a t i o n of A m a j o r - m i n o r , two p r o c e d u r e s f i g u r e s i g n i f i -c a n t l y i n c o m p l i c a t i n g o t h e r w i s e pure c o n v e n t i o n a l i t y : one i s the occur-rence of passing tones and r e s o l u t i o n s o f tendency tones a semitone "too high" o r "too low"; and the oth e r , o f t e n the r e s u l t o f the f i r s t , i s the a f o r e m e n t i o n e d i n t e r m i x i n g o f m a j o r and m i n o r r e s o u r c e s . The f i r s t v i o l i n ' s Db and Eb i n m. 2 a r e n o t d i a t o n i c t o t h e u n d e r l y i n g A m i n o r but are, r a t h e r , a semitone below r e s p e c t i v e d i a t o n i c c o n s t i t u e n t s . The same s i t u a t i o n o c c u r s i n t h e second v i o l i n , m. 4, and i n t h e c e l l o , m. 8. The i n f l e c t i o n s i n br a c k e t s and squares above these t h r e e i n s t a n c e s on s y s t e m (a) a r e t h o s e r e q u i r e d t o r e n d e r t h e n o t e s d i a t o n i c t o t h e u n d e r l y i n g harmony, the squares being used f o r those which would become c h o r d - t o n e s as a r e s u l t o f t h e i n f l e c t i o n s . The r e s u l t i s a t r i a d i c s t r u c t u r e w h i c h i s " t a i n t e d , " so t o speak, by c o n f l i c t i n g s e m i t o n a l l y r e l a t e d nonharmomc notes. I t might be noted t h a t i t i s the s t r i c t p r e s e n t a t i o n and t r a n s p o s i t i o n o f t h e p r i m a r y m o t i v e t h a t r e s u l t s i n n o t e s w h i c h " c o n f l i c t " w i t h t h e a s s e r t e d t e r t i a n harmonies. 173 Major-minor m i x t u r e i s a p p l i e d t o the submediant harmony, which, o c c u r s a s v i ( i . e . , a m i n o r t r i a d on s c a l e d egree 6) a s w e l l as bVI ( i . e . , a m a j o r t r i a d on s c a l e d egree b6). A t t h e b e g i n n i n g o f m. 3, f o r example, v i f r o m A m a j o r o c c u r s . Not o n l y i s t h e o p e n i n g i n A m i n o r , b u t t h e v e r t i c a l i t y s o u n d i n g a t t h e end o f m. 2 (fT)) i s a V o f bVI ( i . e . , t h e V I f o u n d i n t h e m i n o r mode). Thus we have t h e do m i n a n t o f bVI r e s o l v i n g t o v i . T h i s e x a c t p r o g r e s s i o n r e t u r n s i n mm. 7-8 a s i n d i c a t e d a t f^. Here, then, i s a case o f complete harmonies r e s o l v i n g one semitone "too high" w i t h a r e s u l t a n t blend o f major and minor h a r -monic resources, a unique type o f de c e p t i v e p r o g r e s s i o n and r e s o l u t i o n . Example 4.2 a l s o i n d i c a t e s t h a t , a p a r t from l o c a l t o n i c i z a t i o n o f t h e C-minor t r i a d i n m. 13, t h r o u g h a d i s p o s i t i o n d o m i n a n t ( ( 3 ) ) / t h e r e i s l i t t l e i f any d i a t o n i c i m p l i c a t i o n o f t h a t key e a r l i e r i n the phr a s e . A l t h o u g h v e r t i c a l a l i g n m e n t o f t h e f o u r p a r t s on a co n s o n a n t t r i a d i c s o n o r i t y , a c l i m a x o f dynamic i n t e n s i f i c a t i o n , and e x t r e m e r e g i s t r a l s e p a r a t i o n of the o u t e r p i t c h e s , are among the f a c t o r s which h e l p expose t h e C-minor t r i a d i n m. 13 as an a r r i v a l p o i n t , none o f these c h a r a c t e r i s t i c s i m p l i e s e a r l y i n the phrase t h a t t h i s p a r t i c u l a r outcome i s probable. T h i s , however, i s n o t t o say t h a t a r r i v a l o f t h e C-minor t r i a d i n m. 13 i s w i t h o u t p r e p a r a t i o n . As the top two staves o f system (a) i n Ex. 4.3 show, t h e f i r s t v i o l i n and c e l l o — t h e t h e m a t i c v o i c e s — m a y be heard t o form a two-voice c o u n t e r p o i n t which i s s y s t e m a t i c i n approach t o the C-minor t r i a d a t the end of the phrase. The approach i s system-a t i c because o f the c o n s i s t e n t use of two foreground p a t t e r n s : one com-p r i s e d o f a c h r o m a t i c p a s s i n g n o t e and a c h r o m a t i c , i n c o m p l e t e upper 174 neighbour note, resulting i n a semitone encirclement of the next struc-tural pitch i n the linear progression ((?)); and the other, a descending sixth, which at (2) effects linear connection of D to F#, "compensating" for the absence of an ascending step connection of D to F# at £3) . Concatenation of the encirclement and descending-sixth motives i n the upper voice y i e l d s a step progression connecting C to Eb ((?)), which may be understood as a large-scale unfolding, and resultant prolonga-t i o n , of the minor t h i r d of the f i n a l t r i a d . In that the o v e r a l l progression acquires functional significance upon i t s conclusion, i t i s an example of a contextually directed linear progression as defined i n the second and third chapters. The linear organization of the cello part i s more complex as i t involves two progressions: a PC ascent from F# to E (^))—again derived from the linking of transposed thematic-motivic material—and a descent from E to C (f^))- In the f i r s t of these progressions, the descending-sixth motive from the f i r s t v i o l i n (^) occurs twice: at (^), the lower note of the sixth, B, may be construed as an incomplete upper neighbour to the next s t r u c t u r a l note i n the progression (Bb); and a t ^T), the lower note (E) represents, on the one hand, the durationally emphasized f i n a l member of t h i s F#-E progression, and on the other, the i n i t i a l member of the descending E-C progression. The ascending progression from F# to E may be interpreted as an unfolding and prolongation of the F#-E interval i n the disposition dominant which resolves at the end of the phrase (f^)). Through r e p e t i t i o n and tr a n s p o s i t i o n of a one-bar motive ( n.0j , i n the score), the descending E-C progression articulates 175 a 1-1-2 IC p a t t e r n ( ( ^ ) , which i s a t e m p o r a l l y expanded v e r s i o n o f the IC p a t t e r n i n the f i r s t v i o l i n s opening motive ( (^) ). The procedures o u t l i n e d above e x e m p l i f y two important aspects o f i n t e r a c t i o n between determinants o f t o n a l o r i e n t a t i o n : the generation o f l i n e a r p r o gressions t h r o u g h s u c c e s s i v e , o f t e n s t e p - r e l a t e d , t r a n s p o s i t i o n s o f p r i m a r y them a t i c and m o t i v i c m a t e r i a l — a s i n the o u t e r v o i c e s o f t h i s opening p h r a s e — a n d the r e l a t i o n between c o n t e x t u a l l y d i r e c t e d p r ogressions and p r o l o n g a t i o n a l l i n e a r u n f o l d i n g s where p i t c h e x t r e m i t i e s o f the former a r e d i s p o s i t i o n n o t e s d e f i n i n g e n d p o i n t s o f t h e l a t t e r , as i n t h e u n f o l d i n g o f F#-E. B e f o r e c o n s i d e r i n g subsequent p h r a s e s I o f f e r a d i f f e r e n t , though not i n c o m p a t i b l e , i n t e r p r e t a t i o n o f t o n a l o r g a n i z a t i o n and cen-t r i c o r i e n t a t i o n i n t h i s opening g e s t u r e — a n i n t e r p r e t a t i o n which b r i n g s t o l i g h t an element o f i m p l i c a t i o n o f the phrase-ending C-minor t r i a d back i n m. 7, and u n c o v e r s m i d - l e v e l p r o j e c t i o n o f an i m p o r t a n t and r e c u r r e n t foreground motive. The middle staves o f system (b) i n Ex. 4.3 i n t e r p r e t t h e o u t e r v o i c e s o f t h i s o p e n i n g p h r a s e as s u c c e s s i o n s o f foreground, unfolded t h i r d s . A whole-tone r e l a t i o n i s noted a t [ l p and a " r o t a t i o n " a t | l p - I n t h i s r o t a t i o n , t h e D-F# t h i r d p i v o t s about an F# a x i s t o y i e l d an F#-A t h i r d , w h i c h i n t u r n moves up by s t e p ((15) ), as a t {13} . Were the c o n c l u d i n g t h i r d o f t h i s second r o t a t i o n (G#-C) t o p i v o t a b o u t i t s a x i s (C), t h e o r i g i n a l C-Eb t h i r d w o u l d o c c u r ((l6\ ). T h i s i m p l i c a t i o n o f C minor i s , o f course, u n f u l f i l l e d u n t i l t h e end of t h e p h r a s e ( ^J} ). The element which appears i n p l a c e o f the i m p l i e d C-Eb t h i r d i n m. 7 i s an A-C t h i r d ((^j) ), which i s subsequently connected t o the C-Eb 176 t h i r d o f the cadence through an i n t e r v a l l i c a l l y augmented, l a r g e - s c a l e p r o j e c t i o n o f the foreground motive i d e n t i f i e d a t Q). As i n d i c a t e d a t (l9), t h e p a t t e r n i n v o l v e s a p a s s i n g e l e m e n t and an i n c o m p l e t e upper n e i g h b o u r t o t h e f i n a l t h i r d . I n t h e f o r e g r o u n d p a t t e r n w h i c h b e g i n s the movement, the p a s s i n g element moves by semitone, thereby d e c o r a t i n g a w h o l e - t o n e s t e p (C t o D), whereas i n t h e a u g m e n t a t i o n t h e p a s s i n g e l e m e n t moves f i r s t by w h o l e - t o n e , t h e n by s e m i t o n e , r e s u l t i n g i n an o v e r a l l t r a v e r s a l o f a m i n o r t h i r d (A t o C). The s e m i t o n a l l y r e l a t e d incomplete upper-neighbour motion—Eb-D a t the end of ( T )—is r e t a i n e d i n t h e m o t i o n C# (as Db) t o C. The c e l l o p a r t i s r e g a r d e d i n t h i s a l t e r n a t e i n t e r p r e t a t i o n i n much the same way as represented on system ( a ) . The opening phrase, then, r e l i e s on conventional determinants o f t o n a l s t r u c t u r e — f u n c t i o n a l l y r e l a t e d t e r t i a n harmonies and t r a d i t i o n a l means o f t o n i c i z a t i o n — a s w e l l as l e s s c o n v e n t i o n a l d e v i c e s — h a r m o n i c r e s o l u t i o n and v o i c e l e a d i n g a semitone "too hi g h " o r "too low," i n t e r -v a l l i c u n f o l d i n g and p r o l o n g a t i o n t h r o u g h l a r g e - s c a l e c o n t e x t u a l l y d i r e c t e d l i n e a r p r o g r e s s i o n s , and t o n i c i z a t i o n of the f i n a l r e f e r e n t i a l t r i a d through a d i s p o s i t i o n dominant. The r e l a t i o n s h i p o f t h i s opening p h r a s e (and t h e r e f e r e n t i a l t r i a d w i t h w h i c h i t ends) t o t h e o v e r a l l t o n a l d u a l i t y o f D m a j o r and F m a j o r , however, i s one w h i c h w i l l come i n t o focus o n l y upon examination of subsequent phrases. The second p h r a s e , mm. 13-22 (Ex. 4.4), i s l e s s c o n c e r n e d w i t h u n d e r l y i n g chromatic t o n a l procedure and t r i a d i c s t r u c t u r e than w i t h the type of independent l i n e a r c o n t i n u i t y and c o n t e x t u a l d i r e c t e d n e s s asso-177 elated with the outer parts i n the f i r s t phrase. Here, the motivic foreground encirclement pattern at (T) i n Ex. 4.3 i s used to e f f e c t a mid-level step descent i n the outer parts ((T)), followed by an ascent i n the three upper parts ((2}) and a continued descent i n the lower part ((J)). These l i n e a r progressions culminate at the end of the phrase, m. 22, marked by the c o l l e c t i o n (reading up) E-C#-A#-G#. Reference (4) reveals the large-scale voice exchange between E and Gi i n the f i r s t v i o l i n and cello. This phrase i s more systematic than the f i r s t phrase i n that the encirclement pattern i s used consistently i n a l l four parts. Also, the opening of the phrase i s more implicative of i t s a r r i v a l point because of the aforementioned voice exchange. These details render the phrase prolongational i n overall design and serve to demonstrate further the i n t e r a c t i o n between l i n e a r progression, prolongation, and motivic structure. System (b) i l l u s t r a t e s the v e r t i c a l i t i e s which, although not conventionally t e r t i a n , are nevertheless s i g n i f i c a n t i n the present context. As indicated, the i n d i v i d u a l l i n e s produce o f f s e t IC 4s descending by IC 2, mm. 13-17, followed by o f f s e t IC 2 c o l l e c t i o n s ascending by IC 2. The end of system (b) indicates that the two vio l i n s move only a semitone to the cadential sonority; were they to move a whole-tone, as does the v i o l a (and as suggested by the established pattern), the sonority at ^ } would result. This collection, although denied, i s a more conventional V of D, one of the two main r e f e r e n t i a l triads. System (c) i s a more detailed view of the harmonic flow i n mm. 16-22 which results from the superimposition of linear components; i t reveals a common-tone procedure whereby connection of adjacent vertica-178 l i t i e s i s rendered smooth and gradual. As a r e s u l t o f t h e p a t t e r n d e p a r t u r e d i s c u s s e d above, whereby sem i t o n a l motion t o the c a d e n t i a l s o n o r i t y r e p l a c e s the normative whole-tone connection, the c a d e n t i a l s o n o r i t y may be construed as dominant t o b o t h D and F, t h e two r e f e r e n t i a l t r i a d s c o n f i r m e d a t t h e end o f t h e movement. As a do m i n a n t i n F m a j o r , i . e . , E-G#-Bb-Db, t h e " r o o t " i s th e b a s s n o t e E and p r o d u c e s , w i t h t h e C r o o t and bas s o f t h e f i r s t phrase's f i n a l v e r t i c a l i t y , a l a r g e - s c a l e whole-tone e n c i r c l e m e n t o f the u l t i m a t e g o a l D (the whole-tone e n c i r c l e m e n t an expansion o f the f o r e -ground semitone e n c i r c l e m e n t p a t t e r n a t f^ ) i n Ex. 4.3). As a dominant i n D m i n o r , i . e . , C#-E-G#-Bb, i t c r e a t e s , w i t h t h e cadence o f t h e f i r s t phrase, a chromatic PC-step approach t o the pri m a r y goal D i n terms o f r o o t r e l a t i o n s C-C#-D, the o t h e r component i n the foreground e n c i r c l e -ment p a t t e r n . Although D i n these two l a r g e - s c a l e m o t i v i c i m i t a t i o n s of the opening foreground p a t t e r n has not y e t emerged as f o c a l , the l a r g e -s c a l e u n f o l d i n g o f the i n i t i a l p a r t o f the p a t t e r n suggests t h a t expo-sure of D as a p o i n t o f t o n a l focus i s imminent. I t i s , i n f a c t , i n t h e t h i r d p h r a s e , mm. 22-39, t h a t D and i t s m a j o r - t r i a d a f f i l i a t e s F# and A f i n a l l y b e g in t o emerge, a l b e i t gradu-a l l y . F i r s t , t h e r e i s the apparent C#-D completion o f the second v i o -l i n ' s . F##-C by t h e v i o l a and c e l l o i n m. 25, i n d i c a t e d a t i n Ex. 4.5. I s a y a p p a r e n t because i t t u r n s o u t t o be t h e b e g i n n i n g o f a t r i t o n e t r a n s p o s i t i o n o f t h e theme f r o m mm. 22-24 ( @ ) . R h y t h m i c e l o n g a t i o n o f t h e C#-D dyad, however, t e n d s t o g i v e , t h r o u g h a g o g i c a c c e n t , an i n i t i a l , i f o n l y t e n t a t i v e , f e e l i n g o f a r r i v a l on D. F o l -179 lowing this , at .^ p, coincidence of D i n the v io l ins and F# in the viola and cello further suggests D major, even i f the feeling of arrival i s offset by the cello's F# occurrence i n the middle of a thematic gesture. This confluence of D and F# completes an inflected voice exchange between the two violins and the viola and cello.. The inflec-t ion concerns the upper note, F, of the f i r s t v e r t i c a l i t y i n the ex-change (D-F), which is superseded by F.# in the second verticality i(Q)r thereby demonstrating the parallel major-minor relationship alluded to at the opening of this chapter. In m. 29 (^)) the art iculat ion of D major is stronger yet, as i t comes on the downbeat of the measure, with the root preceded by a t r i l l on E (the second scale degree), and the f i f t h now preceded by i t s leading-tone G#. F inal ly , in mm. 35-36 (f^) the D-major referential triad is stated explicitly and is prolonged for two bars. Components in this gradual emergence of D major are summa-rized on system (b) of Ex. 4.5 which, when compared to the score, reveals the increasing temporal distance separating occurrences of the emerging referential tr iad . The f i r s t hint of D i s i n m. 25, then m. 26, m. 29, and finally mm. 35-36 (one-, three-, and six-bar intervals, respectively). Also noteworthy is the fact that the gradual emergence of D major within this phrase reflects a comparable emergence of tonal clarity occurring over the movement as a whole. System (c) of Ex. 4.5 reveals that mm. 31-34—the measures immediately preceding the resolute arr iva l of D major in mm. 35-36— comprise a prolongation of V; note, in part icular, the extended #4 disposition note—G#—-in the ce l lo of these measures (^ p). Also apparent on system (c) is the fact that the version of V articulated in 180 m. 34 i s , with Bb, the exact sonority which ended the second phrase. A large-scale connection between the two seems relevant as i t t i e s i n the arr i v a l point of the second phrase to the important a r r i v a l on D i n mm. 35-36 and completes the two large-scale motivic patterns i n i t i a t e d by the cadences of the f i r s t two phrases. The whole-tone encirclement pattern i s noted at (B), and the chromatic passing motion at (9). This, then, i s an example of i n t e r a c t i o n between phrase-length r e f e r e n t i a l elements and large-scale motivic parallelism. The phrase, however, does not conclude with this patent expres-sion of the D-major tr i a d but, rather, passes through i t , concluding on a v e r t i c a l i t y which could be construed as another version of the domi-nant of D, particularly i n i t s outer-voice augmented sixth, Eb-C# (Db i n the score). The cello's descending step motion from A 3 i n m. 35 to Eb-} i n m. 39, of which A 3 ~ F # 3 i n mm. 35-36 supports the prolongation of D discussed above, would seem to suggest continuation to D 3 , as this would complete an unfolding of the outer f i f t h of the D t r i a d , prolonged i n mm. 35-36, and would r e s u l t i n a larger-scale prolongation of that primary referential triad. Such an a r r i v a l , however, i s delayed u n t i l later. The brief phrase which follows, mm. 40-45, provides a degree of symmetry and thematic closure as i t i s a restatement of the opening theme at i t s original transposition (see Ex. 4.6).3 The brief phrase i s 3The thematic material to this point has been used as the basis for the introductions to the f i r s t three movements. In the movement under examination, however, this thematic section takes up forty-five of the total eighty-six measures and i s thus integral to the movement proper, and not merely introductory. 181 not, however, c l o s e d t o n a l l y . The theme i s harmonized t r i a d i c a l l y but n o n f u n c t i o n a l l y ; r o o t s o f t h e u n d e r l y i n g h a r m o n i e s move f o r t h e most p a r t by ascending step, a r r i v i n g on a v e r t i c a l i t y comprised of the major t h i r d and f i f t h o f the r e f e r e n t i a l D-major t r i a d , as w e l l as the f l a t -tened second s c a l e degree, a d i s p o s i t i o n note t o the r o o t D T h i s nonharmonic element forms, w i t h the f i f t h o f the r e f e r e n t i a l t r i a d , one of the o b l i q u e l y r e s o l v i n g t r i t o n e s d i s c u s s e d i n Chapter I I , and p r o -v i d e s a sense o f i m p e t u s i n t o t h e n e x t p h r a s e . R e s o l u t i o n o f t h e t r i -tone i s r h y t h m i c a l l y d i s p l a c e d through a r p e g g i a t i o n o f the r e f e r e n t i a l D major-minor t r i a d , as i n d i c a t e d a t The next phrase, mm. 46-54, may be understood t o d i v i d e i n t o two segments, each d e f i n e d by an a r p e g g i a t i o n o f the the D major-minor t r i a d i n one o f t h e v i o l i n s , i n d i c a t e d a t ^ ) i n Ex. 4.6. Accompanying t h i s , i n t h e c e l l o , i s a n o t h e r a t t e m p t a t a d e s c e n d i n g f i f t h f r o m A 3 t o D 3 . B o t h t h e m a j o r and m i n o r t h i r d s o f D, o c c u r r i n g i n t h e a r p e g g i a t e d t r i a d s i n the v i o l i n s , occur i n t h i s incomplete descending f i f t h i n the c e l l o r e p r e s e n t i n g another m a n i f e s t a t i o n o f the p a r a l l e l major-m i n o r r e l a t i o n s h i p c h a r a c t e r i z i n g t h e t o n a l i t y o f t h e movement. The l i n e a r descending f i f t h , were i t completed, would r e i n f o r c e the p r o l o n -g a t i o n a l f u n c t i o n o f t h i s phrase. Again, however, the f i f t h i s stopped s h o r t , i t s co n c l u d i n g p i t c h , E 3 , r e i n t e r p r e t e d from s c a l e degree 2 i n D t o 7 i n F. W i t h t h e i n f l e c t i o n o f t h e v i o l a ' s B b 2 (A# i n s c o r e ) t o B 2 i n t h e c e l l o , r e s o l u t i o n o f t h e f i n a l v e r t i c a l i t y o f t h e p h r a s e i s e f f e c t i v e l y r e d i r e c t e d f r o m D t o F - — t h e movement's o t h e r r e f e r e n t i a l t r i a d . The p h r a s e - l i n k i n g , three-note motive i n v o l v i n g t h i s i n f l e c t i o n 182 of Bb i s marked (5) i n Ex. 4.6. Completion of the l i n e a r step progression i n i t i a t e d by the i n f l e c t i o n and subsequent r e d i r e c t i o n of Bb i s to C, the root of the dominant of F. And i t i s this dominant which i n i t i a t e s the prolongation of F major i n mm. 55-60 of the next phrase (Ex. 4.7). This p a r t i c u l a r motive recurs immediately i n the lower l i n e of the f i r s t v i o l i n ((?)), where i t comprises scale degrees 4-#4-5 i n F, and i s redirected i n mm. 59-60 (f^2)), where i t a r t i c u l a t e s scale degrees #4-4-3, also i n F. The order of the B-Bb dyad thus dictates the direction of the motive and the goal note: scale degree 5 i n ascent and 3 i n descent. A tonal determinant of perhaps greater s i g n i f i c a n c e than the three-note motive just cited i s used i n the prolongation of F and beyond to m. 63, the end of the f i r s t h alf of t h i s phrase. I t involves e x p l i -c i t statement of the lower f i f t h of the lydian and phrygian orderings of the d i a t o n i c c o l l e c t i o n , constructs discussed i n Chapter II. In t h i s phrase, phrygian and lydian f i f t h s i n the second v i o l i n span C^ to F 4, connecting the roots of the two functional harmonies i n the prolongation of F, while the f i f t h s delineated by E^ and A 3 i n the viol a connect the thirds of those harmonies. These are indicated on system (a) with large sharp and f l a t symbols. This o s c i l l a t i o n of dominant and tonic e l e -ments, enriched by phrygian and lydian f i f t h s , effects prolongation of the F t r i a d i n a manner reminiscent of c e r t a i n passages the opening movement of the same quartet (Exx. 2.24 and 2.25). In m. 59 the lydian and phrygian f i f t h s , l i n k i n g 1 and 5 i n F, are transposed down a semi-tone, suggesting E (@). A b r i e f instance of overlapping b i t o n a l i t y occurs here: prolongation of F continues f o r one measure while a new 183 r e f e r e n t i a l PC, the s i g n i f i c a n c e o f which w i l l be r e a l i z e d i n the next segment, emerges. Analogy w i t h the opening movement i n v o l v e s more than the o s c i l -l a t o r y p r o l o n g a t i o n d e s c r i b e d above: below the emerging r e f e r e n t i a l PC E, the lower t h r e e instruments r e s o l v e t o F one f i n a l t i m e and continue t o progress along a c i r c l e o f f i f t h s t o n a l l y independent o f the i m p l i c a -t i o n o f E i n t h e upper p a r t . ( B o t h e x c e r p t s f r o m t h e f i r s t movement, r e f e r r e d t o above, continue w i t h d e s c e n d i n g c i r c l e - o f - f i f t h s p r o g r e s -s i o n s . ) The o s c i l l a t o r y p r o l o n g a t i o n o f F and subsequent c i r c l e o f f i f t h s a r e summarized on s y s t e m (b) o f Ex. 4.7. The f i n a l a r r i v a l o f E i n t h e f i r s t v i o l i n i n m. 63 c o i n c i d e s w i t h Eb i n t h e c e l l o — t h e l a s t element i n the c i r c l e o f f i f t h s — a s i n d i c a t e d a t ( V ) . E and Eb o f m. 6 3 — g o a l s o f d i s t i n c t l y d i f f e r e n t t o n a l processes from m. 5 9 — i n i t i a t e independent t e x t u r a l and t o n a l components i n the s e c o n d h a l f o f t h e p h r a s e , as i n d i c a t e d i n Ex. 4.8. E, f o r i n s t a n c e , b e g i n s a d e s c e n d i n g a r p e g g i a t i o n o f t h e d o m i n a n t o f F ( ^ ) , r e l a t i n g back t o the p r o l o n g a t i o n o f t h a t r e f e r e n t i a l t r i a d i n the previous p a r t o f t h e p h r a s e . On r e p e t i t i o n o f t h e a r p e g g i a t i o n ((p), t h e i n c l u s i o n o f C# renders the t e r t i a n c o l l e c t i o n more f l e x i b l e i n t h a t i t now poten-t i a l l y f u n c t i o n s a l s o as dominant o f D, t h e o t h e r p r i m a r y r e f e r e n t i a l t r i a d i n t h e movement (^ ))» And, a l t h o u g h t h e d u a l dominant f u n c t i o n o f t h i s a rpeggiated harmony i s not r e a l i z e d through e x p l i c i t r e s o l u t i o n i n t h i s p a r t i c u l a r phrase, t h e r e i s a t l e a s t a t e n t a t i v e suggestion o f D a t i t s end (m. 71) through a p a r t i a l r e s o l u t i o n o f t h e dominant. Thus, as suggested a t @, C# and A#(as B b ) — d i s p o s i t i o n notes 7 and b6 i n D— 184 may be heard t o r e s o l v e t o D and A, w h i l e E and G, the o t h e r two members of the dominant, ar e h e l d over t o the r e c a p i t u l a t o r y phrase beginning i n m. 72 ((5)). The c e l l o ' s Eb2 i n m. 63 i n i t i a t e s an i n d e p e n d e n t c o n t e x t u a l l y d i r e c t e d l i n e a r p r o g r e s s i o n t o Ab2 (^p)f t h e l a t t e r a r t i c u l a t i n g t h e beginning of the r e c a p i t u l a t i o n . The endpoints o f t h i s a scending-fourth p r o g r e s s i o n , El>2 and Ab2 (the l a t t e r as G#), have p o t e n t i a l s i g n i f i c a n c e i n t h e o v e r a l l t o n a l p l a n , as they w i l l be shown t o f u n c t i o n u l t i m a t e l y as b2 and #4 i n D, a d i s p o s i t i o n p a i r e x t e n s i v e l y documented as impor-t a n t i n Bartok's t o n a l language. I n t h a t t h i s l i n e a r p r o g r e s s i o n c o n -nects two d i s p o s i t i o n notes, l a t e r t o be considered a harmonic element, t h e p r o g r e s s i o n i s b e t t e r u n d e r s t o o d as an u n f o l d i n g and r e s u l t a n t p r o l o n g a t i o n of the d i s p o s i t i o n p a i r . T h i s p r o l o n g a t i o n a l f u n c t i o n w i l l become more e v i d e n t upon recurrence of the u n f o l d i n g i n the next phrase. I t m i g h t a l s o be n o t e d t h a t a l l f o u r d i s p o s i t i o n n o t e s t o D and A — t h e o u t e r f i f t h o f one o f t h e two r e f e r e n t i a l t r i a d s i n t h e m o v e m e n t — a r e represented i n t h i s phrase. And, of these, the two a v a i l a b l e from the major and minor s c a l e s — i . e . , 7 and b6—may be heard t o r e s o l v e , a l b e i t t e n t a t i v e l y , w h i l e r e s o l u t i o n of b2 and #4, from the phrygian and l y d i a n d i a t o n i c p a t t e r n s , i s d e f e r r e d u n t i l l a t e r . A n t i c i p a t i o n o f the r e s o l u -t i o n o f b2 and #4 i s i n t e n s i f i e d through t h i s d elay, and support f o r the p h r y g i a n and l y d i a n c o n s t r u c t s as u n d e r l y i n g r e f e r e n c e s f o r d i r e c t e d motion i s r e i n f o r c e d . A sense of r e c a p i t u l a t i o n may be f e l t i n the phrase beginning i n m. 72 (Ex. 4.9) because o f i t s use ( i n t h e f i r s t v i o l i n and v i o l a ) o f the e n c i r c l e m e n t motive from movement's opening (to be discussed). The 185 phrase extends the ascending fourth i n the cello of the preceding phrase through an ascending perfect f i f t h , Ab2-F±>2, a l s o i n the c e l l o ((p). Reference ( p represents t h i s l i n e a r progression as a prolongational unfolding of the b2-#4 disposition pair i n D—an "inverted" reiteration of the unfolding i n the previous phrase. This Ab-Eb as c e n d i n g - f i f t h manifestation of the b2-#4 p a i r i s fu r t h e r emphasized through i t s reiteration, i n mm. 75-78, by way of a PC descent back to G# also represented on system (b) as an unfolding Upon completion of this f i n a l unfolding, b2 and #4 resolve to D and A ((5}), i n i t i a t i n g the prolongation of D and F major i n the f i n a l phrase of the movement. Correspondences i n this symmetrical unfolding of the b2-#4 disposition p a i r are shown between systems (a) and (b) i n Ex. 4.9. Another example of interaction between linear progressions and prolongational unfoldings of disposition pairs i s apparent here. Two further d e t a i l s i n t h i s phrase are worthy of note. F i r s t , i n the PC descent back to G#, Eb and C# (mm. 75 and 76) are punctuated as the roots of major-minor triads ((6)), and these roots further imply D through t h e i r semitonal r e l a t i o n to that PC. The f i f t h and major t h i r d of the Eb t r i a d are the goals of the m o t i v i c a l l y derived step progressions i n the f i r s t v i o l i n and v i o l a (f^ ) and (^)), r e f e r r e d to above. And, second, i n the f i r s t v i o l i n , m. 75, the descending minor-t h i r d motive, F-E-D, from mm. 24-29, returns and i s compressed and transposed i n mm. 76-78. In mm. 77-78 the f i r s t notes of successive transpositions of the compressed pattern effect the whole-tone PC ascent F#-G#-A#-C (^)) which, i f continued with one more entry, would extend 186 to D; this represents a further element of contextual implication. As noted, the minor-third motive i s here transposed and com-pressed, and i t i s through these processes that the final entry, C-B-Bb i n m. 78, i s transformed into a retrograde version of the motive from mm. 54-55, the latter used in an elided cadence in which the motion was redirected from D to F through the motive's scale degree interpretation as 4-#4-5 in F. This, then, would be a case of la tera l interaction within the thematic-motivic stratum: the alteration of one motive results in i t s being transformed into another. Here, the transformed motive functions as a voice-leading device, just as the original did, i n that the Bb on which i t ends ultimately functions as scale degrees b6 in D and 4 in F. It i s the resolution of this disposition note, with that of #4 to 5 in D, which in i t ia tes the f ina l phrase, analyzed i n Ex. 4.1. This Bb is also redirected—as i t was earlier—through B to C as scale degrees 4-#4-5 i n F, resolving one measure after the prolongational f ina l phrase begins (f^ in Ex. 4.1). This effects an e l i s ion of the type noted from mm. 54 to 55. The Bb-B-C l inear motive i s heard one last time in an inner voice of the harmonic progression linking D and F i n the f ina l cadence ( f^ ) in Ex. 4.1). The detai ls of this f ina l prolongational segment were discussed at the beginning of the analysis and need not be repeated here. From the foregoing phrase-by-phrase analysis i t is possible to assemble a summary of primary determinants and procedures of tonal orientation in the movement, representing them on a single graph to show the large-scale deployment and interaction of these aspects i n the movement as a whole. In that some phrases employ more than one device 187 o r procedure, i t would prove advantageous t o represent each determinant on a s e p a r a t e system. The r e s u l t i n g , s t r a t i f i e d r e p r e s e n t a t i o n , i f f o l l o w e d one system a t a t i m e d u r i n g a hearing, would r e v e a l r e l a t i o n s between adjacent and nonadjacent r e c u r r e n c e s o f each d e t e r m i n a n t . I f v i e w e d v e r t i c a l l y a s t h e p i e c e u n f o l d s , s u c h a r e p r e s e n t a t i o n w o u l d i l l u s t r a t e t h e i n t e r a c t i o n o f v a r i o u s d e v i c e s employed i n a g i v e n phrase. A comprehensive study of a s k e l e t a l framework such as t h i s — o n e t a k i n g i n t o account both h o r i z o n t a l and v e r t i c a l d i m e n s i o n s — w o u l d p r o -v i d e the l i s t e n e r w i t h a complex m a t r i x o f r e l a t i o n s w i t h i n and between phrases by which l a r g e - s c a l e coherence i s achieved. Example 4.10 i s a g r a p h i c r e p r e s e n t a t i o n o f the type d e s c r i b e d above. Each phrase i n the movement i s represented on one o r more s y s -tems, determined by the s p e c i f i c t o n a l p r i n c i p l e s i t has been shown t o demonstrate. Here, t he phrase-length r e p r e s e n t a t i o n s are s k e l e t a l v e r -s i o n s of the analyses presented e a r l i e r . The bottom system i n d i c a t e s l a r g e - s c a l e p i t c h connections and t o n a l r e l a t i o n s , the c o n s t i t u e n t s o f w h i c h a r e drawn f r o m t h e s k e l e t a l r e d u c t i o n s i n t h e t o p f i v e s ystems. As a means o f c o n c l u d i n g t h e a n a l y s i s , t h i s example w i l l s ummarize s i g n i f i c a n t p o i n t s o f i n t e r a c t i o n which have been r e f e r r e d t o above, and w i l l p rovide a b a s i s f o r the h i e r a r c h i z a t i o n o f the two pr i m a r y r e f e r e n -t i a l t r i a d s i n the movement. R e f e r e n c e s f^ p, f^ p, and f^p i n d i c a t e i n t e r a c t i o n s between t h e m a t i c - m o t i v i c r e c u r r e n c e and m o t i v i c a l l y d e r i v e d , c o n t e x t u a l l y d i r e c t e d l i n e a r p r o g r e s s i o n s i n the f i r s t and second phrases and i n the r e c a p i t u l a t o r y phrase beginning i n m. 72. The two important i n s t a n c e s 188 of interaction between linear, progressions and disposition notes, where the function of the latter was ascribed to endpoints of the former, are indicated at (J) and (5). An i n t e r a c t i o n between large-scale motivic parallelism and large-scale tonality-defining harmonic progressions was shown to occur i n the opening three phrases, coincident with the f i r s t gradual emergence of D as root of a referential triad; this interaction i s indicated at Reference (7} identifies the lateral interaction involving transformation, of the motive at m. 24 into the one at 55, the point of transformation being m. 78, the beginning of the f i n a l phrase. And, an i n t e r a c t i o n might be noted i n mm. 55-63 (^ )) between the prolongation of F through o s c i l l a t i o n of conventional dominant and tonic harmonies, and the connection of the roots of those harmonies through the less conventional phrygian and lydian patterns. One f i n a l and very important mode of i n t e r a c t i o n concerns the tonicizing agents employed i n the movement. It was noted at the begin-ning of this chapter that one element of conventionality i n the movement was i t s use of the traditional dominant and a number of what I referred to as dominant substitutes, harmonies comprising alterations of degrees from the major and minor scales. One important r e s u l t of extensive a l t e r a t i o n , addition, and i n f l e c t i o n of chord tones i s an increased semitonal relation between the tonicizing agent and the tonic. Bartok uses conventional dominant variants of the type described above, begin-ning with the f i r s t phrase, where a conventionally functional tertian framework i s i n evidence, and extending well into the piece after such a framework has been abandoned. Bars 12, 22, 34, 39, and 52, for example, in d i c a t e a dominant function on the top system of Ex. 4.10. In each of 189 t h e s e c a s e s — m a r k e d [9J—a t h i c k , d o t t e d , v e r t i c a l l i n e e x t e n d s down f r o m t h e dominant t o a c o l l e c t i o n on t h e t h i r d s t a f f , i n d i c a t i n g t h a t the s e m i t o n a l r e l a t i o n o f t h e members of the dominant can be e x p l a i n e d t h r o u g h means o t h e r t h a n a l t e r a t i o n o f c o n v e n t i o n a l d o m i n a n t f o r m s . S p e c i f i c a l l y , they may be heard t o d e r i v e from the u n d e r l y i n g r e f e r e n -t i a l phrygian and l y d i a n octave p a t t e r n s , shown t o be o p e r a t i v e a t the s u r f a c e o f t h e m u s i c i n mm. 55-63. I n t h i s d e r i v a t i o n , t h e y a r e n o t a l t e r e d n o t e s a t a l l b u t a r e " d i a t o n i c , " so t o speak, t o t h e p h r y g i a n -l y d i a n composite p a t t e r n , a p a t t e r n which comprises two o r d e r i n g s o f the se v e n - n o t e d i a t o n i c c o l l e c t i o n , i n t e r s e c t i n g o n l y a t s c a l e d e g r e e s 1 and 5. T h i s p a r t i c u l a r t y p e o f i n t e r a c t i o n , t h e n , c o n c e r n s a d u a l i n t e r p r e t a t i o n o f t h e s e t o n i c i z i n g a g e n t s : a p p r e h e n s i b l e , on t h e one hand, as c o n v e n t i o n a l , i f a l t e r e d , d o m i n a n t s i n t h e o p e n i n g q u a s i -c o n v e n t i o n a l c o n t e x t , and on t h e o t h e r hand a p p r e c i a b l e i n l i g h t o f d i a t o n i c , t h ough n o n c o n v e n t i o n a l , r e f e r e n t i a l o c t a v e p a t t e r n s . The l a t t e r d e r i v a t i o n s e r v e s as a b a s i s f o r t h e g e n e r a t i o n o f i n d i v i d u a l " c o n t e x t u a l l y d i a t o n i c " d i s p o s i t i o n n o t e s s u c h as b2 and #4, two t e n -dency notes not a v a i l a b l e i n t h e major-minor system w i t h o u t i n v o k i n g the n o t i o n o f " a l t e r a t i o n . " The bottom system o f Ex. 4.10 shows the l a r g e - s c a l e o s c i l l a t i o n o f s e c t i o n s i n D and F, the two p r i m a r y r e f e r e n t i a l t r i a d s , and provides s u f f i c i e n t ground t o a s s e r t t h e s u p e r i o r i t y o f D o v e r F i n t h i s d u a l t o n a l r e l a t i o n . D, f o r example, i s f i r s t t o emerge as f o c a l , t h i s i n i t i a l o r i e n t a t i o n complemented by the l a r g e - s c a l e m o t i v i c p a r a l l e l i s m 190 a t ^p. F u r t h e r , t h e most s u b s t a n t i a l s e c t i o n i n F, mm. 55-65, o c c u r s between more l e n g t h y s e c t i o n s i n D and i s , as a r e s u l t , h e a r d as a d e p a r t u r e f r o m D t o a s e c o n d a r y t o n a l a r e a . And f i n a l l y , t h e l a s t phrase o f the movement i s , as noted e a r l i e r , more c o n s i s t e n t l y o r i e n t e d t o D, t h e f i n a l m o t i o n t o F b e i n g a r e f l e c t i v e r e f e r e n c e t o t h e move-ment s secondary r e f e r e n t i a l t r i a d . 191 CHAPTER V CONCLUSION A t t h e b e g i n n i n g o f t h i s p a p e r i t was a s s e r t e d t h a t , a l t h o u g h t h e r e e x i s t a g r e a t number o f s o u r c e s d e a l i n g w i t h t h e m u s i c o f B e l a B a r t o k , few a d d r e s s t h e c o n c e p t o f t o n a l i t y i n a t r u l y p e n e t r a t i n g , a n a l y t i c a l way. I t was f u r t h e r s t a t e d t h a t those sources t h a t d e a l w i t h t o n a l s t r u c t u r e are o f t e n i m p r e c i s e i n t h e i r s p e c i f i c a t i o n o f the means by which conventional p r i n c i p l e s o f t o n a l o r i e n t a t i o n are adapted t o the o f t e n n o n t r a d i t i o n a l contexts found i n Bartok, and inadequate i n t h e i r e x p l a n a t i o n o f how conv e n t i o n a l and nonconventional t o n a l determinants i n t e r a c t t o e f f e c t a u n i f i e d , coherent system o f r e l a t i o n s . I n seeking t o i l l u s t r a t e f a c t o r s o f t o n a l i t y i n Bartok's s t r i n g q u a r t e t s — a medium which spans h i s c o m p o s i t i o n a l c a r e e r , r e f l e c t i n g the most s i g n i f i c a n t and r e p r e s e n t a t i v e changes i n h i s m u s i c a l l a n g u a g e — t h e f o r e g o i n g s t u d y has t a k e n as a p o i n t o f d e p a r t u r e a b r o a d l y c o n c e i v e d concept of t o n a l i t y which views PC c e n t r i c i t y as a fundamental property, achieved through i n t e r a c t i o n s o f con v e n t i o n a l and nonconventional d e t e r -minants, thereby embracing a concept o f t o n a l i t y f r e e d from i t s s t r i c t h i s t o r i c a l a s s o c i a t i o n w i t h the common-practice p e r i o d . I t was a s s e r t e d t h a t the devices and processes by which t o n a l coherence i s achieved may be c l a s s i f i e d b r o a d l y i n t o p r o g r e s s i o n and p r o l o n g a t i o n , the s u b j e c t s o f d e t a i l e d i n v e s t i g a t i o n and e x e m p l i f i c a t i o n i n C h a p t e r s I I and I I I 192 r e s p e c t i v e l y . I t was noted t h a t the musical language o f Bartok's e a r l y quar-t e t s embodies many p r o p e r t i e s o f t h e l a t e n i n e t e e n t h c e n t u r y : e.g., i r r e g u l a r r e s o l u t i o n , c o n t i n u o u s t o n a l f l u c t u a t i o n , m u l t i p l e t o n a l i m p l i c a t i o n , t o n a l ambiguity, modal mi x t u r e , and harmonic s u b s t i t u t i o n . Excerpts from the f i r s t q u a r t e t s opening movement, f o r example, were c i t e d as demonstrative o f these p r o p e r t i e s i n a r e l a t i v e l y c o n s i s t e n t , c o n v e n t i o n a l l y f u n c t i o n a l t e r t i a n framework. I t was a l s o noted t h a t the most f u n c t i o n a l of p r o g r e s s i o n s — t h a t between the dominant and t o n i c — i s found i n many of Bartok's otherwise n o n t r a d i t i o n a l c o n t e x t s , where i t serves t o a r t i c u l a t e i d e n t i f i a b l e p o i n t s o f t o n a l o r i e n t a t i o n , between which l e s s c o n v e n t i o n a l p r i n c i p l e s o f p i t c h o r g a n i z a t i o n a r e op e r a t i v e . O f t e n , s u c h c o n v e n t i o n a l p a t t e r n s a r e used t o p u n c t u a t e t h e b e g i n n i n g a nd/or end o f l e s s t r a d i t i o n a l l y s t r u c t u r e d s e c t i o n s o r movements. C o n v e n t i o n a l l y f u n c t i o n a l r o o t r e l a t i o n s were shown t o govern t o n a l l y -o r i e n t i n g harmonic progressions over broad spans, where c o n s t i t u e n t s o f those progressions a r e n o n t e r t i a n . The b a s i c p r o g r e s s i o n o f dominant t o t o n i c was shown t o be the b a s i s f o r t o n i c i z i n g p r o g r e s s i o n s e m p l o y i n g d o m i n a n t and t o n i c a n a -logues, the former r e f e r r e d t o as c o n t e x t u a l t o n i c i z i n g agents and the l a t t e r as r e f e r e n t i a l elements. Among t h e d i s p a r a t e r e f e r e n t i a l e l e -ments i d e n t i f i e d a r e s i n g l e PCs, v e r t i c a l i t i e s of superimposed f i f t h s (termed h o m o i n t e r v a l l i c ) , and e n t i r e d i a t o n i c c o l l e c t i o n s . The contex-t u a l t o n i c i z i n g agent was demonstrated t o have commensurate v a r i e t y i n i n t e r v a l l i c s t r u c t u r e . I t was e x p l a i n e d t h a t , i n the absence o f func-t i o n a l r e l a t i o n s i n h e r e n t i n t h e m a j o r - m i n o r system, most c o n t e x t u a l 193 t o n i c i z i n g a g e n t s a c q u i r e c o m p a r a b l e i m p l i c a t i v e p r o p e r t i e s through r e t r o s p e c t i o n — i . e . , a f t e r t h e i r g o a l s a r e p u n c t u a t e d t h r o u g h p a t e n t f a c t o r s o f s u r f a c e exposure—and through frequency of a s s o c i a t i o n w i t h a p a r t i c u l a r r e f e r e n t i a l element. A s p e c i a l k i n d o f t o n i c i z i n g agent i n Bartok was termed a d i s p o -s i t i o n dominant, and d e f i n e d as one whose c o n s t i t u e n t s a r e s e m i t o n a l l y r e l a t e d t o members o f t h e r e f e r e n t i a l e l e m e n t w i t h w h i c h i t i s a s s o -c i a t e d and t o w h i c h i t p r o g r e s s e s . The t e n d e n c y f o r r e s o l u t i o n was shown t o be f o r t i f i e d i f such a dominant's component d i s p o s i t i o n notes were i n h e r e n t l y "unstable" by v i r t u e o f t h e i r p o s i t i o n i n a p a r t i c u l a r o r d e r i n g of the d i a t o n i c c o l l e c t i o n , o f which the major and minor s c a l e s and p h r y g i a n and l y d i a n modes were a c c o r d e d p a r t i c u l a r s i g n i f i c a n c e . I n t e r r u p t i o n from a predominantly whole-tone succession was c i t e d as the p r i m a r y c r i t e r i o n whereby s e m i t o n a l motions i n the phrygian and l y d i a n p a t t e r n s have t o n i c i z i n g f u n c t i o n . A t o n i c i z i n g agent r e f e r r e d t o as an o b l i q u e l y r e s o l v i n g t r i t o n e , shown t o have a b a s i s i n the phrygian and l y d i a n p a t t e r n s c i t e d above, was i d e n t i f i e d as an important c o n s t r u c t as i t commonly r e s o l v e s t o a p e r f e c t f i f t h — a harmonic i n t e r v a l o f r e l a t i v e c o n t e x t u a l s t a b i l i t y and r e f e r e n t i a l s i g n i f i c a n c e i n Bartok. The p e r f e c t f i f t h as an i n t e r v a l o f r o o t motion, p a r t i c u l a r l y i n a d e s c e n d i n g d i r e c t i o n , i s f u n d a m e n t a l t o t h e m a j o r - m i n o r system. Through i t s p a l p a b l e a s s o c i a t i o n w i t h t h e c o n v e n t i o n a l p r o g r e s s i o n o f dominant t o t o n i c , the descending f i f t h r e t a i n s i t s d i r e c t i v e p o t e n t i a l i n p assages where t h e s t r u c t u r e s e r e c t e d on c o n t e x t u a l l y d e s i g n a t e d r o o t s moving by t h a t i n t e r v a l are themselves nonconventional. Bartok's 194 m a n i f e s t a l l e g i a n c e t o t r a d i t i o n i s r e p r e s e n t e d i n p a r t by h i s use o f the p e r f e c t f i f t h as a melodic i n t e r v a l o f r o o t motion i n a v a r i e t y o f c o n t e x t s , s u p p o r t i n g d i s p a r a t e h a r m o n i c s t r u c t u r e s . P r o g r e s s i o n o f t e r t i a n harmonies along a descending c i r c l e o f f i f t h s , f o r example, was shown t o imbue c e r t a i n passages i n Bartok's q u a r t e t s w i t h an unequivocal sense o f c o n v e n t i o n a l l y f u n c t i o n a l d i r e c t e d motion. In other e x c e r p t s , t h e p e r f e c t f i f t h was i d e n t i f i e d as t h e i n f e r r e d r o o t m o t i o n between n o n t r a d i t i o n a l v e r t i c a l i t i e s . A t h i r d deployment of the p e r f e c t f i f t h was f o u n d i n t h e i n t e r v a l o f t r a n s p o s i t i o n o f t h e m a t i c g e s t u r e s i n i m i t a t i v e t e x t u r e s (not u n l i k e s i m i l a r procedures i n major-minor music of the common-practice p e r i o d ) . L i n e a r p r o g r e s s i o n i s t h e f o u r t h and f i n a l c l a s s i f i c a t i o n o f p r o g r e s s i o n d e a l t w i t h i n C h a p t e r I I . I t was s u g g e s t e d t h a t , i n t h e absence o f i n h e r e n t t e n d e n c i e s a s s o c i a t e d w i t h t h e m a j o r and m i n o r s c a l e s , l i n e a r c o n s t r u c t s i n n o n t r a d i t i o n a l contexts a r e o f t e n accorded d i r e c t i v e s i g n i f i c a n c e o n l y i n r e t r o s p e c t , a f t e r the g o a l of the succes-s i o n i s r e a l i z e d as primary through o t h e r , more patent f a c t o r s of punc-t u a t i o n and emphasis. T h i s t y p e o f c o n s t r u c t was r e f e r r e d t o as a c o n t e x t u a l l y d i r e c t e d l i n e a r p r o g r e s s i o n — a p r o g r e s s i o n whose s t e p and PC-step o r g a n i z a t i o n i s the s o l e f a c t o r o f d i r e c t i v e p o t e n t i a l . Because l y d i a n and phrygian p a t t e r n s were advanced as analogues of the major and minor s c a l e s , l i n e a r p r o g r e s s i o n s whose s t r u c t u r e i m i t a t e s those octave p a t t e r n s were termed i n h e r e n t l y d i r e c t e d . Components of these two types o f m i d - l e v e l p r o g r e s s i o n — c o n t e x t u a l l y d i r e c t e d and i n h e r e n t l y d i r e c t e d — a r e s e l e c t e d f r o m t h e s u r f a c e a c c o r d i n g t o f a c t o r s s u c h as 195 dynamic s t r e s s , m e t r i c p l a c e m e n t , d u r a t i o n a l emphasis, and r e g i s t r a l exposure. Where c o n s t i t u e n t s are accorded membership i n a l i n e a r p r o -g r e s s i o n based on t h e i r a n a l o g o u s p o s i t i o n i n concatenated t r a n s p o s i -t i o n s o f a p a r t i c u l a r motive ( f r e q u e n t l y the case i n B a r t o k ) , t he l i n e a r c o n s t r u c t s were s a i d t o be s y s t e m a t i c a l l y d e r i v e d . Chapter I I I d e a l t w i t h f o r e g r o u n d , m i d - l e v e l , and l a r g e - s c a l e p r o l o n g a t i o n a l processes, u s i n g H e i n r i c h Schenker's theory o f prolonga-t i o n i n major-minor music as a p o i n t of departure f o r the d e r i v a t i o n o f analogous and comparable though n o n t r a d i t i o n a l procedures. I t was s a i d t h a t t r a d i t i o n a l foreground motion w i t h i n a chord i s r e l e v a n t t o those p a s s a g e s o f t h e q u a r t e t s w h i c h e x h i b i t a c o n v e n t i o n a l l y f u n c t i o n a l t e r t i a n harmonic b a s i s ; m i d - l e v e l harmonic p r o l o n g a t i o n was a l s o shown t o be o f s i g n i f i c a n c e i n t h e s e p a r t i c u l a r s e c t i o n s . The t r a d i t i o n a l concept o f m i d - l e v e l l i n e a r u n f o l d i n g , i n which a v e r t i c a l i n t e r v a l i s h o r i z o n t a l i z e d , was i d e n t i f i e d as r e l e v a n t , the d i r e c t i v e p o t e n t i a l o f such a l i n e a r c o n s t r u c t a t ti m e s based on i t s l y d i a n o r phrygian s t r u c -t u r e . Apart from these p r o l o n g a t i o n a l p r i n c i p l e s , understood as ana-logues o f co n v e n t i o n a l procedure, i t was i n connection w i t h m i d - l e v e l spans i n n o n t r a d i t i o n a l c o ntexts t h a t a l t e r n a t i v e concepts o f expansion t e c h n i q u e s were i d e n t i f i e d as r e l e v a n t . R e i t e r a t i o n and o s c i l l a t i o n were i d e n t i f i e d a s two s u c h p r o c e s s e s o f e x p a n s i o n . O f t e n , t h e s e methods of expansion a r t i c u l a t e one t o n a l - t e x t u r a l stratum, over which a second stratum emerges. The superimposed l a y e r may be t o n a l l y support-i v e of o r opposed t o the u n d e r l y i n g stratum. I t may a l s o t a k e t h e form o f a p a t t e r n o f r e i t e r a t i o n and/or o s c i l l a t i o n , t h e r e b y d e f i n i n g an 196 o v e r a l l t e x t u r e o f c o m p a r a b l e s t r a t a , o r i t may p r e s e n t a t h e m a t i c gesture, r e s u l t i n g i n a "theme w i t h accompaniment" t e x t u r a l c o n f i g u r a -t i o n . The f i n a l c l a s s i f i c a t i o n o f p r o l o n g a t i o n , i n f a c t , d e a l s w i t h e x c e r p t s w h i c h s u p p o r t more t h a n one r e f e r e n t i a l e l e m e n t s i m u l -t a n e o u s l y — t h r o u g h t h e d u a l r e i t e r a t i o n / o s c i l l a t i o n format d e s c r i b e d above, b u t a l s o t h r o u g h o t h e r means d e f i n e d f o r p r e v i o u s c l a s s i f i c a -t i o n s . S t r u c t u r e s s u p p o r t i n g more t h a n one r e f e r e n t i a l e l e m e n t a r e o f t e n termed " b i t o n a l . " I n t h i s s e c t i o n s i m u l t a n e o u s l y prolonged e l e -ments are shown t o be a t t i m e s the r e s u l t o f o v e r l a p p i n g t o n a l - f o r m a l boundaries. I n some i n s t a n c e s , dual r e f e r e n t i a l elements can be h i e r -a r c h i z e d , w h i l e i n o t h e r s the d i f f i c u l t y o f p e r c e p t u a l s e p a r a t i o n and h i e r a r c h i z a t i o n may be u n d e r s t o o d as a t r a n s i t i o n a l o r d e v e l o p m e n t a l d e v i c e , employed d e l i b e r a t e l y t o e f f e c t t o n a l m o b i l i t y . Some examples i n C h a p t e r s I I . a n d I I I were used t o i l l u s t r a t e more than one t o n a l determinant: some o f these demonstrated d i s p a r a t e types of p r o g r e s s i o n , o t h e r s i l l u s t r a t e d d i f f e r e n t elements of prolonga-t i o n , and s t i l l o t h e r s r e v e a l e d f a c t o r s of p r o g r e s s i o n and p r o l o n g a t i o n . That such a m u l t i d i m e n s i o n a l view of these passages i s p o s s i b l e — e v e n n e c e s s a r y — a t t e s t s t o t h e c o m p l e x i t y and v i t a l i t y o f Bartok's m u s i c . Indeed, most of h i s music c o n s i s t s of i n t e r a c t i o n s between co n v e n t i o n a l and nonconventional p r o g r e s s i v e and p r o l o n g a t i o n a l determinants of t o n a l o r i e n t a t i o n , and i t i s o n l y t h r o u g h r e c o g n i t i o n o f t h e r e l a t i o n s h i p s between s u c h i n t e r a c t i v e e l e m e n t s t h a t a t h o r o u g h u n d e r s t a n d i n g o f Bartok's t o n a l language i s p o s s i b l e . 197 Chapter IV presented an analysis of the sixth quartet's f ina l movement with a view of such interactions as i t s specific goal. Each phrase was studied individual ly for progressive and prolongational determinants, and for i t s role i n sustaining tonal ambiguity or ef-fecting tonal c l a r i t y . The movement was found to employ many of the devices and processes studied in Chapters II and III. For example, contextually directed and inherently directed linear progressions are of v i t a l importance to the language of the movement, at times effecting prolongational unfoldings. Conventionally functional progressions of tertian harmonies and descending-fifth progressions were accorded sig-nificance as conventional means of directed motion. Of the contextual tonicizing agents relevant to the movement, disposition notes, disposi-t ion dominants, and obliquely resolving tritones were found to be the most common. Aside from prolongation through conventionally functional progressions and linear unfoldings, the contextual prolongational pro-cesses of oscillation and reiteration were shown to play a minor role. Phrygian and lydian scalar patterns were seen to be at times explicit in their interaction with descending- and ascending-fifth progressions, serving as an underlying basis according to which special directive potential was ascribed to the frequently used disposition notes b2 and #4. A final comprehensive sketch of this movement was used to i l lus -trate interactions between disparate tonal determinants employed simul-taneously, as well as interactions of particular devices as employed recurrently throughout the movement. This particular mode of represen-198 tation f a c i l i t a t e d a view of the piece as a unified structure of inter-related and not merely coexisting tonal elements. In this study, I have elected to focus on a restricted number of classifications of progression and prolongation i n Bartok's string quar-tets . These s p e c i f i c c l a s s i f i c a t i o n s were chosen because they are either direct adaptations of certain traditional properties or analogues of those properties. That i s , the classifications identified here have strong relation to convention, i n spite of their varied appearances and nontraditional contexts i n which they occur i n Bartok's music. Further-more, I have documented interrelations between these conventional and quasi-conventional progressions and prolongations, suggesting factors of overlap where conventional determinants serve as identifiable prototypes for less conventional devices. Although I have focussed on c e r t a i n basic t r a d i t i o n a l l y tonal motions—e.g., those of the descending f i f t h and the semitone—other, perhaps less conventional principles of tonal organization and centric orientation are undoubtedly of commensurate validity. Some such p r i n c i -ples (symmetry, f o r example) have been alluded to i n the foregoing study, although they have not been of immediate concern. References to sources dealing s p e c i f i c a l l y with those nonconventional means of pitch organization have been given throughout the study and are found i n the selected bibliography. What remains f o r a complete understanding of Bartok's musical language i s a study of interactions between conven-t i o n a l p r i n c i p l e s and analogues—some of which are i d e n t i f i e d i n the present paper—and less t r a d i t i o n a l means of tonal organization. The 19  r e s u l t a n t i n t r i c a t e m a t r i x o f i n t e r a c t i v e p r o p e r t i e s w o u l d i l l u m i n a t e j u n c t u r e s s i m u l t a n e o u s l y r e i n f o r c e d by c o n v e n t i o n a l and nonconventional elements, as w e l l as those exposed p r i m a r i l y through t r a d i t i o n a l means and those b e s t understood through newer, nonconventional determinants. Bartok's m u s i c a l language w o u l d i n d e e d be b e t t e r u n d e r s t o o d t h r o u g h p r e c i s e and thorough documentation o f the changing balance o f emphasis on c o n v e n t i o n a l and n o n c o n v e n t i o n a l p r i n c i p l e s . I t i s hoped t h a t , by f o c u s i n g on i n t e r a c t i o n s between c o n v e n t i o n a l and q u a s i - c o n v e n t i o n a l determinants of t o n a l o r i e n t a t i o n , t h i s study has taken a p r e l i m i n a r y s t e p on the way t o such a comprehensive v i e w o f the music of t h i s most important t w e n t i e t h - c e n t u r y composer. 200 GLOSSARY Contextual tonicizing agent Contextually directed linear progression Disposition dominant Disposition note Dominant prefix Embellishing pattern Functional A PC, ver t i ca l i ty , or col lect ion of PCs which immediately precedes, and is subsequently associated with, an identif iable referential element. A succession of step- or PC-step-related pitches and/or PCs which are comprehended as to direct ive potential only after their endpoints are otherwise punctuated as primary. A verticality comprised of disposition notes. A PC which is semitonally related to a constituent of a referential element (from above or below). Harmonies (other than the tonic) which precede the dominant in a functional progression. They are most commonly root related to the dominant by whole-tone (e.g., IV/ iv , V l / v i ) , by semitone (e.g., v i i of V, augmented sixth), or by descending f i f t h (e.g., i i , V of V). A succession of at least four notes which, when expressed as PCs, can be shown to begin and end with the same note (prolongational), or begin and end with notes which are PC-step-related (progressive). Motion between endpoints of the pattern is as f o l -lows: a leap from the f i r s t note, followed by step or PC-step motion to the final note; step or PC-step motion away from the f irst note, followed by a leap to the f ina l note; or step or PC-step motion away from the opening note an back to the final note. Functionally related and functionally directed har-monies are those whose root relations effect orien-tation to a particular tonic in the major-minor system. The term "functional" without further qualification thus means conventiona1ly functional. 201 H c m o i n t e r v a l l i e v e r t i c a l i t y o r c o l l e c t i o n I n h e r e n t l y d i r e c t e d l i n e a r p r o g r e s s i o n M i d - l e v e l p r o g r e s s i o n / p r o l o n g a t i o n M o t i v i c a l l y d e r i v e d l i n e a r p r o g r e s s i o n O b l i q u e l y r e s o l v i n g t r i t o n e P r o l o n g a t i o n a l p r o g r e s s i o n R e f e r e n t i a l element One whose c o n s t i t u e n t s , when expressed as PCs, may be arranged such t h a t they a r e separated by the same i n t e r v a l ; i n such arrangements, the lowest PC (i.e., the "PC-lowest" c o n s t i t u e n t ) i s designated as "root" f o r t h e p u r p o s e s o f d e f i n i n g " r o o t r e l a t i o n s " i n s t r u c t u r a l p r o g r e s s i o n s . A s u c c e s s i o n o f s t e p - o r P C - s t e p - r e l a t e d p i t c h e s and/or PCs w h i c h a r e comprehended as t o d i r e c t i v e p o t e n t i a l i n l i g h t o f t h e i r membership i n an i d e n t i f i a b l e o r d e r i n g o f t h e d i a t o n i c c o l l e c t i o n (e.g., major s c a l e , 1 y d i a n . o r d e r i n g ) . One whose c o n s t i t u e n t s a r e n o n c o n t i g u o u s and f r e -q u e n t l y e l a b o r a t e d by i n t e r v e n i n g p i t c h and PC e v e n t s . I t may o c c u r o v e r a b r i e f segment as w e l l as a passage o f much broader temporal span. A c o n t e x t u a l l y d i r e c t e d l i n e a r p r o g r e s s i o n whose c o n s t i t u e n t s are i n f e r r e d through s u c c e s s i v e t r a n s -p o s i t i o n s o f m o t i v i c m a t e r i a l . A t r i t o n e comprised o f s c a l e degrees 1 and #4 o r b2 and 5, t h e f o r m e r f u r n i s h e d by t h e l y d i a n o r d e r i n g o f t h e d i a t o n i c c o l l e c t i o n and t h e l a t t e r by t h e p h r y g i a n o r d e r i n g . The l y d i a n - d e r i v e d t r i t o n e commonly r e s o l v e s t o t h e p e r f e c t f i f t h b u i l t o f degrees 1 and 5 ( w i t h s c a l e degree 1 i n common), and the phrygian-derived t r i t o n e t o the same f i f t h b ut w i t h s c a l e degree 5 i n common. See U n f o l d i n g . The a n a l o g u e o f a c o n v e n t i o n a l t o n i c t r i a d . " R e f e r e n t i a l " d e n o t e s t h e f u n c t i o n o f s u c h a s o n o r i t y as the t o n a l "point o f refe r e n c e " t o which o t h e r p i t c h e v e n t s a r e r e l a t e d as s u b o r d i n a t e i n some c o n t e x t u a l l y d e f i n e d manner (explained i n each case). "Element" suggests the v a r i e t y of "sonorous q u a l i t i e s " w h i c h t h e r e f e r e n c e may t a k e . F o r 202 example, t h e t e r m s " r e f e r e n t i a l v e r t i c a l i t y " and " r e f e r e n t i a l PC" w i l l be u s e d w h e r e f u r t h e r d i s t i n c t i o n o r p r e c i s i o n i s r e q u i r e d i n s p e c i f y i n g t h e f o r m o f t h e r e f e r e n t i a l e l e m ent. The f i r s t o f these r e f e r s t o a v e r t i c a l i t y heard as f o c a l , w h i l e the second denotes the single, most fundamental and f o c a l PC i n a g i v e n context. " R e f e r e n t i a l element" i s thus a g l o b a l term i n c l u d i n g both s p e c i f i c types d e s c r i b e d above. A t t i m e s the p r i m a r y r e f e r e n t i a l e l e m e n t o f a p i e c e i s a p a r t i c u l a r PC, r e p r e s e n t e d t h r o u g h o u t by s e v e r a l d i s p a r a t e r e f e r e n t i a l v e r t i -c a l i t i e s and/or c o l l e c t i o n s ; a t o t h e r t i m e s a par-t i c u l a r v e r t i c a l i t y o r c o l l e c t i o n i s m a i n t a i n e d throughout as the s o l e r e p r e s e n t a t i o n o f the p i e c e s primary r e f e r e n t i a l element. Any p r i n c i p l e o r s e t o f p r i n c i p l e s by w h i c h a p a r -t i c u l a r PC o r PC co m p l e x ( i . e . , a r e f e r e n t i a l e l e -ment) i s e s t a b l i s h e d as p r i m a r y i n a g i v e n c o n t e x t and whose p r i m a c y i s m a i n t a i n e d a t a p a r t i c u l a r l e v e l o f s t r u c t u r e . A p r o g r e s s i o n i n which two members o f a harmony a r e t e m p o r a l l y separated and c o n n e c t e d l i n e a r l y . A l s o r e f e r r e d t o as a p r o l o n g a t i o n a l progression. 203 SELECTED BIBLIOGRAPHY Abraham, Gerald. "Bartok: S t r i n g Quartet No. 6." The Music Review 3 (1942). Antokoletz, E l l i o t . The Music of Bela Bartok: A Study of Tonality and  Progression i n 20th-century Music. Berkeley: University of Cal-if o r n i a Press, 1983. ' "The Music of Bartok: Some Theoretical Approaches i n the U.S.A." Studia Musicologica 24 suppl. (1982): 67-74. . "The Musical Language of Bartdk's 14 Bagatelles for Piano." Tempo 137 (June, 1981): 8-16. . "Pitch-Set Derivations from the Folk Modes i n Bartdk's Music." Studia Musicologica 24/3-4 (1982): 265-74. . "Principles of Pitch Organization i n Bartdk's Fourth String Quartet." In Theory Only 3/6 (1977): 3-22. . Principles of Pitch Organization i n Bartok's Fourth String Quartet. Ph.D. dissertation, City University of New York, 1975. Ayrey, Craig. "Berg's vScheideweg': A n a l y t i c a l Issues i n Op. 2 / i i . " Music Analysis 1/2 (1982): 189-202. Babbitt, Milton. "The S t r i n g Quartets of Bartdk." The Musical Quar- te r l y 35 (1949): 377-85. Bachmann, Tibor and Maria. Studies i n Bartdk's Music. 3 Vols. Media, PA: Bartdk Society of America, 1984. Baker, James. "Schenkerian Analysis and Post-Tonal Music." In Aspects  of Schenkerian Theory, ed. David Beach. New Haven: Yale Univer-si t y Press, 1983. Bares, Karen A. The F i f t h S t r i n g Quartet of Bela Bartdk: An Analysis Based on the Theories of Erno Lendvai. Ph.D. d i s s e r t a t i o n , University of Arizona, 1986. Bartok, Bela. "The Relation Between Folk Music and Art Music." In Bela Bartdk Essays, ed. Benjamin Suchoff. London: Faber & Faber, 1976. 204 Benjamin, William, "pour l e s Sixtes: An Analysis." Journal of Music  Theory 22/2 (1978): 253-90. Bernard, Jonathan. "Space and Symmetry i n Bartok." Journal of Music  Theory 30/2 (1986): 185-202. Berry, Wallace. "Symmetrical Interval Sets and Derivative Pitch Mate-r i a l s i n Bartok's String Quartet No. 3." Perspectives of New  Music 18 (1979-80): 287-379. . St r u c t u r a l Functions i n Music. Englewcod C l i f f s : Prentice H a l l , 1976. Cone, Edward. "The Uses of Convention: Stravinsky and His Models." In Stravinsky: A New Appraisal of His Work, ed. Paul Henry Lang. New York: W. W. Norton & Company, Inc., 1963. Crow, Todd ed. Bartok Studies. Detroit: Information Coordinators, 1976. De Bruyn, Randall. Contrapuntal Structure i n Contemporary Tonal Music: A Preliminary Study of T o n a l i t y i n the Twentieth Century. D.MA dissertation, University of I l l i n o i s , 1975. Dobszay, L. "The Absorption of Folksong i n Bartok's Composition." Studia Musicologica 24/3-4 (1982): 303-14. Forte, A l l a n . "Bartdk's S e r i a l Composition." The Musical Quarterly 46/2 (April, 1960): 233-45. . Contemporary Tone Structures. New York: Bureau of Publica-tions, Teachers College, Columbia University, 1955. Forte, Allan, and G i l b e r t , Steven. Introduction to Schenkerian Analy- s i s . New York: W. W. Norton & Company, Inc., 1982. Gow, David. "Tonality and Structure i n Bartok's F i r s t Two String Quar-tets." The Music Review 34/3-4 (Aug.-Ncv., 1973): 259-71. Haun, E. Modal and Symmetrical P i t c h Constructions i n Be l a Bartok's Sonata f o r Two Pianos and Percussion. D.M.A. d i s s e r t a t i o n , University of Texas at Austin, 1982. Hawthorne, R. "The Fugal Technique of Bel a Bartok." The Music Review 10 (Nov., 1949): 277-85. Jonas, Oswald. Introduction to the Theory of Heinrich Schenker. Trans-lated and edited by John Rothgeb. New York: Longman, Inc., 1982. 205 Kapst, Erich. Die "Polymodale Chrcmatik' Be la Bartoks. Ein Beitrag zur stilkritschen Analyse. Ph.D. dissertation, Leipsig, 1969. Karpati, Janos. Bartok's String Quartets. Hungary: Corvina Press, 1967. . "Tonal Divergences of Melody and Harmony: A Characteristic Device i n Bartok's Musical Language." Studia Musicologica 24/3-4 (1982): 373-80. Laufer, Edward. Review of Der freie Satz, by Heinrich Schenker. Music  Theory Spectrum 3 (1981):. 158-84. Lendvai, Erno. "Duality and Synthesis i n the Music of Bela Bartok." In Crow, Bartok Studies, Detroit: Information Studies, 1976, pp. 39-62. . Bela Bartok: An Analysis of His Music. London: Kahn and A v e r i l l , 1971. . The Workshop of Bartok and Kodaly. Budapest: Edition Musica, 1983 Lewin, Harold. "A Graphic Analysis of Bela Bartok's vMajor Seconds Broken and Together', Mikrokosmos, Vol. V, No. 132." Theory and  Practice 6/2 (1981): 40-46. McNamee, Ann. " B i t o n a l i t y , Mode, and Interval i n the Music of Karol Szymanowski." Journal of Music Theory 29/1 (1985): 61-84. Mason, Col i n . "An Essay i n Analysis: Tonality, Symmetry, and Latent S e r i a l i s m i n Bartdk's Fourth Quartet." The Music Review 18 (1957): 189-201. Monelle, Raymond. "Notes on Bartok's Fourth Quartet." The Music Review 29/2 (May, 1968): 123-29. Oster, Ernst. "Re: A New Concept of T o n a l i t y (?)." Journal of Music  Theory 4 (1960): 85-98. Parks, Richard. "Harmonic Resources i n BartrSk's Fourths." Journal of  Music Theory 25/2 (1981): 245-74. Perle, George. "Symetrical Formations i n the String Quartets of Bela Bartok." The Music Review 16 (1955): 300-312. . "Berg's Master Array of the Interval Cycles." The Musical Quarterly 63 (1977): 1-30. 206 Reaves, F. A. Bartok's Approaches to Consonance and Dissonance i n Selected Late Instrumental Works. Ph.D. dissertation, Univer-s i t y of Kentucky, 1983. Salzer, Felix. Structural Hearing: Tonal Coherence i n Music. New York: Dover Publications, Inc., 1952. Samson, Jim. Music i n Transition. London: J. M. Dent & Sons, Ltd., 1977. Schenker, Heinrich. Der f r e i e Satz. Translated and edited by Ernst Oster. New York: Longman, Inc., 1979. _ . Harmony. Edited by Oswald Jonas, translated by Elisab e t h Mann Borgese. Chicago: Chicago University Press, 1954; paper-back e d i t i o n , Boston: M.I.T. Press, 1973. Schoffman, Nahum. "Expanded Unisons i n Bartok." Journal of Musicologi- cal Research 4 (1982): 21-38. Stevens, Halsey. The L i f e and Music of Bela Bartok. New York: Oxford U n i v e r s i t y Press, 1964, rev. ed.. Suchoff, Benjamin. "Structure and Concept i n Bartok's Sixth Quartet." Tempo 83 (Winter, 1967-68): 2-11. Suchoff, Benjamin ed. Bela Bartok Essays. London: Faber & Faber, 1976. Szentkiralyi, Andras. Bartok's Second Sonata for V i o l i n and Piano. Ph.D. dissertation, Princeton University, 1976. . "Some Aspects of Bela Bartok's Compositional Techniques." Studia Musicologica 20 (1978): 157-82. Thomason, Leta. S t r u c t u r a l S i g n i f i c a n c e of the Motive i n the S t r i n g Quartets of Bela Bartok. Ph.D. d i s s e r t a t i o n , Michigan State University, 1965. Travis, Roy. "Tonal Coherence i n the F i r s t Movement of Bartok's Fourth String Quartet." Music Forum 2 (1970): 298-371. . "Toward a New Concept of Tonality." Journal of Music Theory 3 (1959): 257-84. Tre i t l e r , Leo. "Harmonic Procedure i n the Fourth Quartet of,Bartok." Journal of Music Theory 3/2 (1959): 292-98. Vauclain, Constant. "Bartok: Beyond Bi-Modality." The Music Review 42 (1981): 243-51. 207 Walbauer, I. "Intellectual Construct and Tonal Direction in Bartok's Divided Arpeggios." Studia Musicologica 24/3-4 (1982): 527-36. Walker, Mark. Thematic, Formal, and Tonal Structure in the Bartok String Quartets. Ph.D. dissertation, Indiana University, 1955. Whittall, Arnold. "Music Analysis as Human Science? Le Sacre du  Printemps in Theory and Practice." Music Analysis 1/1 (1982): 33-54. Wilson, Paul. Atonality and Structure in Works of Bela Bartok's Middle Period. Ph.D. dissertation, Yale University, 1982. . "Concepts of Prolongation and Bartok's Opus. 20." Music Theory Spectrum 6 (1984): 79-89. . Review of The Music of Bela Bartok: A Study of Tonality and Progression in Twentieth-Century Music, by E l l i o t Antokoletz. Journal of Music Theory 30/1 (1986): 113-121. 208 TABLE OF CONTENTS VOLUME 2 LIST OF EXAMPLES 210 GRAPHIC SYMBOLS ' 214 MUSIC EXAMPLES 217 EXAMPLE AND TEXTUAL REFERENCES TO QUARTET MOVEMENTS (LISTED IN CHRONOLOGICAL ORDER) 291 209 LIST OF EXAMPLES 2.1. Quartet No. 1, I, mm. 1-8 . 217 2.2. Quartet No. 1, I, mm. 8-16 218 2.3. Quartet No. 1, I, mm. 23-32 219 2.4. Quartet No. 1, I, mm. 65-71 220 2.5a. Quartet No. 5, III, mm. 3-9 . 221 2.5b. Quartet No. 5, III, mm. 92-93 221 2.6a. Quartet No. 2, I, mm. 171-180 222 2.6b.. Quartet No. 2, II, mm. 6-9, 14-16 222 2.7a. Quartet NO. 6, II, mm. 17-19 223 2.7b. Quartet No. 6, II, mm. 122-123 223 2.8. Quartet No. 1, III, mm. 156-160 224 2.9. Quartet No. 1, III, mm. 1-14 225 2.10. Quartet No. 5, II, mm. 1-4 226 2.11. Quartet No. 4, V, mm. 295-367 227 2.12. Quartet No. 5, II, mm. 6-7, 9-10, 19-22, 45-46, 54-56 . . . 228 2.13. Quartet No. 1, III, mm. 368-372 229 2.14. Interval structure of the lydian and phrygian octave patterns 230 2.15. Quartet No. 6, IV, mm. 12-13 . . 231 2.16. Quartet No. 5, I, mm. 23-25 231 2.17. Quartet No. 2, I, mm. 31-32 231 2.18a. Quartet No. 6, I, mm. 52-53 232 210 2.18b. Quartet No. 6, I, mm. 59-60 . . . 232 2.19. Quartet No. 6, I, mm. 80-82 232 2.20. Derivation of obliquely resolving tritones in the lydian and phrygian octave patterns 233 2.21. Quartet No. 2, II, mm. 1-7 . 234 2.22a. Quartet No. 4, V, mm. 14-18 235 2.22b. Quartet No. 4, V, mm. 391-392 235 2.23. Quartet No. 3, Seconda parte, mm. 56-61 236 2.24. Quartet No. 6, I, mm. 81-99 237 2.25. Quartet No. 6, I, mm. 312-332 238 2.26. Quartet No. 6, I, mm. 342-354 239 2.27. Quartet No. 3, Prima parte, mm. 65-72 240 2.28. Quartet No. 5, III, mm. 39-53 241 2.29. Quartet No. 4, V, mm. 156-182 242 2.30a. Quartet No. 4, III, mm. 1-13 243 2.30b. Quartet No. 4, III, mm. 64-71 243 2.31. Quartet No. 4, II, mm. 1-12 244 2.32a. Quartet No. 4, IV, mm. 6-14 245 2.32b. Quartet No. 4, IV, mm. 35-37 245 2.33. Quartet No. 3, Seconda parte, mm. 103-149 246 2.34. Quartet No. 5, I, mm. 6-13 . . 247 2.35. Quartet No. 5, I, mm. 11-25 248 2.36. Quartet No. 5, II, mm. 39-46 249 2.37. Quartet No. 4, V, mm. 102-143 250 2.38. Quartet No. 4, V, mm. 236-297 251 2.39. Quartet No. 1, III, mm. 115-122 252 211 2.40. Quartet No. 6, I, mm. 126-143 253 2.41. Quartet No. 5, III, mm. 1-39 254 2.42. Quartet No. 4, V, mm. 183-195 255 3.1. Quartet No. 6, I, mm. 60-82 256 3.2. Quartet No. 1, III, mm. 107-112 257 3.3. Quartet No. 6, I, mm. 1-13 258 3.4. Quartet No. 4, V, mm. 374-385 259 3.5. Quartet No. 5, I, mm. 44-58 260 3.6. Quartet No. 6, I, mm. 141-157 261 3.7. Quartet No. 5, II, mm. 26-29 262 3.8. Quartet No. 3, Prima parte, mm. 76-83 . . 263 3.9. Quartet No. 4, V, mm. 196-213 264 3.10. Quartet No. 2, III,-mm. 47-55 265 3.11. Quartet No. 2, I, mm. 60-69 266 3.12. Quartet No. 5, I, mm. 23-29 267 3.13. Quartet No. 4, V, mm. 214-237 268 3.14. Quartet No. 6, I, mm. 352-390 269 3.15. Quartet No. 4, V, mm. 1-5, 11-18, 23-26, 29-34, 37-45 . . . 270 3.16. Quartet No. 4, V, mm. 47-49, 52-53, 56-61, 63-75 271 3.17. Quartet No. 4, V, mm. 75-79, 81-87, 89-92, 97-104 272 3.18. Quartet NO. 4, V, mm. 320-332 . 273 3.19. Quartet No. 2, I, mm. 14-32 274 3.20. Quartet No. 1, I, mm. 33-53 275 3.21. Quartet No. 3, Prima parte, mm. 27-33 276 3.22. Quartet No. 3, Prima parte, mm. 35-43 277 3.23. Quartet No. 3, Prima parte, mm. 53-64 278 212 3.24. Quartet No. 6, I, mm. 31-60 279 3.25. Quartet No. 5, I, mm. 1-2, 8, 24-25, 44-45,'59-60, 126-127, 132-133, 146-148, 159-160, 167-168 280 4.1. Quartet No. 6, IV, mm. 78-86 281 4.2. Quartet No. 6, IV, mm. 1-13 282 4.3. Quartet No. 6, IV, mm. 1-13 . 283 4.4. Quartet No. 6, IV, mm. 13-22 284 4.5. Quartet No. 6, IV, mm. 22-39 285 4.6. Quartet No. 6, IV, mm. 40-54 286 4.7. Quartet No. 6, IV, mm. 55-63 • 287 4.8. Quartet No. 6, IV, mm. 62-72 . 288 4.9. Quartet No. 6, IV, mm. 72-79 289 4.10. Quartet No. 6, IV, mm. 1-86 290 213 GRAPHIC SYMBOLS A b b r e v i a t i o n s : d.d. = d i s p o s i t i o n dominant TIC+5 = ascending t r a n s p o s i t i o n by i n t e r v a l c l a s s 5. (descending t r a n s p o s i t i o n s denoted by a minus s i g n ) p r o g r e s s i o n o f s c a l e degrees as r e l a t e d t o the i n d i c a t e d r e f e r e n t i a l PC r e f e r e c e number 5, corresponding t o the t e x t (where t he number i s s i m i l a r l y enclosed) D: #4-5 = § -Note-heads: = nonharmonic notes = harmonic notes — i n t e r t i a n t e x t u r e s a t i n i t i a l l e v e l s o f d i s t i n c t i o n between s t r u c t u r a l a n d e l a b o r a t i v e notes J (# ) [* ] = subordinate harmonic elements and s i n g l e p i t c h e s and PCs — i n t e r t i a n a n d n o n t e r t i a n t e x t u r e s and a t a l l l e v e l s o f s t r u c t u r e = r e f e r e n t i a l e l e m e n t s ( i . e . , s t r u c t u r a l harmonic elements and s i n g l e p i t c h e s and PCs) — = enharmonic e q u i v a l e n t of a note g i v e n i n the score = PC ( i . e . , a note i n d i c a t e d on the graph i n a d i f f e r e n t octave f r o m i t s p l a c e m e n t i n t h e score) = i n f e r r e d PC, not a c t u a l l y present a t t h a t p l a c e i n the score 214 A c c i d e n t a l s ; A n a t u r a l - s i g n w i l l be g i v e n o n l y where the immediately preceding note i s an i n f l e c t i o n o f the same PC. [#] = i n f e r r e d a c c i d e n t a l fT| = i n f e r r e d a c c i d e n t a l which transforms the g i v e n nonharmonic note i n t o a chord-tone p h r y g i a n - f i f t h descent rjjr ^ = l y d i a n - f i f t h ascent ## = double sharp (the c o n v e n t i o n a l "x" re s e r v e d f o r enharmonically s p e l l e d notes as i n d i c a t e d above) Stems: r note which i s h i e r a r c h i c a l l y s u p e r i o r t o a f i l l e d note-head without a stem s t e p - r e l a t e d (whole-tone and/or semitone) e l a b o r a t i v e v e r t i -c a l i t y ) i n Exx. 2.29, 2.42, and 3.13, an a n a c r u s i s t o a p r i m a r y n o t e (stemmed) i n a p a r t i c u l a r motive = v o i c e exchange ^ t i o n s o f the f i r s t S l u r s and beams: > = connection o f h i e r a r c h i c a l l y s u p e r i o r notes ( f i l l e d by step, PC-step, o r l e a p ) — = recurrences o f the same p i t c h o r PC ^ ^ = order of notes i n score i s re v e r s e d on graph f o r i n f e r e n c e of l i n e a r c o n t i n u i t y 215 l i n e a r p r o g r e s s i o n b r o a d l y spaced recurrences of the same element u n f o l d i n g ( i . e . , l i n e a r i z a t i o n ) o f a v e r t i c a l i n t e r v a l a r p e g g i a t i o n o f a t r i a d r e f e r r e d t o i n t e x t s p e c i f i c motive r e f e r r e d t o i n t e x t 216 Ex. 2-.1. Quartet No. 1, I, mm. 1-8. 217 Ex. 2.2. Quartet No. 1, I, mm. 8-16. tfim. | F- i HL vi Y Iii p p LV: "2 - 3 Dt i i i "6* Bela Bartok - STRING QUARTET I Used by permission of Boosey & Hawkes (Canada) Ltd. 216 Used by permission of Boosey & Hawkes (Canada) Ltd. 219 Ex. 2.4. Quartet No. 1, I, mm. 65-71. Bela Bartok - STRING QUARTET I Used by permission of Boosey & Hawkes (Canada) Ltd. 220 Ex. 2.5a. Quartet No. 5, I I I , mm. 3-9. P'» «rro Bela Bartok - STRING QUARTET IV Copyright 1929 by Universal Edition A.G. Copyright renewed A l l Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 221 Ex. 2.6a. Quartet No. 2, I, mm. 171-180. A= i 222 Ex. 2.6b. Quartet No. 2, II, mm. 6-9, 14-Bela Bartok - STRING QUARTET II Copyright 1920 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. Ex. 2.7a. Quartet No. 6, Ex. 2.7b. I I , mm. 17-19. Quartet No. 6, | I I , mm. 122-123. Bela Bartok - STRING QUARTET VI Used by permission of Boosey & Hawkes (Canada) Ltd. 223 Ex. 2.8. Quartet No. 1, I I I , mm. 156-160. 224 Ex. 2.9. Quartet No. 1, I I I , mm. 1-14. 2 2 5 Ex. 2.10. Quartet No. 5, I I , mm. 1-4. mm. 1 2 3 4-Bela Bartok - STRING QUARTET V Copyright 1936 by Universal Edition A.G. Copyright renewed A l l Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian ag»nt for Universal Edition. 226 Ex. 2.11. Quartet No. 4, V, mm. 295-367. ~ '—i—f~ < ] A mil • : •f H _ p - P — r o l I r g n o . - -mm. 296 Bela Bartok - STRING QUARTET IV Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American **usic Distributors Corporation, sole Canadian agent for Universal Edition. 227 Ex. 2.12. Quartet No. 5, II, mm. 6-7, 9-10, 19-22, 45-46, 54-56. j 1 Bela Bartok - STRING QUARTET V Copyright 1936 by Universal Edition A.G. Copyright renewed A l l Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 228 Ex. 2.13. Quartet No. 1, I I I , mm. 368-372. Bela Bartok - S T R I N G Q U A R T E T I Used by permission of Boosey & Hawkes (Canada) Ltd. 229 Ex. 2.14. Interval s t r u c t u r e of the lydi a n and phrygian octave patterns. LYDIAN: IC"- 2 2 1 PHRYGIAN: IC 1 2 2 1 LYDIAN-PHRYGIAN COMPOSITE: „ o 1 1C: 2 2 2 'i__2 2 1 230 Ex. 2.15. Quartet No. 6, IV, mm. 12-13. mm.12 13 Ex. 2.16. Quartet No. 5, I, mm. 23-25. Ex. 2.17. Quartet No. 2, I, mm. 31-32. mm. 31 32 (a) 4 . d d - i (b)(j| M Bela Bartok - STRING QUARTET VI Used by permission of Boosey & Hawkes (Canada) Ltd. C'-dd. Bela Bartok - STRING QUARTET V Copyright 1936 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. (a) ( b ) # 4?#: dd. p 4V 2—13 7—1 Bela Bartok - STRING QUARTET II Copyright 1920 by Universal Edition A.G. Copyright renewed A l l Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 231 Ex. 2.18a. Quartet No. 6, I, mm. 52-53. Ex. 2.18b. Quartet No. 6, I, mm. 59-60. i i 1 >• s / ^ " ~ ~ ^ < m m . 5 2 5 3 I f f 5 9 60 3) •7 - t — Mr w B j b ^ - i f >6 > 5 * 3 D-d.d-1 Bela Bartok - STRING QUARTET VI Used by permission of Boosey & Hawkes (Canada) Ltd. 232 Bela Bartok - STRING QUARTET VI Used by permission of Boosey & Hawkes (Canada) Ltd. Ex. 2.20. Derivation of obliquely resolving tritones in the lydian and Phrygian octave patterns. i LYDIAN FIFTH: k #4-E PHRYGIAN FIFTH: k T 1 1 5 - — - 5 5E b2-2 3 3 Ex. 2.21. Quartet No. 2, II, mm. 1-7. mm. 1 2 3 4- 5 6 7 Bela Bartok - STRING QUARTET II Copyright 1920 by Universal Edition A.G. Copyright renewed A l l Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 2 3 4 Ex. 2.22a. Quartet No. 4, V, mm. 14-18. Ex- 2.22b. Quartet No. 4, V, mm. 391-392. Pesante, J * too Bela Bartok - STRING QUARTET IV Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 2 3 5 Ex. 2.23. Quartet No. 3, Seconda parte, mm. 56-61. Bela Bartok - STRING QUARTET III Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 2 3 6 Ex. 2.24. Quartet No. 6, I , mm. 81-99. 237 Ex. 2.25. Quartet No. 6, I, mm. 312-332. Used by permission of Boosey & Hawkes (Canada) Ltd. 238 Ex. 2.26. Quartet No. 6, I, rrm. 342-354. , fc*^—1 * t J-1 a - J ' 1 +1> (D:VJ JL -Y 1 ) Bela Bartok - STRING QUARTET VI Used by permission of Boosey & Hawkes (Canada) Ltd. 239 Ex. 2.27. Quartet No. 3, Prima p a r t e , mm. 65-72. mm.65 66 6 7 68 69 70 7] 72 Bela Bartok - STRING QUARTET III Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian aaent for Universal Edition. 240 Ex. 2.28. Quartet No. 5, I I I , mm. 39-53. Bela Bartok - STRING QUARTET V Copyright 1936 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 241 Ex. 2.29. Quartet No. 4, V, mm. 156-182. Bela Bartok - STRING QUARTET IV Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 242 Ex. 2.30a. Quartet No. 4, I I I , mm. 1-13. Ex. 2.30b. Quartet No. 4, I I I , mm. 64-71. A l l Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. Ex. 2.31. Quartet No. 4, II, irm. 1-12. mm.l 2 3 4- 5 6 7 8 9 10 11 12 Bela Bartok - STRING QUARTET IV Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 244 Ex. 2.32a. Quartet No. 4, IV, mm. 6-14. Ex. 2.32b. Quartet No. 4, IV, mm. 35-37. mm.6 7 8 9 10 11 12 13 14- 35 36 37 Bela Bartok - STRING QUARTET IV Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 2 4 5 Ex. 2.33. Quartet No. 3, Seconda p a r t e , mm. 103-149. Piii mojjo, J . . 8 0 - » 2 Bela Bartok - STRING QUARTET III Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 246 Ex. 2.34. Quartet No. 5, I , rrm. 6-13. mm. 6 8 9 10 11 12 13 Bela Bartok - STRING QUARTET V Copyright 1936 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 247 Ex. 2.35. Quartet No. 5, I , mm. 11-25. 19 20 21 ' 22 23 24 25 Bela Bartok - STRING QUARTET V Copyright 1936 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 248 Ex. 2.36. Quartet No. 5, I I , ram. 39-46. Bela Bartok - STRING QUARTET V Copyright 1936 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 249 Ex. 2.37. Quartet No. 4, V, mm. 102-143. 250 Bela Bartdk - STRING QUARTET IV Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. Ex. 2.38. Quartet No. 4, V, mm. 236-297. ,-, • *—• - /«" •e. rc. — i r 1 fmarc. • ft 248 249 2 50 f 1 , M J tr t i f if cr 260 261 262 263 B SECTION "77 <-A' SECTION 251 Bela Bartok - STRING QUARTET IV Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. Ex. 2.39. Quartet No. 1, I I I , mm. 115-122. 252 Ex. 2.40. Quartet No. 6, I , nm. 126-143. mm. 126 127 128 129 130 131 132 133 13+ 135 136 137 138 139 140 141 142 14-3 Bela Bartok - STRING QUARTET VI Used by permission of Boosey & Hawkes (Canada) Ltd. 2 5 3 Ex. 2.41. Quartet No. 5, I I I , mm. 1-39. 0, fe^n*. I'l' ' - ' 1 mm. Bela Bartok - STRING QUARTET V Copyright 1936 by Universal Edition A.G. Copyright renewed A l l Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 254 Ex. 2.42. Quartet No. 4, V, mm. 183-195. j Ex. 3.1. Quartet No. 6, I , mm. 60-82. 256 Bela Bartok - STRING QUARTET VI Used by permission of Boosey & Hawkes (Canada) Ltd Ex. 3.2. Quartet No. 1, i n , mm. 107-112. Bela Bartok - STRING QUARTET I Used by permission of Boosey & Hawkes (Canada) Ltd. 257 Ex. 3.3. Quartet No. 6, I , mm. 1-13. Ex. 3.4. Quartet No. 4, V, rrm. 374-385. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. I Ex. 3.5. Quartet No. 5, I, mm. 44-58. poco ritr-. Bete Bartok - STRING QUARTET V Copyright 1936 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 260 i Ex. 3.6. Quartet No. 6, I , nm. 141-157. Ex. 3.7. Quartet No. 5, II, mm. 26-29. r>.' I —Y — I Y - I Bela Bartok - STRING QUARTET V Copyright 1936 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 262 Ex. 3.8. Quartet No. 3, Prima par t e , mm. 76-83. mm. 76 Bela Bartok - STRING QUARTET III Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 263 Ex. 3.9. Quartet No. 4, V, mm. 196-213. Bela Bartok - STRING QUARTET IV Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 264 Ex. 3.10. Quartet No. 2, III, mm. 47-55. Bela Bartok - STRING QUARTET II Copyright 1920 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 2 6 5 Ex. 3.11. Quartet No. 2, I, mm. 60-69. Bela Bartok - STRING QUARTET II Copyright 1920 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. Ex. 3.12. Quartet No. 5, I, nm. 23-29. mm. 23 24 25 26 27 28 29 Bela Bartok - STRING QUARTET V Copyright 1936 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 267 Ex. 3.13. Quartet No. 4, V, mm. 214-237. Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 268 i mm.352 353 3 5 4 3 5 5 3 5 6 3 5 7 3 5 8 359 3 6 0 361 3 6 2 3 6 3 3 6 4 3 6 5 3 6 6 3 6 7 368 369 3 7 0 371 372 3 7 3 374 375 376 377 3 7 8 379 3 8 0 381 382 3 8 3 384 3 8 5 386 387 388 389 390 D--I 12 : Y I Bela Bartok - STRING QUARTET VT Used by permission of Boosey & Hawkes (Canada) Ltd. I 269 Ex. 3.15. Quartet No. 4, V, mm. 1-5, 11-18, 23-26, 29-34, 37-45. Bela Bartok - STRING QUARTET IV Copyright 1929 by Universal Edition A.G. Copyright renewed A l l Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 270 Ex. 3.16. Quartet No. 4, V, nm. 47-49, 52-53, 56-61, 63-75 ^ r ±. .h 1 r i • ^ t j H — ^ -^tS : : = J  1 — : ' • • •h , , , - . , -, , . ^ (b) Bela Bartok - STRING QUARTET IV Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 271 Ex. 3.17. Quartet No. 4, V, mm. 75-79, 81-87, 89-92, 97-104. mm.75 76 77 78 79 81 82 83 8 4 8 5 86 87 89 eo 91 92 97 98 99 100 101 102 103 104 A l l Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 272 Ex. 3.18. Quartet No. 4, V, mm. 320-332. mm. 320 321 322 323 324 325 326 327 328 329 330 331 332 ( b ) # ^ -g 273 5-Bela Bartok - STRING QUARTET IV Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. Ex. 3.19. Quartet No. 2, I, mm. 14-32. Ex. 3.20. Quartet No. 1, I, mm. 33-53. Used by permission of Bobsey & Hawkes (Canada) Ltd. 275 Ex. 3.21. Quartet No. 3, Prima parte, mm. 27-33 Bela Bartok - STRING QUARTET III Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 276 Ex. 3.22. Quartet No. 3, Prima parte, mm. 35-43. Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. Ex. 3.23. Quartet No. 3, Prima parte, mm. 53-64 d|)~i F~I » n i i r a • n n r n all»rn>ndO. _» poco a poco allargando n. Ir! f •• ^5 k. t K hi — / k \ k > \ V c ^ • Y (b) Bela Bartok - STRING QUARTET III Copyright 1929 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 278 Ex. 3.24. Quartet No. 6, I , ram. 31-60. Used by permission of Boosey & Hawkes (Canada) Ltd. 279 Ex.' 3.25. Quartet No. 5, I, mm. 1-2, 8, 24-25, 44-45, 59-60, 126-127, 132-133, 146-148, 159-160, 167-168. B M 4 - 5 Bela Bartok - STRING QUARTET V Copyright 1936 by Universal Edition A.G. Copyright renewed All Rights Reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for Universal Edition. 280 281 Ex. 4.2. Quartet No. 6, IV, mm. 1-13. 282 Bela Bartok - STRING QUARTET VI Used by permission of Boosey & Hawkes (Canada) Ltd. Ex. 4.3. Quartet No. 6, IV, mm. 1-13. Bela Bartok - STRING QUARTET VI Used by permission of Boosey & Hawkes (Canada) Ltd. 283 Ex. 4.4. Quartet No..6, IV, mm. 13-22. 284 Ex. 4.5. Quartet No. 6, IV/ mm. 22-39. Bela Bartok - STRING QUARTET VI Used by permission of Boosey & Hawkes (Canada) Ltd. 2 8 5 Ex. 4.6. Quartet No. 6, IV, mm. 40-54. Ex. 4.7. Quartet No,. 6, IV, mm. 55-63. mm.55 56 57 58 59 60 61 62 63 Es 1 - § T 5 T F : Y 1 Y 1 Y 1 Bfc Y 1 r-W _ _ f Bela Bartok - STRING QUARTET VI Used by permission of Boosey & Hawkes (Canada) Ltd. 287 Ex. 4.8. Quartet No. 6, IV, mm. 62-72. Ex. 4.9. Quartet No. 6, IV, mm. 72-79. 289 Ex. 4.10. Quartet No. 6, IV, mm. 1-86. mm. 1 3 4 5 6 7 8 9 10 11 12 13 7172 73 7% 75 76 77 78 79 80 81 83 84 85 86 (A) CONVENTIONAL HARMONIC PROGRESSIONS (B) Bl TONAL AND RELATIVE MAJOR-MINOR DUAL RELATIONSHIPS (Q DISPOSITION-NOTE RESOLUTIONS AND PHRYGIAN, LYDIAN PATTERNS CONTEXTUALLY DIRECTED LINEAR PROGRESSIONS (E) THEMATIC, MOTIVIC RECURRENCES (F) LARGE-SCALE PITCH CONNECTIONS EXAMPLE AND TEXTUAL REFERENCES TO QUARTET MOVEMENTS (LISTED IN CHRONOLOGICAL ORDER) Quartet No. 1: I - (2.1, 217), 26, 120;* (2.2, 218), 30, 113, 120; (2.3, 219), 32, 113, 120; (2.4, 220), 34; (2.13, 229),' 48; (3.20, 275), 154. I l l - (2.8, 224), 40; (2.9, 225), 40, 127; (2.39, 252), 98; (3.2, 257), 123. Quartet No. 2: I - (2.6a, 222), 38; (2.17, 231), 50; (3.11, 266), 138; (3.19, 274), 152. II - (2.6b, 222), 39; (2.21, 234), 53. I l l - (3.10, 265), 137. Quartet No. 3: Prima parte - (2.27, 240), 65; (3.8, 263), 135; (3.21, 276), 156; (3.22, 277), 156; (3.23, 278), 157. Seconda parte - (2.23, 236), 57; (2.33, 246), 76. Quartet No. 4: II - (2.31, 244), 72, 87. I l l - (2.30, 243), 70. IV - (2.32, 245), 74, 84. if Example number and page number in Volume 2 are given i n parentheses, followed by page numbers of textual references in Volume 1. 291 Quartet No. 4 (continued): V - (2.11, 227), 41, 55; (2.22, 235), 54, 126, 145; (2.29, 242), 67, 106, 122; (2.37, 250), 90, 166; (2.38, 251), 95; (2.42, 255), 107; (3.4, 259), 126; (3.9, 264), 136; (3.13, 268), 141; (3.15, 270), 144, 165; (3.16, 271), 147, 166; (3.17, 272), 149, 166; (3.18, 273), 151. Quartet No. 5: I - (2.16, 231), 50; (2.34, 247), 84; (2.35, 248), 88, 122; (3.5, 260), 128; (3.12, 267), 140; (3.25, 280), 167.. II - (2.10, 226), 41; (2.12, 228), 46; (2.36, 249), 89; (3.7, 262), 135. I l l - (2.5, 221), 37; (2.28, 241), 66; (2.41, 254), 103. Quartet No. 6: I - (3.14, 269), 41; (2.18, 232), 51; (2.19, 232), 51; (2.24, 237), 61, 83, 133; (2.25, 238), 61, 83, 133; (2.26, 239), 64; (2.40, 253), 100, 123; (3.1, 256), 113, 140; (3.3, 258), 125; (3.6, 261), 129, 143; (3.14, 269), 143; (3.24, 270), 159. II - (2.7, 223), 39. IV - (2.15, 231), 50; (4.1, 281), 172, 187; (4.2, 282), 173; (4.3, 283), 174; (4.4, 284), 177; (4.5, 285), 179; (4.6, 286), 181; (4.7, 287), 183; (4.8, 288), 184; (4.9, 289), 185; (4.10, 290), 188. 292 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0097482/manifest

Comment

Related Items