Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Aspects of musical language in György Ligeti’s Ten pieces for wind quintet (1968) Morrison, Charles Douglas 1983

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

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1983_A8 M67_3.pdf [ 10.5MB ]
Metadata
JSON: 831-1.0095760.json
JSON-LD: 831-1.0095760-ld.json
RDF/XML (Pretty): 831-1.0095760-rdf.xml
RDF/JSON: 831-1.0095760-rdf.json
Turtle: 831-1.0095760-turtle.txt
N-Triples: 831-1.0095760-rdf-ntriples.txt
Original Record: 831-1.0095760-source.json
Full Text
831-1.0095760-fulltext.txt
Citation
831-1.0095760.ris

Full Text

ASPECTS OF MUSICAL LANGUAGE IN GYORGY LIGETI'S TEN PIECES FOR WIND QUINTET (1968) by CHARLES DOUGLAS MORRISON B.Mus., The U n i v e r s i t y of Manitoba, 1981 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n THE FACULTY OF GRADUATE STUDIES (Department of Music) We accept t h i s t h e s i s as conforming to the req u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA September 1983 © Charles Douglas Morrison, 1983 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department o r by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department o f MU^Kl The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date OCTOBER S, 1 ^ 8 3 )E-6 (3/81) ABSTRACT Gyorgy L i g e t i ' s Ten Pieces for Wind Quintet (1968) i s a work r e p r e s e n t a t i v e of h i s s t y l e i n t h e m i d d l e s i x t i e s ; i t i l l u s t r a t e s many c o m p o s i t i o n a l p r o c e d u r e s i n a medium c o n s i d e r a b l y more "compact" than t h a t of many of h i s o t h e r works. Moreover, r e f i n e m e n t s of t e c h n i q u e s from e a r l i e r p i e c e s a r e apparent throughout the q u i n t e t . The f i r s t c h a p t e r t r a c e s the development of L i g e t i ' s c o m p o s i t i o n a l s t y l e from h i s e a r l y p e r i o d i n Hungary to h i s more mature p e r i o d , t h e s t y l e of which began to e v o l v e i n 1956 w i t h h i s move to V i e n n a . Major works a r e c i t e d , e x c e r p t s g i v e n , and s t y l i s t i c f e a t u r e s d e f i n e d and s u b s t a n t i a t e d , o f t e n by L i g e t i ' s own c h a r a c t e r i z a t i o n s of h i s changing m u s i c a l language. Chapter I I i s o l a t e s c e r t a i n m u s i c a l p a r a m e t e r s — f o r m , t e x t u r e , rhythm, and p i t c h — a n d d i s c u s s e s them i n d e p e n d e n t l y of each o t h e r , d e f i n i n g d e t a i l s of t h e i r s t r u c t u r e s and i l l u s t r a t i n g them i n e x c e r p t s from p i e c e s 2 to 9 of t h e q u i n t e t . C o n c e r n i n g a s p e c t s of form, subgroupings of p i e c e s w i t h i n t h e q u i n t e t as a whole a r e s u g g e s t e d , w h i l e d e l i n e a t i n g f a c t o r s w i t h i n i n d i v i d u a l p i e c e s a r e d i s c u s s e d i n t h e l i g h t of t h e parameters e f f e c t i n g such segment-a t i o n . The s e c t i o n d e a l i n g w i t h t e x t u r e i d e n t i f i e s two p r e v a l e n t arrangements i n the work, i . e . , "ensemble" and " s o l o i s t i c , " and o u t l i n e s g e n e r a l and s p e c i f i c t e x t u r a l a s p e c t s of each t y p e ( e . g . , modes of instrument i n t e r a c t i o n ) . Rhythmic p r i n c i p l e s a r e d i s c u s s e d n e x t , and t h e r o l e s of meter and o t h e r r h y t h m i c g r o u p i n g s a r e d e f i n e d and i l l u s t r a t e d . And f i n a l l y , the s e c t i o n on p i t c h o r g a n i z a t i o n t r e a t s l i n e a r and harmonic d e t a i l s s e p a r a t e l y . R egarding the former, v a r i o u s means of l i n e a r c o n n e c t i o n and p i t c h - c l a s s u n f o l d i n g a r e exposed, w h i l e i n t h e l a t t e r , harmonic s t r u c t u r e s a r e i i i i i c l a s s i f i e d and r e l a t e d a c c o r d i n g to a d e r i v e d system of consonance-d i s s o n a n c e f a c t o r s . Chapter I I , t h r o u g h the e x a m i n a t i o n p r o c e d u r e s o u t l i n e d above, p r o v i d e s a b a s i c u n d e r s t a n d i n g of t e c h n i q u e s and d e v i c e s i n p r e p a r a t i o n f o r t h e d e t a i l e d a n a l y s e s which f o l l o w i n Chapters I I I and IV. C hapters I I I and IV d e a l e x c l u s i v e l y and e x t e n s i v e l y w i t h t h e f i r s t and l a s t p i e c e s r e s p e c t i v e l y . A g a i n , m u s i c a l parameters a r e s t u d i e d i n d i v i d u a l l y , and many c o n c e p t s i n t r o d u c e d i n Chapter I I a r e f u r t h e r d i s c u s s e d . These and o t h e r c o n c e p t s ( t h e l a t t e r b e i n g i n t r o d u c e d w i t h s p e c i f i c r e f e r e n c e to t h e f i r s t and/or l a s t p i e c e s ) a r e a l s o approached on a l a r g e r s c a l e , p r o v i d i n g a comprehensive view of the p i e c e s ' o v e r a l l m u s i c a l s t r u c t u r e s . I n s t a n c e s of i n t e r a c t i o n between parameters a r e r e f e r r e d to i n t h i s r e g a r d . I n a d d i t i o n , t h e s e two d e t a i l e d a n a l y s e s i n c l u d e a s p e c t s of c o n n e c t i o n between the f i r s t and t h i r d p i e c e s of the q u i n t e t , and between the n i n t h and t e n t h . In Chapter V, c o n c l u s i o n s a r e g i v e n which p e r t a i n to t h e q u i n t e t as r e p r e s e n t a t i v e of L i g e t i ' s music of t h i s p e r i o d , as e v i d e n c e d i n f i n d i n g s r e s u l t i n g from the a n a l y s i s . TABLE OF CONTENTS ABSTRACT i i LIST OF EXAMPLES v i i ACKNOWLEDGMENTS x i EDITORIAL NOTES x i i Chapter I. INTRODUCTION 1 I I . ASPECTS OF MUSICAL LANGUAGE IN GYORGY LIGETI'S TEN PIECES FOR WIND QUINTET 23 I n t r o d u c t i o n 23 Formal O r g a n i z a t i o n o f t h e Work as a Whole 24 A s p e c t s of T e x t u r a l S t r u c t u r e 25 T e x t u r a l d e t a i l s i n ensemble p i e c e s 26 T e x t u r a l d e t a i l s i n s o l o i s t i c p i e c e s 32 Summary 39 P r i n c i p l e s of Rhythmic and M e t r i c D e s i g n 40 Summary 64 Modes o f P i t c h O r g a n i z a t i o n 66 L i n e a r d e t a i l s 66 Summary 85 Harmonic d e t a i l s 86 Summary 103 Summary 104 I I I . ANALYSIS OF PIECE NO. 1 105 I n t r o d u c t i o n 105 D e l i n e a t i n g F a c t o r s o f Formal Segmentation 105 Summary 106 A s p e c t s of T e x t u r a l S t r u c t u r e 107 T e x t u r a l q u a l i t y 107 T e x t u r a l space 110 Summary 112 i v V P r i n c i p l e s of Rhythmic and M e t r i c Design 112 Element-rhythms 113 Rhythm of impulse-density f l u c t u a t i o n 113 Rhythm of dynamically exposed p i t c h - p a i r groups . . . 116 Rhythm of t e x t u r a l - d e n s i t y f l u c t u a t i o n 119 Rhythm of t e x t u r a l q u a l i t y f l u c t u a t i o n 119 Rhythm of harmonic-density f l u c t u a t i o n 120 Rhythm of tempo change 120 I n t e r a c t i o n of element-rhythms 120 Summary 123 Modes of P i t c h O rganization . . . . . 124 Lin e a r d e t a i l s 124 Outer-voice p r o l o n g a t i o n 124 Linear progressions i n v o l v i n g l a t e r a l v o i c e c r o s s i n g . 133 Timbral connections 134 Connection through dynamic exposure 134 Connection through a r t i c u l a t i o n a f t e r a r e s t . . . . 136 Connections between dynamically exposed p i t c h - p a i r s . 140 Summary 144 Harmonic d e t a i l s 144 Measures 1-12 145 Measures 13-15 (the t r a n s i t i o n ) and the 'b'-section . 151 Summary 154 Connective Factors Between the F i r s t and T h i r d Pieces and I n t e r r u p t i v e Aspects of the Second 155 Summary 158 Summary 158 IV. ANALYSIS OF PIECE NO. 10 160 I n t r o d u c t i o n 160 D e l i n e a t i n g Factors of Formal Segmentation 160 Summary 161 Aspects of T e x t u r a l S t r u c t u r e 162 Formal s t r u c t u r e as defined by t e x t u r a l c o n d i t i o n s . . . 163 Te x t u r a l progressions as manifest i n d e n s i t y and s p a t i a l f l u c t u a t i o n s 167 T e x t u r a l - d e n s i t y . , 167 Te x t u r a l space 171 Summary 172 P r i n c i p l e s of Rhythmic and M e t r i c Design 173 Summary 178 Modes of P i t c h O rganization 179 Lin e a r d e t a i l s 179 Linear r e g i s t r a l connections 179 PC u n f o l d i n g 188 Summary 193 Harmonic d e t a i l s 194 Consonance-dissonance q u a l i t y of c o l o r a t i o n s 194 S p e c i f i c placement and content of c o l o r a t i o n s . . . . 198 S p e c i f i c placement of octave and unison doublings . . 200 Summary 201 Connective Factors Between the Ni n t h and Tenth Pieces '. . . 201 Summary 203 Summary 204 V. CONCLUSION 205 WORKS CITED 209 SELECTED BIBLIOGRAPHY 210 LIST OF EXAMPLES 1. Atmospheres, measures 1-6, showing s t a t i c , c h r o m a t i c sound mass 4 2. Atmospheres, measures 30-34, showing g r a d u a l l y t r a n s f o r m i n g s o n o r i t i e s 7 3. Atmospheres, measures 52-53, showing m i c r o p o l y p h o n y . . . . . 10 4. Volumina, r e h e a r s a l nos. 1 to 2, showing s t a t i c , c h r o m a t i c sound mass 12 5. Requiem, second movement, measures 67-72, showing m i c r o p o l y p h o n y 14 6. Apparitions, second movement, measures 10-17, showing a r a p i d s u c c e s s i o n of d i s p a r a t e t e x t u r e s 16 7. Aventures, measures 1-11, showing a r a p i d s u c c e s s i o n of d i s p a r a t e t e x t u r e s 18 8. Double Concerto, f i r s t movement, measures 68-74, showing a more t r a n s p a r e n t polyphony w i t h independent components . . 21 9. I n s t r u m e n t a t i o n - d e n s i t y and subgrouping of t h e t e n p i e c e s . . 24 10. P i e c e No. 5, measures 1-5, showing a s i n g l e t e x t u r a l element , 28 11. P i e c e No. 9, measures 8-13, showing one t e x t u r a l element . . . 29 12. P i e c e No. 3, measures 7-10, showing a subgrouping of components i n the t r a n s i t i o n a l passage 30 13. P i e c e No. 7, measures 3-8 and 40-41, showing d i s p a r a t e t e x t u r e s c h a r a c t e r i z i n g a d j a c e n t f o r m a l s e c t i o n s 31 14. P i e c e No. 2, measures 1-4, showing a two-element t e x t u r e . . . 33 15. P i e c e No. 6, measures 1-4, showing a two-element t e x t u r e . . . 34 16. P i e c e No. 8, measures 1, 2, 5, 10, and 12, showing an " e n s e m b l e - l i k e " t e x t u r e as an accompanimental element . . . 36 17. P i e c e No. 2, measures 12-15, showing one t e x t u r a l element w i t h one p r i m a r y and f o u r secondary components 37 v i i v i i i 18. Piece No. 4, measures 1-4, showing one t e x t u r a l element w i t h one primary and two secondary components 38 19. P i e c e No. 8, measures 1-16, impulse-density graph 43 20. P i e c e No. 8, measures 12-16 (horn part o n l y ) , showing l o w - l e v e l metric u n i t s 45 21. Piece No. 8, measures 1 (beats 1-2) and 10 (beats 3-4), showing p o t e n t i a l pulse d e f i n i t i o n 47 22. Piece No. 8, measure 5, showing rhythmic and l i n e a r patterns . 48 23. Piece No. 4, impulse-density graph 50 24. Pi e c e No. 4, l a r g e - s c a l e impulse-density u n i t s 52 25. P i e c e No. 3, impulse-density graph 53 26. P i e c e No. 3, me t r i c u n i t s 55 27. Piece No. 3, measures 10-12, rhythmic and me t r i c design . . . 57 28. Piece No. 5, impulse-density graph 58 29. Piece No. 7, measures 38-44, impulse-density graph 60 30. Piece No. 2, l o c a l a r r i v a l p o i n t s (measures 9-12 and 23-24) . 62 31. P i e c e No. 6, l o c a l a r r i v a l / d e p a r t u r e p o i n t s (measures 8-9 and 10-11) 63 32. P i e c e No. 8, measures 26-32, showing consecutive d i s p a r a t e musical ideas 65 33. Piece No. 2, measures 12-15, two simultaneous l i n e a r i z a t i o n s . 68 34. Pi e c e No. 2, measures 21-22 and 29, two simultaneous l i n e a r i z a t i o n s 68 35. P i e c e No. 4, measures 1-8, simultaneous l i n e a r connections . . 71 36. Piece No. 7, measures 38-44, l i n e a r progression of t r i t o n e s . 73 37. P i e c e No. 5, PC o r d e r i n g s , showing PC p a i r and IC o r d e r i n g r e l a t i o n s h i p s 74 38. Pieces 5 and 6, PC p a i r and IC ordering r e l a t i o n s h i p s . . . . 75 39. Pieces 9, 5, and 6, patterns of PC u n f o l d i n g 77 40. PC connection between the f i f t h and s i x t h pieces 79 41. P i e c e No. 8, measures 1-12, wedge-patterned l i n e a r i z a t i o n s . 80 i x 42. P i e c e No. 8, measures 1-12, p a t t e r n e d p i t c h u n f o l d i n g as compared to r h y t h m i c a c t i v i t y 80 43. P i e c e No. 3, measures 1-8, l i n e a r components through u n i s o n t r a n s f e r and p i t c h i n t e r c h a n g e 83 44. P i e c e No. 3, measures'1-8, harmonic complexes 88 45. P i e c e No. 3, measures 1-8, c o n s o n a n c e - d i s s o n a n c e c r i t e r i a and harmonic q u a l i t y f l u c t u a t i o n 89 46. P i e c e No. 5, measures 1-8, l i n e - g r a p h r e p r e s e n t a t i o n of l i n e a r and harmonic e x p a n s i o n 92 47. P i e c e No. 9, measures 8-15, l i n e - g r a p h r e p r e s e n t a t i o n of l i n e a r and harmonic e x p a n s i o n 94 48. P i e c e No. 2, measures 12-13; and p i e c e No. 4, measure 1, harmonic i n t e r v a l f l u c t u a t i o n t h r o u g h v o i c e l e a d i n g . . . . 97 49. P i e c e No. 4, measures 7-9 and 23-26, harmonic i n t e r v a l f l u c t u a t i o n t h r o u g h v o i c e l e a d i n g 98 50. P i e c e No. 2, harmonic o r g a n i z a t i o n 101 51. P i e c e No. 7, measures 1-38, harmonic o r g a n i z a t i o n 101 52. L i n e - r e p r e s e n t a t i o n of t e x t u r a l components, showing t e x t u r a l q u a l i t y 109 53. T e x t u r a l spaces of f o r m a l segments I l l 54. Two l e v e l s o f i m p u l s e - d e n s i t y f l u c t u a t i o n 115 55. U n i t s of d y n a m i c a l l y exposed p i t c h - p a i r groups 118 56. I n t e r a c t i o n of s i x element-rhythms 122 57. O u t e r - v o i c e p r o l o n g a t i o n i n measures 1-16 126 58. L i n e a r s t r u c t u r e of t h e ' b ' - s e c t i o n and i t s r e l a t i o n s h i p to t h e ' a ' - s e c t i o n 132 59. Two i n s t a n c e s of t i m b r a l c o n n e c t i o n i n l a t e r a l v o i c e -c r o s s i n g e v e n t s 135 60. One i n s t a n c e of c o n n e c t i o n t h r o u g h dynamic exposure 135 61. One i n s t a n c e of c o n n e c t i o n through a r t i c u l a t i o n a f t e r a r e s t . 136 Examples 52-67 ( i n c l . ) p e r t a i n to p i e c e No. 1. X 62. L i n e a r p r o g r e s s i o n s i n v o l v i n g l a t e r a l v o i c e c r o s s i n g i n measures 1-12 139 63. C o n n e c t i o n s t h r o u g h d y n a m i c a l l y exposed p i t c h - p a i r s i n measures 1-14 142 64. Harmonic s t r u c t u r e 147 65. Consonance-dissonance c r i t e r i a and C-D f a c t o r s 149 66. R e c u r r i n g s e t s of e q u a l harmonic q u a l i t y i n u n i t s of d y n a m i c a l l y exposed p i t c h - p a i r s 153 67. P i t c h r e l a t i o n s h i p s between t h e f i r s t and t h i r d p i e c e s . . . . 157 c68. L i n e - g r a p h r e p r e s e n t a i o n 165 69. Four modes of t e x t u r a l - d e n s i t y f l u c t u a t i o n 170 70. Impulse-number p r o p o r t i o n s of p h r a s e fragments and i m p u l s e - d e n s i t y graph 176 71. M o t i v i c d e f i n i t i o n of r e g i s t e r s i and i i 180 72. F i r s t and second l e v e l s of l i n e a r p i t c h s t r u c t u r e 183 73. T h i r d and f o u r t h l e v e l s o f l i n e a r p i t c h s t r u c t u r e 187 74. M o t i v i c o r g a n i z a t i o n i n r e g i s t e r s i , i i , and i i i 188 75. PC c o n t e n t of f o r m a l segments 191 76. Consonance-dissonance f a c t o r s of c o l o r a t i o n v e r t i c a l i t i e s . . 197 77. L i n e a r p r o g r e s s i o n r e l a t i o n s h i p between t h e n i n t h and t e n t h p i e c e s ..' .' 202 78. Twelve-note a g g r e g a t e c o m p l e t i o n from the n i n t h to the t e n t h p i e c e 203 Examples 68-78 ( i n c l . ) p e r t a i n to p i e c e No. 10. ACKNOWLEDGMENTS 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 , t h e f o l l o w i n g p u b l i s h e r s a r e 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 Canadian agent f o r B. S c h o t t ' s Soehne; C. F. P e t e r s C o r p o r a t i o n , New York; and U n i v e r s a l E d i t i o n A.G., Wien. I would l i k e to e x p r e s s my utmost g r a t i t u d e t o Dr. W a l l a c e B e r r y f o r h i s c a r e f u l s u p e r v i s i o n and i n v a l u a b l e s u g g e s t i o n s throughout the c o u r s e of t h i s p r o j e c t . A l s o , I wish to extend my thanks to Dr. Gregory B u t l e r f o r h i s r e a d i n g o f t h e paper and h e l p f u l comments. To Dr. W i l l i a m Benjamin, f o r h i s gu i d a n c e i n t h e e a r l y s t a g e s of t h i s p r o j e c t and f o r h i s r e a d i n g of the t h e s i s , 1 o f f e r my a p p r e c i a t i o n . x i EDITORIAL NOTES Subheadings of the s e c t i o n s w i t h i n chapters of t h i s paper are rank-ordered i n the f o l l o w i n g manner: F i r s t - L e v e l Subheading Second-Level Subheading T h i r d - l e v e l subheading F o u r t h - l e v e l subheading R e g i s t r a l l y s p e c i f i c p i t c h e s are designated according to 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 1 c 2 c 3 c 4 c 5 c 6 c 7 ^Y. ) z -/ ° —( •) V J. i -e-Upper-case l e t t e r s w i t h s u p e r s c r i p t numbers thus denote r e g i s t r a l l y s p e c i f i c 4 3 p i t c h e s , e.g., E , D , e t c . P i t c h - c l a s s e s ( i . e . , r e g i s t r a l l y n o n - s p e c i f i c p i t c h e s ) are i n d i c a t e d by upper-case l e t t e r s , e.g., D, F//, etc. PC stands f o r p i t c h - c l a s s , IC f o r i n t e r v a l - c l a s s , and C-D f a c t o r f o r consonance-dissonance f a c t o r (explained at the appropriate point i n the text). x i i CHAPTER I INTRODUCTION The year 1956 may be considered a major t u r n i n g point i n Gyorgy L i g e t i ' s l i f e , f o r i t was the move from Hungary ( h i s place of b i r t h i n 1923) to Vienna i n that year which put him i n contact w i t h s e v e r a l l e a d i n g European avant-garde composers such as Eimert, Koenig, and Stockhausen. ^" The r e s u l t of t h i s exposure was a marked change i n L i g e t i ' s compositional s t y l e . L i g e t i ' s works p r i o r to 1956 may be d i v i d e d i n t o three smaller groups. His e a r l i e s t works, composed between 1938 and 1942, c o n s i s t mainly 2 of unpublished piano p i e c e s , chamber works, and songs. From the middle to l a t e f o r t i e s , however, the p o l i t i c a l s i t u a t i o n l a r g e l y r e s t r i c t e d the 3 composition of new music to mere folksong arrangements. And f i n a l l y , i n the e a r l y f i f t i e s , when the r e s t r i c t i o n s were somewhat r e l a x e d , L i g e t i began to develop a new s t y l e : About 1950 I r e a l i z e d that f u r t h e r development i n the post-Bartok s t y l e i n which I had been composing was not the way f o r w a r d f o r me. . . . I n 1951 I s t a r t e d to experiment w i t h simple s t r u c t u r e s of rhythm and sound i n order, i n a manner of speaking, to b u i l d up a new music from nothing. . . . I asked myself: what can I do w i t h a s i n g l e note? what can I do w i t h i t s octave? what w i t h one i n t e r v a l ? what w i t h two i n t e r v a l s ? what w i t h d e f i n i t e rhythmic r e l a t i o n s h i p s which could form the foundations of a whole based on rhythm and i n t e r v a l ? In t h i s way s e v e r a l small *0ve Nordwall, " L i g e t i , Gyorgy," The New Grove Dictionary of Music and Musicians, e d i t e d by Stanley Sadie, v o l . 10, p.854. 2 Ibid. ^Ibid. 1 , 2 pieces were composed, c h i e f l y f o r the piano. His Musica ricercata (11 Pieces f o r Piano, 1951-53) was composed i n the wake of these questions."' While t h i s work contains some of the seeds of L i g e t i ' s new s t y l e , a f r e e l y t o n a l language remains prominent i n the Ba r t o k - i n f l u e n c e d S t r i n g Quartet No. 1 - Metamorphoses nocturnes (1953-54), and Ejszaka, Reggel (1955) f o r chorus. In 1956, w i t h the move to Vienna, L i g e t i developed the s t y l e which brought him i n t e r n a t i o n a l a c c l a i m — a s t y l e which he maintained f o r about a decade. Apparitions (1958-59) and Atmospheres (1961), both f o r o r c h e s t r a , are the works which were l a r g e l y r e s p o n s i b l e f o r t h i s immediate widespread r e c o g n i t i o n . Atmospheres i s c h a r a c t e r i z e d by the use of s t a t i c , chromatic sound masses, g r a d u a l l y transforming s o n o r i t i e s , and micropolyphony. The f i r s t of these three t e x t u r e s , as i l l u s t r a t e d i n Example 1, i s defined as a sustained chromatic c l u s t e r . In t h i s p a r t i c u l a r excerpt, the sound block inc l u d e s every p i t c h from 6 T - 7 " a m e t r i c a l l y " as though suspended i n space. ^ - t o j y f r * except CJ. ^ , sustained 4 Gyorgy L i g e t i , quoted i n Ove Nordwall, l i n e r notes f o r Musica ricercata (1951-53), on Duo Pohjola (Grammofonfirma BIS 18, recorded i n W. Germany, 1974). Given the u n a v a i l a b i l i t y of published sources by L i g e t i , of sources which quote L i g e t i , i n f o r m a t i o n gleaned from l i n e r notes such as t h i s has proved i n v a l u a b l e i n a s c e r t a i n i n g L i g e t i ' s own c h a r a c t e r i z a t i o n s of the techniques of h i s musical language. 5Ibid. 6 This sustained sound mass may be considered "ametric" because of the absence of p e r c e i v a b l e , accent-delineated m e t r i c u n i t s ; the 4 time signature and notated b a r l i n e s are e s s e n t i a l l y n o t a t i o n a l conveniences. 7My c h a r a c t e r i z a t i o n of these measures i s corroborated by Thomas C l i f t o n i n h i s recent book, Music as Heard (New Haven: Yal e U n i v e r s i t y P r ess, 1983), pp. 155-56. C l i f t o n s t a t e s : "The most elemental kinds of surface occur under three c o n d i t i o n s : the f i r s t r e q u i r e s the absence of movement; the second, the absence of any c o n t r a s t i n dynamics; and the t h i r d , an absence of t i m b r a l complexity. The opening measures of L i g e t i ' s Atmospheres r e v e a l the 3 Example 1. Atmospheres, measures 1-6, showing s t a t i c , c h r o m a t i c sound mass. unmerklich einsetzen / imperceptible ottack die Tremoli so dicht wie moglich / the tremolos as thick as possible 1) without the hair of the bow 2) scarcely audible 0 1 9 6 3 by Universal Edition A . G . Reprint with permission of Universal Edition Wien 5 Example 2, a l s o from Atmospheres, i l l u s t r a t e s a t e x t u r e which c o n s i s t s of g r a d u a l l y changing s o n o r i t i e s . In t h i s process, each member g of an e s t a b l i s h e d v e r t i c a l s o n o r i t y moves independently of others u n t i l a new v e r t i c a l i t y has evolved. This p a r t i c u l a r excerpt f e a t u r e s the i n t e r a c t i o n of s e v e r a l sound b l o c k s , each of which goes through the metamorphic process described above. For ins t a n c e , i n measure 30, the - ) — 9 ^ 0 » > t n e p i t c h e s of which move one second v i o l i n s are s u s t a i n i n g by one u n t i l -s 1 i s formed i n bar 32 and subsequently:sustained. Occurring r h y t h m i c a l l y independent o f , but nevertheless concurrent w i t h , the second v i o l i n s ' t r ansformation i s a progression from f to i n the v i o l a s , e f f e c t e d through the same process. The p i c c o l o s , oboes, c l a r i n e t s , trumpets, f i r s t v i o l i n s , and c e l l o s are a l s o engaged i n independent s o n o r i t y transformations throughout these measures. "Micropolyphony," as i l l u s t r a t e d i n Example 3, i s defined by L i g e t i as: . . . a technique by which instrumental p a r t s are interwoven and crowded together i n t o a dense contrapuntal t e x t u r e . There are so many p a r t s , and t h e i r polyphonic interweaving i s so complex, that the i n d i v i d u a l p a r t s are completely submerged i n t o a micropolyphonic web, and the o v e r a l l musical p a t t e r n which emerges from t h i s technique imposes a formal shape on the work.^ u f i r s t two of these c o n d i t i o n s . W i t h i n these measures—I t h i n k p a r t i c u l a r l y of the f i r s t s i x — o n e experiences very l i t t l e sensation of change. Without change, which i s c o n s t i t u t i v e of rhythm, time i t s e l f i s suspended. . . . A c c o r d i n g l y , the t e x t u r e of the opening measures of Atmospheres can be described as s y n t h e t i c , i n the sense that i n d i v i d u a l elements are absorbed i n t o t h i s amorphous mass of sound." g An " e s t a b l i s h e d v e r t i c a l s o n o r i t y " i s one which has sounded long enough, without i n t e r n a l p i t c h change, to be recognized as a s t a t i c v e r t i c a l i t y . 9 The black v e r t i c a l bar i n d i c a t e s a chromatic c l u s t e r , i . e . , a l l p i t c h e s between and i n c l u d i n g the two i n d i c a t e d . ^Gyorgy L i g e t i , l i n e r notes f o r Ligeti: Melodien for Orchestra (Decca Headline, Head 12, 1976). 6 Example 2. Atmospheres, measures 30-34, showing g r a d u a l l y t r a n s f o r m i n g s o n o r i t i e s . 8 The denseness of the polyphonic interweaving i n Example 3 i s the r e s u l t of the complex composite rhythm o f , and r e l a t i v e l y narrow ambitus, :ne rover which the f o r t y - e i g h t independent l i n e a r events operate. The o v e r a l l e f f e c t undoubtedly outweighs that of any one of i t s components. S t a t i c sound b l o c k s , gradual s o n o r i t y transformations, and micropolyphony are the main t e x t u r a l c h a r a c t e r i s t i c s of other works i n the e a r l y to middle s i x t i e s , as evidenced i n Volumina (1961-62) f o r organ, movements one and two of the Requiem (1963-65) f o r two choruses and o r c h e s t r a , the f i r s t movement of the Cello Concerto (1966), Lux aeterna (1966) f o r chorus, and Lontano (1967) f o r l a r g e o r c h e s t r a , three of which (Volumina, Cello Concerto, and Requiem) are discussed i n more d e t a i l below-.-Example 4 c o n s i s t s of the opening of Volumina, which g r a p h i c a l l y i l l u s t r a t e s the concept of s t a t i c sound mass. Notice i n t h i s excerpt t h a t , although the dynamics f l u c t u a t e as a r e s u l t of r e g i s t r a t i o n changes, p i t c h content remains s t a t i c throughout. The opening movement of the Cello Concerto t y p i f i e s a s l i g h t l y d i f f e r e n t a p p l i c a t i o n of s l o w l y changing s o n o r i t i e s from that of the b l o c k - l i k e c l u s t e r s of Atmospheres. Here, a mode of l i n e a r expansion may be discerned. S p e c i f i c a l l y , the unison E^ of measure 11 g r a d u a l l y expands to more complex v e r t i c a l i t i e s , p i t c h e s being added i n the f o l l o w i n g order: Km. 11 m. 17 m. 26 m. 28 . f 1 ' & faW The second movement of the Requiem contains p o r t i o n s e x h i b i t i n g complex micropolyphonic te x t u r e s such as the excerpt given as Example 5. Here, as i n the excerpt from Atmospheres, the complex interweaving of l i n e a r components occurs w i t h i n a narrow range, s p e c i f i c a l l y from O l to ~)  ^ # . Linear independence i s consequently rendered subordinate to 9 Example 3. Atmospheres, measures 52-53, showing m i c r o p o l y p h o n y . 1) scorcely audible 2) scraps 3) stop suddenly @1963 by Universal Edition A.G. Reprint with permission of Universal Edition Wien 11 Example 4. Volumina, r e h e a r s a l nos. 1 to 2, showing s t a t i c , c h r o m a t i c sound mass. r (dCt ?if{ti-« btzCeHcn ttch imf die- btc^t-le-jttn Anm tr-ie u.n.g ti) „ / / / / Remitter - eLitniniten <to (wJe Cm M<LMU«.0. W Unker F u i j A. 13 t h e e f f e c t o f t h e whole. Apparitions, t h e o t h e r work u n d e r l y i n g L i g e t i ' s immediate r e c o g n i t i o n i n t h e l a t e f i f t i e s , i s somewhat d i f f e r e n t from t h e p i e c e s i l l u s t r a t e d above. Rather than a c o n t i n u o u s sound s t r u c t u r e o f s l o w l y t r a n s f o r m i n g t e x t u r e s , i t f e a t u r e s a s u c c e s s i o n o f a b r u p t l y changing t e x t u r e s (one o f which i s m i c r o p o l y p h o n y ) . T h i s "fragmented" q u a l i t y i s a l s o d i s c e r n i b l e i n s e v e r a l of L i g e t i ' s o t h e r p i e c e s from t h e m i d d l e s i x t i e s such as Aventures (1964) and Nouvelles Aventures (1964) f o r t h r e e s o l o v o i c e s and seven i n s t r u m e n t s , t h e t h i r d movement of t h e Requiem, and second movement o f t h e Cello Concerto. Example 6 i s an e x c e r p t from Apparitions, and Example 7, from Aventures, b o t h of which i l l u s t r a t e t h i s more d i s j u n c t s t y l e . I n t h e f i r s t o f t h e s e (from Apparitions) a change of m u s i c a l element o c c u r s on almost e v e r y beat, each element b e i n g d e f i n e d by d i f f e r e n t o r c h e s t r a t i o n , r e g i s t e r , r h y t h m i c d e s i g n , l e n g t h , m e l o d i c shape, dynamics, and a r t i c u l a t i o n . N o t i c e t h a t by measure 16 t h e independent elements b e g i n to o v e r l a p , t r a n s f o r m i n g t h e former "patch-work" t e x t u r e ( i . e . , one o f j u x t a p o s i t i o n ) t o one o f complex s u p e r i m p o s i t i o n o f d i s p a r a t e m u s i c a l i d e a s . The e x c e r p t from Aventures a l s o r e v e a l s s u c c e s s i v e and superimposed, c o n t r a s t i n g elements o f t e n i n v o l v i n g n o n - t r a d i t i o n a l v o c a l t e c h n i q u e s . Around 1965 L i g e t i began t o a l t e r h i s m u s i c a l s t y l e once more: S i n c e about t h e m i d d l e s i x t i e s I have g r a d u a l l y been t r a n s f o r m i n g t h e t e c h n i q u e o f mic r o p o l y p h o n y , ai m i n g t o make the s e p a r a t e l i n e s c l e a r e r and more i n d i v i d u a l l y d i s t i n g u i s h a b l e . The p o l y p h o n i c p a t t e r n i s s t i l l complex, but t h e polyphony i t s e l f i s l e s s " m i c r o " i n t h a t t h e p o s s i b i l i t y now e x i s t s of d e s i g n i n g autonomous, d i v e r g e n t , m u t u a l l y c o n t r a s t e d ''''''Two o b s e r v a t i o n s r e g a r d i n g t h i s example a r e noteworthy, t h e f i r s t o f which i s t h e f a c t t h a t the v o i c e p a r t s a r e doubled i n t h e s t r i n g s ; t h r e e c h o r a l s e c t i o n s — s o p r a n o , mezzo, and a l t o — a r e i n o p e r a t i o n . The second d e t a i l c o n c e r n s t h e t e x t u r e i t s e l f . W i t h i n each s e c t i o n , m i c r o p o l y p h o n y i s e f f e c t e d t h r o u g h a f o u r - v o i c e canon. A l t h o u g h t h e s e canons a r e not r h y t h m i c a l l y s t r i c t , t h e s u c c e s s i o n ( i . e . , u n f o l d i n g ) o f p i t c h e s i s t h e same i n each case. 14 Example 5. Requiem, second movement, measures 67-72, showing micro polyphony. © 1966 by Henry L i t o l f f ' s Verlag Reprint with permission of C.F.Peters Music Publishers Frankfurt 15 Example 6. Apparitions, second movement, measures 10-17, showing a r a p i d s u c c e s s i o n o f d i s p a r a t e t e x t u r e s . * Sie»*« Efklo'ufg "* Sa-ta 14 / Sea eoienct on ** o" peg* 14 II (harsh/ oudbia) 2) from rhe b'-dgedownwa'di over m« fince*fceo'd T-a nointr of tt'o>ei J 3oc3«^ ata. 3l conpVely sont.cello **" Siehe FMI6rung $*,<« 14 / See e«Dlonoior *" on poge I* *" "nge'nagei del G'rtf-nge'i ouf die So.ta dtuc*en./• - Pill.; Presi noil ol the (e-t-hond-finoer on rhe (tring. 1) fno' flvtter-tonguel 21 bowed 3] S'fott dekoielv end continually ove> the Hio witn b'uiH, 4) g'oduollyJul totto 51 iul tgsto, grodoofiy.-* to porvictllo 61 groduoNyul toito 7) bowed * Fc'i «*'ne VK'ccpe vo'handen ;it, sp.ele men d.,' ti no 8*ey i avovabfe. play 0. H no'Sfy oudb'e 21 on *fe edge of ma ikin 3l witn d-umit'CK 4| bo*«d 5i g'odajiiy completely iul pom calto 61 JU ! fci'O, grodi<3:!v-*ord. 7) Tha lymbt* ot l"0*a» :»t oppronmo'e. Wl^out •'O'f. ©1964 by Universal Edition A.G. Reprint with permission of Universal Edition Wien 17 Example 7. Aventures, measures 1-11, showing a r a p i d s u c c e s s i o n o f d i s p a r a t e t e x t u r e s . 01964 by Henry Litolff's Verlag Reprint with permission of C.F.Peters Music Publishers Frankfurt 19 m e l o d i c p r o c e s s e s , which l e a d an independent e x i s t e n c e w i t h i n t h e o v e r r i d i n g c o n t r a p u n t a l n e t w o r k . ^ T h i s newly e s t a b l i s h e d , more t r a n s p a r e n t t e x t u r e i s a d i s t i n g u i s h i n g f e a t u r e of such works as t h e Ten Pieces for Wind Quintet (1968), Chamber Concerto (1968-70), Melodien (1971) f o r o r c h e s t r a , Double Concerto (1972) f o r f l u t e , oboe, and o r c h e s t r a , and San Fransisco Polyphony (1973-74) f o r o r c h e s t r a . An example o f t h e more p e r s p i c u o u s t e x t u r e , s t i l l r h y t h m i c a l l y complex but w i t h l i n e s e x h i b i t i n g i n c r e a s e d independence and d i r e c t i o n , i s found i n t h e f i r s t movement o f t h e Double Concerto, an e x c e r p t from which i s g i v e n i n Example 8. I t s h o u l d be c l e a r from t h i s example t h a t , a l t h o u g h t h e r h y t h m i c 3 . . . . 5 s t r u c t u r e i s s t i l l complex (e.g., | [ | a g a i n s t | | | | a g a i n s t | | | | J ) , each o f t h e l i n e a r components r e v e a l s independence i n terms of m e l o d i c d i r e c t i o n and g o a l o f motion. F o r i n s t a n c e , t h e f i r s t v i o l a moves from A^ to by measure 70, w h i l e t h e t h i r d v i o l a t r a v e l s from i t s i n i t i a l B -1 i n bar 68 t o by measure 72, and so on. A l t h o u g h t h e " t o t a l i t y " o f t h e r e s u l t i n g complex p o l y p h o n i c web i s an important a s p e c t , so too a r e t h e i n d i v i d u a l components which comprise t h e o v e r a l l t e x t u r e . Other a s p e c t s of m u s i c a l language of t h i s second phase o f L i g e t i ' s mature p e r i o d a r e d i s c l o s e d i n t h e f o l l o w i n g q u o t a t i o n : The m u s i c a l language o f t h i s work [chamber Concerto], as i n t h e case i n a l l my c o m p o s i t i o n s s i n c e t h e m i d d l e s i x t i e s , i s n e i t h e r t o n a l n or a t o n a l . There a r e no t o n a l c e n t r e s , n or a r e t h e r e any harmonic c o m b i n a t i o n s o r p r o g r e s s i o n s which can be f u n c t i o n a l l y a n a l y z e d ; on the o t h e r hand t h e t w e l v e n o t e s of t h e c h r o m a t i c s c a l e a r e not t r e a t e d as n o t e s o f e q u a l importance, as i n a t o n a l and s e r i a l music. There a r e s p e c i f i c predominant arrangements o f i n t e r v a l s , which determine t h e c o u r s e o f t h e music and t h e development o f t h e form. The complex polyphony o f t h e i n d i v i d u a l p a r t s i s embodied i n a h a r m o n i c - m u s i c a l f l o w , i n which t h e harmonies ( i . e . , t h e v e r t i c a l c o m b i n a t i o n s of i n t e r v a l s ) do not change suddenly, but merge i n t o one an o t h e r ; one c l e a r l y d i s c e r n i b l e i n t e r v a l c o m b i n a t i o n i s g r a d u a l l y b l u r r e d , and 12 L i g e t i , l i n e r n o t e s f o r Melodien. 20 Example 8. Double Concerto, f i r s t movement, measures 68-74, showing a more t r a n s p a r e n t polyphony w i t h independent components. 21 J = 80 (Piu mosso) „ Accelerando poco a p o c o P ® <to al . "Ftpr1. - err, -0 1974 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of B. Schott's Soehne Mainz O B O E SOLO Oar.. s p i e l Cel. A r p a V c l . fif- con fuoco i/rn rirt Roaenmetturf . , c o r l l r v * to ?wnaf >wi -73T-- - t~ Iw 22 from t h i s c l o u d i n e s s i t i s p o s s i b l e t o d i s c e r n a new i n t e r v a l 1 o c o m b i n a t i o n g r a d u a l l y t a k i n g shape. 14 L i g e t i ' s Ten Pieces for Wind Quintet, t h e s u b j e c t o f t h i s paper, adheres t o t h e c o m p o s i t i o n a l p r o c e d u r e s s t a t e d above to a c o n s i d e r a b l e degree (as w i l l become a p p a r e n t ) , a l t h o u g h t h e q u o t a t i o n was made w i t h s p e c i f i c r e f e r e n c e t o t h e Chamber Concerto. In f a c t , t h e wind q u i n t e t o f f e r s an e x t r e m e l y d i v e r s e s e l e c t i o n o f t e c h n i q u e s r e p r e s e n t a t i v e o f L i g e t i ' s works from the m i d d l e t o l a t e s i x t i e s , some of t h e t e c h n i q u e s b e i n g r e f i n e m e n t s of t h o s e found i n e a r l i e r works. A l s o , t h e q u i n t e t , b e i n g a chamber work, i s more a c c e s s i b l e than t h e l a r g e r o r c h e s t r a l works f o r th e t y p e o f a n a l y s i s p r e s e n t e d h e r e . In Chapter I I , a s p e c t s of m u s i c a l language i n t h e quintet-§form, t e x t u r e , rhythm, and p i t c h — w i l l be examined i n d i v i d u a l l y , w i t h i n t e r -r e l a t i o n s h i p s n o t e d where a p p l i c a b l e . D e t a i l e d s t u d i e s of a l l t e n p i e c e s would have been a t a s k too g r e a t f o r t h i s paper; c o n s e q u e n t l y , t h e f i r s t and l a s t p i e c e s were chosen to be a n a l y z e d i n d e t a i l because each r e p r e s e n t s one of t h e two p r e v a l e n t t e x t u r a l c o n f i g u r a t i o n s found i n t h e work. These d e t a i l e d a n a l y s e s a r e found i n C h a p t e r s I I I ( p i e c e No. 1) and IV (No. 10) and, l i k e Chapter I I , a p p roach t h e v a r i o u s m u s i c a l parameters i n d i v i d u a l l y . S p e c i f i c d e t a i l s p e r t a i n i n g t o t h e s e p a r t i c u l a r p i e c e s w i l l be d i s c l o s e d , as w i l l extended a p p l i c a t i o n s of c o n c e p t s i n t r o d u c e d i n Chapter I I . A summary of c o n c l u s i o n s w i l l f o l l o w i n Chapter V. The Ten Pieces for Wind Quintet i s , h e n c e f o r t h , r e f e r r e d t o as " t h e q u i n t e t . " CHAPTER I I c ASPECTS OF MUSICAL LANGUAGE IN GYORGY LIGETI'S TEN PIECES FOR WIND QUINTET I n t r o d u c t i o n The i n t e n t o f t h i s c h a p t e r i s t o d e f i n e and e x e m p l i f y c e r t a i n a s p e c t s o f m u s i c a l language i n t h e t e n p i e c e s , thus p r o v i d i n g a b a s i s f o r the d e t a i l e d a n a l y s e s i n Chapters I I I and IV. The main s e c t i o n s o f t h i s c h a p t e r a r e as f o l l o w s : Formal O r g a n i z a t i o n o f t h e Work as a Whole A s p e c t s of T e x t u r a l S t r u c t u r e P r i n c i p l e s o f Rhythmic and M e t r i c D e s i g n Modes of P i t c h O r g a n i z a t i o n L i n e a r D e t a i l s Harmonic D e t a i l s Summary. Many of t h e c o n c e p t s d i s c u s s e d i n t h i s c h a p t e r a r e of g e n e r a l s i g n i f i c a n c e i n t h e work, p e r t a i n i n g to s e v e r a l p i e c e s or s e c t i o n s w i t h i n p i e c e s , w h i l e o t h e r s expose t e c h n i q u e s of more l i m i t e d a p p l i c a t i o n . Because t h e f i r s t and l a s t p i e c e s of t h e q u i n t e t a r e t h e s u b j e c t s of Cha p t e r s ITT and IV, r e s p e c t i v e l y , p r e s e n t r e f e r e n c e s t o them a r e m i n i m a l . 23 24 Formal O r g a n i z a t i o n o f t h e Work as a Whole Perhaps t h e most s i g n i f i c a n t f o r m a l a s p e c t of t h e work as a whole i s t h e r e g u l a r a l t e r n a t i o n between "ensemble" and " s o l o i s t i c " pieces.'' S p e c i f i c a l l y , t h e odd-numbered p i e c e s a r e o f t h e ensemble t y p e , w h i l e t h e even-numbered ones a r e s o l o i s t i c . The o r d e r o f t h e f e a t u r e d i n s t r u m e n t s i n t h e s o l o i s t i c p i e c e s i s as f o l l o w s : No. 2 - c l a r i n e t , No. 4 - f l u t e , No. 6 - oboe, No. 8 - horn, and No. 10 - bassoon. F l u c t u a t i o n s i n i n s t r u m e n t a t i o n - d e n s i t y ( i . e . , t h e number of i n s t r u m e n t s sounding) from p i e c e t o p i e c e , as w e l l as v a r i a n c e s i n a c t u a l i n s t r u m e n t a t i o n , suggest 2 subgroupings w i t h i n t h e q u i n t e t . I n Example 9, t h e i n s t r u m e n t a t i o n -d e n s i t y of each p i e c e (and each s e c t i o n w i t h i n a p i e c e — t o be e x p l a i n e d below) i s g i v e n w i t h the suggested subgroupings i n d i c a t e d by b r a c k e t s . Example 9. I n s t r u m e n t a t i o n - d e n s i t y and s u b g r o u p i n g of t h e t e n p i e c e s . P i e c e No.: 1 2 3 4 5 6 7 8 9 10 I n s t r u m e n t a t i o n -d e n s i t y : 5 5 5 3 4 5 5-4 3 -4-53 4-5 Subgroupings: I I I I I 1 I I I I I I C o n c e r n i n g f l u c t u a t i o n s i n i n s t r u m e n t a t i o n - d e n s i t y and i n s t r u m e n t a t i o n , s e v e r a l d e t a i l s a r e noteworthy. The a l t o f l u t e i s used i n th e f i r s t t h r e e p i e c e s , r e s e r v i n g t h e f l u t e f o r i t s s o l o i s t i c treatment i n t h e f o u r t h p i e c e . A l t h o u g h t h e s e two c l a s s i f i c a t i o n s a r e d e f i n e d i n d e t a i l i n t h e next s e c t i o n , t h e y r e f e r e s s e n t i a l l y t o p i e c e s i n which a l l of t h e s c o r e d i n s t r u m e n t s p a r t i c i p a t e e q u a l l y (ensemble) and t h o s e i n which one p a r t i c u l a r i n s t r u m e n t i s f e a t u r e d ( s o l o i s t i c ) . 2 Other subgroupings o f p i e c e s may be i n t e r p r e t e d a c c o r d i n g t o f a c t o r s o t h e r than i n s t r u m e n t a t i o n - d e n s i t y and i n s t r u m e n t a t i o n . These, however, a r e d i s c l o s e d i n t h e l i g h t of t h e s p e c i f i c parameters e f f e c t i n g such c o n n e c t i o n s . 25 The e n g l i s h horn appears i n t h e f i r s t two p i e c e s , t h e oboe d' amore i n t h e t h i r d , and n e i t h e r i n t h e f o u r t h and f i f t h ; t h e oboe i s saved f o r No. 6 where i t i s t h e f e a t u r e d i n s t r u m e n t . I n t e r n a l f l u c t u a t i o n s i n i n s t r u m e n t a t i o n - d e n s i t y i n d i c a t e d i n p i e c e s 7 t o 10 a r e based on c o n d i t i o n s s i m i l a r to t h o s e l i s t e d above. In the second f o r m a l s e c t i o n o f t h e s e v e n t h p i e c e , f o r example, the horn i s s i l e n t i n p r e p a r a t i o n f o r No. 8 where i t i s f e a t u r e d . A good p o r t i o n o f t h e e i g h t h p i e c e , however, o c c u r s w i t h o u t t h e horn; i t s e n t r y , a l o n g w i t h t h a t o f t h e oboe l a t e r i n t h e p i e c e , i s r e s p o n s i b l e f o r t h e " s t e p p e d " d e n s i t y i n d i c a t e d i n Example 9. The bassoon does not p a r t i c i p a t e i n t h e n i n t h p i e c e , a g a i n i n p r e p a r a t i o n f o r i t s s o l o i s t i c t reatment . ( i n t h e f i n a l p i e c e ) . F i n a l l y , a l t h o u g h t h e l a s t p i e c e i s s c o r e d f o r f i v e i n s t r u m e n t s , o n l y on one s i x t e e n t h - n o t e i n t h e e n t i r e p i e c e do t h e y a c t u a l l y sound t o g e t h e r ( s p e c i f i c a l l y , a t t h e c u l m i n a t i o n p o i n t o f t h e main body of t h e p i e c e i n bar 15). Other a s p e c t s of o r g a n i z a t i o n and f a c t o r s of l a r g e - s c a l e g r o u p i n g a r e d e f i n e d i n subsequent s e c t i o n s of t h i s c h a p t e r , as w e l l as i n C h a p t e r s I I I and IV. D e t a i l s of f o r m a l s t r u c t u r i n g w i t h i n i n d i v i d u a l p i e c e s a r e examined i n the l i g h t o f t h e v a r i o u s parameters (e.g., t e x t u r e , rhythm, e t c . ) which e f f e c t t h e f o r m a l d e l i n e a t i o n s . A s p e c t s of T e x t u r a l S t r u c t u r e As s t a t e d i n t h e p r e v i o u s s e c t i o n , t h e q u i n t e t i s o r g a n i z e d i n a l t e r n a t i n g ensemble and s o l o i s t i c p i e c e s . T e x t u r e p l a y s a most d e c i s i v e r o l e i n d e f i n i n g t h e s e t y p e s . A l t h o u g h each p i e c e e x p l o r e s a unique mode o f t e x t u r a l c h a r a c t e r i z a t i o n ( i . e . , u nique i n d e t a i l ) , t h e r e e x i s t s e v e r a l a s p e c t s of t e x t u r e which have widespread s i g n i f i c a n c e i n t h e ensemble p i e c e s , and o t h e r s , of e q u a l importance, which a r e s p e c i f i c t o t h e s o l o i s t i c p i e c e s . These two t y p e s of p i e c e s and c o r r e s p o n d i n g t e x t u r a l d e t a i l s w i l l 26 now be d i s c u s s e d i n d e t a i l . T e x t u r a l D e t a i l s i n Ensemble P i e c e s E s s e n t i a l l y two t e x t u r a l c o n f i g u r a t i o n s a r e found i n th e ensemble 3 p i e c e s : one which c o n s i s t s of o n l y one t e x t u r a l element t h r o u g h o u t , and one which f e a t u r e s s e v e r a l c o n s e c u t i v e elements. Only on one o c c a s i o n a r e two d i s p a r a t e t e x t u r a l elements sounded s i m u l t a n e o u s l y ( t h i s d e p a r t u r e to be d i s c u s s e d s h o r t l y ) . T e x t u r e , t h e parameter which b e s t d i f f e r e n t i a t e s ensemble and s o l o i s t i c p i e c e s , i s a l s o an important f a c t o r i n t h e d e l i n e a t i o n o f form w i t h i n i n d i v i d u a l ensemble p i e c e s . S u c c e s s i v e t e x t u r a l 4 elements, i n f a c t , most o f t e n c o r r e s p o n d t o main f o r m a l s e c t i o n s , i n which c a s e t h e y u s u a l l y i n v o l v e a l l of t h e i n s t r u m e n t s f o r which the p i e c e i s s c o r e d , as w e l l as t o t r a n s i t i o n a l passages, which may f e a t u r e a r e d u c t i o n i n the number of components.^ The f i f t h and n i n t h p i e c e s a r e each comprised o f one, c o n t i n u o u s t e x t u r a l element which i n v o l v e s a l l of t h e s c o r e d i n s t r u m e n t s t h r o u g h o u t . "A t e x t u r a l element i s a homogeneous mode o f i n t e r a c t i o n between i n s t r u m e n t s , as i n a p o l y p h o n i c o r homophonic t e x t u r e . The i n d i v i d u a l p a r t s i n such a t e x t u r a l element a r e r e f e r r e d to as "sounding components" o r s i m p l y , "components." A t e x t u r a l element may a l s o be comprised of o n l y one component as i n a s i n g l e - l i n e melody. The t e x t u r e o f a p i e c e a t any g i v e n time may c o n s i s t o f one o r more t e x t u r a l elements, each h a v i n g one o r more components £e.g., v e r t i c a l t h r e e - n o t e chords (one element, t h r e e components), w i t h a s i n g l e - l i n e melody (one element, one component)}. T h i s mode of t e x t u r a l c h a r a c t e r i z a t i o n i s i n f l u e n c e d i n p a r t by W a l l a c e B e r r y ' s v i e w s . See i n t h i s r e g a r d h i s Structural Functions in Music (Englewood C l i f f s : P r e n t i c e - H a l l , I n c . , 1976), Ch. 2. 4 The c o n t r a r y , however, i s not always t r u e . In o t h e r words, a p i e c e which f e a t u r e s one c o n t i n u o u s t e x t u r a l element may have s e v e r a l f o r m a l s e c t i o n s d e l i n e a t e d by v a r i a n c e s i n o t h e r parameters. ^Where such a r e d u c t i o n o c c u r s , however, the components l e f t sounding c o n t r i b u t e to o n l y one t e x t u r a l element. 27 The t e x t u r e of the f i f t h piece i s one of polyphony, while that of the n i n t h i s a three-part canon. 7 In the l a t t e r , the t e x t u r a l c o n t i n u i t y corresponds to the u n i s e c t i o n a l form, while i n the former, d e s p i t e i t s continuous t e x t u r e , formal segmentation occurs through v a r i a n c e s i n other parameters such as t e x t u r a l space and rhythmic i n t e n s i t y (each of which i s discussed l a t e r ) . Examples 10 and 11 c o n s i s t of excerpts from No. 5 and No. 9 , r e s p e c t i v e l y , each r e v e a l i n g a s i n g l e t e x t u r a l element. Of the remaining ensemble p i e c e s , each of which contains s e v e r a l successive t e x t u r a l elements, the f i r s t piece i s d e t a i l e d i n the next chapter. Measures 1-7 of piece No. 3, however, provide another example of a t e x t u r a l element which fe a t u r e s equal and t o t a l involvement of the g instruments f o r which i t i s scored. The t h i r d piece a l s o provides the one instance of simultaneous t e x t u r a l elements i n an ensemble piece. In measures 10-12, the octave-doubled theme represents one t e x t u r a l element, 9 while the t r i l l ( c l a r i n e t ) and sustained note (horn) represent the other. "The components of t h i s p a r t i c u l a r polyphonic t e x t u r e are extremely " a r t i c u l a t e " i n t h e i r use of repeated staccatissimo notes. The i m p l i c a t i o n s of t h i s surface d e t a i l w i t h respect to rhythmic design are de a l t w i t h i n the next s e c t i o n . A l s o , the s p e c i f i c mode of p i t c h o r g a n i z a t i o n o p e r a t i v e i n t h i s p a r t i c u l a r polyphonic element i s explained i n the f i n a l s e c t i o n of t h i s chapter. 7 The canonic treatment employed here i s a prime example of l i n e a r independence w i t h i n a polyphonic t e x t u r e . That i s , apart from c o n t r i b u t i n g to the e f f e c t of the whole, the i n d i v i d u a l components e x h i b i t a considerable degree of independence and d i r e c t i o n . As noted i n the previous chapter, t h i s increased independence i s c h a r a c t e r i s t i c of many of the polyphonic t e x t u r e s i n L i g e t i ' s music of the l a t e s i x t i e s . g The d e t a i l s of the l i n e a r s t r u c t u r e i n t h i s p a r t i c u l a r t e x t u r a l element w i l l be examined i n the s e c t i o n on p i t c h o r g a n i z a t i o n . A l s o , i t might be noted that t h i s t e x t u r a l element comprises almost h a l f the pie c e . I t i s , i n f a c t , c h a r a c t e r i s t i c of the ensemble pieces that a t e x t u r a l element, once e s t a b l i s h e d , continues to operate over a s u b s t a n t i a l p o r t i o n of the piece. 9 The doubling of the "theme" i n octaves i n t h i s s e c t i o n negates any s o l o i s t i c i m p l i c a t i o n . 28 Example 10. P i e c e No. 5, measures 1-5, showing a s i n g l e t e x t u r a l element. •) 5 (1, t £ £ e,c.) b e d e u t e t : T o n r e p e t i t i o n S t a c c a t i s s i m o (JjJJJmm e:c.) so s c h n c l l wie m o g l i c h . Die n o i i e r t e n Dauerwerte w e r d e n m i t s o l c h e n stacca-l i s s i m o - T o n f o l g e n ausgeftillt , w o b e i jedes I n s t r u m e n t , von den anderen I n s i r u m e n i e n unabhangig u n d o h n e RLicksicht auf die T a k l e i n t e i l u n g , so s c h n e l l stacca -tiert , wie das seine t e c h n i s c h e Eigenart u n d die Lage, in der es s p i e l t , zulaUt. E i n f a c h e r b z w . d o p p e l t e r , bei der Klote ad l i b . dreifacher Z u n g e n s t o f i . K c i n e F l a t - terzungel S t e i s d i s t i n k t e . gesonderte A t t a e k e n . Z u m R h y t h m i s c h e n : W a h r e n d die Einsatze u n d A b -satze e x a k t angegeben s i n d , ist die innere D i c h t e der s t a c c a t o - F o l g e n r h y t h m i s c h f r e i . *) D y n a m i s c h e Balance = s/jp a n n a h e r n d gleich in alien I n s t r u m e n t e n . /5 =fe i £ \ *; ^ \o, o, m, 0. ere.) means: repeated tones staccatissimo (JjJJJjJ etc.) as fast as possible. The given note-values are filled with these staccatissimo repeated tones; each instrument plays as fast a staccato as its technique and register permit, independently of the other instruments and with no regard for subdivi-sion of bars Single tonguing, double tonguing. Flute triple tonguing ad lib. So fluttertongue! Distinct, separated attacks throughout. Rhythm: Entries and cut- offs are indicated precisely; the density of the staccato sequences, however, is rhyth-mically free. **y Balance of dynamics: sjp approximately equal in all instruments. @1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne. 29 © 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne. The two t e x t u r a l l y d e f i n e d f o r m a l s e c t i o n s o u t l i n e d above ( i . e . , measures 1-7 and 10-12) a r e b r i d g e d by a r h y t h m i c a l l y i n t e n s i f i e d p o l y p h o n i c element which d i m i n i s h e s i n d e n s i t y from f o u r t o t h r e e components, and descends i n r e g i s t e r , c u l m i n a t i n g on the t r i l l i n b a r 9 (one of t h e two s i m u l t a n e o u s t e x t u r a l elements of t h e second s e c t i o n ) . T h i s t r a n s i t i o n a l element, f e a t u r i n g a r e d u c t i o n or subgrouping o f components i s g i v e n as Example 12. 30 Example 12. Piece No. 3, measures 7-10, showing a subgrouping of components i n the t r a n s i t i o n a l passage. end of first section-\ transition-8 Ft.Sol +J c CJ — s OJ •H q OJ OJ c 0 & E / 3 0 ' +J 0 OJ SH +J 3 O OJ Ms 0 © 1969 B. Schott's Soehne, Mainz A l l r i g h t s reserved Used by permission of European American Music D i s t r i b u t o r s Corporation, sole Canadian agent for B. Schott's Soehne. The seventh piece i s perhaps the most e x p l i c i t example of consecutive, d i s p a r a t e t e x t u r a l elements c h a r a c t e r i z i n g adjacent formal s e c t i o n s . ^ The ^The s p e c i f i c t e x t u r a l elements are extremely c o n s i s t e n t throughout each s e c t i o n , again r e v e a l i n g the a t t r i b u t e of t e x t u r a l c o n t i n u i t y . v e r t i c a l homorhythmic s o n o r i t i e s of t h e ' a ' - s e c t i o n (measures 1-37) f e a t u r e e q u a l involvement o f a l l t h e i n s t r u m e n t s . A l t h o u g h t h e c l a r i n e t s u s t a i n s a n o t e out o f t h e v e r t i c a l complex i n bar 6, a l l t h e i n s t r u m e n t s w i l l have f o l l o w e d s u i t by the c l o s e of t h e s e c t i o n ( c f . b a r s 12, 15, and 34). The ' b ' - s e c t i o n (measures 38 to t h e end), i n i t i a t e d w i t h o u t a t r a n s i t i o n , f e a t u r e s f o u r o f t h e f i v e i n s t r u m e n t s i n a c o n t r a s t i n g p o l y p h o n i c t e x t u r e ( t h e horn b e i n g s i l e n t i n p r e p a r a t i o n f o r t h e e i g h t h p i e c e ) . These d i v e r s e t e x t u r a l c o n f i g u r a t i o n s a r e i l l u s t r a t e d i n t h e two e x c e r p t s i n Example 13. Example 13. P i e c e No. 7, measures 3-8 and 40-41, showing d i s p a r a t e t e x t u r e s c h a r a c t e r i z i n g a d j a c e n t f o r m a l s e c t i o n s . C l a r i n c t t o in Si t C o r n o in l a F a g o t t o ri. Ob. Cl.$i\> Cor. Fa Fag. © 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne. 32 T e x t u r a l D e t a i l s i n S o l o i s t i c P i e c e s A l t h o u g h i t i s somewhat more d i f f i c u l t t o g e n e r a l i z e about the s o l o i s t i c p i e c e s , . b e c a u s e each instrument i s f e a t u r e d i n a much d i f f e r e n t way, two modes of t e x t u r a l s t r u c t u r e may n e v e r t h e l e s s be d i s c e r n e d . One i n v o l v e s t h e e s t a b l i s h m e n t of an accompanimental t e x t u r a l element c o m p r i s i n g a l l of t h e i n s t r u m e n t s (or a l l but t h e f e a t u r e d one), out o f which ( o r o v e r which) the f e a t u r e d instrument a s s e r t s i t s e l f i n a d i s t i n c t , second t e x t u r a l c h a r a c t e r . In some ca s e s t h e accompanimental element resembles a p a r t i c u l a r ensemble t e x t u r e found elsewhere i n t h e q u i n t e t . I n t h e second p i e c e ( f e a t u r i n g t h e c l a r i n e t ) , f o r example, a l l f i v e i n s t r u m e n t s c o n t r i b u t e to t h e accompanimental f i v e - n o t e v e r t i c a l s o n o r i t i e s ( e .g., measures 1-11, 15, and 20-21). These v e r t i c a l i t i e s a r e s e p a r a t e d by r e s t s , some o f which a r e p a r t i a l l y f i l l e d by t h e l i n e a r i z a t i o n s of t h e c l a r i n e t ( t h e s e b e i n g t h e second t e x t u r a l e l e m e n t ) . Note, however, t h a t t h e accompanimental v e r t i c a l complexes a r e s i m i l a r i n e f f e c t (and harmonic q u a l i t y ) t o t h o s e o f t h e s e v e n t h p i e c e ( ' a ' - s e c t i o n o n l y ) . The opening f o u r measures of the second p i e c e , i l l u s t r a t i n g t h e two-element t e x t u r e a r e g i v e n as Example 14. The accompanimental element of the s i x t h p i e c e ( f e a t u r i n g t h e oboe) i s a second example o f a t e x t u r e borrowed from another p i e c e . I n t h i s case t h e accompaniment ( b a r s 1-8) i s comparable t o the whole o f the p r e c e d i n g ensemble p i e c e i n s e v e r a l ways: i t i n v o l v e s t h e same f o u r i n s t r u m e n t s , the tempo i s t h e average o f t h e two i n t h e p r e v i o u s p i e c e , and t h e performance i n s t r u c t i o n s r e g a r d i n g a r t i c u l a t i o n a r e t h e same.'''''' The oboe i s i s o l a t e d ''"'''Regarding performance i n s t r u c t i o n s see Gyorgy L i g e t i , Ten Pieces for Wind Quintet (Mainz: B. S c h o t t ' s Soehne, 1969), pp. 18 and 20. A l s o , i t was n o t e d i n t h e s e c t i o n on f o r m a l a s p e c t s t h a t subgroupings of p i e c e s o c c u r t h r o u g h a v a r i e t y of p a r a m e t r i c v a r i a n c e s ( i n a d d i t i o n to t h o s e i n v o l v i n g i n s t r u m e n t a t i o n - d e n s i t y and a c t u a l i n s t r u m e n t a t i o n ) . The f i f t h and s i x t h p i e c e s may be c o n s i d e r e d one such subgroup, w i t h t h e t h r e e 33 Example 14. P i e c e No. 2, measures 1-4, showing a two-element t e x t u r e . Prestissimo minaccioso e burlesco** •) A u l i e r den sff u n d - A k z e n t e n ste ls g le ichmaf t ig *) Play very evenly, except for the sff and sfaccen. s p i e l e n , so daft e ine T a k t e i n t c i l u n g n icht w a h r n e h m b a r ruations, so that the subdivision into bars is not w i r d . D ie T a k l e u n d T a k t e i n t e i l u n g e n d i e n e n als O r i e n - perceptible. Bar lines serve as a means of orienta -l i e r u n g , e ine m e t r i s c h e P u l s a t i o n gibt es n i c h t . tton; there is no metrical pulsation. © 1969 B. Schott's Soehne, Mainz A l l r i g h t s reserved Used by permission of European American Music D i s t r i b u t o r s Corporation, sole Canadian agent for B. Schott's Soehne. from t h e accompanimental t e x t u r e t h r o u g h dynamic exposure, a r t i c u l a t i v e d i f f e r e n t i a t i o n , and t i m b r a l q u a l i t y , as shown i n Example 15. c r i t e r i a a l r e a d y s t a t e d as c o n n e c t i v e f a c t o r s ( i . e . , i n s t r u m e n t a t i o n , tempo, and a r t i c u l a t i o n ) . S e v e r a l a d d i t i o n a l f a c t o r s may be added t o t h e l i s t , one o f which i s t h e attacca i n d i c a t i o n a t t h e end o f t h e f i f t h p i e c e . Other c o n n e c t i v e f a c t o r s , which i n v o l v e l i n e a r p i t c h - c l a s s c o n n e c t i o n s , w i l l be d i s c l o s e d i n d e t a i l l a t e r i n t h i s c h a p t e r . 34 Example 15. P i e c e No. 6, measures 1-4, showing a two-element t e x t u r e . Presto staccatissimo e leggiero ffpp * ) £ = T o n r e p e t i t i o n s t a c c a t i s s i m o , wie in Satz S •) T o n r e p e t i t i o n bei der O b o e : s t a c c a t i s s i m o , sehr d i -s t i n k t , so s c h n e l l wie m o g l i c h . Die Spielart ist iden-tisch m i t der 3. n o t i e r t e n Spielart der Ubrigen Instru-mente ( etc. ). Die andersgeartete N o t a t i o n bezieht sich l e d i g l i c h a u f die K h y t h m i k : bei der No-t a t i o n eP ist die Dauer der T o n f o l g e gegeben, die A n z a h l der Schlage j e d o c h f r e i , bei der N o t a t i o n ist die A n z a h l der Schlage festgelegt, die Dauer der T o n f o l g e j e d o c h f r e i (so k u r z wie m o g l i c h , da T o n r e p e t i t i o n so raseh wie m b g l i c h ) . Bei der N u -t a t i o n ist der Kinsatz des ersten T o n e s m e t r i s c h festgelegt ( f i x i e r t e r l J latz tm T a k t d u r c h vorangehende Pausen), darauf folgt die T o n r e p e t i t i o n unabhangig v o m M e t r u m . Die 1'ausen in K l a m m e r n sind eine imaginare met rise he Krganzung der N o t a -t i o n , s i e w e r d e n z u m 'I'eil v o n der T o n r e p e t i t i o n v e r s c h l u n g e n ; z. B. b e d e u l e t 7 7 1*2 [i\ : e i n s e l z e n im d r i t t e n T r i o l e n a c h l e l , die Pause [7] ist eine v i r t u -elle E r g a n z u n g . *) ~£ = staccatissimo repeated tones as in Movement 5 **) Repeated tones in the Oboe staccatissimo. very di-stinct, as fast as possible. The manner of playing is identical to the manner of playing notated £ in the other instruments ( , e^, etc. ). The different no-tation refers only to the rhythm: in the notation £ the duration of the sequence is fixed, but the numbei of the attacks is free; in the notation fJjJJ the number of the attacks is fixed but the duration of tht sequence is free (as short as possible, since the tones are repeated as fast as possible). In the notation i^J ^1 J fl the entrance of the first tone is metrically fixed by the rests preceding it, whereupon the tones are repeated independently of the metre. The rests in brackets are the imaginary completion of the metre, and will be absorbed in part by the repeated tones. For example, y 1 [7] means: attack the third quaver of the triplet; the rest [V] is the virtual com -pletion of the triplet. © 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne. The accompaniment of t h e f i r s t s i x t e e n measures of the e i g h t h p i e c e , a l t h o u g h not s u g g e s t i v e o f any o t h e r t e x t u r e i n t h e q u i n t e t , n e v e r t h e l e s s f e a t u r e s t h e f l u t e , c l a r i n e t , and bassoon i n what c o u l d v e r y w e l l be an ensemble t e x t u r e , a c c o r d i n g to t h e c r i t e r i a o u t l i n e d i n t h e ensemble p i e c e s . That i s to say, t h e t h r e e i n s t r u m e n t s i n t e r a c t w i t h i n a c o n t i n u o u s p o l y p h o n i c t e x t u r e i n which no p a r t i c u l a r instrument predominates, the main e f f e c t b e i n g t h a t of t h e whole. I t i s , i n f a c t , o n l y when t h e horn e n t e r s i n bar 12 w i t h a c o n t r a s t i n g s u s t a i n e d q u a l i t y t h a t t h e i m p l i c a t i o n of a s o l o i s t i c t e x t u r e i s r e a l i z e d . The " e n s e m b l e - l i k e " t e x t u r e and e v e n t u a l horn e n t r y a r e i l l u s t r a t e d i n t h e e x c e r p t g i v e n as Example 16. I t was n o t e d e a r l i e r t h a t two modes of t e x t u r a l s t r u c t u r e may be d i s c e r n e d i n t h e s o l o i s t i c p i e c e s . T'tue second mode i s one i n which o n l y one t e x t u r a l element i s i n o p e r a t i o n , t h e f e a t u r e d i n s t r u m e n t g e n e r a l l y b e i n g t h e most c o n t i n u o u s and d y n a m i c a l l y exposed of a l l t h e components i n v o l v e d . The accompanying components, taken s e p a r a t e l y , f a i l t o d e f i n e a t e x t u r a l element w i t h enough independence and c o n t i n u i t y to be c o n s i d e r e d s e p a r a t e from t h e f e a t u r e d component. Rather, the components i n t e r a c t w i t h t h e f e a t u r e d i n s t r u m e n t i n ways which suggest one o v e r a l l t e x t u r a l element w i t h one p r i m a r y and s e v e r a l s e c o n d a r y components. Two examples w i l l s e r v e to i l l u s t r a t e t h i s mode of t e x t u r a l s t r u c t u r e . Measures 12-15 of t h e second p i e c e r e v e a l a c o n t i n u o u s c l a r i n e t l i n e w i t h numerous p o l y p h o n i c fragments c o n t r i b u t e d by t h e r e m a i n i n g f o u r 12 i n s t r u m e n t s . A g a i n , t h e s e fragmented " o v e r l a y s " do not comprise a t e x t u r a l element o f t h e i r own, but a r e , r a t h e r , i n t e g r a l t o t h e s i n g l e 12 T h i s t y p e of component i n t e r a c t i o n w i t h i n a s i n g l e t e x t u r a l element i s one o f two t o be d i s c u s s e d i n Chapters I I I and IV as f a c t o r s of " t e x t u r a l q u a l i t y . " Example 16. P i e c e No. 8, measures 1, 2, 5, 10, and 12, showing an " e n s e m b l e - l i k e " t e x t u r e as an accompanimental element. Allegro C O n delicatezza (sehr gleichmafiig, ohne jede Betonung der Takte bzw. Taktunterteilungen.) (J 72) (very evenly, without any accentuation of the bars or their subdivisions.) 1 *) fliefiend, alle neuen Einsfitze sehr weich / fluently, every new entry very SOJI x s s 1 5 ~l2 e_ Clarinetto in Sit Fagotto ') fliefiend, alle neuen Einsfitze sehr weich / fluently, every new entry very soft r £ S I PP sivtUU *) fliefiend, alle neuen Einsatze sehr weich / fluently, every new entry very soft PP 3 ) Dynamische Balance: pp gleich in F16te, Klarinette, Fagott. Klarinette verhalthismafcig etwas starker blasen. *J Balance of dynamics: pp equal in Flute, Clarinet Bassoon. Play the clarinet somewhat louder in rela-tion. **) Fagott, con sordino: Ein Tuch, in die Schalltiffnung ** ; Bassoon,con sordino: a cloth stuffed into the upper gestopft. joint. _ Fl. Cl.$i\> Fag. Fl. Cl.Siv Cor.Fa Fag. © 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne. 37 13 o v e r a l l t e x t u r e i n which t h e c l a r i n e t i s p r i m a r y . T h i s i s i l l u s t r a t e d i n Example 17. Example 17. P i e c e No. 2, measures 12-15, showing one t e x t u r a l element w i t h one p r i m a r y and f o u r secondary components. Foco meno mosso , 12 CJ = 144) Fl.Sol C.Ing. Cl.Siv Cor.Fa Fag; Fl.Sol C.Ing. Ct.$i\> Cor.Fa Fag. PPrpossibile ©1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne. T h i s i s a p a r t i c u l a r l y c l e a r example o f f o r m a l d e l i n e a t i o n t h r o u g h t e x t u r a l d i v e r s i t y . The opening of t h e second p i e c e was shown e a r l i e r t o c o n s i s t o f two si m u l t a n e o u s , d i s p a r a t e t e x t u r a l elements w h i l e i n t h e passage j u s t d i s c u s s e d and i l l u s t r a t e d a b o v e — a second f o r m a l s e c t i o n - — o n l y one element o p e r a t e s . These f o r m a l segments a r e f u r t h e r d e f i n e d ". thro u g h v a r i a n c e s i n tempo and dynamics. 38 The f o u r t h piece features a s i n g l e polyphonic t e x t u r e i n which the f l u t e i s dynamically, r e g i s t r a l l y , and r h y t h m i c a l l y exposed r e l a t i v e to the other two components. The c l a r i n e t and bassoon (the l a t t e r being c o n s i d e r a b l y more fragmented than the other two instrumental parts) c o n t r i b u t e more to the o v e r a l l polyphony than to a d i s p a r a t e t e x t u r a l element. An excerpt from No. 4 i s given as Example 18 . Example 18. Piece No. 4, measures 1-4, showing one t e x t u r a l element w i t h one primary and two secondary components. © 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne. In b o t h i n s t a n c e s o u t l i n e d above ( i . e . , t h e second and f o u r t h p i e c e s ) , t h e primacy of the f e a t u r e d i n s t r u m e n t and s u g g e s t i o n o f a s i n g l e -element (but multi-component) t e x t u r e a r e r e i n f o r c e d by s t r o n g harmonic a f f i l i a t i o n between t h e pr i m a r y and secondary c o m p o n e n t s — a d e t a i l which w i l l be d e a l t w i t h i n t h e f i n a l s e c t i o n o f t h i s c h a p t e r . C o n c e r n i n g t e x t u r a l s t r u c t u r e , a p a r a l l e l i s m between L i g e t i ' s e a r l i e r works (mentioned i n Chapter I) and t h e p i e c e s of t h e q u i n t e t may be drawn. The ensemble p i e c e s were s a i d e a r l i e r t o p o s s e s s a c e r t a i n degree of t e x t u r a l c o n t i n u i t y , t h e i n d i v i d u a l t e x t u r e s o f t e n c o n s i s t i n g o f s l o w l y changing s o n o r i t i e s . I n t h i s r e g a r d t h e y a r e s u g g e s t i v e of e a r l i e r p i e c e s of which Atmospheres i s r e p r e s e n t a t i v e . The s o l o i s t i c p i e c e s , t e x t u r a l l y d i f f e r e n t i a t e d from t h e ensemble p i e c e s , a l s o c o n t r a s t w i t h t h e l a t t e r i n t h a t t h e y f e a t u r e f r e q u e n t and, o f t e n , abrupt t e x t u r e changes. The second, s i x t h , e i g h t h , and t e n t h p i e c e s , f o r example, each c o n t a i n from f o u r t o s i x t e x t u r e changes, o f t e n accompanied by changes i n tempo, n o t a t e d meter, dynamics, r e g i s t e r , d e n s i t y , and g e n e r a l "mood." In t h i s sense t h e y a r e s u g g e s t i v e o f t h e s t y l e o f Apparitions and Aventures. A l t h o u g h t h e s c a l e o f t h e q u i n t e t p i e c e s i s much s m a l l e r than t h a t o f t h e a f o r e m e n t i o n e d r e l a t e d p i e c e s , t h e p a r a l l e l mode of d i f f e r e n t i a t i o n i s o f s i g n i f i c a n c e i n th e c h a r a c t e r i z a t i o n o f t e x t u r e s i n t h e q u i n t e t . Summary T e x t u r e has been c i t e d here asa'^major f a c t o r , i n t h e c h a r a c t e r i z a t i o n o f "ensemble" and " s o l o i s t i c " p i e c e s . W hile ensemble p i e c e s were shown t o i n v o l v e e s s e n t i a l l y one t e x t u r a l element a t a time ( e i t h e r throughput a complete p i e c e o r a t l e a s t a f o r m a l s e c t i o n ) , one i n s t a n c e o f s i m u l t a n e o u s , d i s p a r a t e t e x t u r a l elements was noted i n t h e t h i r d p i e c e . Two c o n f i g u r a t i o n s 40 were s a i d to c h a r a c t e r i z e t h e s o l o i s t i c p i e c e s : one i n which two simu l t a n e o u s , c o n t r a s t i n g t e x t u r a l elements o c c u r , t h e f e a t u r e d i n s t r u m e n t p r o v i d i n g one o f them; and one i n which o n l y a s i n g l e element i s ap p a r e n t , w i t h t h e f e a t u r e d i n s t r u m e n t emerging as p r i m a r y t h r o u g h dynamic and/or r e g i s t r a l exposure, a s - w e l l a s c o n t i n u i t y of s t r u c t u r e . F i n a l l y , t h e ensemble p i e c e s were l i k e n e d to a group o f L i g e t i ' s e a r l i e r works of which Atmospheres i s r e p r e s e n t a t i v e , and t h e s o l o i s t i c p i e c e s t o a group t y p i f i e d by Apparitions and Aventures. P r i n c i p l e s of Rhythmic and M e t r i c D e s i g n While i t i s not t h e i n t e n t i o n here t o attempt t o e x p l i c a t e c o m p l e t e l y t h e r h y t h m i c s t r u c t u r e s o f a l l t e n p i e c e s , s e v e r a l a s p e c t s o f rh y t h m i c and m e t r i c d e s i g n a r e a c c e s s i b l e , noteworthy, and n e c e s s a r y f o r even a moderate u n d e r s t a n d i n g of t h e m u s i c a l language o f t h e work. The most u n i v e r s a l and, perhaps, most s i g n i f i c a n t a s p e c t of rhythm i n a l l of t h e p i e c e s i s t h e r a r i t y o f o p e r a t i v e meter a t t h e l e v e l of t h e n o t a t e d measure. Meter i n t h e p r e s e n t c o n t e x t r e f e r s t o one p a r t i c u l a r mode of 14 rhythm — s p e c i f i c a l l y , one i n which impulse g r o u p i n g s a r e d e f i n e d by p a t t e r n s of a c c e n t e d ^ and unaccented b e a t s . These p a t t e r n e d g r o u p i n g s , c a l l e d measures, r e p r e s e n t t h e l o w e s t - l e v e l m e t r i c u n i t . Meter, t h e n , depends on a c c e n t ; m e t r i c u n i t s a r e d e l i n e a t e d by a c c e n t e d i m p u l s e s . I n s a y i n g , t h e r e f o r e , t h a t meter i s h a r d l y ever o p e r a t i v e a t t h e l e v e l of 14 Other "element-rhythms" w i l l be d e f i n e d i n Chapter I I I w i t h s p e c i f i c r e f e r e n c e to t h e f i r s t p i e c e . ^ A p a r t i c u l a r a r t i c u l a t i o n o r impulse may be a c c e n t e d t h r o u g h r e g i s t r a l and/or dynamic exposure, a r t i c u l a t i v e a c c e n t s ( e . g . , - - , >, A , e t c . ) , and/or extended d u r a t i o n r e l a t i v e to s u r r o u n d i n g i m p u l s e s . In s h o r t , a c c e n t here r e f e r s to emphasis i n h e r e n t i n t h e music, not imposed by t h e performer. the notated measure i n the pieces, the suggestion i s that patterned u n i t s of strong and weak beats are r a r e l y e s t a b l i s h e d i n a way that makes notated, apparent m e t r i c u n i t s p e r c e i v a b l e as such. The i m p l i c a t i o n s of t h i s phenomenon are con s i d e r a b l y d i f f e r e n t i n pieces or s e c t i o n s i n which the notated meter i s constant, as compared to those i n which i t i s f l u c t u a n t . In the former, b a r l i n e s appear p r i m a r i l y f o r ease of reading; these pieces (or sections) may be considered "ametric" at the l e v e l of the notated measure (because of the l a c k of accent-delineated m e t r i c u n i t s of that s i z e ) . H i g h e r - l e v e l impulse groupings (not n e c e s s a r i l y l a r g e - s c a l e metric u n i t s i n the sense of a c c e n t - a r t i c u l a t e d groupings) may, however, be discerned. For i n s t a n c e , l a r g e r phrases without i n t e r n a l m e t r i c s u b d i v i s i o n s (at the l e v e l of the measure) may be f e l t as continuous gestures which d i s p l a y p a r t i c u l a r rhythmic s t r u c t u r e s (to be s p e c i f i e d below). The l o w e s t - l e v e l impulse u n i t , then, becomes the phrase i t s e l f , not the notated bar. Most o f t e n these continuous gestures or phrases are not s i n g l e - l i n e melodies, but r a t h e r t e x t u r a l elements c o n s i s t i n g of s e v e r a l sounding components. We may, f o r example, speak of a "homophonic phrase," i n which a l l of the components move i n s t r i c t v e r t i c a l alignment, or a "polyphonic phrase," i n which the components are engaged i n a complex interweaving considered together as a s i n g l e gesture of f l u c t u a t i n g rhythmic i n t e r a c t i o n . In the case of the more common polyphonic phrase, one fundamental aspect of rhythmic design concerns the p r o p e r t i e s of "progression" and " r e c e s s i o n " ' ^ i n the l e v e l of rhythmic a c t i v i t y of the t e x t u r a l element as a whole. Although such continuous polyphonic phrases are found most f r e q u e n t l y 16 "Progression" and " r e c e s s i o n " are terms and concepts used e x t e n s i v e l y by Wallace Berry. See h i s Structural Functions, Chapters 2 and 3.. 42 i n ensemble pieces (because, as noted e a r l i e r , they c h a r a c t e r i s t i c a l l y f e a t u r e only one t e x t u r a l element at a time), s e v e r a l s o l o i s t i c pieces o f f e r examples. The accompanimental element ( i . e . , f l u t e , c l a r i n e t , and bassoon) of the f i r s t s i x t e e n measures of piece No. 8, f o r i n s t a n c e , o f f e r s an e x c e l l e n t example of rhythmic progression and r e c e s s i o n w i t h i n a s i n g l e , continuous polyphonic phrase. Example 19 c o n s i s t s of a graphic r e p r e s e n t a t i o n of the a c t i v i t y l e v e l i n t h i s s e c t i o n (accompanimental element only) as to the number of impulses per quarter-note i n the composite rhythm (henceforth termed " i m p u l s e - d e n s i t y " ) . ^ Ignoring the horn part f o r now, the graph r e v e a l s a l a r g e - s c a l e progression and r e c e s s i o n of rhythmic a c t i v i t y which peaks i n bar 11 (22 impulse s/ J ) followed by an abrupt d e c l i n e i n a c t i v i t y commencing i n bar 14. These, then, represent two l a r g e - s c a l e impulse u n i t s which consider " q u a n t i t a t i v e " aspects of rhythmic design ( i . e . , a c t i v i t y l e v e l s e x h i b i t i n g growth and d e c l i n e ) , r a t h e r than s p e c i f i c patterns of accent and unaccent ( i . e . , " q u a l i t a t i v e " aspects i n connection w i t h s p e c i f i c m e t r i c u n i t s ) . While the "downbeat" d e l i n e a t e s m e t r i c u n i t s , we might speak of a "turn-around p o i n t " as being a d e l i n e a t o r of impulse-density u n i t s . Such a j u n c t u r e may be c h a r a c t e r i z e d as the point at which the rhythmic progression ceases and the r e c e s s i o n begins (as i n t h i s p a r t i c u l a r case) or v i c e v e r s a . In t h i s piece the turn-around point occurs on the t h i r d beat of measure 14 as i n d i c a t e d i n Example 19. The accompanimental element, t h e r e f o r e , r e v e a l s i t s own mode of l a r g e - s c a l e rhythmic s t r u c t u r e — o n e which may a l s o be seen to i n t e r a c t w i t h the horn part (the second d i s t i n c t t e x t u r a l element). This i n t e r a c t i o n ^ I f more than one instrument sounds i n s t r i c t v e r t i c a l alignment, i t counts as one impulse o n l y f o r the purposes of the impulse-density graph. 43 Example 19. P i e c e No. 8, measures 1-16, i m p u l s e - d e n s i t y graph. \ measure no. r e s u l t s from s e v e r a l c o n d i t i o n s . F i r s t , t h e l a t t e r e n t e r s when t h e former i s at i t s maximum l e v e l o f a c t i v i t y ( i . e . , 22 im p u l s e s / J , measure 12). In a sense the opening r h y t h m i c p r o g r e s s i o n i n t h e accompaniment may be heard to f u n c t i o n a n a c r u s t i c a l l y t o t h e horn e n t r y ( a l t h o u g h t h e l a t t e r does not o c c u r i n a r e g i s t r a l l y o r d y n a m i c a l l y exposed manner), w h i l e r e t a i n i n g t h e c o n t i n u i t y w i t h i n i t s own t e x t u r a l element. Second, t h e maintenance o f peak a c t i v i t y i n t h e accompaniment l a s t s f o r t w e l v e q u a r t e r - n o t e s , r o u g h l y c o i n c i d e n t w i t h the opening s u s t a i n e d and d y n a m i c a l l y i n t e n s i f y i n g p i t c h 44 i n t h e horn. The f i r s t p i t c h change i n t h e horn (measure 1 4 ) , marked poco in relievo i s , c u r i o u s l y , t h e p o i n t at which t h e d e c l i n e i n a c t i v i t y i n t h e accompaniment b e g i n s ( i . e . , t h e t u r n - a r o u n d p o i n t ) . And t h i r d , as t h e graph r e v e a l s , t h e a c t i v i t y c u r v e of t h e horn p a r t i s i t s e l f a s m a l l - s c a l e v e r s i o n of t h a t of t h e accompaniment, b o t h c o i n c i d i n g j u s t p r i o r t o t h e z e r o - a c t i v i t y l e v e l i n bar 1 6 . Apart from t h e s e i n t e r a c t i v e f e a t u r e s , t h e horn p a r t e x h i b i t s i t s own l o w e r - l e v e l m e t r i c u n i t s , d e f i n e d not by t h e n o t a t e d measures of the s c o r e , but a f l u c t u a t i n g meter based on t h e lowest common denominator o f the r h y t h m i c d i v i s i o n s i n o p e r a t i o n ( i . e . , | | I* | I ! I x FI 1 I I = 6 0 / J ) . " ^ Example 2 0 c o n s i s t s o f t h e horn p a r t (measures 1 2 - 1 6 ) i n t h e m e t r i c c o n f i g u r a t i o n found i n t h e s c o r e (bottom s t a f f o f example), and a re-metered v e r s i o n , perhaps more i n d i c a t i v e o f t h e p e r c e i v e d a c c e n t p a t t e r n . Three suggested l e v e l s o f m e t r i c s t r u c t u r e a r e r e p r e s e n t e d by t h e arrows d e p i c t i n g upbeats and downbeats. The c r i t e r i a f o r t h e downbeat c h a r a c t e r i z a t i o n s a t l e v e l (a) i n c l u d e a s p e c t s of d u r a t i o n and r e g i s t e r p r i m a r i l y . The f i r s t A ^ may be c o n s i d e r e d a l o c a l downbeat s i m p l y because i t i s t h e f i r s t p i t c h of t h e l i n e ( a l t h o u g h i t s e n t r y , as no t e d e a r l i e r , i s somewhat overpowered by t h e accompaniment), and t h e r e a r e no o t h e r p a t t e r n e d i m p ulses t o suggest o t h e r w i s e . The dynamic c u l m i n a t i o n on t h e change of p i t c h t o B ^ c o n t r i b u t e s t o i t s downbeat c h a r a c t e r i z a t i o n , w h i l e r e g i s t e r ( i . e . , the h i g h e s t p i t c h i n t h e l i n e ) and l i n e a r approach ( i . e . , a f t e r t h e d e l a y o f p r o g r e s s i o n t o D^5) g i v e s t h e E^-* a l o c a l downbeat q u a l i t y . The l e a p from B^, s t e p w i s e approach 18 i By c o n s i d e r i n g t h e p u l s e u n i t t o be 6 0 / 4, any impulse w i t h i n t h e m e t r i c c o n f i g u r a t i o n s i n v o l v i n g I 3 I I , I I I I , and I l 5 l I I , t h e t h r e e o p e r a t i v e i n t h e p i e c e , may q u a l i f y as a downbeat, on c o n d i t i o n t h a t i t : i s a c c e n t - d e f i n e d t h r o u g h r e g i s t e r , dynamics, d u r a t i o n , e t c . Example 20. P i e c e No. 8, measures 12-16 (horn p a r t o n l y ) , showing l o w - l e v e l m e t r i c u n i t s . t (t) 1 (») W r e -m e t e r e d t I 1 1 11% r 'MM' (no. of 60 t h s ) f (!) I 1 1 I M J I J -(50) (42) (24) (39) (15)(15X39) mm. 12 from over t h e d e l a y of p r o g r e s s i o n ) , and l o n g e r d u r a t i o n a r e f a c t o r s which emphasize the — a l s o a downbeat a t t h i s p a r t i c u l a r l e v e l . F i n a l l y , t h e G ^ , h a v i n g been approached l i n e a r l y from t h e s u s t a i n e d G^, has t h e f e e l of an a r r i v a l p o i n t a i d e d , i n p a r t , by t h e t e r m i n a t i o n of a c t i v i t y i n 19 t h e o t h e r t h r e e components. At t h e l e v e l of t h e u n i t s d e l i n e a t e d by t h e l o c a l downbeats s p e c i f i e d above [i.'.e'. , l e v e l (b) on Example 2u] , two impulses c o n t i n u e t o emerge as downbeats or a r r i v a l p o i n t s . The B ^ i s f e l t as such because o f t h e a p p r o a c h i n g dynamic i n t e n s i f i c a t i o n which c u l m i n a t e s w i t h i t s a r t i c u l a t i o n . The f i n a l G ^ i s t h e o n l y o t h e r downbeat of any s t r u c t u r a l v a l u e and, i n f a c t , i s t h e a r r i v a l p o i n t of t h e whole l i n e as suggested i n l e v e l ( c ) . A g a i n t h e c e s s a t i o n o f r h y t h m i c a c t i v i t y i n t h e accompanying components i s a prime f a c t o r i n t h e a c c e n t u a l s i g n i f i c a n c e a t t r i b u t e d t o t h e f i n a l G ^ . W h i l e t h e f i r s t s e c t i o n o f t h e e i g h t h p i e c e p r o v i d e s a c l e a r example of r h y t h m i c p r o g r e s s i o n and r e c e s s i o n i n a c o n t i n u o u s phrase ( e . g . , i n t h e accompaniment), as w e l l as one o f t h e few i n s t a n c e s of l o w - l e v e l m e t r i c s u b d i v i s i o n ( e . g . , t h e horn p a r t ) , one a d d i t i o n a l a s p e c t of r h y t h m i c d e s i g n i n t h i s s e c t i o n i s noteworthy. S p e c i f i c a l l y , t h e accompanimental element comes c l o s e r than any s e c t i o n i n t h e q u i n t e t to d e f i n i n g a r e g u l a r C i f 20 u n d i f f e r e n t i a t e d by a c c e n t ) p u l s e . As i n d i c a t e d i n Example 21, measures 1 ( b e a t s 1-2) and 10 ( b e a t s 3-4) o f t h e p i e c e , t h e t h r e e i n s t r u m e n t a l p a r t s c o i n c i d e on each q u a r t e r - n o t e , w h i l e i n t e r a c t i n g i n a complex way d u r i n g 19 The harmonic s t r u c t u r e which o c c u r s a c r o s s b a r s 15-16 i s a B major chord w i t h an added second; the r e l a t i v e consonance of t h i s s o n o r i t y p l a y s an important r o l e i n t h e a r r i v a l - p o i n t q u a l i t y of t h e s u s t a i n e d p i t c h e s ( i n both t e x t u r a l e l e m e n t s ) . 20 L i g e t i does, however, s p e c i f y i n t h e s c o r e : " v e r y e v e n l y , w i t h o u t any a c c e n t u a t i o n o f t h e b a r s o r t h e i r s u b d i v i s i o n s . " See L i g e t i , Ten Pieces, p. 27. 47 the balance of each beat. Even without any performer-imposed s t r e s s , the quarters are marked through the concurrence of a r t i c u l a t i o n . Example 21. Pi e c e No. 8, measures 1 (beats 1-2) and 10 (beats 3-4), showing p o t e n t i a l pulse d e f i n i t i o n . B S N As the i n t e r a c t i o n between rhythmic patterns becomes more complex and, e s p e c i a l l y i n the l i g h t of the l i n e a r p i t c h patterns which occur out-of-phase w i t h the rhythmic p a t t e r n s , the quarter-note pulse i s e f f e c t i v e l y 21 obscured i n favor of three r h y t h m i c a l l y independent l i n e a r events. Example 22(a) c o n s i s t s of measure 5 of the score w i t h the aforementioned l i n e a r p a t t e r n s marked w i t h s l u r s . This c l e a r l y r e v e a l s the l a c k of synchronization between rhythmic and l i n e a r p a t t e r n s . In (b) of Example 22, the f i r s t notes of the l i n e a r p a t t e r n s i n each instrument are i n d i c a t e d by noteheads w i t h t h i c k stems, a l l of which are connected by a t h i c k beam. The stems between the beamed notes 21 These three events, however, are s t i l l components of the one t e x t u r a l element i n operation at t h i s p o i n t . 48 r e p r e s e n t t h e r h y t h m i c c o n f i g u r a t i o n s of each p a r t , t h e r e b y showing the d i s t a n c e s between p a t t e r n r e c u r r e n c e s . Not o n l y i s t h e l a c k o f s y n c h r o n i z a t i o n between r h y t h m i c and l i n e a r p a t t e r n s , apparent i n system ( a ) , f u r t h e r i l l u s t r a t e d , but an element-rhythm o t h e r than meter i s , here, r e v e a l e d — t h e rhythm of l i n e a r p a t t e r n r e c u r r e n c e . Three d i s t i n c t rhythms a r e i n o p e r a t i o n (one i n each i n s t r u m e n t ) , t h e i n t e r a c t i o n o f which o b s c u r e s t h e q u a r t e r - n o t e p u l s e , as i n d i c a t e d e a r l i e r , and r e i n f o r c e s t h e r h y t h m i c a l l y p r o g r e s s i v e and r e c e s s i v e q u a l i t i e s o f t h e t e x t u r e as a whole. Example 22. P i e c e No. 8, measure 5, showing r h y t h m i c and l i n e a r p a t t e r n s . P i e c e No. 4, f e a t u r i n g t h e f l u t e , i s n o t a t e d c o m p l e t e l y i n ^  ( t h e 22 meter b e i n g e s s e n t i a l l y n o n - f u n c t i o n a l as t o p e r c e i v e d e f f e c t ) , and i s t e x t u r a l l y s t r u c t u r e d so t h a t t h e f l u t e i s engaged i n two c o n t i n u o u s phrases w i t h t h e accompanying i n s t r u m e n t s p r o v i d i n g t h e ( o f t e n fragmented) c o u n t e r p o i n t . The r e s u l t i n g s i n g l e t e x t u r a l element i s one of pseudo-polyphony e f f e c t e d by the rh y t h m i c " p h a s i n g " o f the f l u t e w i t h t h e c l a r i n e t and bassoon. That i s , t h e accompanying i n s t r u m e n t s move i n and out o f r h y t h m i c s y n c h r o n i z a t i o n w i t h t h e f l u t e , a p p e a r i n g more independent 23 than t h e y a c t u a l l y a r e . The p h a s i n g i s , however, i n p a r t r e s p o n s i b l e f o r t h e l o c a l p r o g r e s s i v e and r e c e s s i v e t e n d e n c i e s i n t h e p i e c e , b o t h phrases o f which r e v e a l an o v e r a l l move from an a c t i v e t o an i n a c t i v e s t a t e . Example 23 c o n s i s t s o f a g r a p h i c r e p r e s e n t a t i o n of t h e r h y t h m i c a c t i v i t y ( i . e . , i m p u l s e - d e n s i t y o f t h e composite rhythm) of t h e f o u r t h p i e c e . The g e n e r a l r h y t h m i c r e c e s s i o n i n t h e f i r s t phrase (measures 1-9) i s o b v i ous from t h e graph. The second phrase, however, i s c o n s i d e r a b l y more complex as i t c o n t a i n s s e v e r a l i n t e r r u p t i o n s , one o f which a l t e r s t h e o v e r a l l f l o w o f r h y t h m i c a c t i v i t y ( e . g . , the fe r m a t a over t h e r e s t i n bar 18). The f l u t e i s s i l e n t d u r i n g t h e o t h e r i n t e r r u p t i o n s , which f e a t u r e abrupt changes i n r e g i s t e r and dynamics i n t h e c l a r i n e t and bassoon (e.g.,. measures 11-12, 16, and 17); i t i s , t h e r e f o r e , o n l y t h e r h y t h m i c f l o w o f the f l u t e p a r t which i s a f f e c t e d . The f l u t e resumes i t s l e v e l o f a c t i v i t y immediately upon r e - e n t e r i n g . 22 L i g e t i u n d e r s c o r e s t h i s by t h e performance n o t e s i n t h e s c o r e ; "Apart from t h e i n d i c a t e d a c c e n t s , always p l a y v e r y e v e n l y and w i t h o u t a c c e n t u a t i o n , so t h a t t h e s u b d i v i s i o n s i n t o b a r s does not become p e r c e p t i b l e . " See L i g e t i , Ten Pieces, p. 15. 23 T h e i r r e l a t i o n s h i p t o t h e f l u t e l i n e w i l l become more apparent i n the next s e c t i o n . Example 23. P i e c e No. 4, i m p u l s e - d e n s i t y graph. measure 51 Rhythmic s t r u c t u r e o f t h e f l u t e p a r t i n t h e second phrase i s " f r u s t r a t e d " as a r e s u l t of r e c u r r i n g i n t e r r u p t i o n s n o t e d above. Even t h e f i n a l r e c e s s i o n o f r h y t h m i c a c t i v i t y i n measures 19 t o t h e end ( b o t h i n t h e f l u t e a l o n e , as w e l l as i n t h e t r i o ) , seems somewhat d i v o r c e d from t h e p r e v i o u s measures because of t h e abrupt " b r e a k i n g o f f " o f t h e f l u t e l i n e , c o n c u r r e n t w i t h t h e extreme r e g i s t e r and dynamic s h i f t i n t h e o t h e r p a r t s . A l t h o u g h t h e o v e r a l l r h y t h m i c d r i v e i s brought c o n v i n c i n g l y t o a c l o s e , one g e t s t h e i m p r e s s i o n t h a t t h e f l u t e i s l e f t i n a s t a t e of 24 u n f u l f i l l m e n t back i n bar 19. A l t h o u g h i n the f o u r t h p i e c e t h e n o t a t e d measure i s not . o p e r a t i v e as a m e t r i c u n i t , l a r g e - s c a l e u n i t s of i m p u l s e - d e n s i t y , n ot u n l i k e t h o s e n o t e d i n c o n n e c t i o n w i t h t h e e i g h t h p i e c e , may be d i s c e r n e d h e r e as w e l l . In t h e f i r s t phrase, f o r example, t h e f i r s t s i x b a r s may be d e f i n e d as a p r o g r e s s i v e u n i t w i t h t h e t u r n - a r o u n d p o i n t o c c u r r i n g on t h e f i r s t beat o f bar 7. The c r i t e r i a f o r t h i s i n t e r p r e t a t i o n a r e t h r e e f o l d : f i r s t , t h e maximum i m p u l s e - d e n s i t y o f t h e phrase o c c u r s on t h e l a s t beat of bar 6 (e.g., a d e n s i t y o f 6 ) ; second, t h e f l u t e i t s e l f o f f e r s a l o c a l r h y t h m i c i n t e n s i f i c a t i o n towards t h a t p o i n t , c u l m i n a t i n g w i t h t h e f i r s t q u i n t u p l e t i n t h e p i e c e ( i . e . , r"T~| f^f\ I j I I I J )» a n t * t h i r d , t h e a c t i v i t y l e v e l d rops c o n s i d e r a b l y w i t h t h e absence o f t h e f l u t e commencing on t h e f i r s t beat o f bar 7. The r e c e s s i v e u n i t spans measures 7-9, whereupon t h e r h y t h m i c t e n s i o n i s c o m p l e t e l y r e l a x e d w i t h t h e s u s t a i n e d v e r t i c a l dyad C^-D^. The f i r s t p h rase, a s two l a r g e - s c a l e u n i t s of i m p u l s e - d e n s i t y (one p r o g r e s s i v e and one r e c e s s i v e ) might be d e p i c t e d as i n Example 24. 24 I f one compares t h e " r e c e s s i o n " i n t h e two p h r a s e s , one n o t i c e s t h a t , i n t h e f i r s t , t h e f l u t e changes r e g i s t e r smoothly and wi t h o u t i n t e r -r u p t i o n ( e .g., bar 2 ) . In t h e second phrase, t h e f l u t e s t o p s suddenly and r e s t s b e f o r e r e - e n t e r i n g at t h e lower r e g i s t e r and dynamic l e v e l ( e . g . , bar 19). 52 Example 24. P i e c e No. 4, l a r g e - s c a l e impulse-density u n i t s . large-scale progressive unit large-scale recessive unit The second phrase i s more d i f f i c u l t to c h a r a c t e r i z e as to u n i t s of rhythmic progression and r e c e s s i o n . However, because the o v e r a l l rhythmic flo w i s e s s e n t i a l l y unaffected by the i n t e r r u p t i o n s (apart from the r e s t i n bar 18), the l a r g e - s c a l e progressive u n i t might a l s o be considered unaffected. Even the r e s t i n bar 18 might be f e l t to heighten the t e n s i o n because i t i s not approached by an app r e c i a b l e d e c l i n e i n rhythmic a c t i v i t y . The problem l i e s i n f i n d i n g the turn-around p o i n t . In c o n s i d e r a t i o n of the impulse-d e n s i t y curve (Example 23), one i n t e r p r e t a t i o n f o r such a point i s measure 21—the beginning of the f i n a l rhythmic r e c e s s i o n . I f , on the other hand, one takes i n t o account t e n s i o n through r e g i s t r a l and dynamic exposure, the second beat of bar 19 might be more persuasive. A f t e r a l l , the f i r s t beat of bar 19 i s unquestionably the r e g i s t r a l and dynamic climax point of the piece, w h i l e the second beat i n i t i a t e s a r e l a x i n g trend w i t h i n those same parameters (but not w i t h i n the parameter of rhythm). In any case, the f o u r t h piece does e x h i b i t the p o t e n t i a l f o r c h a r a c t e r i z a t i o n as to l a r g e - s c a l e u n i t s of impulse-density w i t h i n a rhythmic s t r u c t u r e of progressive and r e c e s s i v e q u a l i t i e s . The t h i r d piece (an ensemble type) provides an example of l a r g e - s c a l e 53 rhythmic progression and r e c e s s i o n w i t h i n an extended polyphonic phrase which spans the e n t i r e piece. Example 25 c o n s i s t s of the impulse-density curve of the piece and, although i t s shape i s g e n e r a l l y s i m i l a r to that of the excerpt from the ei g h t h piece c i t e d e a r l i e r (even the emergence of a simultaneous second t e x t u r a l element occurs i n both), No. 3 i s d i f f e r e n -t i a t e d by one important s t r u c t u r a l f a c t o r . S p e c i f i c a l l y , the s i n g l e , continuous t e x t u r a l element, i n d i c a t e d on the graph, i s composed of four consecutive t e x t u r a l elements. Three of these c o n t r i b u t e to the l a r g e -s c a l e progression (measures 1-8, 8-9, and 9-13), and one comprises the rec e s s i o n (measures 14 to the end). (The rhythmic i m p l i c a t i o n s of the octave-doubled theme i n bars 1 0 - 1 2 — i . e . , the simultaneous second t e x t u r a l e l e m e n t — w i l l be de a l t w i t h s h o r t l y . ) Example 25. • Piece No. 3, impulse-density graph. turn-around point tr.H 1 15 measure no. 54 The d i f f e r e n c e i n the l e v e l s of o v e r a l l a c t i v i t y i n the three stages of progression are l a r g e l y the r e s u l t of rhythmic and t e x t u r a l p a r t i c u l a r s ( i . e . , surface d e t a i l s ) of the i n d i v i d u a l components of each consecutive polyphonic element. For example, i n measures 1-8, the 25 components move r e l a t i v e l y slowly and i n a fragmented f a s h i o n ; the i n c r e a s i n g complexity of i n t e r a c t i o n between components provides the o v e r a l l rhythmic progression. In the second stage, bars 8-9, each part moves more continuously and i n smaller note v a l u e s . The i n t e r a c t i o n of components, each of which undergoes a rhythmic i n t e n s i f i c a t i o n , y i e l d s the sharp increase i n t o t a l rhythmic a c t i v i t y represented on the graph 2 6 by the almost v e r t i c a l l i n e . The t h i r d stage of progression i s e f f e c t e d by the c l a r i n e t t r i l l (e.g., an i n d e f i n i t e number of impulses per quarter-note) . The beginning of each of the three stages of rhythmic progression (defined above) as w e l l as that of the r e c e s s i v e gesture i s marked by a concurrence of a r t i c u l a t i o n . In c o n s i d e r a t i o n of t h i s d e t a i l , one may wish to a t t r i b u t e metric accentual s i g n i f i c a n c e to these p a r t i c u l a r impulses, thereby q u a l i f y i n g the four consecutive elements as m e t r i c u n i t s — u n i t s which are l a r g e r than the notated measure but smaller than the u n i t s of impulse-density to be exposed l a t e r . These are i n d i c a t e d i n Example 26 and, once again, i n order that i m p u l s e s — n o t a t e d " o f f - t h e - b e a t " i n the s c o r e — b e considered l o c a l downbeats, the m e t r i c i n d i c a t i o n s must be based on a pulse 25 The c o n t i n u i t y inherent i n the l i n e a r components of t h i s p a r t i c u l a r t e x t u r a l element, d e s p i t e the apparent fragmentation of the instrumental p a r t s , i s discussed i n the next s e c t i o n on l i n e a r d e t a i l s of p i t c h o r g a n i z a t i o n . 2 6 This sharp increase i n rhythmic a c t i v i t y , concurrent w i t h the instrumentation-density r e d u c t i o n , was r e f e r r e d to e a r l i e r as a t r a n s i t i o n a l s e c t i o n between the two main formal s e c t i o n s of the piece. 55 r a t e which w i l l accommodate such c h a r a c t e r i z a t i o n s . Example 26. P i e c e No. 3, m e t r i c u n i t s . mm. 1 7 8 9 14 16 Taken as one c o n t i n u o u s statement, t h e p i e c e (not y e t c o n s i d e r i n g t h e o c t a v e - d o u b l e d theme) may be viewed as a l a r g e - s c a l e u n i t of r h y t h m i c p r o g r e s s i o n f o l l o w e d by one of r h y t h m i c r e c e s s i o n , the t u r n - a r o u n d p o i n t o c c u r r i n g a t t h e b e g i n n i n g o f measure 14 (as i n d i c a t e d i n Example 25). With r e s p e c t to t h i s p a r t i c u l a r mode of r h y t h m i c s t r u c t u r e , t h e o v e r a l l d e s i g n ( i . e . , at t h e h i g h e s t l e v e l ) i s not c o m p l e t e l y u n l i k e t h a t of t h e e x c e r p t from No. 8 c i t e d e a r l i e r . A l s o s i m i l a r to t h e No. 8 e x c e r p t i s t h e emergence of a s i m u l t a n e o u s , second t e x t u r a l element a t t h e peak o f r h y t h m i c a c t i v i t y . The r h y t h m i c a l l y p r o g r e s s i v e p o r t i o n o f t h e c o n t i n u o u s t e x t u r e may be f e l t as a n a c r u s t i c to t h e o c t a v e - d o u b l e d theme, w h i l e 56 27 r e t a i n i n g t h e c o n t i n u i t y w i t h i n i t s own l a r g e - s c a l e s t r u c t u r e . Apart from t h e i n t e r a c t i o n between t h e two s i m u l t a n e o u s elements, t h e o c t a v e - d o u b l e d theme may be heard to r e v e a l i t s own l o w - l e v e l m e t r i c 2 8 s t r u c t u r e ( a g a i n , not u n l i k e t h a t of the horn l i n e i n No. 8 ) . By d e f i n i t i o n , m e t r i c u n i t s r e q u i r e a c c e n t - d i f f e r e n t i a t e d impulses which a r e d e f i n e d h e r e , as i n p i e c e No. 8, by r e g i s t r a l and/or dynamic exposure, l i n e a r approach, d u r a t i o n , and/or n o t a t e d a r t i c u l a t i v e m arkings. I g n o r i n g t h e n o t a t e d meter s i g n a t u r e , one might c o n c e i v e t h e E a t t h e end of bar 10 as an a c c e n t e d , l o c a l downbeat because of i t s d u r a t i o n and l i n e a r approach ( r e f e r to Example 27). The next p i t c h o f comparable d u r a t i o n a l exposure, t h e F o f bar 11, may a l s o be h e a r d as a l o c a l a r r i v a l p o i n t , e s p e c i a l l y i n 29 view of t h e l e a p which approaches i t . A l t h o u g h t h e C of b a r s 11-12 i s comparable i n d u r a t i o n and has added emphasis t h r o u g h r e g i s t r a l exposure, i t comes too soon a f t e r t h e F to be heard as a m e t r i c d o w n b e a t — t h a t i s , one which a r t i c u l a t e s t h e b e g i n n i n g of a m e t r i c u n i t a t a l e v e l comparable t o t h a t of t h e p r e v i o u s u n i t . I t i s t h e r e f o r e c o n s i d e r e d s u b o r d i n a t e to t h e p r e v i o u s E and F i n terms of m e t r i c s t r e n g t h . F i n a l l y , t h e A i n bar 12 " ' I t i s i n t e r e s t i n g t o n o t e t h a t t h e c o n t i n u o u s statement would seem to d r i f t i n and out o f t e x t u r a l "primacy." I n o t h e r words, t h e t h r e e s t a g e s of r h y t h m i c p r o g r e s s i o n a r e t h e p r i m a r y t e x t u r e s i n t h e opening s e c t i o n ( t h e y a r e t h e o n l y o n e s ) . As t h e r h y t h m i c a c t i v i t y r e a c h e s i t s peak ( i . e . , the t r i l l ) , however, the i n s t r u m e n t a t i o n - d e n s i t y d e c r e a s e s and t h e r e g i s t e r and dynamics become l e s s i n t e n s e , r e d u c i n g t h e s t a t u s of t h a t p a r t i c u l a r t e x t u r a l element ( i . e . , t h e t r i l l ) . The o c t a v e - d o u b l e d theme which emerges ov e r the l a t t e r i s c o n s i d e r e d p r i m a r y u n t i l i t d i s s o l v e s i n bar 12, where-upon the r e c e s s i v e g e s t u r e ( w i t h i n t h e l a r g e c o n t i n u o u s statement) emerges as p r i m a r y . 28 An a d d i t i o n a l g e n e r a l s i m i l a r i t y between p i e c e No. 3 and t h e e x c e r p t from No. 8 may be d i s c e r n e d : t h e r h y t h m i c a c t i v i t y c u r v e of t h e emerging theme, i n each case, m i r r o r s on a s m a l l e r s c a l e t h a t o f t h e l a r g e r c o n t i n u o u s element. Note a l s o t h e h i g h e r - l e v e l s t e p w i s e approach from the E o f bar 11. 57 may be heard as the u l t i m a t e a r r i v a l point of the theme ( i t i s the l a s t p i t c h to be doubled i n octaves) and i s , t h e r e f o r e , considered to be of accentual and m e t r i c s i g n i f i c a n c e . Because of the l a c k of e x p l i c i t l y a r t i c u l a t e d p u l s e — e s p e c i a l l y one which concurs w i t h the three downbeats defined above—a pulse f a c t o r derived from the rhythmic d i v i s i o n s of the theme i t s e l f may be assumed f o r & the purpose of determining the m e t r i c i n d i c a t i o n s . I f a pulse of 111111 i s used, f o r example, two equal m e t r i c u n i t s of 17^ are d e l i n e a t e d by the E, F, and A, w i t h the accented C f a l l i n g w i t h i n the second u n i t (e.g., a "syncopation" of s o r t s ) . This rhythmic/metric c o n f i g u r a t i o n i s i l l u s t r a t e d i n Example 27. Example 27. Piece No. 3, measures 10-12, rhythmic and m e t r i c design. mm. 10 11 12 | 17x1 | 1 7 x | I B S N . I I ' ) - ~ re-metered T 6 ^Again, l o w e r - l e v e l metric o r g a n i z a t i o n i s revealed w i t h i n a l a r g e r , more continuous rhythmic statement, the l a t t e r e x h i b i t i n g impulse groupings considerably l a r g e r than the asserted m e t r i c u n i t s of the theme i t s e l f . 58 While the f i f t h , seventh, and n i n t h pieces ( a l l being of the ensemble type) a l s o r e v e a l continuous rhythmic statements, some i n v o l v i n g progression and r e c e s s i o n , the statements l a c k the presence of e x p l i c i t turn-around p o i n t s comparable to those exposed i n the pieces discussed thus f a r . In the f i f t h p iece, f o r instance, four s e c t i o n s are d e l i n e a t e d by a l t e r n a t i n g tempi and dynamics (e.g., J= 120 J= 132 J= 120 J= 132). sfz ff sfz ff 4 3 4 4 The impulse-density curve of t h i s piece i s given in; Example 28. In t h i s p a r t i c u l a r piece, because the mode of a r t i c u l a t i o n throughout i s one of repeated staccatissimo notes, the impulse-density i s a c t u a l l y r e p r e s e n t a t i v e of the rhythm.'.of p i t c h change. The i m p l i c a t i o n s of t h i s d e t a i l w i l l soon become c l e a r . Example 28. P i e c e No. 5, impulse-density graph. 59 Within the f i r s t s e c t i o n ( J = 120, measures 1-8), the a c t i v i t y l e v e l of the h i g h l y a r t i c u l a t e polyphonic t e x t u r e i s r e l a t i v e l y constant, suggesting n e i t h e r progression nor r e c e s s i o n . The second s e c t i o n i s i n t e n s i f i e d through the abrupt tempo change ( i . e . , to J = 132) and marginal increase i n impulse-density, while the t h i r d s e c t i o n (back to J = 120) i n v o l v e s a rhythmic r e c e s s i o n to the o r i g i n a l l e v e l of a c t i v i t y and beyond to 0 i m p u l s e s / J f o r s e v e r a l consecutive beats i n bar 11. While the j u n c t u r e s at which rhythmic a c t i v i t y changes d i r e c t i o n £i.e., from one of progression to one of r e c e s s i o n (e.g., measure 9) , or v i c e versa (.e.g., measure 12)J might be viewed as turn-around p o i n t s , the d i f f e r e n c e i n magnitude of impulse-density i s h a r d l y enough to warrant such a 30 c h a r a c t e r i z a t i o n . The e f f e c t of an increase i n impulse-density from 2 to 4 / J , f o r example, i s s i g n i f i c a n t l y overpowered by the mode of a r t i c u l a t i o n ( i . e . , the continuous, arhythmic note r e p e t i t i o n s ) . The staccatissimo r e i t e r a t i o n s , i n f a c t , prevent a f e e l i n g of rhythmic repose even when the p i t c h e s are kept constant (e.g., i n measure 11). The rhythmic i n t e n s i f i c a t i o n i n the second s e c t i o n of the seventh piece (bars 3 8 - 4 4 ) — e s s e n t i a l l y a s i n g l e s e c t i o n which i s " t o r n o f f " at the peak of i t s rhythmic a c t i v i t y — r e s u l t s from gradual independence of the four sounding components. Each time a component enters, i t does so i n rhythmic unison w i t h a part already i n progress. Soon a f t e r e n t r y , however, the new component branches o f f on i t s own rhythmic course (e.g., oboe and c l a r i n e t i n measure 39, and bassoon i n bar 40), thus i n t e n s i f y i n g the i n t e r a c t i o n between parts and u l t i m a t e l y the l e v e l of the composite 30 In t h i s piece the d i f f e r e n c e between the most a c t i v e and i n a c t i v e s t a t e s i s only 4 impulses/ J ; compare t h i s w i t h 22 i n No. 8, 8 i n No. 4, and at l e a s t 15 i n No. 3 ("at l e a s t " because of the i n d e f i n i t e number provided by the t r i l l ) . 60 r h y thmic a c t i v i t y . Example 29 o f f e r s a g r a p h i c r e p r e s e n t a t i o n of r h y t h m i c a c t i v i t y as to i m p u l s e - d e n s i t y . Example 29. P i e c e No. 7, measures 38-44, i m p u l s e - d e n s i t y graph. 38 39 40 41 42 43 44 measure no. A l t h o u g h the n i n t h p i e c e c o n s i s t s of one, c o n t i n u o u s t e x t u r a l element throughout ( i . e . , t h e t h r e e - p a r t canon mentioned e a r l i e r ) , a g r a p h i c r e p r e s e n t a t i o n o f t h e i m p u l s e - d e n s i t y o f i t s composite rhythm would r e v e a l a r a t h e r u n i n t e r e s t i n g o s c i l l a t i o n between 0 and 2 impulses per q u a r t e r - n o t e — c l e a r l y not t h e most s i g n i f i c a n t a s p e c t of r h y t h m i c s t r u c t u r e i n the p i e c e . I n f a c t , p i t c h u n f o l d i n g and r e g i s t r a l a s c e n t a r e more important f a c t o r s of p r o g r e s s i o n i n t h e p i e c e than r h y t h m i c i n t e n s i f i c a t i o n . Rhythm does, however, p l a y a v i t a l r o l e i n t h e independence o f t h e c a n o n i c components. Each of the t h r e e p a r t s moves i n m u l t i p l e s of a d i f f e r e n t d u r a t i o n a l u n i t : 6 1 5 3 p i c c o l o - | | | | , oboe - | I | I I , and c l a r i n e t - | 1 I . T h i s d e t a i l i n rhythmic d e s i g n p r e v e n t s the i m i t a t i o n from becoming too r e g u l a r (or s t r i c t ) . At t h e b e g i n n i n g of the p r e s e n t s e c t i o n on rh y t h m i c a s p e c t s , i t was noted t h a t t h e consequences of n o n - o p e r a t i v e meter a t t h e l e v e l of t h e n o t a t e d measure a r e d i f f e r e n t i n p i e c e s w i t h c o n s t a n t n o t a t e d meter from those w i t h f l u c t u a t i n g meter. In c o n s i d e r a t i o n of t h e l a t t e r t y p e ( s p e c i f i c a l l y , f o u r of the f i v e s o l o i s t i c p i e c e s ) a number of examples e x i s t where the b a r l i n e s would a p p e a r to be s t r a t e g i c a l l y p l a c e d t o h e i g h t e n the downbeat q u a l i t y of c e r t a i n p o i n t s (be th e y a r r i v a l and/or d e p a r t u r e p o i n t s ) , a l r e a d y exposed t h r o u g h o t h e r means of a c c e n t u a t i o n ( e . g . , i n c r e a s e d dynamics, a r t i c u l a t i v e markings, e t c . ) . The second p i e c e o f f e r s two i n s t a n c e s of e x p l i c i t l y d e f i n e d downbeats as a r r i v a l p o i n t s . The f i r s t o c c u r s i n bar 1 1 , approached from bar 9 , w h i l e t h e second t a k e s p l a c e on t h e downbeat of bar 2 4 , approached from t h e l a s t beat of the p r e v i o u s measure. These e x c e r p t s a r e g i v e n i n Example 30 (a) and (b) r e s p e c t i v e l y . G i v e n t h e r h y t h m i c a l l y complex environment i n which t h e s e two downbeats o c c u r , t h e i r placement would seem to be of s t r u c t u r a l s i g n i f i c a n c e . The f i r s t one may be heard t o c l o s e o f f t h e opening s e c t i o n , t h e c o n t i n u a t i o n i n t h e c l a r i n e t (bar 1 1 ) s e r v i n g as a c o n n e c t i o n t o t h e next f o r m a l s e c t i o n ( J = 1 4 4 , poco meno mosso). The downbeat of bar 2 4 would appear t o end t h e main body of the p i e c e , w h i l e e l i d i n g w i t h t h e c o n n e c t i n g l i n k to t h e coda ( i . e . , measures 2 8 to t h e end). 62 Example 30. P i e c e No. 2, l o c a l a r r i v a l p o i n t s . (a) measures 9-11 (b) measures 23-24 © 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributor; Corporation, sole Canadian agent for B. Schott's Soehne. 63 Two i n s t a n c e s o f l o c a l downbeats i n t h e s i x t h p i e c e a r e o f s i g n i f i c a n c e . Each i s approached by a c a d e n z a - l i k e passage i n t h e oboe (t h e f e a t u r e d i n s t r u m e n t ) , marked senza tempo, and each f u n c t i o n s as an e l i d e d d o w n b e a t — t h a t i s , a sim u l t a n e o u s a r r i v a l and d e p a r t u r e p o i n t . Example 31 i l l u s t r a t e s t h e two p o i n t s i n q u e s t i o n . Example 31. P i e c e No. 6, l o c a l a r r i v a l / d e p a r t u r e p o i n t s , (a) measures 8-9 ^ 8 senza tempo (Presto) J A  Fl. Ob. Cl.SH, Cor.Fa Fag. Tempo: Poco sostenuto.legato dolcissimo 9 v-JSL (b) measures 10-11 j 0 senza tempo: Prestiss., staccatiss. Poco sostenuto prestissimo possibile —LL. = — j — = = —f- —f- — — T T r«|*TT"rtl*"rtf tartyluil'gkjr'-crescenao motto -t r * -is u ;  A - ^ V senza sord.\aa ±^L±J •1' Jig rT\ pp moito calmo Fl. Ob. Cl.Si\> Cor. Fa. Fag. ©1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne. 64 A second f u n c t i o n of the b a r l i n e s and metric i n d i c a t i o n s may be one of rhythmic grouping without a c c e n t - d e l i n e a t i o n . In other words, a musical idea may r e q u i r e the time-span of f i v e quarter-notes at a given tempo so i t would be l a b e l l e d as 4 without any m e t r i c ( i . e . , accent) i m p l i c a t i o n such > > > > a s ^ r * p | * | * or f f |* |* f ' T n^- S would appear to be the s i t u a t i o n i n parts of the e i g h t h piece. In measures 26-32, f o r instance, f i v e d i s p a r a t e musical ideas are presented i n succession, each r e q u i r i n g a d i f f e r e n t time-span (not n e c e s s a r i l y a d i f f e r e n t p a t t e r n of accented and unaccented p u l s e s ) . Example 32 c o n s i s t s of these seven measures from the score. Notation i n s t r a i g h t ^ would be next to impossible and would, almost c e r t a i n l y , undermine 31 the dramatic impact of the d i s p a r a t e musical ideas presented i n the excerpt. Summary Concerning rhythmic and metric design, three main p r i n c i p l e s were found to be of s i g n i f i c a n c e i n the q u i n t e t . The f i r s t i n v o l v e s the f l u c t u a t i o n i n composite rhythmic a c t i v i t y , termed "impulse-density," and i t s v i t a l i n f l u e n c e on progressive and r e c e s s i v e tendencies i n s e c t i o n s and pieces c o n s i s t i n g p r i m a r i l y of polyphonic t e x t u r e s . The second p r i n c i p l e concerns the f a c t that notated meter i s l a r g e l y i n o p e r a t i v e i n the pieces and, i n f a c t , a c c e n t - a r t i c u l a t e d u n i t s at the l e v e l of the notated measure were judged to be e s s e n t i a l l y i r r e l e v a n t . However, l o w - l e v e l metric u n i t s ( d e l i n e a t e d by f a c t o r s other than notated b a r l i n e s ) were s a i d to operate i n the horn part of piece No. 8 and the octave-doubled theme of No. 3. The t h i r d p r i n c i p l e stated t h a t , i n pieces w i t h a constant notated meter, b a r l i n e s were found to be n o t a t i o n a l conveniences. In pieces e x h i b i t i n g 31 The e a r l i e r p a r a l l e l drawn between the s o l o i s t i c pieces of the quintet and the l a r g e r pieces c h a r a c t e r i z e d by the s t y l e of Apparitions and Aventures i s e x e m p l i f i e d i n t h i s p a r t i c u l a r excerpt. Example 32. P i e c e No. 8, measures 26-32, showing c o n s e c u t i v e d i s p a r a t e m u s i c a l i d e a s . Agitato capriccioso " as @ 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne. 66 f l u c t u a t i n g , n o t a t e d meter, however, f a c t o r s of downbeat c h a r a c t e r i z a t i o n and time-span c o n s i d e r a t i o n s of d i s p a r a t e m u s i c a l i d e a s were found to be r e l e v a n t i n a d d i t i o n to t h a t of n o t a t i o n a l c o n v e n i e n c e . While o t h e r d e t a i l s , and p r i n c i p l e s of g r e a t e r consequence, may be found to o p e r a t e w i t h i n t h e r h y t h m i c and m e t r i c d e s i g n of t h e s e p i e c e s , i t i s hoped t h a t the i s s u e s d i s c u s s e d i n t h i s s e c t i o n w i l l s e r v e as a p o i n t from which a g r e a t e r u n d e r s t a n d i n g of t h i s m u s i c a l language may be d e v e l o p e d . Modes of P i t c h O r g a n i z a t i o n L i n e a r D e t a i l s The l i n e a r d e t a i l s o f p i t c h o r g a n i z a t i o n , f o r t h e purposes o f t h i s study, r e f e r t o ( p r e d o m i n a n t l y ) s t e p w i s e p a t t e r n s of r e g i s t r a l l y s p e c i f i c 32 p i t c h e s and/or p i t c h - c l a s s e s ( P C ' s ) . As one might expect to f i n d many such l i n e a r p a t t e r n s i n music o f t h i s language, our c o n c e r n w i l l f o c u s on l i n e a r c o n n e c t i o n s which tend to move toward and/or away from s p e c i f i c s t r u c t u r a l p o i n t s i n the p i e c e s , t h e r e b y s u g g e s t i n g elements o f p r o g r e s s i o n and r e c e s s i o n . Two a s p e c t s of l i n e a r c o n n e c t i o n to be s t u d i e d a r e modes of p i t c h / PC s t r u c t u r i n g w i t h i n the v a r i o u s p i e c e s , and l a r g e - s c a l e c o n n e c t i o n s 33 between p i e c e s . In t h e former, t h e c o n n e c t i o n s may be found to o c c u r i n one p a r t i c u l a r i n s t r u m e n t ( i . e . , one component w i t h i n a l a r g e r t e x t u r a l 32 A c c o r d i n g t o Edward Cone, s t e p w i s e c o n n e c t i o n s a r e v i t a l t o t h e p e r c e p t i o n o f l i n e a r s t r u c t u r e as " t h e ear w i l l n a t u r a l l y connect each tone w i t h t h o s e n e a r e s t i t i n p i t c h . The a d j a c e n t p i t c h e s may be d i a t o n i c or t h e y may be c h r o m a t i c ; t h e y may be a c t u a l l y a d j a c e n t o r d i s p l a c e d by one o r more o c t a v e s ; t h e y may be p r e s e n t by i m p l i c a t i o n o n l y . " See " A n a l y s i s Today," The Musical Quarterly ( A p r i l 1960): 177-78. 33 Re g a r d i n g t h e l a t t e r , such i n s t a n c e s may be c o n s i d e r e d a d d i t i o n a l modes of l a r g e - s c a l e c o n n e c t i o n o r p i e c e subgrouping, s e v e r a l of which were o u t l i n e d e a r l i e r i n t h i s c h a p t e r . 67 element), o r t h e y may be the r e s u l t o f the i n t e r a c t i o n of components ( t h e l i n e a r i z a t i o n s , themselves, b e i n g a d d i t i o n a l components of s o r t s ) . A l t h o u g h s i g n i f i c a n t l i n e a r c o n n e c t i o n s may be found i n a l l of t h e p i e c e s , t h e s t r u c t u r a l d e t a i l s or p a r t i c u l a r s o f l i n e a r i z a t i o n a r e o f t e n d i f f e r e n t from p i e c e to p i e c e . The second p i e c e , f o r example, r e v e a l s two l i n e a r i z a t i o n s e f f e c t e d by t h e a r p e g g i a t i o n d e s i g n of t h e c l a r i n e t p a r t . I n the ' b ' - s e c t i o n , measures 12-15, t h e upper and lower p i t c h e s of t h e s u c c e s s i v e a r p e g g i o s c r e a t e s i m u l t a n e o u s , d i f f e r e n t l i n e a r 34 c o n t i n u i t i e s . In b o t h a s c e n d i n g e v e n t s , t h e f i n a l p i t c h e s a r e marked by t h e l e a p o f a t h i r d which i s f u r t h e r d i s p l a c e d by an o c t a v e . These c o n n e c t i v e p a t t e r n s , which p r o v i d e l i n e a r d i r e c t i o n t o t h e f o u r measures at hand, a r e i l l u s t r a t e d i n Example 33. A second l i n e a r event r e s u l t i n g from a s i m i l a r a r p e g g i o d e s i g n may be d i s c e r n e d i n measures 21-22 and c o n t i n u e d i n bar 29. The upper n o t e s of t h e c o n s e c u t i v e two and t h r e e - n o t e p a t t e r n s ( i . e . , o s c i l l a t i o n s and a r p e g g i o s ) c r e a t e an a s c e n d i n g l i n e from D^ -> t o G^-* ( b a r s 21-22) which i s c o n t i n u e d from A ^ to A ^ i n bar 29. The lower n o t e s c o n t r i b u t e t o a s i m u l t a n e o u s l y a s c e n d i n g l i n e from to B-> and an o v e r l a p p i n g d e s c e n d i n g l i n e from t o D^-\ Example 34 p o r t r a y s t h e s e i n t e r a c t i n g l i n e a r e v e n t s . While c o n t i n u e d l i n e a r i z a t i o n o f t h e lower n o t e s does not o c c u r i n t h e f i n a l measure, t h e resumption o f t h e a s c e n d i n g l i n e i n t h e upper p a r t i s r e s p o n s i b l e f o r t h e d i r e c t e d tendency towards t h e h i g h e s t p i t c h of t h e p i e c e ( A 1 * 6 ) . 34 W h i l e t h e " i n n e r " p a r t s of t h e a r p e g g i o s may a l s o r e v e a l l i n e a r r e l a t i o n s h i p s , t h e " o u t e r " v o i c e s a r e most r e a d i l y p e r c e i v e d a t the o p e r a t i v e tempo,J = 144. Example 33. P i e c e No. 2, measures 12-15, two simultaneous l i n e a r i z a t i o n s . mm. 12 13 14 15 41 C L ( inC), % y M f=±=z 111 I IIiff 51? L^^L3Z^ L^^L^0 iX^Li^EJ ^ E J LLLU Uill 1  Bf 5 5 6 6 6 Example 34. P i e c e No. 2, measuresv2I-22 and 29, two simultaneous l i n e a r i z a t i o n s . ON oo mm. 21 2 2 2 9 69 Much of t h e f l u t e p a r t i n t h e f o u r t h p i e c e i s c o n s t r u c t e d o f s u c c e s s i v e , two-note o s c i l l a t i o n s , t h e upper and lower n o t e s of which may be heard to d e f i n e independent l i n e a r i z a t i o n s , not u n l i k e t h o s e o f the second p i e c e . A l t h o u g h t h e c l a r i n e t p a r t ( i n No. 4) opens i n a r e l a t i v e l y s t e p w i s e f a s h i o n , i t a l s o e x h i b i t s a b i - l i n e a r s t r u c t u r e from t h e m i d d l e of bar 2 t o bar 8. Example 35 shows the f l u t e and c l a r i n e t p a r t s from t h e s c o r e w i t h t h e suggested l i n e a r i z a t i o n s i n t h e f l u t e (above t h e s c o r e ) and i n t h e c l a r i n e t (below). A l t h o u g h t h e c o n n e c t i o n s a r e s e l f - e x p l a n a t o r y , two d e t a i l s a r e noteworthy. F i r s t , r e g a r d i n g r e g i s t r a l space, i t i s s i g n i f i c a n t t h a t t h e p o i n t o f o r i g i n o f t h e f l u t e ' s t op l i n e a r event, (bar 1 ) , i s t h e a r r i v a l p o i n t o f i t s lower a s c e n d i n g l i n e ( i n measure 2 ) . The d o t t e d l i n e c o n n e c t s t h e two, s u g g e s t i n g a c o n j o i n e d l i n e a r i z a t i o n o f E^ to F#6 t h r o u g h p r o l o n g a t i o n o f t h e C^. Second, the b i - l i n e a r s t r u c t u r e o f t h e f l u t e p a r t , which t e r m i n a t e s a b r u p t l y a t t h e end of bar 6, may be heard t o c o n t i n u e i n t h e c l a r i n e t p a r t , as suggested by t h e arrow from b a r s 6-7. The l i n e a r -p r o g r e s s i v e t e n d e n c i e s , i n i t i a t e d i n t h e f l u t e and c l a r i n e t a t t h e o n s e t of t h e p i e c e , a r e brought t o a c o n v i n c i n g c l o s e i n measures 7-8 by t h e c l a r i n e t and bassoon, t h e a r r i v a l p o i n t s on and c o i n c i d i n g w i t h t h e 35 a f o r e m e n t i o n e d r h y t h m i c r e p o s e . In t h e ' b ' - s e c t i o n o f the s e v e n t h p i e c e (measures 38 t o t h e end), a l i n e a r event may be d i s c e r n e d which r e s u l t s from dynamic, d u r a t i o n a l , and r e g i s t r a l exposure, as w e l l as m o t i v i c r e c u r r e n c e . The peaks of t h e r e c u r r i n g dynamic " s w e l l s " a r e o f t e n c o n c u r r e n t w i t h a s u s t a i n e d p i t c h which has been approached by an a s c e n d i n g a r p e g g i o and, more immediately, 35 The sense o f cadence a t t h i s p o i n t i n t h e p i e c e a l s o r e s u l t s from a p a r t i c u l a r harmonic d e t a i l t o be e x p l a i n e d l a t e r . 70 Example 35. P i e c e No. 4, measures 1-8, simultaneous l i n e a r connections.. 71 by a t r i t o n e ( a s c e n d i n g o r d e s c e n d i n g ) . The l i n e a r p a t t e r n i n q u e s t i o n i n v o l v e s t h e p r o g r e s s i o n of t h e r e c u r r i n g t r i t o n e s ( a l t h o u g h , i n t h i s 3 6 p a r t i c u l a r example, movement by s t e p i s exceeded). The t o p s t a f f o f Example 36 r e v e a l s t h e t r i t o n e s exposed t h r o u g h the means d e s c r i b e d above. 37 System (b) i l l u s t r a t e s t h e v a r i o u s " i n v e r s i o n " and i n t e r l o c k i n g r e l a t i o n -s h i p s i n h e r e n t i n t h e s u c c e s s i o n of t r i t o n e s , w h i l e system (c) shows the d e r i v e d l i n e a r p r o g r e s s i o n . I n t e r v a l - c l a s s e s (IC's) between c o n t i g u o u s t r i t o n e s o f the p r o g r e s s i o n a r e i n d i c a t e d below system ( c ) , t h e "-" r e p r e s e n t i n g a d e s c e n t , and "+" an a s c e n t . The t r a n s p o s i t i o n and n e a r -i n v e r s i o n r e l a t i o n s h i p between the opening and c l o s i n g t r i t o n e s o f t h e l i n e a r i z a t i o n a r e summarized on systems (d) and ( e ) . Once a g a i n a complete f o r m a l s e c t i o n i s t r a v e r s e d by a l i n e a r event, t h e s t e p w i s e a s c e n d i n g s t r u c t u r e o f which c o n t r i b u t e s to a " d i r e c t e d " tendency towards i t s c o n c l u s i o n . The opening of t h e ' b ' - s e c t i o n (of t h e s e v e n t h p i e c e ) i s noteworthy f o r r e a s o n s of p i t c h / P C o r g a n i z a t i o n o t h e r than t h o s e i n v o l v i n g l i n e a r c o n n e c t i o n s . I t i s an example of a c a r e f u l l y c o n t r o l l e d u n f o l d i n g of PC c o n t e n t ; t h e twelve PC's a r e sounded once b e f o r e any a r e r e p e a t e d . A l t h o u g h t h e t w e l v e - n o t e o r d e r i n g i s not f u r t h e r t r e a t e d t r a n s p o s i t i o n a l l y o f i n v e r s i o n a l l y , as an a c t u a l t w e l v e - t o n e "row," i t does r e p r e s e n t one mode of PC o r g a n i z a t i o n which i s o p e r a t i v e i n o t h e r p i e c e s of the q u i n t e t . The PC c o n t e n t of p i e c e No. 5, f o r example, u n f o l d s a c c o r d i n g to f o u r d i f f e r e n t t w e l v e - n o t e o r d e r i n g s , c o n c u r r e n t , f o r the most p a r t , w i t h t h e 3 6 B o t h t h e r e c u r r i n g l i n e a r t r i t o n e s and g e n e r a l a r p e g g i o approaches t o s u s t a i n e d p i t c h e s may be c o n s i d e r e d m o t i v i c . 37 I n v e r s i o n r e l a t i o n s h i p r e f e r s t o t h e v e r t i c a l o r d e r of t h e t r i t o n e members (even though a t r i t o n e , as such, i s not i n v e r t i b l e w i t h r e s p e c t t o a c t u a l I C ) . 73 Example 36. P i e c e No. 7, measures 38-44, l i n e a r p r o g r e s s i o n o f t r i t o n e s . 74 four s e c t i o n s of the piece (as d e l i n e a t e d through other parameters already-mentioned) . In the f i r s t and t h i r d s e c t i o n s some PC's are repeated before a l l twelve have sounded, the t w e l f t h PC s i g n i f y i n g the end of the f i r s t 38 s e c t i o n and, i n the l a t t e r case, the beginning of the f o u r t h . The second and f o u r t h s e c t i o n s c o n t a i n no such r e p e t i t i o n s ; once the twelve PC's have sounded i n each case, the s e c t i o n i s over. Although"the four PC orderings are not t r a n s p o s i t i o n a l l y or i n v e r s i o n a l l y r e l a t e d , many i n t e r n a l PC p a i r s are r e t a i n e d (bracketed i n Example 37), as i s one p a r t i c u l a r IC ord e r i n g ("boxed" i n Example 37). Example 37. Piece No. 5, PC orde r i n g s , showing PC p a i r and IC ordering r e l a t i o n s h i p s . I (mm.l-8.8fp1 D E ^ C D ^ E F B B * II (mm.8-9.ff) E III (mm.9-12.sfp) C D B* B BE (mm.12-14,ff) The completion of the t h i r d PC ord e r i n g ( i . e . , the E ^ ) c o i n c i d e s with the f i r s t note of the f i n a l s e c t i o n (as defined by tempo and dynamics). The f i n a l s e c t i o n , t h e r e f o r e , contains t h i r t e e n notes: The E ^ from the end of the t h i r d ordering and the twelve notes of i t s own ord e r i n g , which a l s o ends on E K 75 The beginning of the s i x t h piece continues the o r g a n i z a t i o n a l concept of the twelve-note ordering but, u n l i k e i n the f i f t h p iece, o n l y one ordered u n f o l d i n g occurs, a f t e r which the PC's do not appear to be arranged i n s p e c i f i c p a t t e r n s . The i n i t i a l o rdering i s , however, of i n t e r e s t as i t r e t a i n s some of the PC p a i r s and the recu r r e n t IC ordering from the PC patterns used i n the previous piece. Example 38 r e v e a l s the PC p a i r r e l a t i o n s h i p s between the f i r s t o r d e r i n g of the s i x t h - p i e c e and the f i r s t and l a s t of the f i f t h piece (bracketed i n the example), as w e l l as the r e c u r r i n g IC o r d e r i n g (boxed i n the example). Example 38. Pieces 5 and 6, PC p a i r and IC ordering r e l a t i o n s h i p s . No. 5, I No. 6 No. 5, 3 E C Br*D E ^ | A * A » G G ^ E F O ^ C B ^ B A G ^ F E E ^ F i n a l l y , w i t h regard to ordered PC u n f o l d i n g , the n i n t h piece deserves mention. The whole piece c o n s i s t s of one, nine-note o r d e r i n g which un f o l d s c a n o n i c a l l y i n the p i c c o l o , oboe, and c l a r i n e t . Although the unison E^ i s repeated i n the opening, the remaining PC's of the ordering are a r t i c u l a t e d only once ( i . e . , once per instrument). • 76 ; An important a s p e c t of p r o g r e s s i v e ( i . e . , d i r e c t e d ) l i n e a r c o n n e c t i o n may be a s s o c i a t e d w i t h the o r d e r i n g s o f the t h r e e p i e c e s j u s t examined. Apart from c o n t r o l l i n g t h e i n t r o d u c t i o n of PC's, t h e a c t u a l p a t t e r n s of u n f o l d i n g r e v e a l l i n e a r and w e d g e - l i k e c o n t i n u i t i e s , t h e l a t t e r c o n s i s t i n g of s i m u l t a n e o u s l y a s c e n d i n g and d e s c e n d i n g l i n e a r i z a t i o n s . In Example 39 t h e o r d e r i n g s of t h e n i n t h , f i f t h , and s i x t h p i e c e s a r e n o t a t e d as PC's, r e g i s t r a l l y a r r a n g e d to i l l u s t r a t e t h e l i n e a r and/or wedge p a t t e r n s i n h e r e n t i n t h e i r o r d e r i n g s . The p a t t e r n i n t h e n i n t h p i e c e ( t o p s t a f f o f Example 39) i s , i n f a c t , t h e r e g i s t r a l c o n f i g u r a t i o n of t h e c a n o n i c theme, a p a r t from t h e C^ which a c t u a l l y sounds an o c t a v e h i g h e r ( a s i n d i c a t e d by t h e b l a c k n o t e i n p a r e n t h e s e s ) . The a s c e n d i n g f o u r t h E^6 to A ^ , the a s s e r t e d l i n e a r p r o g r e s s i o n i n t h e p i e c e , has added s i g n i f i c a n c e i n t h e l i g h t o f t h e l i n e a r d e t a i l s o f t h e f i n a l p i e c e — a c o n n e c t i v e f e a t u r e which w i l l be d e a l t w i t h i n Chapter IV. I n t h e c a s e of t h e f i r s t and t h i r d s e c t i o n s of p i e c e No. 5, t h e PC p a t t e r n s i n Example 39 a r e a l s o t h e r e g i s t r a l l y s p e c i f i c p i t c h e s of t h e p i e c e , a p a r t from t h o s e w i t h a b l a c k n o t e above o r below. (I n th e l a t t e r c a s e s , t h e b l a c k n o t e s a r e t h e a c t u a l sounding r e g i s t e r s o f t h e n o t e s . ) The p i t c h e s of t h e second and f o u r t h s e c t i o n s , however, a r e r e g i s t r a l l y d i s p e r s e d o v e r f o u r and o n e - h a l f o c t a v e s ; t h e l i n e a r p a t t e r n s i l l u s t r a t e d i n Example 39 a r e , t h e r e f o r e , more p r o b l e m a t i c as " s t e p w i s e " e v e n t s . Apart from r e v e a l i n g i n t e r n a l l i n e a r p a t t e r n s , t h e o r d e r i n g s of t h e f i f t h p i e c e e x h i b i t i n t e r r e l a t e d d i r e c t i v e t e n d e n c i e s . The w e d g e - l i k e " s p a t i a l " e x pansion of the opening s e c t i o n i s p r e p a r a t o r y f o r t h e e x t r e m e l y wide coverage of t h e r e g i s t r a l l y d i s p e r s e d second s e c t i o n , and i n t h i s sense tends t o " p o i n t " towards i t . The energy g e n e r a t e d i n the l a t t e r i s 77 Example 39. P i e c e s 9, 5, and 6, p a t t e r n s of PC u n f o l d i n g . 78 somewhat d i s s i p a t e d by t h e r e g i s t r a l l y compact l i n e a r i t y of t h e t h i r d s e c t i o n — a l i n e a r descent which a l s o t e n ds to r e c e d e towards a p o i n t of r e p o s e , a s s i s t e d by t h e d e c l i n e i n r h y t h m i c a c t i v i t y n o t e d e a r l i e r . The e x p l o s i v e f o u r t h s e c t i o n would appear t o i n t e r r u p t t h e l i n e a r d e s c e n t , which may be seen t o c o n t i n u e w i t h the f i n a l f o u r p i t c h e s of t h e p i e c e . The c o n d i t i o n most r e s p o n s i b l e f o r t h e s u g g e s t i o n of such a c o n t i n u a t i o n i s t h e PC and r e g i s t r a l e q u a l i t y of t h e f i n a l f o u r members o f the t h i r d and f o u r t h o r d e r i n g s . C o n c e r n i n g r e g i s t r a l e q u a l i t y , a d e t a i l a l l u d e d to e a r l i e r i s noteworthy. While the G^, F^, and o f t h e t h i r d o r d e r i n g o c c u r e a r l y i n t h e t h i r d s e c t i o n , t h e f i n a l o c c u r s an o c t a v e lower and as t h e f i r s t p i t c h o f t h e f i n a l s e c t i o n (as d e f i n e d by tempo and dynamics). T h i s may be i n d i c a t i v e of an a v e r t e d l i n e a r d e s c e n t , the i n t e n d e d c o n n e c t i o n coming at t h e end of t h e f o u r t h s e c t i o n where t h e r e g i s t e r o f t h e f i n a l E^ i s c o n s i s t e n t w i t h t h e p r e c e d i n g t h r e e p i t c h e s . D e s p i t e t h e c o n t i n u a t i o n of t h e l i n e a r i z a t i o n , as suggested above, the p i e c e would appear to c o n c l u d e i n an "open" f a s h i o n w i t h r e s p e c t to PC 39 u u n f o l d i n g . S e v e r a l c o n d i t i o n s r e i n f o r c e t h e n o t i o n t h a t D 4 would q u a l i f y as a f i n a l a r r i v a l p o i n t : f i r s t , t h e p i e c e opens w i t h an emphatic D^ ( r e i t e r a t e d i n u n i s o n ) ; second, t h e f o u r t h s e c t i o n b e g i n s on D5 and p r o g r e s s e s t h r o u g h a d e s c e n d i n g seventh; and t h i r d , t h e f i n a l f o u r p i t c h e s of t h e f o u r t h s e c t i o n p o i n t l i n e a r l y t o , but f a l l s h o r t o f , D4. T h i s a p p a r e n t l y " i n c o m p l e t e " c l o s e may, however, have f u n c t i o n a l s i g n i f i c a n c e . A l t h o u g h the u n f o l d i n g of p i t c h e s i n t h e o p e n i n g of t h e s i x t h p i e c e does not conform t o t h e r e g i s t r a l c o n f i g u r a t i o n o f t h e wedge 39 T h i s i s f u r t h e r r e i n f o r c e d by t h e n o t e i n t h e s c o r e : " s t o p as though t o r n o f f . " See L i g e t i , Ten Pieces, p. 19. p a t t e r n noted on the bottom s t a f f of Example 39, i t i s r e s p o n s i b l e , i n PC 40 terms, f o r an aspect of connection between the two pieces . For example, while the end of the f i f t h piece approaches D from above ( i . e . , G^, F, E, E&), the opening of the s i x t h piece approaches i t from below ( i . e . , A#, B, C, C#, the a c t u a l order being B, C#, C, A#). The D ( f i f t h PC of the ordering) i s the featured oboe's f i r s t note. The d i f f e r e n c e i n timbre as w e l l as a r t i c u l a t i o n (as s p e c i f i e d i n the scor e ) , render the long-awaited D more emphatic. The PC connection between the f i f t h and s i x t h pieces i s summarized i n Example 40. Example 40. PC connection between the f i f t h and s i x t h p i e c e s . registrally specific pitches No. 5 mm. 13 i t ch -classes No. 6 1 _ / o b o e \ Before l e a v i n g the concept of l i n e a r wedge-patterns, the opening twelve measures of the e i g h t h piece should be examined. Although twelve-note orderings are not i n operation here, the expansion and c o n t r a c t i o n of the "outer v o i c e s " c o n t r i b u t e to the d i r e c t i v e q u a l i t y which p o i n t s to the horn e n t r y i n bar 12. "Outer v o i c e s , " here, r e f e r to the highest and lowest p i t c h e s of the o v e r a l l r e g i s t r a l space created by the i n t e r a c t i o n of the 40 Other aspects c i t e d e a r l i e r i n c l u d e tempo, a r t i c u l a t i o n , instrumentation, and the attacca i n d i c a t i o n at the end of the f i f t h piece. 80 three instruments. Example 41 summarizes these p i t c h e x t r e m i t i e s and r e v e a l s the aforementioned wedge-like p a t t e r n of l i n e a r i z a t i o n . Example 41. P i e c e No. 8, measures 1-12, wedge-patterned l i n e a r i z a t i o n s . mm. 1 2 3 4 7 7 8 10 11 12 The horn entry i s marked by the c o n t r a c t i o n to the minor second, i n the accompanimental element. The i n t e r a c t i o n between p i t c h and rhythmic patterns i n these opening twelve measures i s noteworthy. In the s e c t i o n on rhythm, the horn entry was s a i d to be marked by the maximum i n composite rhythmic a c t i v i t y . During t h i s steady increase i n impulse-d e n s i t y , the p i t c h s t r u c t u r e has revealed a twofold wedge p a t t e r n . The i n t e r a c t i o n of both patterns ( i . e . , rhythm and p i t c h ) may be represented as i n Example 42. Example 42. Piece No. 8, measures 1-12, patterned p i t c h u n f o l d i n g as compared to rhythmic a c t i v i t y . pitch unfolding: rhythmic a c t i v i t y : (impulse-density) 81 A u n i q u e mode of l i n e a r c o n n e c t i o n may be d i s c e r n e d i n t h e opening e i g h t measures of t h e t h i r d p i e c e . A l t h o u g h a l l f i v e i n s t r u m e n t s c o n t r i b u t e to t h e p o l y p h o n i c t e x t u r a l element, o n l y t h r e e components a r e a c t u a l l y p r e s e n t i n t h e f i r s t f o u r measures. I n b a r s 5-7 t h e number of components i n c r e a s e s to f o u r and, f i n a l l y , f i v e . The c o n t i n u o u s l i n e a r components, as d i s t i n c t from t h e o f t e n fragmented i n s t r u m e n t a l p a r t s of t h e s c o r e , a r e i l l u s t r a t e d i n Example 43. The components i n d i c a t e d i n t h e example a r e c r e a t e d t h r o u g h t h e use of a d e v i c e I have termed " u n i s o n t r a n s f e r . " E s s e n t i a l l y i t r e f e r s t o t h e c o n n e c t i o n of two fragments of a s i n g l e l i n e a r component through an o v e r l a p p i n g u n i s o n i n t h e two i n s t r u m e n t s i n v o l v e d i n t h e t r a n s f e r . I n t h e second measure ( r e f e r to t h e s c o r e ) , f o r example, t h e a l t o f l u t e sounds a C# 5, c o n c u r r e n t w i t h the horn e n t r y , a l s o on C#5. Once the horn has assumed the p i t c h , t h e f l u t e drops out. The l i n e a r component has, h e r e , been t r a n s f e r r e d from t h e f l u t e to t h e horn v i a t h e u n i s o n o v e r l a p ( r e f e r t o Example 43). As i n t h e i n c i d e n t c i t e d above, i n s t r u m e n t s a r e most o f t e n s i l e n t i mmediately b e f o r e and a f t e r p r e s e n t i n g a p o r t i o n of a p a r t i c u l a r l i n e a r 41 component. On o c c a s i o n , however, b o t h i n s t r u m e n t s c o n t i n u e to sound a f t e r a t r a n s f e r has o c c u r r e d . T h i s i s t h e c a s e i n bar 5, f o r example, where t h e c l a r i n e t c o n t i n u e s to sound i t s E^ (and the r e s t of i t s component) a f t e r t h e l a t t e r has been assumed by t h e f l u t e . Here, the u n i s o n t r a n s f e r may be s a i d to have spawned a f o u r t h component, t h e r e b y a f f e c t i n g t h e t e x t u r a l -41 One p a r t i c u l a r d e p a r t u r e from t h i s s t a n d a r d p r o c e d u r e o c c u r s i n bar 5. The oboe d' amore c o n t i n u e s i t s a f t e r t h a t p i t c h i s assumed by the bassoon, and o n l y when i t r e a c h e s D^5, s e v e r a l b e a t s l a t e r , does i t r e s t , a f t e r t h e i S ) i n t u r n , p i c k e d up by t h e horn. T h i s e x c e p t i o n may be seen as an "extended" o v e r l a p . 82 Example 43. P i e c e No. 3, measures 1-8, l i n e a r components t h r o u g h u n i s o n t r a n s f e r and p i t c h i n t e r c h a n g e . 83 *These brackets indicate the span over which a particular instrument sounds; the dotted portion at the end of each indicates the point of "unison transfer" and the other instrument involved. 'These diagonal lines indicate instances of "pitch interchange. " 84 d e n s i t y . Unison t r a n s f e r i s a l s o r e s p o n s i b l e f o r t h i n n i n g the t e x t u r e . In bar 7, the horn 's G#4 i s assumed by the bassoon (already sounding a l i n e a r component), a f t e r which the horn drops out, thereby ending one component. An example of an incomplete unison t r a n s f e r accounts f o r the b r i e f fragment B 4-A 4 i n the f l u t e , measures 4-5. The i n i t i a l B i n the f l u t e does not come from an e x i s t i n g B i n another instrument, as i n the normal t r a n s f e r s . In t h i s respect the t r a n s f e r i s incomplete. The c l o s i n g A, however, i s assumed by the bassoon w i t h the c h a r a c t e r i s t i c unison overlap. " P i t c h interchange" i s a second v o i c e - l e a d i n g device employed i n t h i s p a r t i c u l a r s e c t i o n of the piece. While components u s u a l l y move independently of one another, the rhythmic d i v i s i o n s of two components engaged i n a p i t c h interchange are i d e n t i c a l . This p a r t i c u l a r device u s u a l l y i n v o l v e s the exchange of p i t c h e s between two d i s p a r a t e components (and not an exchange of the a c t u a l components themselves), and i s o c c a s i o n a l l y r e s p o n s i b l e f o r the generation and termin a t i o n of l i n e a r components (not u n l i k e unison t r a n s f e r ) , thereby a s s i s t i n g i n the c o n t r o l of t e x t u r a l - d e n s i t y . R e f e r r i n g again to Example 43, p i t c h interchange i s used i n measure 7 to spawn a new component. The F4 a n d $k Q f t ^ e bassoon are interchanged w i t h the A^ 4 and F 4 of the f l u t e . Just as the i n i t i a l three components of the piece were engaged i n p i t c h interchanges at t h e i r onset, so the technique i s employed here to introduce a f i f t h component. Occurring simultaneously to the emergence of the l i n e j u s t mentioned, i s the ter m i n a t i o n of an already e x i s t i n g one, ef f e c t e d through p i t c h interchange. In measure 7, the components i n the c l a r i n e t and oboe d' amore are inv o l v e d i n a p i t c h interchange a f t e r which the oboe continues but the c l a r i n e t drops out. While the techniques of unison t r a n s f e r and p i t c h interchange may be 85 important f a c t o r s i n l i n e a r p i t c h o r g a n i z a t i o n i n t h e components of t h e s e opening measures, t h e sense o f p r o g r e s s i o n towards bar 6 and t h e f e e l i n g of c l i m a x i n t h a t measure a r e l a r g e l y t h e r e s u l t o f t h e expanding r e g i s t r a l 42 b o u n d a r i e s d i c t a t e d by t h e l i n e a r components themse l v e s . The a s c e n d i n g and d e s c e n d i n g l i n e a r i z a t i o n s which o u t l i n e t h e p r o g r e s s i v e wedge-pattern a r e i n d i c a t e d on system (b) of Example 43. Summary S e v e r a l modes of l i n e a r p i t c h and PC c o n n e c t i o n have been found t o 43 o p e r a t e i n t h e p i e c e s of t h e q u i n t e t . I n the second and f o u r t h p i e c e s , f o r example, t h e f e a t u r e d i n s t r u m e n t s were n o t e d as c o n s i s t i n g of l i n e a r i z a t i o n s i n v o l v i n g t h e upper and lower p i t c h e s of s u c c e s s i v e a r p e g g i o s . I n t h e f i f t h , s i x t h , seventh, and n i n t h p i e c e s , s p e c i f i c o r d e r i n g s (most o f t e n t w e l v e - n o t e s u c c e s s i o n s ) were found t o c o n t r o l t h e i n t r o d u c t i o n o f PC c o n t e n t . Many of t h e o r d e r i n g s were shown t o c o n t a i n common PC p a i r s and one p a r t i c u l a r IC o r d e r i n g , a l t h o u g h t h e s u c c e s s i o n s a r e not t r a n s p o s i t i o n a l l y o r i n v e r s i o n a l l y r e l a t e d . Apart from t h e c o n t r o l o f PC c o n t e n t , t h e p a t t e r n s o f PC u n f o l d i n g were seen t o r e v e a l d i r e c t e d l i n e a r i z a t i o n s , some i n t h e form o f wedge-l i k e e x p a n s i o n s and c o n t r a c t i o n s . F i n a l l y , a wedge-pattern was a l s o found i n t h e t h i r d p i e c e ; i t was sugg e s t e d t h a t t h e components o f t h i s p a t t e r n r e s u l t from t h e t e c h n i q u e s of u n i s o n t r a n s f e r and p i t c h i n t e r c h a n g e . One a t t r i b u t e , common :to a l l of t h e l i n e a r e v e n t s n o t e d above, r e g a r d l e s s of v a r y i n g d e t a i l s o f s t r u c t u r e , i s t h e sense of d i r e c t e d a c t i v i t y and c o n t i n u i t y which t h e y e f f e c t . 42 r The c l i m a x i s formed by t h e h i g h e s t p i t c h i n t h e s e c t i o n , G-5, as w e l l as t h e w i d e s t r e g i s t r a l space which accompanies i t , F 4-G^. 43 Other s c e r t a i n l y e x i s t , s e v e r a l of which w i l l be e x e m p l i f i e d i n the next two c h a p t e r s . 86 Harmonic D e t a i l s Two c e n t r a l i s s u e s of harmonic o r g a n i z a t i o n i n t h e q u i n t e t a r e consonance and d i s s o n a n c e i n v e r t i c a l i t i e s , and f u n c t i o n a l r e l a t i o n s h i p s between s o n o r i t i e s . Such c h a r a c t e r i z a t i o n s and r e l a t i o n s h i p s , however, depend l a r g e l y on t h e t e x t u r a l environment i n which t h e y o c c u r . For example, a most p r e v a l e n t t e x t u r a l c o n d i t i o n was n o t e d e a r l i e r as t h e s i n g l e , p o l y p h o n i c element c o n s i s t i n g o f from t h r e e t o f i v e components. In t h i s p a r t i c u l a r s i t u a t i o n , t h e v e r t i c a l s o n o r i t i e s a r e s l o w l y , but c o n t i n u o u s l y , changing ( o f t e n one n o t e a t a t i m e ) , r e s u l t i n g i n a continuum of consonance-d i s s o n a n c e f l u c t u a t i o n . The opening seven measures of t h e t h i r d p i e c e , j u s t examined i n t h e l i g h t o f l i n e a r o r g a n i z a t i o n , e x e m p l i f y such harmonic f l u c t u a t i o n . System (a) of Example 44 c o n s i s t s of t h e l i n e a r components, as s t a t e d e a r l i e r , w h i l e system (b) i n d i c a t e s t h e harmonic changes, d e l i n e a t e d by t h e v e r t i c a l l i n e s t h r o u g h b o t h systems. V e r t i c a l i t i e s may be c l a s s i f i e d as consonant 44 o r d i s s o n a n t a c c o r d i n g t o t h e i r semitone and whole-tone co n t e n t as i n d i c a t e d on t h e l e f t o f Example 45 (see page 8 9 ) . These a r e then p l o t t e d on t h e graph (Example 45) r e v e a l i n g t h e f l u c t u a t i o n i n harmonic q u a l i t y . (The numbers from 1-25 on t h e graph c o r r e s p o n d to t h e complexes of Ex. 44.) " T h e c r i t e r i o n of semitone c o n t e n t i s a suggested " f i r s t s t e p " towards t h e c h a r a c t e r i z a t i o n o f consonance and d i s s o n a n c e i n v e r t i c a l i t i e s . In t h e a n a l y s i s of t h e f i r s t p i e c e (Chapter I I I ) t h i s i n i t i a l s t e p s e r v e s as a p o i n t o f d e p a r t u r e f o r a more d e t a i l e d s e t o f c r i t e r i a used t o d i f f e r e n t i a t e consonant and d i s s o n a n t s o n o r i t i e s i n t h e opening p o l y p h o n i c s e c t i o n . I t i s c l e a r , however, t h a t i n t h i s p a r t i c u l a r m u s i c a l language the r e f e r e n c e p o i n t s f o r v e r t i c a l consonance and d i s s o n a n c e a r e r a d i c a l l y d i f f e r e n t from t h o s e of t r i a d i c music. A whole-tone may t a k e on t h e r o l e o f a consonance i n r e l a t i o n t o semitone s t r u c t u r e s . Perhaps t h e most b l a t a n t example of t h i s comes at t h e end of t h e t h i r d p i e c e . The s i m u l t a n e o u s , but o u t - o f - p h a s e , o s c i l l a t i o n between A^ and B ^ r e s u l t s i n a r e i t e r a t e d minor second. The f i n a l major second, A^-B-^, sounds ex t r e m e l y c o n v i n c i n g as a p o i n t o f r e s o l u t i o n ; i t s s t a t u s as a consonance can h a r d l y be d i s p u t e d . 87 Example 44. P i e c e No. 3, measures 1-8, harmonic complexes. 88 Example 45. P i e c e No. 3, measures 1-8, consonance-dissonance c r i t e r i a and harmonic q u a l i t y f l u c t u a t i o n . i ; I diss. vertical complexes as to Example No. 44. 90 I t must be remembered, however, t h a t t h e s e v e r t i c a l complexes a r e e s s e n t i a l l y p o i n t s a l o n g a continuum and, w h i l e t h e i r i n d i v i d u a l consonance-d i s s o n a n c e q u a l i t i e s may be p e r c e i v e d i n i s o l a t i o n , i t i s , perhaps, t h e i r c o n t r i b u t i o n s t o t h e l a r g e - s c a l e p r o g r e s s i o n of harmonic q u a l i t y which i s more s i g n i f i c a n t h e r e . The h i g h e r - l e v e l p r o g r e s s i o n from consonance >• d i s s o n a n c e >• consonance, suggested by the c u r v e above the graph on Example 45, f o r i n s t a n c e , i s analogous i n dimension to t h e l e v e l of r h y t h m i c 45 and m e t r i c c h a r a c t e r i z a t i o n n o t e d e a r l i e r . The harmonic s t r u c t u r e of t h e f i f t h and n i n t h p i e c e s , l i k e t h a t of t h e t h i r d , r e v e a l c o n t i n u o u s l y changing v e r t i c a l i t i e s and, hence, f l u c t u a t i n g c o n sonance-dissonance q u a l i t y . Rather than s t a f f n o t a t i o n , t h e f i r s t s e c t i o n of t h e f i f t h p i e c e and measures 7-15 of t h e n i n t h a r e , here, r e p r e s e n t e d by l i n e - g r a p h s , g i v e n as Examples 46 and 47. The i n c r e a s e i n s p a t i a l d e n s i t y (see below) of the harmonic complexes ( r e p r e s e n t a t i v e o f c o n sonance-dissonance f l u c t u a t i o n ) i s e f f e c t i v e l y p o r t r a y e d t h r o u g h t h i s means. The e x p a n s i o n i n r e g i s t r a l space, which r e s u l t s from the p r e v i o u s l y e s t a b l i s h e d wedge-pattern o f p i t c h u n f o l d i n g , i s a p r i m a r y f a c t o r i n t h e 46 p e r c e i v e d d i s s o n a n c e of t h e s o n o r i t y . The c o n t i n u o u s l y expanding r e g i s t r a l b o u n d a r i e s i n t h e s e two p i e c e s r e p r e s e n t i n t h i s sense a g r a d u a l r e d u c t i o n i n p e r c e i v e d d i s s o n a n c e — a p a t t e r n which may, a g a i n , be c o n s i d e r e d t h e h i g h e s t , most g e n e r a l , s t r u c t u r a l l e v e l o f harmonic q u a l i t y f l u c t u a t i o n . 45 In t h e f o r e g o i n g s e c t i o n s o f t h i s c h a p t e r , t h e s e seven measures were c h a r a c t e r i z e d as one c o n t i n u o u s g e s t u r e w i t h r e s p e c t to r h y t h m i c i n t e n s i f i c a t i o n , m e t r i c s t r u c t u r e , and l i n e a r o r g a n i z a t i o n . The l a r g e - s c a l e p r o g r e s s i o n of harmonic q u a l i t y i s congruent w i t h t h e span of f u n c t i o n a l u n i t y suggested by t h e s e p a r a m e t r i c c h a r a c t e r i z a t i o n s . 46 For example, v e r t i c a l i t i e s may c o n s i s t of s e v e r a l o c c u r r e n c e s of IC 1, but i n compound forms ( e . g . , minor n i n t h , e t c . ) . I n t h e s e i n s t a n c e s , t h e p e r c e i v e d d i s s o n a n c e o f t h e IC 1 i s presumably somewhat reduced. 91 Example 46. P i e c e No. 5, measures 1-8, l i n e - g r a p h r e p r e s e n t a t i o n o f l i n e a r and harmonic expansion. 91 E -D -C -A « -G«-F*-E— D - • C -A « -G*-F* E -D -C -A* E -D -C -i r i r 1 T measure no. f lute / / * / clarinet horn * bassoon — 93 Example 47. P i e c e No. 9, measures 8-15, l i n e - g r a p h r e p r e s e n t a t i o n l i n e a r and harmonic ex p a n s i o n . 9+ a B A G F - | E H unison to this point) 1 1 h ' -f=i 1 _ J _ l 8 10 (unison t o e n d K ^ F L U T E O B O E C L A R I N E T 11 12 measure no. 13 14 15 16 I t was a s s e r t e d a t t h e b e g i n n i n g of t h i s s e c t i o n on harmonic d e t a i l s t h a t t e x t u r a l environment i n f l u e n c e s t h e approach to harmonic c l a s s i f i c a t i o n s 47 and f u n c t i o n a l r e l a t i o n s h i p s . In t h e second, f o u r t h , and t e n t h p i e c e s , a second t e x t u r a l s i t u a t i o n i s p r e v a l e n t — o n e i n which a p r i m a r y l i n e i n t e r a c t s w i t h secondary components, the l a t t e r o c c u r r i n g i n a fragmented c a p a c i t y a t t i m e s . R e v e a l i n g a s p e c t s of harmonic o r g a n i z a t i o n i n t h i s t e x t u r a l environment c e n t r e around r e l a t i o n s h i p s between the p r i m a r y and secondary components. In t h e t h r e e p i e c e s c i t e d , t h e tempo and r h y t h m i c a c t i v i t y r e n d e r t h e i n d i v i d u a l harmonic r e l a t i o n s h i p s too f l e e t i n g t o be o f s i g n i f i c a n c e , t h e l i n e a r i t y of t h e t e x t u r e , once a g a i n , b e i n g t h e f o c a l p o i n t . The harmonic q u a l i t y which i s p e r c e i v e d on a more g l o b a l l e v e l , however, i s the r e s u l t o f t h e d e t a i l e d r e l a t i o n s h i p s a l o n g t h e way. Example 48 c o n s i s t s of two e x c e r p t s , measures 12 and 13 of t h e second p i e c e , and measure 1 o f t h e f o u r t h , b o t h of which a r e n o t a t e d without stems and beams f o r ease o f r e a d i n g . The groups of p i t c h e s which sound t o g e t h e r 48 a r e boxed, numbered, and d e t a i l e d on t h e second system o f each e x c e r p t . As t h e d e t a i l s i n the example r e v e a l , a f f i l i a t i o n s between n o t e s of t h e p r i m a r y and secondary components u s u a l l y i n v o l v e s d i s s o n a n c e f o l l o w e d by r e l a t i v e consonance. Conc e r n i n g t h e a f o r e m e n t i o n e d a f f i l i a t i o n , a concept o f consonance-d i s s o n a n c e r e l a t i o n s may be p o s i t e d . In measure 13 of t h e second p i e c e , 47 The t e n t h p i e c e i s d e a l t w i t h i n Chapter IV. 48 The s c o r e s h o u l d be c o n s u l t e d f o r u n d e r s t a n d i n g of t h e r h y t h m i c c o n f i g u r a t i o n s of t h e v e r t i c a l i t i e s . O f t e n , f o r example, a s u b t l e r h y t h m i c v a r i a t i o n between components w i l l produce c o n s e c u t i v e v e r t i c a l i t i e s . In t h e r h y t h m i c c o n f i g u r a t i o n • — - J ^ f o r i n s t a n c e , two v e r t i c a l i t i e s n n sound, a l t h o u g h v e r y b r i e f l y . 96 Example 48. P i e c e No. 2, measures 12-13, and p i e c e No. 4, measure 1, harmonic i n t e r v a l f l u c t u a t i o n t h r o u g h v o i c e l e a d i n g . one textural element 3 ft < 0) 0) w </> (0 (0 ma ro I co Wr -I I co I "<g> 98 f o r example, a r e l a t i v i t y p r i n c i p l e a l l o w s t h a t t h e whole-tone i s c o n s i d e r e d as a consonance or a d i s s o n a n c e , depending on t h e i n t e r v a l which p r o c e e d s o r f o l l o w s i t , an i d e a a l r e a d y a l l u d e d to i n c o n n e c t i o n w i t h t h e end of t h e t h i r d p i e c e . T h i s concept i s a l s o r e l e v a n t to t h e ends of the two p h r a s e s which comprise t h e f o u r t h p i e c e . Here, t h e r h y t h m i c a c t i v i t y has r e l a x e d s u f f i c i e n t l y t o a l l o w p e r c e p t i o n o f t h e f l u c t u a t i n g harmonic q u a l i t y . The two i n s t a n c e s i n q u e s t i o n a r e shown i n Example 49. The u l t i m a t e a r r i v a l p o i n t on t h e whole-tone (from t h e " d i s s o n a n t " semitone) r e i n f o r c e s t h e concept of r e l a t i v i t y and a l s o r a i s e s t h e p o s s i b i l i t y o f t h i s p a r t i c u l a r r e l a t i o n s h i p b e i n g c o n s i d e r e d as a r e s o l u t i v e c a d e n t i a l d e v i c e . Example 49. P i e c e No. 4, measures 7-9 and 23-26, harmonic i n t e r v a l f l u c t u a t i o n t h r o u g h v o i c e l e a d i n g . mm. 7 8 finC) B S N . 1 - 2 - 1 - 2 - 2 - 1 - 2 1 - 2 mm. 2 3 2 4 2 5 26 F L C L (inC) 1 J JJ - 1 - 1 IvA J Ik [) ill J\ - 2 - 1 J _ e _ 1 .0 ^ »•*! 99 P a r t s of the second and seventh pieces fea t u r e v e r t i c a l i t i e s , the component parts of which are simultaneously a r t i c u l a t e d ( i . e . , they occur i n s t r i c t v e r t i c a l alignment). In t h i s t e x t u r a l environment the harmonic aspect i s primary, w i t h the p o s s i b i l i t y of derived l i n e a r r e l a t i o n s h i p s , rather than the other way around. In the second piece, the v e r t i c a l .•: s o n o r i t i e s comprise the secondary t e x t u r a l element i n the opening s e c t i o n , over which the c l a r i n e t i s f e a t u r e d . Five v e r t i c a l complexes are sounded i n t h i s p a r t i c u l a r s e c t i o n (measures 1-11), the f i r s t three c o n s i s t i n g e n t i r e l y of adjacent semitones. The l a s t two f e a t u r e semitone and whole-tone c o n t e n t — a s u b t l e , yet i m p l i c a t i v e departure from the opening s o n o r i t y . The f i v e - n o t e v e r t i c a l i t i e s appear l a t e r i n the piece (e.g., bars 15, 20, and 21) and serve to r e c a l l the opening s e c t i o n . In these three recurrences, the content i s e x a c t l y that of the t h i r d complex of the piece ( i . e . , consecutive semitones from to G//3—a t r a n s p o s i t i o n of the f i r s t complex i n the p i e c e ) . In t h i s sense they r e s o l v e the harmonic departure of the s o n o r i t i e s which end the opening s e c t i o n . F i n a l l y , i n bar 29, a v e r t i c a l i t y occurs which r e c a l l s PC's D#, E, and F from the opening s o n o r i t y (where they appear as the lowest three p i t c h e s ) , thereby p r o v i d i n g a degree of PC c l o s u r e . These harmonic complexes are i n d i c a t e d on the second s t a f f of Example 50 ( a l l the p i t c h e s w i t h i n each box sounding tog e t h e r ) . The outer i n t e r v a l of each s i m u l t a n e i t y ( v a r i e d through i n t e r n a l combinations of semitones and whole-tones) i s given on the t h i r d system. Three a d d i t i o n a l d e t a i l s i n Example 50 are worth n o t i n g . F i r s t , the three harmonies which conclude the piece e x h i b i t another instance of f u n c t i o n a l consonance-dissonance r e l a t i o n , as p o s i t e d i n connection w i t h 100 the t h i r d and f o u r t h pieces. The three s o n o r i t i e s i n question, along w i t h the IC's of the consonance >>• dissonance progressions are a l s o 49 included on the second s t a f f of Example 50. Second, a l i n e a r p a t t e r n may be imposed on the complexes i n d i c a t e d on the second s t a f f ( i . e . , the complexes which c h a r a c t e r i z e the 'a'-section and subsequent a l l u s i o n s to i t ) . The p a t t e r n i n v o l v e s the connection of PC's which represent p i t c h e x t r e m i t i e s of each complex, the upper ascending l i n e c o n t r i b u t i n g to the o v e r a l l PC progression, and the lower l i n e p r o v i d i n g a departure from, and r e t u r n t o , the PC representing the lowest p i t c h of the opening s o n o r i t y . These l i n e a r events are i n d i c a t e d on the top s t a f f of Example 5 0 . A n d f i n a l l y , the upper ascending l i n e a r connection j u s t mentioned i s , i n a sense, "summarized" by the s o n o r i t i e s which c l o s e the piece. This r e l a t i o n s h i p i s noted on the t h i r d s t a f f of the example. The i n t e r v a l make-up of the r e c u r r i n g v e r t i c a l i t i e s found at the beginning of the seventh piece i s the same as that of the opening s o n o r i t y of the second p i e c e . S p e c i f i c a l l y , they are comprised of f i v e adjacent semitones, f i r s t , from G^ to (measures 1-23), and then from D to F# ( r e g i s t r a l l y dispersed) i n bars 30 and 34. V a r i e t y i n the r e i t e r a t e d s o n o r i t i e s based on G^ i s provided by the va r i o u s instrumental v o i c i n g s i n which i t occurs. (Refer to Example 51.) While the r e i t e r a t e d harmonies remain based on G^, the sustained s o n o r i t i e s which grow out of them are v a r i e d and, i n themselves, e x h i b i t 49 Here i s another instance to r e i n f o r c e the n o t i o n of the semitone to whole-tone " r e s o l u t i o n " f u n c t i o n i n g as a c a d e n t i a l device. ~^As "stepwise" events these p a r t i c u l a r l i n e a r i z a t i o n s are admittedly more problematic (than previous examples) because of the . r e g i s t r a l d i s p e r s i o n of t h e i r members. Linear events i n v o l v i n g such octave-displaced "steps," however, may be viewed as an important aspect of l i n e a r o r g a n i z a t i o n i n t h i s musical language. Example 50. P i e c e No. 2, harmonic o r g a n i z a t i o n . n — 1 J „ 1 — J — — — i J * , 1 mm. 1,2 3 4 11 15,20,21 29 ^*±±-±— ufsh =—^=f=i 1 V \fy V 1 T-j ' (ic: 2 - 3 1 - 2 ) r r r r — n - H - r ^ — r * . , y^±J^%: ^ "*T> \ j * . xJ. l_!Li \t*—JL. —a j i l j » ic: 4 4 6 5 4 Example 51. P i e c e No. 7, measures 1-38, harmonic o r g a n i z a t i o n . sustained sonorities ^ * s mm. 1-12 12-15 15-19 23 30,34 102 a d i r e c t e d f l u c t u a t i o n . For i n s t a n c e , t h e f i r s t s u s t a i n e d element i s t h e B* 7 4 (measures 6 f f . ) , f o l l o w e d by t h e t r i c h o r d G 4-A 4-B' 7 4 ( b a r s 12 f f . ) , and f i n a l l y t h e f o u r - n o t e s o n o r i t y G// 4-A 4-A# 4-B 4 ( b a r s 15 f f . ) — t h e top f o u r p i t c h e s of t h e o r i g i n a l f i v e - n o t e complex. The t e x t u r a l t h i c k e n i n g of t h e s u s t a i n e d s o n o r i t i e s p r o v i d e s d i r e c t i o n towards t h e emphatic d i s p l a y of t h e f i v e - n o t e v e r t i c a l i t i e s i n bar 23."^ The change of s o n o r i t y to t h e f i v e - n o t e complex b u i l t on D i s a l s o marked by t h e r e g i s t r a l l y d i s p e r s e d s p a c i n g o f t h e ch o r d . Between t h e two v e r t i c a l i t i e s — o n e based on G, t h e o t h e r on D — a l l PC's from D to B a r e r e p r e s e n t e d . A l t h o u g h the harmonic a s p e c t s i n t h i s p a r t i c u l a r s e c t i o n a r e c o n s i d e r a b l y more s t r a i g h t f o r w a r d , compared to th o s e of the second p i e c e , i t i s i n t e r e s t i n g t h a t they b o t h use, as a "harmonic r e f e r e n c e , " a f i v e - n o t e v e r t i c a l i t y which c o n s i s t s of a d j a c e n t semitones. A l s o , b o t h e x h i b i t d e p a r t u r e s from, and r e v e r s i o n s t o , the a l l - s e m i t o n e complex. The f i n a l harmonic d e t a i l to be examined i n t h i s c h a p t e r c o n c e r n s the use of u n i s o n and o c t a v e d o u b l i n g . The widespread u se of h i g h l y -c h r o m a t i c s o n o r i t i e s and complex r h y t h m i c i n t e r a c t i o n s c r e a t e s an environment i n which t h e l e a s t expected m u s i c a l event i s a m o t i v e o r theme which i s doubled i n u n i s o n or o c t a v e s . The use of t h i s mode of d o u b l i n g i n t h e p i e c e s o f t h e q u i n t e t (and i t o c c u r s i n a l l but t h e f o u r t h ) thus has an ex t r e m e l y p o t e n t e f f e c t . W h i l e t h e f u n c t i o n and o c c u r r e n c e o f such d o u b l i n g i n t h e f i r s t and l a s t p i e c e s w i l l be d e a l t w i t h i n t h e next two c h a p t e r s , i n s t a n c e s i n o t h e r p i e c e s a r e noteworthy h e r e . Most of the mo t i v e s and themes i n v o l v i n g u n i s o n and/or o c t a v e s have, i n f a c t , been mentioned i n c o n n e c t i o n w i t h o t h e r a s p e c t s of the ^ N o t i c e i n t h e s u c c e s s i v e v e r t i c a l i t i e s o f bar 23 t h a t p i t c h c o n t e n t remains t h e same; o n l y the i n s t r u m e n t a l d i s t r i b u t i o n v a r i e s . 103 musical language. The three-note, octave-doubled motive i n the second piece (bar 23), f o r example, was introduced e a r l i e r as le a d i n g i n t o one of the few a u r a l l y perceived downbeats i n the piece. The octave-doubled theme i n the middle of the t h i r d piece (measures 10-12) was c h a r a c t e r i z e d as one of the two simultaneously sounding t e x t u r a l elements i n the p i e c e — the only occurrence of such a te x t u r e i n a p a r t i c u l a r ensemble piece. The f i f t h and n i n t h pieces open with a r e i t e r a t e d and sustained unison, r e s p e c t i v e l y , each f u n c t i o n i n g as a departure point f o r a wedge-patterned u n f o l d i n g of p i t c h content. The n i n t h piece a l s o concludes on a unison. In the s i x t h p i e c e , a b r i e f theme which opens i n unison and concludes i n octaves introduces the coda; see measures 11-14 i n t h i s regard. The unison treatment i n the seventh piece has a l s o been a l l u d e d to e a r l i e r . In the 'b'-section (bars 38 to the end) each l i n e a r component, upon e n t e r i n g , doubles an e x i s t i n g part at the unison, a f t e r which i t gains independence both l i n e a r l y and r h y t h m i c a l l y . F i n a l l y , i n the e i g h t h piece the sustained octave B^ (measures 23-26), the b r i e f octave motive (measure 29), and the unison motive .(measure 30) represent the d i s p a r a t e m u s i c a l ideas noted e a r l i e r as being i n d i c a t i v e of the s t y l e of Apparitions and Aventures. The intense unison motive i n bar 30 provides a dramatic i n t r o d u c t i o n to the sustained s o n o r i t i e s of the calm f i n a l s e c t i o n . Summary In the foregoing d i s c u s s i o n of harmonic d e t a i l s , consonance and dissonance i n v e r t i c a l i t i e s , and f u n c t i o n a l harmonic r e l a t i o n s h i p s were stated as being the two main i s s u e s . T e x t u r a l environment was asserted as i n f l u e n c i n g such c h a r a c t e r i z a t i o n s . Three tex t u r e s were examined: polyphony, pseudo-polyphony ( i n which one component i s primary), and homophony. Regarding the f i r s t of these, the t h i r d , f i f t h , and n i n t h 104 p i e c e s were seen t o c o n s i s t of a continuum o f f l u c t u a t i n g v e r t i c a l consonance and d i s s o n a n c e . S p e c i f i c a l l y , t h e s o n o r i t i e s were n o t e d as i n v o l v i n g s u b t l e changes i n semitone and whole-tone c o n t e n t . In c o n n e c t i o n w i t h the second t e x t u r e , t h e harmonic a f f i l i a t i o n s between p r i m a r y and secondary components were examined, and a concept o f conso n a n c e - d i s s o n a n c e r e l a t i o n s p o s i t e d . The second and f o u r t h p i e c e s were c i t e d i n t h i s r e g a r d . The homorhythmic v e r t i c a l i t i e s o f t h e t h i r d t e x t u r e , as found i n t h e second and s e v e n t h p i e c e s , a l s o r e v e a l e d a consonance-dissonance f l u c t u a t i o n i n v o l v i n g semitone and whole-tone c o n t e n t . F i n a l l y , t h e use of u n i s o n and o c t a v e d o u b l i n g was found t o be of dr a m a t i c import i n a l l but the f o u r t h p i e c e . Summary T h i s c h a p t e r aims t o e s t a b l i s h a b a s i s f o r u n d e r s t a n d i n g t h e m u s i c a l language o f L i g e t i ' s Ten Pieces for Wind Quintet v i a t h e d e f i n i t i o n and i l l u s t r a t i o n o f g e n e r a l and s p e c i f i c a s p e c t s of form, t e x t u r e , rhythm, meter, and l i n e a r and harmonic p i t c h o r g a n i z a t i o n . Concepts i n t r o d u c e d i n c o n n e c t i o n w i t h t h e examples s t u d i e d w i l l s e r v e as a b a s i s f o r d e t a i l e d a n a l y s e s of t h e f i r s t and l a s t p i e c e s o f t h e q u i n t e t , s u b j e c t s o f t h e next two c h a p t e r s . CHAPTER I I I ANALYSIS OF PIECE NO. 1 I n t r o d u c t i o n The f o l l o w i n g a n a l y s i s of p i e c e No. 1 resembles, i n format, t h e p r e v i o u s c h a p t e r on a s p e c t s of L i g e t i ' s m u s i c a l language. That i s , each parameter i s d e a l t w i t h s e p a r a t e l y w i t h i n t e r r e l a t i o n s h i p s n o t e d where a p p l i c a b l e . The main s e c t i o n s of t h i s c h a p t e r a r e as f o l l o w s : D e l i n e a t i n g F a c t o r s of Formal Segmentation A s p e c t s of T e x t u r a l S t r u c t u r e P r i n c i p l e s of Rhythmic and M e t r i c Design Modes of P i t c h O r g a n i z a t i o n L i n e a r D e t a i l s Harmonic D e t a i l s C o n n e c t i v e F a c t o r s Between the F i r s t and T h i r d P i e c e s and I n t e r r u p t i v e A s p e c t s of t h e Second Summary. Some c o n c e p t s i n t r o d u c e d i n Chapter I I w i l l be shown to have a p p l i c a t i o n i n t h e f i r s t p i e c e . O f t e n , however, d e t a i l s o f p a r a m e t r i c o r g a n i z a t i o n a r e s p e c i f i c to p i e c e No. 1; t h e s e w i l l a l s o r e c e i v e c l o s e a t t e n t i o n . D e l i n e a t i n g F a c t o r s of Formal Segmentation The f i r s t p i e c e e x h i b i t s a c l e a r l y d e f i n e d two-part f o r m a l s t r u c t u r e , measures 1-16 c o m p r i s i n g t h e ' a ' - s e c t i o n , and 16-22, t h e ' b ' - s e c t i o n . A b r i e f t r a n s i t i o n i n b a r s 15-16 b r i d g e s t h e two main d i v i s i o n s and an "echo" of the ' a ' - s e c t i o n (to be e x p l a i n e d l a t e r ) o c c u r s a t th e end of t h e p i e c e ( i . e . , measures 22-24). A b r i e f summary o f d e l i n e a t i n g f a c t o r s of f o r m a l 105 106 segmentation i s g i v e n below, a l l o f which a r e d e a l t w i t h i n g r e a t e r d e t a i l l a t e r i n the c h a p t e r . C o n c e r n i n g a s p e c t s o f t e x t u r e , t h e ' a ' - s e c t i o n f e a t u r e s complex polyphony o p e r a t i n g over t h e range >y • - , d y n a m i c a l l y from pianissimo 1 to mezzoforte. The l a t t e r p o r t i o n of t h e p i e c e ( i . e . , measures 16-22) c o n s i s t s of p a i r e d e n t r i e s a t fff, l e s s i n t e r a c t i o n between p a r t s , and a c o n t r a s t i n g r e g i s t e r and t e x t u r a l space, e.g., ) f • . A l e g a t o c h a r a c t e r and molto sostenuto e calmo, dolcissimo marking accompany t h e opening s e c t i o n , w h i l e a r e i t e r a t i v e q u a l i t y (marked tutta la forza) d i s t i n g u i s h e s t h e ' b ' - s e c t i o n . I n terms of rh y t h m i c d e f i n i t i o n , t h e a c t i v i t y l e v e l i n t h e ' a ' - s e c t i o n i s much h i g h e r t h a n t h a t df the 'b'-s e c t i o n , and i n s t r u m e n t s i n t h e former u t i l i z e t h e rh y t h m i c d i v i s i o n s 3 _ S 3 | | 1, I I I I, and | | | | |, w h i l e i n t h e l a t t e r , o n l y | | l a n d | | I 1 a r e found. With r e s p e c t t o tempo, t h e two s e c t i o n s a r e marked J = 40 and J = 48, r e s p e c t i v e l y . The f i n a l tempo change back t o J = 40 i n bar 22, a l o n g w i t h t h e quasi eco i n d i c a t i o n and r e t u r n to pianissimo axe f a c t o r s which suggest an a l l u s i o n to t h e ' a ' - s e c t i o n . ^ Summary The a f o r e m e n t i o n e d f a c t o r s of d e l i n e a t i o n c o n t r i b u t e t o a c l e a r l y d e f i n e d f o r m a l s t r u c t u r e i n the f i r s t p i e c e . Some d e t a i l s a r e s t r a i g h t -f o r w a r d , such as tempo and dynamics, w h i l e o t h e r s a r e more complex, e.g., l e v e l s of r h y t h m i c a c t i v i t y and t e x t u r a l c h a r a c t e r i s t i c s . A l l f a c t o r s , however, w i l l be d e a l t w i t h i n d e t a i l i n subsequent s e c t i o n s . The PC c o n t e n t o f t h e f i n a l dyad, C and D, i s a n o t h e r a s p e c t s u g g e s t i n g r e l a t i o n s h i p to t h e ' a ' - s e c t i o n ; t h i s , however, w i l l r e c e i v e c l o s e r a t t e n t i o n i n the s e c t i o n d e a l i n g w i t h l i n e a r d e t a i l s o f p i t c h o r g a n i z a t i o n . 107 A s p e c t s of T e x t u r a l S t r u c t u r e T e x t u r a l c h a r a c t e r i s t i c s of p i e c e No. 1 a r e g e n e r a l l y c o n s i s t e n t w i t h t h o s e d e f i n e d i n t h e p r e v i o u s c h a p t e r as s p e c i f i c t o ensemble p i e c e s . The f i r s t p i e c e , f o r example, f e a t u r e s o n l y one t e x t u r a l element at a time, and i s comprised o f e s s e n t i a l l y two c o n s e c u t i v e t e x t u r e s c o r r e s p o n d i n g t o t h e main f o r m a l s e c t i o n s . A l s o c o n s i s t e n t i s t h e t r a n s i t i o n which f e a t u r e s a r e d u c t i o n i n t e x t u r a l - d e n s i t y to t h r e e components ( y i e l d i n g one t e x t u r a l e l e m e n t ) . In a p p r o a c h i n g t h e t e x t u r a l s t r u c t u r e o f t h e p i e c e , two a s p e c t s w i l l be c o n s i d e r e d : t e x t u r a l q u a l i t y and t e x t u r a l space. T e x t u r a l Q u a l i t y T e x t u r e , as a d e l i n e a t o r o f form, must f i r s t be u n d e r s t o o d t o account f o r t h e ways i n which i n s t r u m e n t s i n t e r a c t i n music. S e c t i o n s of a g i v e n p i e c e may then be d i f f e r e n t i a t e d from each o t h e r by t h e i r s p e c i f i c 2 c h a r a c t e r i s t i c s of inst r u m e n t i n t e r a c t i o n . A fundamental a s p e c t of i n t e r a c t i o n c o n c e r n s t h e r h y t h m i c s t r u c t u r e o f t h e i n d i v i d u a l i n s t r u m e n t a l p a r t s . I n s t r u m e n t s (or components) moving i n s t r i c t v e r t i c a l a l i g n m e n t , f o r i n s t a n c e , may be c o n s i d e r e d i n t e r d e p e n d e n t , w h i l e t h o s e moving i n non-3 alignm e n t a r e independent. Such c l a s s i f i c a t i o n s a r e " q u a l i t a t i v e " ; we may t h e r e f o r e speak o f independence among components as one t e x t u r a l q u a l i t y and i n t e r d e p e n d e n c e among components as an o t h e r . Where subg r o u p i n g s of p a r t s o c c u r , v a r i o u s degrees of indepe n d e n c e / i n t e r d e p e n d e n c e may r e s u l t , depending on t h e t e x t u r a l q u a l i t y of each subgroup. In Example 52 a q u a l i t a t i v e a n a l y s i s i s a p p l i e d t o t h e t e x t u r a l 2 Instrument i n t e r a c t i o n i s t h e p r i m a r y f a c t o r i n t h e d e t e r m i n a t i o n of t e x t u r a l elements which i n t u r n d e f i n e o v e r a l l t e x t u r e . 3 The terms "independent" and " i n t e r d e p e n d e n t , " i n r e f e r e n c e t o t h e i n t e r a c t i o n o f components, a r e a s s o c i a t e d w i t h t h e work of W a l l a c e B e r r y . See h i s Structural Functions, Ch. 2. 108 Example 52. L i n e - r e p r e s e n t a t i o n o f t e x t u r a l components, showing t e x t u r a l q u a l i t y . TE = textural element ITC = interdependent component IDC = independent component 109 'a'-section transition 'b'-section a-sect. (echo) mm. 1 ( i i L 5 _ i _ J L 10 J l _ J I L 15 » j i ; i L 20 l J L 25 J i i F L — E H . — C L -HRN.— BSN.— I '•I I TEXTURAL QUALITY 5 IDC 1 T E 4 1 TE 1 T E 0 2ITC-»»2 IDC 0 1 TE ^ 2 ITC >3 IDC >2ITC V3ITC-»6IDC CI 2ITC OVERALL QUALITY V independent independent/interdependent . interdependent 110 components of the f i r s t p i ece. The 'a' - s e c t i o n and t r a n s i t i o n are c h a r a c t e r i z e d by a t e x t u r a l q u a l i t y of independence ( i . e . , polyphony), the t r a n s i t i o n a l s o f e a t u r i n g the d e n s i t y r e d u c t i o n noted e a r l i e r . The 'b'-section i s t e x t u r a l l y contrasted i n that i t i s comprised of subgroups, the components of which move independently at times, and interdependently at other times. The subgroups themselves ( s p e c i f i c a l l y at p o i n t s of interdependence of components) enter independently of one another. F i n a l l y , components of the c l o s i n g dyad enter interdependently. This p a r t i c u l a r instance of v e r t i c a l alignment i s prepared by the interdependence of components w i t h i n the previous subgroups. The s h i f t from t o t a l independence to interdependence i s noted i n Example 52 below the l i n e -r e p r e s e n t a t i o n of t e x t u r a l components. T e x t u r a l Space For the purposes of t h i s paper, t e x t u r a l space r e f e r s to the i n t e r -v a l l i c d i s t a n c e between outermost r e g i s t r a l l y s p e c i f i c p i t c h e s of a p a r t i c u l a r formal s e c t i o n or other s t r u c t u r a l segment. In comparing t e x t u r a l spaces of two se c t i o n s (be they consecutive or n o t ) , r e g i s t e r i s of secondary concern; a f t e r a l l , any p e r f e c t f i f t h i s l a r g e r than any major t h i r d , e t c . , r e g a r d l e s s of r e g i s t e r . The r e g i s t r a l placement of a se c t i o n ' s t e x t u r a l space i s , however, of s i g n i f i c a n c e on a more g l o b a l l e v e l , e.g., that of the whole piece. In the piece under d i s c u s s i o n , four t e x t u r a l spaces may be discerned, as i n d i c a t e d i n Example 53. Below the s p a t i a l r e p r e s e n t a t i o n s are i n t e r v a l l i c r e l a t i o n s h i p s r e v e a l i n g an o v e r a l l p a t t e r n of s p a t i a l expansion followed by c o n t r a c t i o n . For example, the expansion from the 'a' to 'b'-s e c t i o n £i.e., the minor seventh (D^-C^) to the octave (B^-B^)] i s r e i n f o r c e d by the more l o c a l expansion of the t r a n s i t i o n ' s minor t h i r d I l l Example 53. T e x t u r a l spaces of f o r m a l segments. mm. 1-14 15-16 17-21 2 2 - 2 4 (inv.) to t h e ' b 1 - s e c t i o n ' s major t h i r d ( h ere independent o f t h e o c t a v e d o u b l i n g , B^/B ) . S i m i l a r l y , t h e g e n e r a l c o n t r a c t i o n from t h e ' b ' - s e c t i o n ( w i t h or witho u t the o c t a v e B)j to t h e f i n a l dyad i s r e i n f o r c e d by t h e l a r g e - s c a l e c o n t r a c t i o n from t h e ' a ' - s e c t i o n ' s minor s e v e n t h . I n t h i s l a t t e r i n s t a n c e t h e two a r e i n v e r s i o n a l l y r e l a t e d ; e.g., t h e minor seve n t h D-^-C4, when i n v e r t e d , becomes t h e major second C-^ -D-* ( d i s p l a c e d by an o c t a v e ) . (The i m p l i c a t i o n s of t h i s a s s o c i a t i o n a r e e x t r e m e l y important and w i l l be e x p l a i n e d i n d e t a i l l a t e r i n t h e c h a p t e r . ) Regarding r e g i s t r a l placement of t h e s u c c e s s i v e s p a t i a l f i e l d s , t h e l a r g e - s c a l e p r o g r e s s i o n i s one o f a s c e n t , t h e s i g n i f i c a n c e o f which w i l l be e x p l a i n e d i n t h e f i n a l s e c t i o n o f t h i s c h a p t e r (on r e l a t i o n s h i p s between t h e f i r s t and t h i r d p i e c e s ) . 4 A more immediate e x p a n s i o n i s d i s c e r n i b l e w i t h i n t h e ' b ' - s e c t i o n i t s e l f , s p e c i f i c a l l y i n t h e p r o g r e s s i o n from t h e opening u n i s o n C//^  to B 4 and E^5. 112 Summary Two a s p e c t s of t e x t u r a l s t r u c t u r e have been d e a l t w i t h i n t h i s s e c t i o n : t e x t u r a l q u a l i t y and t e x t u r a l space. The former, d e f i n e d by independent and/or i n t e r d e p e n d e n t modes of i n t e r a c t i o n between t e x t u r a l components, was found t o f u n c t i o n as a f o r m a l d e l i n e a t o r i n a d d i t i o n t o i t s r o l e as a b a s i s f o r i t s own p a r t i c u l a r mode o f p r o g r e s s i o n . T e x t u r a l space was r e f e r r e d t o as t h e space d e f i n e d by p i t c h e x t r e m i t i e s i n v a r i o u s f o r m a l segments o f t h e p i e c e . T h i s a s p e c t of t e x t u r a l s t r u c t u r e was a l s o shown to p r o v i d e s m a l l and l a r g e - s c a l e p a t t e r n s r e s u l t i n g i n an a d d i t i o n a l mode o f d i r e c t i o n w i t h i n t h e p i e c e , s p e c i f i c a l l y , one o f s p a t i a l e x pansion f o l l o w e d by c o n t r a c t i o n . R e g i s t r a l l y , t h e f i r s t p i e c e r e v e a l s a l a r g e -s c a l e a s c e n t — a d e t a i l which w i l l g a i n s i g n i f i c a n c e l a t e r i n t h i s c h a p t e r . P r i n c i p l e s o f Rhythmic and M e t r i c D e s i g n The f i r s t p i e c e i s c o n s i s t e n t w i t h t h e o t h e r ensemble p i e c e s w i t h r e g a r d t o meter. That i s , t h e n o t a t e d 4 i s e s s e n t i a l l y u n d e f i n e d by p a t t e r n e d s t r o n g and weak b e a t s ; r a t h e r , i t i s s o l e l y a n o t a t i o n a l c o n v e n i e n c e . Meter was d e f i n e d e a r l i e r as one p a r t i c u l a r mode of r h y t h m i c g r o u p i n g - - s p e c i f i c a l l y , one which groups r h y t h m i c impulses a c c o r d i n g t o acc e n t and u n a c c e n t — a n d , w h i l e t h i s t y p e o f rh y t h m i c u n i t i s not o p e r a t i v e i n t h e f i r s t p i e c e , o t h e r element-rhythms c o n t r i b u t e s i g n i f i c a n t l y t o t h e p r o g r e s s i v e and r e c e s s i v e t e n d e n c i e s i n h e r e n t i n t h e music. To quote W a l l a c e B e r r y : A l l e l e m e n t - p r o c e s s e s a r e r h y t h m i c . I n an important sense, t h e s t u d y of rhythm i s t h e stu d y o f a l l m u s i c a l elements, t h e a c t i o n s , o f t h o s e elements p r o d u c i n g t h e e f f e c t s of pace, p a t t e r n , and g r o u p i n g which c o n s t i t u t e rhythm.-* ^ B e r r y , Structural Functions, p. 301. 113 For our purposes, an element-rhythm may be thought o f as a p a t t e r n of r e c u r r e n c e w i t h r e s p e c t to an event w i t h i n a p a r t i c u l a r element, or a p a t t e r n o f r e c u r r i n g changes w i t h i n a c e r t a i n element.^ In t h e p r e v i o u s c h a p t e r , f o r example, a p a r t i c u l a r element-rhythm was s a i d t o o p e r a t e i n t h e f i r s t s i x t e e n b a r s of t h e e i g h t h p i e c e . S p e c i f i c a l l y , t h e r e c u r r e n c e o f b r i e f l i n e a r p a t t e r n s i n t h e f l u t e , c l a r i n e t , and bassoon were s a i d t o r e s u l t i n t h r e e d i s p a r a t e rhythms. Any g i v e n p i e c e may be h e a r d to c o n s i s t o f many such element-rhythms i n t e r a c t i n g w i t h one another i n v a r y i n g degrees of c o m p l e x i t y . O c c a s i o n a l l y , s t r u c t u r a l s i g n i f i c a n c e may be a t t r i b u t e d to s p e c i f i c p o i n t s which a r e marked by t h e c o n c u r r e n c e of s e v e r a l d i f f e r e n t rhythms. The f o l l o w i n g e x a m i n a t i o n of th e f i r s t p i e c e w i l l expose r h y t h m i c u n i t s based on s i x d i f f e r e n t elements o r parameters: i m p u l s e - d e n s i t y , dynamics, t e x t u r a l - d e n s i t y , t e x t u r a l q u a l i t y , h a r m o n i c - d e n s i t y , and tempo. Element-Rhythms Rhythm o f i m p u l s e - d e n s i t y f l u c t u a t i o n I n t h e p r e v i o u s c h a p t e r , i m p u l s e - d e n s i t y was s a i d t o d e f i n e w i d e spread u n i t s of r h y t h m i c p r o g r e s s i o n and r e c e s s i o n d e l i n e a t e d by a " t u r n - a r o u n d p o i n t . " U n i t s of comparable d e s i g n and d i m e n s i o n a r e a l s o d i s c e r n i b l e i n t h e f i r s t p i e c e , as i n d i c a t e d above t h e graph on system (a) of Example 54 (see " l a r g e - s c a l e u n i t s " ) . These u n i t s ( p a r t i c u l a r l y t h e p r o g r e s s i v e one) may be seen to c o n s i s t of u n d e r l y i n g " s t e p p e d " i n c r e a s e s and d e c r e a s e s i n r h y t h m i c a c t i v i t y , each p l a t e a u b e i n g d e l i n e a t e d by a change i n magnitude i n t h e In t h e former, t h e r e c u r r i n g event i s th e same. For example, meter i s one s p e c i f i c e l e m e n t - r h y t h m — o n e which r e l i e s on r e c u r r i n g a c c e n t -d e l i n e a t e d p a t t e r n s . A p a t t e r n o f r e c u r r i n g change would be, f o r i n s t a n c e , a f l u c t u a t i o n i n i n s t r u m e n t a t i o n - d e n s i t y . The r e c u r r e n t event ( i . e . , a f l u c t u a t i o n ) i s d i f f e r e n t each time; sometimes i t i s an i n c r e a s e i n d e n s i t y , at o t h e r t i m e s i t i s a d e c r e a s e . In e i t h e r case, as w i l l be e x p l a i n e d , a rhythm r e l i e s on a r e c u r r e n c e o f some k i n d . 114 Example 54. Two l e v e l s of i m p u l s e - d e n s i t y f l u c t u a t i o n . us measure no. 116 p r o g r e s s i v e d i r e c t i o n and, a f t e r t h e t u r n - a r o u n d p o i n t , i n t h e r e c e s s i v e d i r e c t i o n £see system (b) o f Example 54^]. Such r e c u r r e n t changes may be p e r c e i v e d as e s t a b l i s h i n g a "rhythm" ( a c c o r d i n g t o t h e c r i t e r i a s t a t e d e a r l i e r ) , t h e i n d i v i d u a l p l a t e a u s r e p r e s e n t i n g s m a l l - s c a l e u n i t s o f imp u l s e -d e n s i t y f l u c t u a t i o n . T h i s p a r t i c u l a r element-rhythm, then, may be viewed as hav i n g two l e v e l s and two s t a n d a r d s of measurement, t h e l o w - l e v e l u n i t s marked by magnitude changes, and t h e h i g h e r - l e v e l u n i t s by t h e t u r n - a r o u n d p o i n t (or change i n d i r e c t i o n ) . Rhythm of d y n a m i c a l l y exposed p i t c h - p a i r groups In t h e f i r s t t w e l v e measures of p i e c e No. 1 each i n s t r u m e n t a l p a r t c o n s i s t s o f a s u c c e s s i o n o f l i n e a r p i t c h - p a i r s s e p a r a t e d by r e s t s . The i n i t i a l p i t c h of each p a i r b e g i n s a t pianissimo and g r a d u a l l y i n t e n s i f i e s d y n a m i c a l l y . A t o r j u s t b e f o r e a r t i c u l a t i o n o f t h e second p i t c h , t h e dynamic i n c r e a s e peaks a t mezzoforte, a t which p o i n t a diminuendo b e g i n s . T h i s p a t t e r n r e p e a t s i t s e l f w i t h each subsequent p i t c h - p a i r . A l t h o u g h t h e peaks of dynamic i n t e n s i f i c a t i o n and c o r r e s p o n d i n g p i t c h changes i n t h e f i v e i n s t r u m e n t s occur i n d e p e n d e n t l y of each o t h e r , t h e y n e v e r t h e l e s s do so i n r e l a t i v e l y c l o s e p r o x i m i t y . The r e s u l t i s a "group" o f d y n a m i c a l l y exposed p i t c h - p a i r s . The next o c c u r r e n c e o f mezzoforte p i t c h changes i n c l o s e p r o x i m i t y c o n s t i t u t e s a n o t h e r group, and so on. These r e c u r r i n g groups of d y n a m i c a l l y i n t e n s i f i e d p i t c h - p a i r s c r e a t e an o v e r a l l , slow p u l s a t i o n — a rhythm o f s o r t s . The f i r s t mezzoforte p i t c h change o f each group may be heard t o a r t i c u l a t e u n i t s of t h i s p a r t i c u l a r rhythm. Example 55 c o n s i s t s of a g r a p h i c r e p r e s e n t a t i o n o f t h e d y n a m i c a l l y exposed p i t c h - p a i r groups i n t h e f i r s t t w e l v e measures. The o u t e r systems of t h e graph i n d i c a t e groups of p i t c h - p a i r s o c c u r r i n g i n c l o s e p r o x i m i t y and, a t t h e same time, u n i t s of o v e r a l l dynamic f l u c t u a t i o n . Two systems 117 Example 55. U n i t s of d y n a m i c a l l y exposed p i t c h - p a i r groups. 118 119 have been employed because of the overlapping of groups; the graph i s to be read by a l t e r n a t i n g between the top and bottom systems. The diagonal arrows above and below the centre l i n e i n d i c a t e the dynamic increase towards the i n i t i a l mezzoforte p i t c h change of each group, the du r a t i o n of p i t c h changes at mezzoforte ( i . e . , the h o r i z o n t a l p o r t i o n ) , and the o v e r a l l diminuendo ( a f t e r the l a s t mezzoforte p i t c h change). The centre l i n e i t s e l f shows only the i n i t i a l mezzoforte point of each group. These p a r t i c u l a r j u n c t u r e s may be heard to d e l i n e a t e r e c u r r i n g u n i t s of dynamically exposed p i t c h - p a i r s — a second element-rhythm d i s c e r n i b l e i n the piece. I n c i d e n t a l l y , a progressive tendency i s revealed i n the dim i n i s h i n g lengths of dynamic u n i t s commencing i n bar 9—a tendency which complements the increase i n impulse-density noted e a r l i e r . ^ Rhythm of t e x t u r a l - d e n s i t y f l u c t u a t i o n While t e x t u r a l independence and interdependence, discussed e a r l i e r , are q u a l i t a t i v e f e a t u r e s , a mode of grouping i s defined by the aspect of t e x t u r a l - d e n s i t y f l u c t u a t i o n — a q u a n t i t a t i v e f e a t u r e . S p e c i f i c a l l y , abrupt changes i n d e n s i t y a r t i c u l a t e a p a r t i c u l a r rhythm, a l b e i t an i r r e g u l a r one. System (c) on Example 56 (p. 122)' c o n s i s t s of the l i n e -r e p r e s e n t a t i o n of t e x t u r a l components used i n Example 52. The rhythm of de n s i t y f l u c t u a t i o n i s i n d i c a t e d by the v e r t i c a l l i n e s marking changes i n the number of sounding components. Rhythm of t e x t u r a l q u a l i t y f l u c t u a t i o n The concept of t e x t u r a l q u a l i t y was discussed i n the previous s e c t i o n . As a p a r t i c u l a r mode of rhythmic grouping, however, o v e r a l l ^Because each mezzoforte marks a p i t c h change, the c l o s e p r o x i m i t y of the i n d i v i d u a l dynamic peaks represents a rhythmic i n t e n s i f i c a t i o n r e f l e c t e d on the impulse-density graph. 120 q u a l i t a t i v e changes f u n c t i o n as r e c u r r i n g events which d e l i n e a t e s p e c i f i c u n i t s . These u n i t s are i n d i c a t e d on system (d) of Example 56. Rhythm of harmonic-density f l u c t u a t i o n In the 'a'-section and t r a n s i t i o n , harmonic-density ( i . e . , the number of v e r t i c a l p i t c h e s sounding) i s e s s e n t i a l l y t i e d to t e x t u r a l -g d e n s i t y ; the number of sounding components equals the number of p i t c h e s . The 'b'-section i s i n t e r e s t i n g i n that the t e x t u r a l and harmonic d e n s i t i e s do not correspond. Despite a five-component t e x t u r e , the harmonic-density begins w i t h a unison C#-* and g r a d u a l l y expands to a te t r a c h o r d by measure 21. Each new p i t c h entry marks a growth i n harmonic-density { w i t h i n the s t a t i c t e x t u r a l - d e n s i t y ) , thereby generating i t s own mode of rhythmic grouping. (The i n t e r a c t i o n of these two d e n s i t i e s i s i l l u s t r a t e d g r a p h i c a l l y i n Example 56, to be introduced s h o r t l y . ) Rhythm of tempo change Tempo change i s another event which recurs i n the piece and, as noted e a r l i e r , tends to c o i n c i d e w i t h changes i n the formal s t r u c t u r e . I t nevertheless a r t i c u l a t e s a widespread rhythmic p a t t e r n , to be revealed i n c onjunction w i t h those already d e f i n e d . I n t e r a c t i o n of element-rhythms Example 56 i s a r e p r e s e n t a t i o n of the s i x element-rhythms defined above. In the case of impulse-density, only the l a r g e - s c a l e p r o g r e s s i v e and r e c e s s i v e u n i t s are noted and are i n d i c a t e d here as s t r a i g h t l i n e s g Two v e r t i c a l i t i e s i n measure 12 represent b r i e f departures from t h i s norm. In these i n s t a n c e s , to be d i s c l o s e d i n a l a t e r s e c t i o n , the f i v e instruments sound a four-note s o n o r i t y . 121 Example 56. I n t e r a c t i o n o f s i x element-rhythms. 122 mm.1 (a) rhythm of impulse-density fluctuation (b) rhythm of dynamically exposed pitch-pair groups FL. (c) rhythm of E.H. textural-density CL-fluctuation HRN. BSN. (d) rhythm of textural quality fluctuation (e) rhythm of ^ 4-harmonic-density g 3-fluctuation "2 2-o I-(f) rhythm of tempo change formal segmentation mm. y-4o mf mf mf mf mf mf ~f 1 I I. I \ mf mf mf independent "a'-section 10 , independent/interdependent , interdependent . — — > H + J.-48 4 -J . 4 0 . transition. - 4 -15 *b'-section —f— 2 0 'a*- echo — r -25 123 o m i t t i n g t h e d e t a i l e d f l u c t u a t i o n s and l o w e r - l e v e l u n i t s i n c l u d e d i n 9 Example 54. The rhythm o f d y n a m i c a l l y exposed p i t c h - p a i r groups i s a l s o s i m p l i f i e d here as o n l y t h e i n i t i a l mezzoforte p i t c h change o f each group i s i n d i c a t e d ( t h e s e b e i n g t h e u n i t d e l i n e a t o r s t a k e n from t h e c e n t r e l i n e o f Example 55). Two p o i n t s of s i g n i f i c a n t c o n c u r r e n c e among element-rhythms a r e i n measures 16 and 22. These j u n c t u r e s , of c o u r s e , mark the main f o r m a l s e c t i o n s . Of l e s s e r f o r m a l import i s t h e t r a n s i t i o n (measures 15-16), a l s o marked by c o i n c i d e n c e of rhythms: t h e rhythms of t e x t u r a l and harmonic d e n s i t i e s . Summary I t was found t h a t t h e f i r s t p i e c e i s c o n s i s t e n t w i t h t h e o t h e r ensemble p i e c e s i n t h e q u i n t e t w i t h r e g a r d to m e t r i c s t r u c t u r e ; s p e c i f i -c a l l y , t h e n o t a t e d 4 does not s i g n i f y m e t r i c g r o u p i n g s as such, but i s , r a t h e r , a n o t a t i o n a l c o n v e n i e n c e . The concept of element-rhythms ( o t h e r than m e t e r ) , however, was found to be o f g r e a t s i g n i f i c a n c e i n t h e p a c i n g , p r o g r e s s i o n , r e c e s s i o n , and f o r m a l d e l i n e a t i o n o f t h e p i e c e . The rhythms examined i n v o l v e t h e parameters (elements) o f i m p u l s e - d e n s i t y , dynamics, t e x t u r a l - d e n s i t y , t e x t u r a l q u a l i t y , h a r m o n i c - d e n s i t y , and tempo. S u b s t a n t i a l c o n c u r r e n c e among t h e s e was noted a t s t r u c t u r a l p o i n t s i n t h e p i e c e , namely, t h e b e g i n n i n g s of f o r m a l s e c t i o n s . The t r a n s i t i o n , a f o r m a l segment o f l e s s e r importance, was a l s o n o t e d as b e i n g d e f i n e d by t h e 9 T h i s i s m e r e l y f o r c l a r i t y ; as w i l l be shown, s i g n i f i c a n t i n t e r a c t i o n o c c u r s o n l y a t t h e t u r n - a r o u n d p o i n t , a d e q u a t e l y r e p r e s e n t e d by t h i s l e s s - d e t a i l e d v e r s i o n . 124 s i multaneous r e d u c t i o n i n t e x t u r a l and harmonic d e n s i t i e s . 10 The r h y t h m i c s t r u c t u r e of p i e c e No. 1, d e s p i t e a l a c k of m e t r i c d e f i n i t i o n , i s one of c o n s i d e r a b l e c o m p l e x i t y , as m a n i f e s t i n t h e i n t e r a c t i o n o f element-rhythms e x e m p l i f i e d above. Modes of P i t c h O r g a n i z a t i o n L i n e a r D e t a i l s As i n the examples c i t e d i n t h e p r e v i o u s c h a p t e r , t h e l i n e a r d e t a i l s o f p i t c h o r g a n i z a t i o n i n t h e f i r s t p i e c e i n v o l v e s t e p w i s e p a t t e r n s of p i t c h and/or PC c o n n e c t i o n s . Three s p e c i f i c modes of l i n e a r c o n n e c t i o n w i l l be examined. The f i r s t i n v o l v e s o u t e r - v o i c e p r o l o n g a t i o n i n t h e ' a ' - s e c t i o n , as w e l l as the PC c o n n e c t i o n t o , and two-voice s t r u c t u r e o f , t h e ' b ' - s e c t i o n . The second mode c o n s i d e r s l i n e a r p r o g r e s s i o n s which, t h r o u g h l a t e r a l v o i c e c r o s s i n g , c o n n e c t p i t c h e x t r e m i t i e s i n t h e ' a ' - s e c t i o n ( t h e l a t t e r b e i n g the p i t c h e s p r o l o n g e d i n the o u t e r v o i c e s r e f e r r e d to abov e ) . L i n e a r i z a t i o n s comprised of d y n a m i c a l l y a c c e n t e d p i t c h - p a i r s d e f i n e the t h i r d mode of l i n e a r c o n n e c t i o n . O u t e r - v o i c e p r o l o n g a t i o n The (five-component) t e x t u r e of the ' a ' - s e c t i o n ' s f i r s t t w e l v e b a r s y i e l d s a continuum o f changing f i v e - n o t e v e r t i c a l s o n o r i t i e s spanning a (above t h e top s t a f f ) i n t h e f i r s t t welve measures marks a new harmonic complex. The p i t c h e s a r e o r g a n i z e d such t h a t the h i g h e s t p i t c h o f each v e r t i c a l i t y ( r e g a r d l e s s of i n s t r u m e n t a t i o n ) appears on t h e top s t a f f , t h e second h i g h e s t on t h e second s t a f f , e t c . The " h i g h e s t " p i t c h e s a r e ^ A l o n g w i t h t h e r e d u c t i o n i n t e x t u r a l and harmonic d e n s i t i e s i n the t r a n s i t i o n i s a d e c r e a s e i n t e x t u r a l space ( e . g . , from a minor s e v e n t h to a minor t h i r d ) and dynamics (to a c o n s t a n t pianissimo l e v e l ) . On system (a) of Example 57 each v e r t i c a l stem 125 Example 57. O u t e r - v o i c e p r o l o n g a t i o n i n measures 1-16. e.p. = embellishing pattern l.n. = lower neighbour u.n. = upper neighbour m.m.u.n. = major-minor upper neighbour m.m.l.n. = major-minor lower neighbour i.m.m.u.n. = incomplete major-minor upper neighbour ant. = anticipation 126 mf mf oo in a> a E CO X LU • C O TJ 0) D C +-> c o o i.m.mxi.n 127 considered l i n e a r l y to form a " v o i c e " as d i s t i n c t from the a c t u a l instrumental p a r t s . The same holds true f o r the second highest p i t c h e s , and so on. The f i v e " v o i c e s , " then, are the r e s u l t of constant p i t c h and frequent p o s i t i o n changes w i t h i n successive v e r t i c a l complexes. Each instrumental part moves from one v o i c e to another depending on the p o s i t i o n of i t s p i t c h i n the v e r t i c a l i t y . P i t c h e s of a given instrumental part are connected by h o r i z o n t a l and diagonal l i n e s and arrows, r e v e a l i n g the motion across v o i c e s as described above. For example, i f a l i n e connects two pi t c h e s on the same s t a f f , i t means they are sounded by the same instrument and the second p i t c h r e t a i n s i t s v o i c e p o s i t i o n i n the v e r t i c a l complex. A r e s t separates the two p i t c h e s i f the l i n e i s notated w i t h a p a r a l l e l s l a s h , e.g., " /• a — . Where a diagonal l i n e connects two, l i k e p i t c h e s on separate staves, i t s v o i c e p o s i t i o n has changed (but not i t s instrumentation) as a r e s u l t of a p i t c h change elsewhere i n the v e r t i c a l i t y . F i n a l l y , where a diagonal arrow connects two d i f f e r e n t p i t c h e s on separate staves, i t i n d i c a t e s a p i t c h and p o s i t i o n change ( w i t h i n the same instrument), again, separated by a r e s t i f the arrow has a p a r a l l e l s l a s h through i t , e.g., 2 Our focus on the outer v o i c e s i n p a r t i c u l a r as one mode of l i n e a r connection i s f o r three r e a s o n s . ^ F i r s t , they are c h a r a c t e r i s t i c a l l y the most r e a d i l y perceived. Second, they r e v e a l prolongations o f D3 and C 4 (the p i t c h e x t r e m i t i e s ) and, hence, c o n t r i b u t e to the d e l i n e a t i o n of form. And t h i r d , the PC's C and D have f u n c t i o n a l import i n the l a r g e - s c a l e l i n e a r s t r u c t u r e of the piece. Concerning the second c o n d i t i o n , r e f e r to ^Measures 13-16 as represented on system (a) of Example 57 w i l l be d e a l t w i t h l a t e r . 128 system (b) of Example 57, where a l l p i t c h e s i n t h e o u t e r v o i c e s a r e i n d i c a t e d . The e x t r e m i t i e s , and C^, a r e n o t a t e d as open n o t e s which a r e stemmed, beamed, and s l u r r e d t o g e t h e r . Neighbour n o t e s to t h e s e p i t c h e s a r e a l s o stemmed but a r e i n d i c a t e d by b l a c k n o t e s . E m b e l l i s h i n g 12 p a t t e r n s , a l s o n o t a t e d as b l a c k n o t e s , a r e stemmed to t h e s l u r which of a "major" and "minor" second a r e n o t a t e d t h u s : n f P f V *—r-1 J , and l a b e l l e d MMUN or MMLN (major-minor upper n e i g h b o u r or major-minor lower n e i g h b o u r ) . Once t h e and e x t r e m i t i e s a r e r e a c h e d i n b a r s 5 and 7, r e s p e c t i v e l y , t h e y a r e p r o l o n g e d i n a s t r a i g h t f o r w a r d manner as i n d i c a t e d on system ( b ) . One p a r t i c u l a r d e t a i l i s noteworthy however. I t concerns t h e d i f f e r e n t i a t i o n between " p r i m a r y " and " s e c o n d a r y " i n s t a n c e s of t h e p i t c h e x t r e m i t i e s . N o t i c e , f o r example, t h a t o c c u r r e n c e s of i n b a r s 7, 9, 11, and 13 a r e a d j a c e n t to t h o s e of t h e lower e x t r e m i t y , D3, w h i l e i n b a r s 5, 8, 11 ( f i r s t b e a t ) , and 13 t h e y a r e w i t h o u t such c o n c u r r e n c e . G i v e n the f u n c t i o n o f and C^ as t h e outermost p i t c h e s and, hence, form d e l i n e a t o r s of t h e ' a ' - s e c t i o n , r e i t e r a t e d i n s t a n c e s o f a d j a c e n t e x t r e m i t i e s would seem to be of " p r i m a r y " importance, w i t h t h e i n t e r v e n i n g o c c u r r e n c e s of C^, " s e c o n d a r y . " System (c) r e p r e s e n t s t h i s mode of d i s t i n c t i o n by i n c l u d i n g o n l y a d j a c e n t , c o r r o b o r a t i n g ( i . e . , p rimary) i n s t a n c e s of and C^ (as open n o t e s ) . The i n i t i a l C^, n o t a t e d b l a c k n o t e , may be heard as an a n t i c i p a t i o n o f t h e f i r s t p r i m a r y a p p e a r i n g i n measure 7. The i n i t i a l " i n c o m p l e t e " major-minor upper as a 12 An e m b e l l i s h i n g p a t t e r n , i n t h i s c o n t e x t , r e f e r s t o s t e p w i s e motion (beyond a major second) away from, and back t o , a p a r t i c u l a r s t r u c t u r a l n o t e . I t may a l s o c o n s i s t o f a l e a p away from t h e main n o t e and s t e p w i s e motion back, o r v i c e v e r s a . • 129 n e i g h b o u r (IMMUN) approach t o D3 i s a l s o i n d i c a t e d i n b l a c k n o t e s on system ( c ) . On system (a) of Example 57, t h e end o f t h e ' a ' - s e c t i o n (measures 13-15), and t r a n s i t i o n (measures 15-16), a r e n o t a t e d d i f f e r e n t l y from t h e p r e c e d i n g b a r s i n t h a t t h e i n s t r u m e n t a l p a r t s of t h e s c o r e a r e g i v e n . Rhythmic i n t e n s i f i c a t i o n , here, r e n d e r s i n d i v i d u a l v e r t i c a l i t i e s d i f f i c u l t t o i s o l a t e ; r a t h e r , t h e l i n e a r c o n t i n u i t y of each i n s t r u m e n t a l p a r t i s more apparent as a f o c u s of a t t e n t i o n . The i n t e r a c t i o n o f t h e i n s t r u m e n t s , n e v e r t h e l e s s , c a r r i e s t h e p r e v i o u s l y e s t a b l i s h e d o u t e r - v o i c e p r o l o n g a t i o n s by c l o s e r e i t e r a t i o n o f and C 4 , and l i n e a r embellishment not u n l i k e t h a t of measures 1-12. On system ( a ) , p i t c h e s w i t h b r a c k e t s above ( e . g . , measures 13-14) c o n t r i b u t e to t h e u p p e r - v o i c e p r o l o n g a t i o n , w h i l e t h o s e w i t h b r a c k e t s below e f f e c t t h e l o w e r - v o i c e maintenance, both o f which a r e i n d i c a t e d on system (b) and t h e h i g h e r - l e v e l system ( c ) . I n c i d e n t a l l y , the l i n e a r i z a t i o n from C 4 to F^ on system (b) (bar 14) s u g g e s t s t h a t , d u r i n g t h e s e t r a n s i t i o n a l measures, the u n d e r l y i n g upper v o i c e p r o l o n g s •5 o 13 F J (the lower r e m a i n i n g on D J) as an i n t e r i m b a s i s . T h i s l o w e r - l e v e l d e t a i l , however, i s not i n c l u d e d on system ( c ) ; D3 and C 4 remain the p r i m a r y r e g i s t r a l r e f e r e n c e p o i n t s f o r t h e ' a ' - s e c t i o n . I n Example 58, system (a) c o n s i s t s of t h e ' b ' - s e c t i o n (measures 16-22) i n s c o r e form. Systems (b) and (c) b e g i n w i t h i d e n t i c a l summaries o f system (c) from Example 57 ( i . e . , measures 1-16), but o f f e r two d i f f e r e n t i n t e r p r e t a t i o n s f o r t h e s t r u c t u r e o f t h e ' b ' - s e c t i o n and i t s r e l a t i o n s h i p to t h e p r e v i o u s l y p r o l o n g e d and C 4. The f i r s t v iews the 13 T h i s i s t h e r e d u c t i o n i n t e x t u r a l space n o t e d e a r l i e r . 130 p r o l o n g e d as a " p i t c h - c l a s s (PC) n e i g h b o u r , " f u n c t i o n i n g w i t h C# 5 o f bar 16 as an i n c o m p l e t e major-minor lower n e i g h b o u r to t h e f i n a l D^, t h e E^ -> o f bar 21 b e i n g i t s i n c o m p l e t e upper n e i g h b o u r . of t h e ' a ' - s e c t i o n i s then viewed c o n v e r s e l y as a PC n e i g h b o u r w i t h C//5 as ah i n c o m p l e t e major-minor upper n e i g h b o u r to t h e f i n a l C^, t h e B^ of bar 20 b e i n g i t s i n c o m p l e t e lower n e i g h b o u r . In t h e second i n t e r p r e t a t i o n {system (c)] , C^ i s c o n s i d e r e d a "PC r e p r e s e n t a t i v e " of t h e f i n a l C^, w i t h 0 f bar 16 and B^ of bar 20 f u n c t i o n i n g , r e s p e c t i v e l y , as complete upper and lower n e i g h b o u r s . D-^  from t h e ' a ' - s e c t i o n i s t r e a t e d here as a PC r e p r e s e n t a t i v e of t h e f i n a l D 5, w i t h C# 5 (bar 16) and E* 7 5 (bar 21) f u n c t i o n i n g , r e s p e c t i v e l y , as complete lower and upper n e i g h b o u r s . In s h o r t , t h e f i r s t i n t e r p r e t a t i o n i n v o l v e s two, s i m u l t a n e o u s i n c o m p l e t e major-minor n e i g h b o u r s , C/C# to D and D/D^ t o C, w h i l e t h e second r e c o g n i z e s two l a r g e - s c a l e PC p r o l o n g a t i o n s , one of C ( i n v o l v i n g C^ and C^), and one of D ( i n v o l v i n g and D^). The end r e s u l t o f e i t h e r  i n t e r p r e t a t i o n i s t h e i n v e r s i o n and r e g i s t e r s h i f t o f t h e p r o l o n g e d p i t c h  e x t r e m i t i e s of t h e ' a ' - s e c t i o n . ^ System (d) of Example 58 summarizes t h i s r e l a t i o n s h i p — o n e which, a l o n g w i t h t h e r e t u r n to t h e o r i g i n a l tempo and dynamics, and quasi eco i n d i c a t i o n i n t h e s c o r e , s t r e n g t h e n s t h e a l l u s i o n t o t h e ' a ' - s e c t i o n suggested e a r l i e r . 14 " P i t c h - c l a s s (PC) n e i g h b o u r " r e f e r s t o r e g i s t r a l l y n o n - s p e c i f i c n e i g h b o u r n o t e s . ^ T h e PC's C and D, i n f a c t , f i g u r e v e r y p r o m i n e n t l y i n t h e a u d i t o r y e x p e r i e n c e as a r e s u l t of t h e a f o r e m e n t i o n e d o u t e r - v o i c e p r o l o n g a t i o n and l i n e a r d i r e c t e d n e s s to measure 22. 131 Example 58. L i n e a r s t r u c t u r e of t h e ' b ' - s e c t i o n and i t s r e l a t i o n s h i p to t h e ' a ' - s e c t i o n . 132. . / ^ (E.H.) (CL.) 9 Iti— — * i I I " • 4 J. _ _i (HRN.) ^ l l l |T |> V l i * — (BSN.) 4 ZZZZZZZZZZZZZZZZZZZZZl m m . 2 7 7-14 15-16 16 17 2 0 20 2| 22-24 i.l.n. (b) (O 133 L i n e a r p r o g r e s s i o n s i n v o l v i n g l a t e r a l v o i c e c r o s s i n g As noted i n Chapter I I , t h e most p e r c e i v a b l e l i n e a r c o n n e c t i o n s i n t h i s i d i o m a r e t h o s e i n v o l v i n g movement by semitones .arid whole-tones. In measures 1-12 each i n s t r u m e n t a r t i c u l a t e s two p i t c h e s between r e s t s and, a l t h o u g h i n t h e f i r s t n i n e o f t h e s e measures movement between r e s t s i s by s t e p , movement a c r o s s r e s t s i s o f t e n by l e a p . I n o r d e r to d i s c e r n more extended l i n e a r c o n n e c t i o n s , s t e p w i s e movement a c r o s s t h e f i v e - v o i c e s t r u c t u r e must be c o n s i d e r e d ( i . e . , l a t e r a l v o i c e c r o s s i n g ) . Two c l a s s i f i c a t i o n s of l i n e a r e v e n t s i n v o l v i n g l a t e r a l v o i c e c r o s s i n g w i l l be d e f i n e d f o r t h e purposes o f t h i s paper: p r i n c i p a l and s u b o r d i n a t e . The former i s c h a r a c t e r i z e d by t r a v e r s a l o f the e n t i r e range o f t h e ' a ' - s e c t i o n , t h e r e b y c o n n e c t i n g p i t c h e x t r e m i t i e s ( i . e . , E-^  and i n measures 2-5, and and by measure 7 ) . V o i c e c r o s s i n g s which connect D-^  and C^ r e p r e s e n t a type o f l a t e r a l p r o l o n g a t i o n — o n e which complements t h e l i n e a r p r o l o n g a t i o n s e f f e c t e d by t h e o u t e r - v o i c e movement j u s t examined. Three c o n d i t i o n s c h a r a c t e r i z e a l a t e r a l v o i c e - c r o s s i n g event as s u b o r d i n a t e : f i r s t , i t may n o t span t h e e n t i r e range o f t h e ' a ' - s e c t i o n (or i t would be a " p r i n c i p a l " p r o g r e s s i o n ) ; second, i t must a r r i v e on one of t h e two p i t c h e x t r e m i t i e s ; and t h i r d , i t must o r i g i n a t e — b e spawned— from a p r i n c i p a l p r o g r e s s i o n a l r e a d y underway. C o n c e r n i n g t h e t h i r d c o n d i t i o n : a t some p o i n t a p r i n c i p a l p r o g r e s s i o n may have two a v a i l a b l e s t e p w i s e c o n n e c t i o n s , one i n t h e d i r e c t i o n i t s t a r t e d ( i . e . , t h e c o n t i n u a t i o n o f t h e p r i n c i p a l p r o g r e s s i o n ) , and the o t h e r i n t h e o p p o s i t e d i r e c t i o n . I f t h e p r o g r e s s i o n which branches o f f i n t h e o p p o s i t e d i r e c t i o n a r r i v e s back a t t h e s t a r t i n g p i t c h of the o r i g i n a l p r i n c i p a l p r o g r e s s i o n 134 16 I t i s c o n s i d e r e d t o be a s u b o r d i n a t e l i n e a r i z a t i o n . Stepwise p i t c h c o n n e c t i o n s e f f e c t i n g t h e s e l a t e r a l v o i c e - c r o s s i n g events i n v o l v e p i t c h e s which emerge as ( a u d i b l y ) prominent t h r o u g h t i m b r a l , dynamic, or a r t i c u l a t i v e exposure. These t h r e e t y p e s of "exposed" c o n n e c t i o n w i l l now be d i s c u s s e d i n g r e a t e r d e t a i l . T i m b r a l c o n n e c t i o n Semitone o f whole-tone movement i n one p a r t i c u l a r i n s t r u m e n t , e i t h e r i n t h e same v o i c e o f a c r o s s v o i c e s , ^ as i n d i c a t e d by a d i a g o n a l arrow, q u a l i f i e s as a t i m b r a l c o n n e c t i o n . In Example 59, two such c o n n e c t i o n s a r e boxed on system ( a ) — t h e same " v o i c i n g " arrangement as Example 5 7 — a n d summarized on system ( b ) . The f i r s t i n s t a n c e o f c o n n e c t i o n i n Example 59 o c c u r s i n t h e same v o i c e , w h i l e t h e second i n v o l v e s v o i c e c r o s s i n g . C o n n e c t i o n t h r o u g h dynamic exposure Movement a t mezzoforte to a p i t c h which i s a semitone o r whole-tone above or below t h e p r e c e d i n g p i t c h of t h e p r o g r e s s i o n (heard i n an o t h e r i n s t r u m e n t and which c o n t i n u e s t o sound) d e f i n e s c o n n e c t i o n t h r o u g h dynamic exposure. T h i s p a r t i c u l a r c o n n e c t i o n always i n v o l v e s two i n s t r u m e n t s , t h e f i r s t one s u s t a i n i n g i t s p i t c h a f t e r t h e second one c o n t i n u e s t h e l i n e a r 18 p r o g r e s s i o n w i t h i t s d y n a m i c a l l y exposed p i t c h ; r e f e r t o Example 60. 16 I f a t some p o i n t a p r i n c i p a l p r o g r e s s i o n has two a v a i l a b l e s t e p w i s e c o n n e c t i o n s , each i n t h e same d i r e c t i o n as i t s t a r t e d ( e . g . , from G to and G t o F ) , b o t h of which c o n t i n u e i n t h a t d i r e c t i o n and a r r i v e on the lower p i t c h e x t r e m i t y ( t h e upper e x t r e m i t y i f t h e l i n e s a r e ascending) t h e s e a r e c o n s i d e r e d to be, and n o t a t e d as, two s e p a r a t e p r i n c i p a l p r o g r e s s i o n s o c c u r r i n g o v e r d i f f e r e n t time spans. ^ V o i c e s , remember, a r e l i n e a r c o n t i n u i t i e s comprised o f ton e s o f equa l p o s i t i o n i n s u c c e s s i v e v e r t i c a l i t i e s ( r e g a r d l e s s of i n s t r u m e n t a t i o n ) . 18 In t h i s p a r t i c u l a r t y p e o f c o n n e c t i o n , dynamic exposure i s o f pr i m a r y importance. Compare t h i s w i t h t h e f i r s t t y p e where mezzoforte a c c e n t i s secondary t o t h e as p e c t o f t i m b r a l c o n s i s t e n c y . -Example 59. Two i n s t a n c e s of t i m b r a l c o n n e c t i o n i n l a t e r a l v o i c e - c r o s s i n g e v e n t s . mm. 2 3 4 5 Example 60. One i n s t a n c e o f c o n n e c t i o n t h r o u g h dynamic exposure. mm. 9 10 W' t connection: 136 C o n n e c t i o n t h r o u g h a r t i c u l a t i o n a f t e r a r e s t When a p i t c h i s a r t i c u l a t e d a f t e r a r e s t , and i s a semitone or whole-tone above o r below t h e p r e c e d i n g p i t c h of t h e p r o g r e s s i o n ( a g a i n , heard i n an o t h e r i n s t r u m e n t and which c o n t i n u e s t o sound), i t may be heard to c o n t i n u e t h e l i n e a r i z a t i o n a c r o s s v o i c e s . Example 61 i l l u s t r a t e s t h i s t h i r d c o n d i t i o n o f l i n e a r p r o g r e s s i o n t h r o u g h l a t e r a l v o i c e c r o s s i n g . Example 61. One i n s t a n c e o f c o n n e c t i o n t h r o u g h a r t i c u l a t i o n a f t e r a r e s t . mm. L connection: N o t i c e i n t h e second and t h i r d c r i t e r i a ( i . e . , Examples 60 and 61) t h a t the i n s t r u m e n t which sounds t h e new p i t c h of t h e p r o g r e s s i o n (be i t t h r o u g h dynamic o r a r t i c u l a t i v e exposure) does not have t o move by s t e p from i t s own p r e c e d i n g n o t e . Rather, t h e s t e p w i s e c o n n e c t i o n o c c u r s from an a l r e a d y sounding i n s t r u m e n t to t h e one which p r o v i d e s t h e exposed p i t c h . W h i l e many b r i e f c o n n e c t i o n s may be d i s c e r n e d , based on any one of 137 t h e t h r e e c r i t e r i a s t a t e d above, i t i s t h e j o i n t c o n s i d e r a t i o n o f t h e s e p r i n c i p l e s w i t h t h e c o n d i t i o n s of p r i n c i p a l and s u b o r d i n a t e l i n e a r e v e n t s , d e f i n e d e a r l i e r , which r e v e a l s l i n e a r c o n t i n u i t y i n t h e opening t w e l v e 19 measures of t h e p i e c e . System (a) of Example 62 c o n s i s t s of t h e same " v o i c e " r e p r e s e n t a t i o n a s Example 57 (used t o i l l u s t r a t e o u t e r - v o i c e p r o l o n g a t i o n ) , here, up t o measure 12 o n l y . System (b) i s comprised of th e v a r i o u s p r i n c i p a l and s u b o r d i n a t e v o i c e - c r o s s i n g e v e n t s d e f i n e d t h r o u g h a p p l i c a t i o n of t h e c r i t e r i a s t a t e d above. A l l o c c u r r e n c e s o f a r e approached by a p r i n c i p a l v o i c e - c r o s s i n g p r o g r e s s i o n ; of ba r s 7 and 10 a r e a l s o d e p a r t u r e pointsff.or l a t e r a l p r o g r e s s i o n s t o C 4 . Of t h e o c c u r r e n c e s o f C 4, a l l a r e approached by a l a t e r a l p r o g r e s s i o n ( p r i n c i p a l or s u b o r d i n a t e ) , but not a l l a r e p o i n t s o f d e p a r t u r e f o r d e s c e n d i n g l a t e r a l c o n n e c t i o n s t o D . As i t t u r n s out, i n s t a n c e s of C 4 which f a i l t o i n i t i a t e v o i c e - c r o s s i n g p r o g r e s s i o n s do not appear a d j a c e n t t o o c c u r r e n c e s o f D^. Remember t h a t , i n t h e p r e c e d i n g d i s c u s s i o n on o u t e r - v o i c e p r o l o n g a t i o n , a C 4 was l a b e l l e d p r i m a r y i f i t o c c u r r e d next t o a D^, and secondary i f i t appeared " a l o n e . " I t i s c o n s i s t e n t , then, t h a t o f t h e C 4 ' s which a r e not i n i t i a t o r s o f d e s c e n d i n g l a t e r a l p r o g r e s s i o n s , a l l a r e secondary by d e f i n i t i o n . System (c) of Example 62 o f f e r s a summary o f t h e i n t e r a c t i n g l a t e r a l p r o g r e s s i o n s . Those on t h e t o p s t a f f p r o g r e s s toward and away from 19 A l t h o u g h b a r s 13-15 a r e p a r t of t h e ' a ' - s e c t i o n , i n c r e a s e d rhythmic a c t i v i t y , slow dynamic f l u c t u a t i o n r e l a t i v e to p i t c h changes, and absence of r e s t s p r e c l u d e l i n e a r c o n n e c t i o n s as d e f i n e d by t h e a s s e r t e d c r i t e r i a o f l a t e r a l v o i c e c r o s s i n g . I t i s i n t e r e s t i n g t h a t , w h i l e b a r s 15-16 have been d e f i n e d as t r a n s i t i o n a l , a d i s s o l u t i o n o f p a r a m e t r i c c o n t i n u i t y i s a l r e a d y emerging i n b a r s 13-15 as suggested by t h e changes n o t e d above ( i . e . , r h y t h m i c , dynamic, and a r t i c u l a t i v e ) , and by t h e c o n d i t i o n a l changes r e g a r d i n g o u t e r - v o i c e p r o l o n g a t i o n d e s c r i b e d e a r l i e r . 138 Example 62. L i n e a r p r o g r e s s i o n s i n v o l v i n g l a t e r a l v o i c e - c r o s s i n g in.measures 1-12. 13? m m . 2 3 8 140 p r o l o n g a t i o n a l p o i n t s n o t e d e a r l i e r , w h i l e t h o s e on t h e bottom a r e more extended and o v e r l a p t h e former p r o g r e s s i o n s . C o n n e c t i o n s between d y n a m i c a l l y exposed p i t c h - p a i r s The concept of d y n a m i c a l l y exposed p i t c h - p a i r s was d e f i n e d e a r l i e r as m a n i f e s t i n g a p a r t i c u l a r mode o f rh y t h m i c g r o u p i n g . To r e c a p i t u l a t e t h e d e r i v a t i o n o f p i t c h - p a i r s , i t was noted t h a t i n measures 1-12 each instrument f e a t u r e s a s u c c e s s i o n of l i n e a r dyads s e p a r a t e d by r e s t s . P i t c h changes between r e s t s o c c u r a t or v e r y near t h e peak of dynamic i n t e n s i f i c a t i o n a t mezzoforte—hence, d y n a m i c a l l y exposed p i t c h - p a i r s . At t h i s p o i n t we a r e concerned w i t h t h e a c t u a l p i t c h c o n t e n t o f such p a i r s , and t h e i r r e l a t i o n s h i p to s u r r o u n d i n g p a i r s . A l t h o u g h c o n t i g u o u s p a i r s do not g i v e r i s e to st e p w i s e c o n t i n u i t i e s which t r a v e r s e o r p r o l o n g o u t e r -p i t c h e x t r e m i t i e s , as i n t h e two modes of l i n e a r c o n n e c t i o n p r e v i o u s l y d e s c r i b e d , t h r e e d e t a i l s of t h i s a s p e c t o f l i n e a r o r g a n i z a t i o n a r e worth n o t i n g . The f i r s t i n v o l v e s l o c a l p r o l o n g a t i o n o f s p e c i f i c p i t c h e s t h r o u g h n e i g h b o u r m otion p r o v i d e d by i n t e r v e n i n g p i t c h - p a i r s . I n Example 63 t h e s e i n s t a n c e s of l o w - l e v e l p r o l o n g a t i o n a r e n o t e d on system ( c ) . System (a) i s t h e p r e v i o u s l y employed l i n e a r r e p r e s e n t a t i o n of p i t c h c o n t e n t , w h i l e system (b) i s a summary of the d y n a m i c a l l y exposed p a i r s . In t h e l a t t e r , each p a i r i s s l u r r e d and t h e f i r s t p i t c h o f each i s n o t a t e d j u s t p r i o r t o changing r a t h e r than a t i t s a c t u a l p o i n t o f i n c e p t i o n {[since i t i s f i r s t a r t i c u l a t e d a t pianissimo and i s t h e r e f o r e most p e r c e p t i b l e j u s t p r i o r t o changing ( i . e . , a t mezzoforte)}. In most p i t c h - p a i r groups ( i . e . , groups as s e p a r a t e d by d o t t e d v e r t i c a l l i n e s and which c o r r e s p o n d t o t h o s e o f Example 54) t h e f i r s t p i t c h i s p r o l o n g e d t h r o u g h e i t h e r a double n e i g h b o u r o r major-minor neighbour as i n d i c a t e d on system (c) o f t h e graph. 141 Example 63. C o n n e c t i o n s t h r o u g h d y n a m i c a l l y exposed p i t c h - p a i r s i n measures 1-14. 143 O c c a s i o n a l l y the i n t e r v a l of a t h i r d w i l l approach the f i n a l p i t c h of the p r o l o n g a t i o n as i n measures 11 and 12. Because the f i r s t p i t c h of each group i s not always a p i t c h extremity of the s e c t i o n (e.g., or C 4 ) , the connection of p i t c h e s i n t h i s manner r e s u l t s , at times, i n low-l e v e l " i n n e r - v o i c e " p r o l o n g a t i o n s , e.g., measures 4-5, 6, 10, and 11-12. Perhaps more s i g n i f i c a n t i s the progressive expansion of i n t e r v a l s o c c u r r i n g between ( l i n k i n g ) p i t c h e s of i n d i v i d u a l p a i r s . Below system ( c ) , the d e s i g n a t i o n m/M2 suggests t h a t , up to measure 10, movement between the r e s t s i n each instrument i s by step. In measure 10 t h i s i s expanded to i n c l u d e minor t h i r d s and by measure 12, major t h i r d s . This might be viewed as another m a n i f e s t a t i o n of the expansion concept discussed i n the preceding chapter. A t h i r d d e t a i l of i n t e r e s t concerns measures 13-15, two bars which have already been mentioned i n connection w i t h the d i s s o l u t i o n of s e v e r a l p a t t e r n s . For example, heightened rhythmic a c t i v i t y i n these measures was s a i d to render v e r t i c a l s o n o r i t i e s and o u t e r - v o i c e prolongations more d i f f i c u l t to d i s c e r n . L a t e r a l v o i c e - c r o s s i n g connections were a l s o found to stop short of bar 13. To be added to t h i s l i s t of departures i s the absence of p i t c h - p a i r s separated by r e s t s ; r a t h e r , l i n e a r c o n t i n u i t y i n  each instrument i s now more apparent. However, one f i n a l dynamic " s w e l l " takes place i n each instrument, again, exposing a p a i r of p i t c h e s . But r a t h e r than o c c u r r i n g c o n t i g u o u s l y , the p a i r s overlap as a r e s u l t of increased rhythmic a c t i v i t y . The dynamically exposed p a i r s i n question are bracketed on system (a) of Example 63. A l o w - l e v e l p r o l o n g a t i o n of C 4 (through a major-minor lower neighbour) i s perhaps the most s i g n i f i c a n t outcome of t h i s dynamic f l u c t u a t i o n [see system (c)l; i t r e i n f o r c e s the 144 2 0 o u t e r - v o i c e p r o l o n g a t i o n o f C 4 i l l u s t r a t e d e a r l i e r . Summary Three modes of l i n e a r c o n n e c t i o n u t i l i z i n g s t e p w i s e motion have been examined i n t h e f o r e g o i n g s e c t i o n : o u t e r - v o i c e p r o l o n g a t i o n s , l a t e r a l v o i c e - c r o s s i n g e v e n t s , and l o w - l e v e l p r o l o n g a t i o n s t h r o u g h dynamic exposure. In t h e f i r s t of t h e s e , and C 4 — t h e p i t c h e x t r e m i t i e s of t h e ' a ' - s e c t i o n — were s i m u l t a n e o u s l y p r o l o n g e d , and a d j a c e n t a r t i c u l a t i o n s of each were l a b e l l e d p r i m a r y . The tw o - v o i c e s t r u c t u r e o f t h e ' b ' - s e c t i o n was shown t o be a c o n t i n u a t i o n of t h e s e p r o l o n g e d p i t c h e x t r e m i t i e s . In t h e second mode of l i n e a r i z a t i o n , t h r e e c r i t e r i a i n v o l v i n g t i m b r e , dynamics, and a r t i c u l a -t i o n were used t o e s t a b l i s h l a t e r a l v o i c e - c r o s s i n g e v e n t s which connect and C 4. O u t e r - v o i c e p r o l o n g a t i o n s and l a t e r a l v o i c e - c r o s s i n g s were s a i d to complement each o t h e r i n m a i n t a i n i n g t h e p i t c h e x t r e m i t i e s o f the 'a'-s e c t i o n . The c o n n e c t i o n of d y n a m i c a l l y exposed p i t c h - p a i r s i n c l o s e p r o x i m i t y r e v e a l e d l o w - l e v e l p r o l o n g a t i o n s o f i n n e r v o i c e s as w e l l as a p a r t i c u l a r mode of expa n s i o n . C o n c e r n i n g t h e l a t t e r , movement between r e s t s was seen t o expand from minor and major seconds i n t h e f i r s t t e n measures t o minor and major t h i r d s i n b a r s 11 and 12. L i n e a r c o n t i n u i t y would seem t o be t i g h t l y c o n t r o l l e d t h r o u g h the-modes of l i n e a r c o n n e c t i o n suggested i n t h i s s e c t i o n . Harmonic D e t a i l s I n t h e p r e v i o u s c h a p t e r , consonance and d i s s o n a n c e i n , and f u n c t i o n a l r e l a t i o n s h i p s between, v e r t i c a l i t i e s were s t a t e d as b e i n g two c e n t r a l i s s u e s of harmonic p i t c h o r g a n i z a t i o n . C o n c e r n i n g t h e f i r s t o f t h e s e , semitone and 2 0 Giv e n t h a t o n l y the p r o l o n g a t i o n o f D^ and not c 4 i s c o n t i n u e d i n the subsequent t r a n s i t i o n (measures 15-16), t h i s f i n a l maintenance o f C 4 t h r o u g h dynamic exposure has added s i g n i f i c a n c e . 145 whole-tone c o n t e n t w i l l be used h e r e , as i t was e a r l i e r , as a main c r i t e r i o n f o r c l a s s i f y i n g harmonic q u a l i t y . Because of t e x t u r a l c o n s i s t e n c y i n t h e f i r s t t w e l v e measures ( a l r e a d y n o t e d ) , t h a t p o r t i o n o f t h e ' a ' - s e c t i o n w i l l be d e a l t w i t h f i r s t . Measures 13-15 ( t h e t r a n s i t i o n ) , and t h e ' b ' - s e c t i o n w i l l then be examined. Measures 1-12 U n d e r l y i n g the f i v e - p a r t independent t e x t u r e o f measures 1-12, h a r m o n i c a l l y , i s a continuum o f changing v e r t i c a l s o n o r i t i e s . A l t h o u g h from one aggregate to t h e next o n l y one p i t c h i s changed, harmonic q u a l i t y may be a f f e c t e d c o n s i d e r a b l y . The r e a d e r i s r e f e r r e d t o Example 64 where, i n system ( a ) , t h e p r e v i o u s l y employed p i t c h r e p r e s e n t a t i o n i s g i v e n . The harmonic q u a l i t y o f each v e r t i c a l i t y must be e s t a b l i s h e d i n o r d e r t h a t h i g h e r - l e v e l r e l a t i o n s h i p s be d i s c e r n e d . The c r i t e r i a f o r c l a s s i f y i n g t h e s e s o n o r i t i e s a r e r e l a t i v e l y s imple f o r two r e a s o n s : a l l but two of them 2 c o n t a i n f i v e members, and the s e t s a r e r e g i s t r a l l y spaced w i t h i n one octave. In t h e l e f t column of Example 65 (p. 149) a l l p o s s i b l e c o m b i n a t i o n s of t h e f i r s t two i n t e r v a l - v e c t o r e n t r i e s f o r five-member s e t s and two c o m b i n a t i o n s f o r four-member s e t s a r e g i v e n . F o r t h e purpose of t h i s study, semitone c o n t e n t i s c o n s i d e r e d t h e p r i m a r y determinant o f consonance-d i s s o n a n c e q u a l i t y ; each i n t e r v a l - c l a s s 1 (per v e r t i c a l i t y ) i s t h e r e f o r e a s s i g n e d a v a l u e o f 4. Whole-tone c o n t e n t i s used as a f u r t h e r c r i t e r i o n to d i f f e r e n t i a t e between s e t s h a v i n g t h e same semitone c o n t e n t ; each i n t e r v a l - c l a s s 2 i s g i v e n a v a l u e of 1. When t h e s e v a l u e s a r e a p p l i e d t o th e c o m b i n a t i o n s i n t h e f i r s t column, q u a l i t a t i v e t o t a l s a r e determined; 21 Semitones and whole-tones would, presumably, have to be t r e a t e d d i f f e r e n t i n s o n o r i t i e s where t h e y appear r e g i s t r a l l y d i s p l a c e d by one or more o c t a v e s ( i . e . , as compound i n t e r v a l s ) . Example 64. Harmonic s t r u c t u r e . 14-7 mm.2 3 4 C - D factors: 7 10 1b 10 9 7 8 IO 12 13 14 7 9 11 11 14 10 9 13 9 [5 5\ 13 11 6 9 13 PlO 10 1ol 9 13 6 1 J 1 1 1 1 1 1 « i 1 1 J 1 . 7 i i i i U l ! J i T i 1 T [T 11 t J M ? tT T ^ V ? T ! [? r ? Ir ? v. DP ti& 3 T T I ? * * 15 16 17 20 21 22 148 Example 65. Consonance-dissonance c r i t e r i a and C-D f a c t o r s . 149 a,b of Interval Vector C-D Quality IC 1=4, IC 2=1 C-D Factor Representative Sets 4,3 19 (Diss.) 15 f 0,1,2,3,4 m. 12 ****** 1 m. i i 3,3 15 14 0,1,2,3,5 m. 3 3,2 14 13 j 0,1,2,4,5 m. 9 7-**-*-3,1 13 12 0,1,2,6,7 m. 4 2,3 11 11 0,2,3,4,6 • » T ' * m. 7 2,2 10 10 0,2,3,4,7 m. 8 2,1 9 9 0,1,4,5,7 m. 9 2,0 8 8 0,1,4,7,8 m. 4 1,3 7 7 0,2,3,5,7 £ m s * m. 6 1,2 6 6 0,2,3,6,8 m. 5 it** 1,1 5 5 0,1,3,6,9 m. 8 0,4 4 4 0,2,4,6,8 | m. 12 0,3 3 3 0,2,4,7,9 1 m. 12 V -0,1 1 2 | 0,2,5,8 1 m. 12 0,0 0 1 1 0,3,6,9 (Cons.) 150 these appear i n the second column. The f a c t o r s 4 and 1 were sel e c t e d i n order that the q u a l i t a t i v e t o t a l s r e f l e c t semitone primacy, p a r t i c u l a r l y across groups where whole-tone content i s r a d i c a l l y d i f f e r e n t . For example, a set w i t h three semitones and one whole-tone i s presumed more dissonant than one w i t h only two semitones and three whole-tones. Higher whole-tone ; content, then, only a f f e c t s harmonic q u a l i t y of s e t s w i t h equal semitone content. Q u a l i t a t i v e t o t a l s are adjusted to consecutive numbers f o r ease of reference and l i s t e d i n column three; these are henceforth termed consonance-dissonance f a c t o r s (or simply C-D f a c t o r s ) . The right-hand column c o n s i s t s of r e p r e s e n t a t i v e sets from the opening twelve measures. The C-D f a c t o r s e s t a b l i s h e d by the process explained above are i n d i c a t e d above the v e r t i c a l i t i e s on system (a) of Example 64. With respect to the frequency of the v a r i o u s f a c t o r s , at l e a s t three s t a t i s t i c a l d e t a i l s are noteworthy. The most f r e q u e n t l y used s o n o r i t i e s are those of f a c t o r s 9 and 10; they occur 12 and 16 times r e s p e c t i v e l y . A l s o , the number of s o n o r i t i e s of C-D f a c t o r 10 and above i s approximately that of f a c t o r 9 and b e l o w — r e s p e c t i v e l y , 39 and 36. V e r t i c a l i t i e s of f a c t o r 9 and 10 might be considered "average" reference p o i n t s based on these data. F i n a l l y , o n l y one v e r t i c a l i t y of C-D f a c t o r 1 i s used and one of f a c t o r 15, and both occur i n r e l a t i v e l y c l o s e p r o x i m i t y (e.g., measure 12). Regarding s p e c i f i c l o c a t i o n s of the v a r i o u s s o n o r i t i e s of a given harmonic q u a l i t y , two important r e l a t i o n s h i p s may be discerned, both of which concern instances of consecutive v e r t i c a l i t i e s of the same C-D f a c t o r . The f i r s t a l s o i n v o l v e s r e c u r r i n g sets of the same f a c t o r . R e f e r r i n g back to Example 64, system (b) c o n s i s t s of the instances of D^  and C^ prolonged through the techniques o u t l i n e d i n the previous s e c t i o n . Noteworthy i s the f a c t that most occurrences of D^  and are a r t i c u l a t e d — 151 i n a sense "harmonized"—by v e r t i c a l i t i e s of C-D f a c t o r s 9 or 1 0 — t h e two most widely used i n the piece. This r e i n f o r c e s the p r e v i o u s l y asserted " r e f e r e n t i a l " property of these two harmonic q u a l i t i e s . These p a r t i c u l a r connections are i n d i c a t e d by the l i n e , -, above each s t a f f on system (b). Also of import i s the use of consecutive v e r t i c a l i t i e s of equal harmonic q u a l i t y i n two of the three instances of adjacent a r r i v a l s on D^  and C^ (defined e a r l i e r as "primary" p o i n t s of p r o l o n g a t i o n ) . In measures 9-10, f o r instance, both p i t c h e x t r e m i t i e s are accompanied by aggregates of C-D f a c t o r 3, while those i n bar 11 are of the f a c t o r 10. These a s s o c i a t i o n s are i n d i c a t e d on system (b) by the diagonal l i n e " ^ v A second important r e l a t i o n s h i p i n v o l v e s i n t e r a c t i o n between harmonic q u a l i t y and dynamic f l u c t u a t i o n . Adjacent C-D f a c t o r s of the same magnitude which represent v e r t i c a l i t i e s involved i n t h i s i n t e r a c t i o n are bracketed above system (a) on Example 64. These f a c t o r s are a l s o i n d i c a t e d on Example 66, a r e p r i n t of an e a r l i e r example used to i l l u s t r a t e the rhythm of dynamically exposed p i t c h - p a i r groups. As the graph r e v e a l s , at l e a s t some contiguous mezzoforte p a i r s w i t h i n a given group occur i n v e r t i c a l s o n o r i t i e s of equal harmonic q u a l i t y . The ebb and flo w of the asserted rhythmic p a t t e r n would seem to be strengthened by t h i s aspect of harmonic s t r u c t u r e . Measures 13-15 (the t r a n s i t i o n ) , and the 'b'-section As noted throughout t h i s chapter, measures 13-15, although part of the ' a ' - s e c t i o n , e x h i b i t departures from the t e x t u r a l and rhythmic design of the preceding measures. The surface "business" of these bars continues i n t o the subsequent t r a n s i t i o n , the l a t t e r f e a t u r i n g f u r t h e r rhythmic i n t e n s i f i c a t i o n as w e l l as a red u c t i o n i n t e x t u r a l - d e n s i t y to. three components, a l l of which operate between D^  and F^. The continuous 152 Example 66. R e c u r r i n g s e t s of e q u a l harmonic q u a l i t y i n u n i t s of d y n a m i c a l l y exposed p i t c h - p a i r s . I S3 | I I I | I I I | I I t | I I I | I I I | I 1 I | I I I | I I I | 1 I 1 | I I I | I I I | I I I | I I I | 1 I I | 7 8 9 measure n o . 10 11 12 13 14 15 154 a r t i c u l a t i o n o f D^, D//3, E^, and i n t h e t r a n s i t i o n g i v e s t h e e f f e c t o f a r e i t e r a t e d f o u r - n o t e s o n o r i t y , d e s p i t e t h e p r e s e n c e o f o n l y t h r e e l i n e a r components. The l a c k o f harmonic e v e n t f u l n e s s i n t h e ' b ' - s e c t i o n r e n d e r s 22 i n d i v i d u a l s o n o r i t i e s e x t r e m e l y p e r c e p t i b l e . Obvious i s t h e w e d g e - l i k e expansion from a u n i s o n C//5 to t h e f o u r - n o t e s e t , C#^-D^-E^; i n t e r e s t i n g i s t h e f a c t t h a t t h i s s e t , d e s p i t e i t s c a r d i n a l i t y , has a C-D f a c t o r o f 1 0 — the most f r e q u e n t o f t h o s e i n t h e ' a ' - s e c t i o n (most of which c o n t a i n f i v e members). F i n a l l y , a d e t a i l of harmonic o r g a n i z a t i o n i n t r o d u c e d i n t h e p r e v i o u s c h a p t e r may have a p p l i c a t i o n i n t h e f i n a l dyad o f t h i s p i e c e . S p e c i f i c a l l y , t h e whole-tone s o n o r i t y may be he a r d as a consonant " r e s o l u t i o n " ( i n a r e l a t i v e sense) from t h e p e n u l t i m a t e c h r o m a t i c v e r t i c a l i t y B-C/Z-D-E^7. In t h i s sense i t i s s u g g e s t i v e of t h e " c a d e n t i a l " a t t r i b u t e o f t h e whole-tone n o t e d a l r e a d y i n t h e t h i r d and f o u r t h p i e c e s . Summary Consonance and d i s s o n a n c e i n , and consequent f u n c t i o n a l r e l a t i o n s h i p s between, v e r t i c a l s o n o r i t i e s were s t a t e d a s b e i n g two main co n c e r n s i n e s t a b l i s h i n g p r i n c i p l e s of harmonic o r g a n i z a t i o n . In measures 1-12, f i v e -n o t e v e r t i c a l i t i e s were i d e n t i f i e d as t o cons o n a n c e - d i s s o n a n c e " f a c t o r s , " a r r i v e d a t t h r o u g h a s s i g n i n g v a l u e s o f 4 and 1 to semitones and whole-tones i n t h e i r make-up. A c o r r e l a t i o n between v e r t i c a l i t i e s w i t h t h e most f r e q u e n t l y used C-D f a c t o r s , 9 and 10, and t h e p r o l o n g a t i o n o f D-* and C^ was r e v e a l e d . A l s o found to be o f s i g n i f i c a n c e i s t h e a s s o c i a t i o n between c o n s e c u t i v e s o n o r i t i e s w i t h t h e same harmonic f a c t o r , and peaks of t h e u n i t s d e f i n e d b y : s u c c e s s i v e d y n a m i c a l l y exposed p i t c h - p a i r s . In t h e 'b'-22 In t h e ' a ' - s e c t i o n , harmonic rhythm i s t i e d t o r h y t h m i c a c t i v i t y i n g e n e r a l because each a r t i c u l a t i o n sounds a new v e r t i c a l i t y . In t h e 'b'-s e c t i o n , t h e harmonic rhythm i s most o f t e n slower than t h e l e v e l of i m p u l s e -d e n s i t y because o f t h e r e i t e r a t i o n o f p i t c h e s . 155 s e c t i o n , t h e l a r g e s t s o n o r i t y ( w i t h r e s p e c t to c a r d i n a l i t y ) i s t h e p e n u l t i m a t e v e r t i c a l i t y i n b a r s 21-22. I t was found t o be of a f a c t o r 1 0— t h e most f r e q u e n t l y used i n t h e p i e c e . F i n a l l y , t h e c l o s i n g dyad o f th e p i e c e was suggested to be another i n s t a n c e o f t h e semitone-to-whole-tone c a d e n t i a l r e s o l u t i o n a s s e r t e d i n Chapter I I . Co n n e c t i v e F a c t o r s Between t h e F i r s t and T h i r d  P i e c e s and I n t e r r u p t i v e A s p e c t s of t h e Second At t h e b e g i n n i n g o f the second c h a p t e r , i n s t r u m e n t a t i o n - d e n s i t y and i n s t r u m e n t a t i o n were s a i d t o be r e s p o n s i b l e f o r apparent subgroupings of p i e c e s i n t h e q u i n t e t . Other c o n n e c t i v e a s p e c t s have s i n c e been d e f i n e d ( e . g . , a r t i c u l a t i v e and tempo s i m i l a r i t i e s i n , and PC c o n n e c t i o n s between, t h e f i f t h and s i x t h p i e c e s ) . A number of f a c t o r s p o i n t to a c h a r a c t e r i z a t i o n o f t h e f i r s t and t h i r d p i e c e s as a l a r g e - s c a l e c o n t i n u i t y , i n t e r r u p t e d by t h e second p i e c e . F o r example, p i e c e s 1 and 3 a r e ensemble p i e c e s a t J= 40, and s c o r e d f o r f i v e i n s t r u m e n t s ( o n l y one o f which i s d i f f e r e n t ) . Each f e a t u r e s an opening p o l y p h o n i c s e c t i o n i n which a l l i n s t r u m e n t s a r e marked dolcissimo, move i n p r e d o m i n a n t l y s t e p w i s e motion, and do so between t h e dynamic range from pianissimo t o mezzoforte. A l s o common to both p i e c e s i s t h e f a c t t h a t each opens i n one c l e a r l y d e f i n e d r e g i s t e r and ends i n a n o t h e r . In t h i s r e g a r d , t h e r e g i s t e r o f t h e f i r s t p i e c e ' s opening i s r e s t o r e d at t h e end of t h e t h i r d p i e c e , and t h e c l o s i n g r e g i s t e r o f t h e f i r s t p i e c e i s t h a t o f t h e t h i r d p i e c e ' s opening. ( T h i s w i l l be i l l u s t r a t e d s h o r t l y . ) I n a d d i t i o n t o t h e s i m i l a r i t i e s l i s t e d above, each p i e c e f e a t u r e s a " d r a m a t i c e v e n t " a f t e r t h e opening p o l y p h o n i c s e c t i o n . I n t h e f i r s t p i e c e i t i s i n t h e form o f a f i v e - p a r t u n i s o n (e.g., C//5 o f bar 16X, w h i l e i n t h e t h i r d , an o c t a v e - d o u b l e d theme p r o v i d e s t h e d r a m a t i c c o n t r a s t . The 156 two pieces may a l s o be seen as r e l a t e d i n terms of p r o p o r t i o n . In each piece the dramatic event begins at the golden s e c t i o n of t h e i r r e s p e c t i v e lengths. P i e c e No. 1, f o r example, i s 100 beats long. The golden s e c t i o n i s 62, and the unison C# enters i n beat 63. In the second piece, 64 beats long, the octave-doubled theme enters i n beat 39, the golden s e c t i o n of 64. On a l a r g e r s c a l e , pieces 1 and 3, taken as an u n i n t e r r u p t e d c o n t i n u i t y , are themselves i n a golden s e c t i o n r e l a t i o n s h i p . The t w e n t y - f i v e measure f i r s t piece i s the golden s e c t i o n of the t o t a l forty-one bars of both pieces. P i t c h r e l a t i o n s h i p s between the opening and c l o s i n g of the f i r s t and t h i r d pieces may a l s o be discerned. These are i n d i c a t e d on the second system of Example 67, the top system being a summary of s t r u c t u r a l p a i n t s i n the pieces. The bottom system i l l u s t r a t e s the aforementioned r e g i s t r a l connections. The f i r s t of two important d e t a i l s i n Example 67 i s the senza diminuendo marking which appears w i t h the f i n a l dyad of the f i r s t p iece, p o s s i b l y suggesting a connection to something which occurs l a t e r (e.g., the opening of No. 3?). The attacca i n d i c a t i o n a t . t h e end of the piece would a l s o seem to imply a c o n t i n u a t i o n . The second d e t a i l concerns the opening i n t e r v a l of a f i f t h i n the f i r s t p iece, l i n e a r i z e d at the end 23 o of the t h i r d piece. In t h i s sense, the B J which i s the u l t i m a t e a r r i v a l point of the t h i r d piece, provides a degree of l a r g e - s c a l e c l o s u r e from the f i r s t piece. While the c o n d i t i o n s o u t l i n e d above suggest connective aspects between pieces 1 and 3, a number of c o n t r a s t i n g f e a t u r e s support c h a r a c t e r i z i n g of the second piece as an i n t e r r u p t i o n . F i r s t , i t i s a 23 In piece No. 1 the f i f t h represents the p i t c h e x t r e m i t i e s of the i n i t i a l s o n o r i t y . In piece No, 3 the l i n e a r i z e d f i f t h occurs i n the ascending t r i l l of the c l a r i n e t i n bars 12-16. 158 s o l o i s t i c p i e c e w i t h an o f t e n fragmented t e x t u r e , f l u c t u a t i n g n o t a t e d meter, and a q u i c k e r tempo. Second, i t has a much wider range than t h e p i e c e s which frame i t , and i t f e a t u r e s f r e q u e n t and abrupt changes i n r e g i s t e r and ..24 dynamics. The n o t e a t t h e end: " s t o p suddenly a s though t o r n o f f , " s u g g e s t s a d e n i a l o f d i r e c t c o n t i n u i t y t o t h e opening o f t h e t h i r d p i e c e . Summary Whi l e i n s t r u m e n t a t i o n - d e n s i t y and i n s t r u m e n t a t i o n were s a i d e a r l i e r to suggest subgroupings, a number o f d i f f e r e n t f a c t o r s add support t o t h e n o t i o n o f a c o n n e c t i o n between t h e f i r s t and t h i r d p i e c e s . Among t h e c o n n e c t i v e f a c t o r s a r e a s p e c t s o f t e x t u r e , tempo, a r t i c u l a t i o n , dynamics, r e g i s t e r , p r o p o r t i o n , and p i t c h c o n n e c t i o n . The use of a u n i s o n or o c t a v e d r a m a t i c event i s a l s o common to both. F i n a l l y , s e v e r a l c o n t r a s t i n g f e a t u r e s of t h e second p i e c e (e.g., t e x t u r e , tempo, and dynamics) were s a i d t o q u a l i f y i t as an i n t e r r u p t i o n o f t h e c o n t i n u i t y between p i e c e s 1 and 3. Summary The f o r e g o i n g c h a p t e r i s a d e t a i l e d a n a l y s i s of t h e f i r s t p i e c e o f t h e q u i n t e t . A s p e c t s of f o r m a l d e l i n e a t i o n , t e x t u r a l s t r u c t u r e , r h y t h m i c and m e t r i c d e s i g n , and p i t c h o r g a n i z a t i o n were d e a l t w i t h i n d i v i d u a l l y and i n t e r r e l a t i o n s h i p s noted where a p p l i c a b l e . The f i r s t p i e c e was found t o be c o n s i s t e n t , i n many ways, w i t h o t h e r ensemble p i e c e s i n t h e q u i n t e t , and c o n c e p t s such as i m p u l s e - d e n s i t y and consonance-dissonance c r i t e r i a , i n t r o d u c e d i n Chapter I I , were found t o have a p p l i c a t i o n here. Other c o n c e p t s ( e . g . , t e x t u r a l q u a l i t y , t e x t u r a l space, and i n t e r a c t i o n o f element-rhythms) a r e s p e c i f i c t o t h e a n a l y s i s o f p i e c e No. 1. F i n a l l y , 24 T . . L i g e t x , Ten Pieces, p. 11. 159 t h e n o t i o n of p i e c e subgrouping, a l s o i n t r o d u c e d i n t h e second c h a p t e r , was found to be r e i n f o r c e d i n elements of c o n n e c t i o n between t h e f i r s t and t h i r d p i e c e s . CHAPTER IV ANALYSIS OF PIECE NO. 10 I n t r o d u c t i o n In the a n a l y s i s of piece No. 10 each parameter i s examined i n d i v i d u a l l y as i n the previous two chapters. The main formal s e c t i o n s are as f o l l o w s : D e l i n e a t i n g Factors of Formal Segmentation Aspects of T e x t u r a l S t r u c t u r e P r i n c i p l e s of Rhythmic and M e t r i c Design Modes of P i t c h O rganization Linear D e t a i l s Harmonic D e t a i l s Connective Factors Between the N i n t h and Tenth Pieces Summary. As i n the a n a l y s i s of the f i r s t p i e c e , some concepts here are extended a p p l i c a t i o n s of those introduced i n Chapter I I , w h i l e others are p a r t i c u l a r to the tenth p i e c e . D e l i n e a t i n g Factors of Formal Segmentation U n l i k e other s o l o i s t i c pieces i n the qu i n t e t (e.g., Nos. 2, 6, and 8 ) , where formal s e c t i o n s and d i s p a r a t e musical ideas o f t e n coalesce i n t o a continuous stream, the tenth piece f e a t u r e s formal segmentation which i s more d i s t i n c t and pronounced. Two main s e c t i o n s may be discerned: measures 1-12 and 13-22 and, although t h e i r surfaces may appear s i m i l a r , many d e t a i l s u n d e r l i e the i n d i v i d u a l i t y of each s e c t i o n . Such d e t a i l s concern parameters 160 161 of t e x t u r e and rhythm, as w e l l as a s p e c t s o f l i n e a r and harmonic p i t c h o r g a n i z a t i o n ; t h e s e w i l l be d i s c l o s e d i n subsequent s e c t i o n s of t h i s c h a p t e r . More o b v i o u s form d e f i n i n g f a c t o r s , however, i n c l u d e t h e generalpause i n measure 12, p r i o r t o , and a f t e r which t h i r t y - o n e b e a t s ( i . e . , q u a r t e r -n o t e s ) o f a c t u a l sound o c c u r . Tempo i n d i c a t i o n s a l s o r e i n f o r c e t h i s p o i n t of segmentation; w i t n e s s the pochiss. rail, i n b a r s 10-12 (accompanied by a w r i t t e n ritardando), and a tempo and ex abrupto i n d i c a t i o n s i n bar 13. The m e l o d i c s t r u c t u r e o f t h e bassoon p a r t i s a n o t h e r f a c t o r of d e l i n e a t i o n . Each f o r m a l s e c t i o n , f o r example, may be heard to c o n s i s t o f a d i s j u n c t p o r t i o n f o l l o w e d by a c o n j u n c t "cadenza." Dynamic i n d i c a t i o n s accompanying t h e s e i n t e r n a l segments a l s o c o n t r i b u t e t o the i n d i v i d u a l i t y of each f o r m a l s e c t i o n . In t h e ' a ' - s e c t i o n t h e d i s j u n c t p o r t i o n i s a t ff and t h e cadenza at p, w h i l e i n t h e ' b ' - s e c t i o n t h e s e a r e r e p l a c e d by fff and pp. In s h o r t , t h e l o u d p a r t o f t h e ' b ' - s e c t i o n g e t s l o u d e r and t h e s o f t p a r t g e t s s o f t e r , r e s u l t i n g i n a p a r t i c u l a r mode of e x p a n s i o n : the ' b ' - s e c t i o n h a v i n g a w i d e r dynamic range. And f i n a l l y , f l u c t u a t i o n i n i n s t r u m e n t a t i o n p a r t i c i p a t i o n i s i n agreement w i t h f o r m a l segmentation as d e f i n e d above. The p i c c o l o , s i l e n t d u r i n g t h e d i s j u n c t p o r t i o n o f each s e c t i o n , e n t e r s i n t h e cadenza, t h u s marking t h e end of each main f o r m a l d i v i s i o n . Many f a c t o r s of f o r m a l segmentation i n v o l v e d e t a i l s o f t e x t u r a l and r h y t h m i c s t r u c t u r e , as w e l l as t h o s e o f p i t c h o r g a n i z a t i o n , to be examined i n f o r t h c o m i n g s e c t i o n s . P a t e n t i n d i c a t o r s of f o r m a l d e l i n e a t i o n , however, i n c l u d e t h e generalpause i n bar 12, tempo markings, m e l o d i c c o n t o u r of the bassoon p a r t , dynamics, and i n s t r u m e n t a t i o n . •pp Summary 1 6 2 A s p e c t s of T e x t u r a l S t r u c t u r e In t h e second c h a p t e r , two t e x t u r a l c o n f i g u r a t i o n s were s a i d t o o p e r a t e i n t h e s o l o i s t i c p i e c e s of t h e q u i n t e t . In one o f t h e s e t y p e s , accompanying i n s t r u m e n t s e s t a b l i s h a p a r t i c u l a r t e x t u r a l p a t t e r n o v e r which the f e a t u r e d i n s t r u m e n t a s s e r t s i t s e l f i n a c o n t r a s t i n g manner. The o t h e r i s comprised of a c o n t i n u o u s l i n e a r event, e f f e c t e d i n t h e f e a t u r e d i n s t r u m e n t , w i t h e i t h e r " c o n t r a p u n t a l fragments" o r " s p o r a d i c d o u b l i n g s and c o l o r a t i o n s " c o n t r i b u t e d by t h e r e m a i n i n g instruments.''' The e s s e n t i a l d i f f e r e n c e , t h e n , i s t h a t i n t h e f i r s t t y p e two s i m u l t a n e o u s t e x t u r a l elements comprise t h e o v e r a l l t e x t u r a l c o n f i g u r a t i o n , w h i l e i n t h e second o n l y one i s o p e r a t i v e . The f i n a l p i e c e of t h e q u i n t e t i s t e x t u r a l l y s t r u c t u r e d a c c o r d i n g t o t h e p r i n c i p l e s of t h e l a t t e r t y p e . S p e c i f i c a l l y , 2 t h e bassoon i s f e a t u r e d i n a n e a r l y c o n t i n u o u s , d i s j u n c t l i n e a r event w h i l e t h e r e m a i n i n g i n s t r u m e n t s p r o v i d e u n i s o n and o c t a v e d o u b l i n g s , and 3 semitone and whole-tone c o l o r a t i o n s t h r o u g h o u t . In a d d i t i o n t o t h e t e x t u r a l arrangement d e f i n e d above, two o t h e r c o n d i t i o n s a r e noteworthy. One i s a "cadenza" f i g u r e c o n s i s t i n g m a i n l y of s t e p w i s e motion ( i n c o n t r a s t t o t h e f i r s t t y p e ) . I n s t a n c e s of t h i s o c cur '''The l a t t e r d e s i g n a t i o n r e f e r s t o t h e t e x t u r a l q u a l i t y o f i n t e r -a c t i o n between the bassoon and o t h e r i n s t r u m e n t s . For example, c o n t r a p u n t a l fragments were no t e d as b e i n g b r i e f , r h y t h m i c a l l y independent passages which appear superimposed on t h e f e a t u r e d i n s t r u m e n t ' s p a r t . T h i s r e s u l t s i n p e r i o d i c fragments of polyphony. D o u b l i n g s and c o l o r a t i o n s , on t h e o t h e r hand, a r e c h a r a c t e r i z e d by r h y t h m i c i n t e r d e p e n d e n c e ; t h e i r v e r t i c a l a l ignment r e s u l t s i n b r i e f i n s t a n c e s of homophony. 2 The d i s j u n c t d i s p o s i t i o n o f t h e bassoon l i n e , f e a t u r i n g a b r u p t and extreme r e g i s t e r changes, s u g g e s t s an i m p l i e d m u l t i - v o i c e d l i n e a r . s t r u c t u r e — one which w i l l be i l l u s t r a t e d l a t e r i n t h e c h a p t e r . 3 Semitone c o l o r a t i o n s r e f e r t o a p i t c h ( i n an accompanying i n s t r u m e n t ) v e r t i c a l l y a l i g n e d w i t h , and a semitone above o r below, a p a r t i c u l a r bassoon °note. That d e s i g n a t e d as a whole-tone c o l o r a t i o n o c c u r s a whole-tone away. 163 i n measures 5-6, 8-9 continued i n 10-11 ( p i c c o l o ) , and 16-18 (the f i r s t bar oc c u r r i n g i n the c l a r i n e t ) . These f i g u r e s c o n t r a s t the d i s j u n c t fragments i n two other r e s p e c t s : they occur at p or pp (rather than ff or fff), and doublings and c o l o r a t i o n s do not occur during t h e i r execution. The t h i r d t e x t u r a l c o n d i t i o n i s one of s i l e n c e — a device which w i l l be shown to have a marked e f f e c t on pacing and progression i n the piece. Two aspects to be examined here are formal s t r u c t u r e as defined by the three t e x t u r a l c o n d i t i o n s stated above, and t e x t u r a l progression as manifest i n d e n s i t y and s p a t i a l f l u c t u a t i o n s . The l a t t e r concept deals w i t h instances of doubling and c o l o r a t i o n s p e c i f i c a l l y . Formal S t r u c t u r e as Defined by T e x t u r a l Conditions As suggested e a r l i e r i n the chapter, the piece:, may be heard to c o n s i s t of two main formal s e c t i o n s , each e x h i b i t i n g the use of the three t e x t u r a l c o n d i t i o n s defined above. For instance, i n Example 68, a l i n e -graph r e p r e s e n t a t i o n of the pie c e , the 'a'-section i s shown to be comprised of two phrases, each of which c o n s i s t s of three d i s j u n c t fragments and a cadenza. Large u n i t s of s i l e n c e separate d i s j u n c t fragments i n the f i r s t 4 phrase w h i l e these are replaced by b r i e f r e s t s i n the second. Generally speaking, the d i s j u n c t p o r t i o n of the second phrase i s more "condensed" as a r e s u l t . Each phrase concludes w i t h a cadenza, approached from the f i n a l d i s j u n c t fragment without i n t e r r u p t i o n . (As w i l l be shown l a t e r i n the chapter, the rhythmic s t r u c t u r e s of the cadenzas have a s i g n i f i c a n t e f f e c t on pacing.) While the 'b'-section a l s o f e a t u r e s two phrases, t h e i r i n t e r n a l 4 In that the use and e f f e c t s of r e s t s concern rhythmic progression and r e c e s s i o n , they w i l l be examined i n the next s e c t i o n , on rhythmic design. 164 Example 68. L i n e - g r a p h r e p r e s e n t a t i o n of p i e c e No. 10. [j] = octave doubling I 'f p.d. = phrase divider I f«A = semitone or whole-tone coloration 165 | | i 166 s t r u c t u r e s a r e somewhat d i f f e r e n t from t h a t of t h e phrases o u t l i n e d above. For i n s t a n c e , t h e f i r s t p h rase i s comprised of o n l y two fragments and does not appear to c o n c l u d e w i t h a cadenza ( a t l e a s t not one which adheres s t r i c t l y t o t h e c h a r a c t e r i s t i c s o f p r e v i o u s c a d e n z a s ) . On c l o s e i n s p e c t i o n , :however, a b r i e f , d i s j u n c t fragment may be heard t o s e p a r a t e the two phrases ( l a b e l l e d "p.d." or "phrase d i v i d e r " on t h e g r a p h ) — o n e which, i n some r e s p e c t s , has a c o n s i d e r a b l y c l o s e r e l a t i o n s h i p t o p r e v i o u s cadenzas, p a r t i c u l a r l y t h e f i r s t one ( i . e . , measures 5-6). I t s reduced dynamics and l a c k o f d o u b l i n g s and c o l o r a t i o n s a r e f a c t o r s s p e c i f i c t o p r e v i o u s cadenzas and, a l t h o u g h i t o c c u r s as a d i s j u n c t fragment, i t s o r d e r o f PC u n f o l d i n g i s c l e a r l y s t e p w i s e : A^-G-G^, E ^ E - F . In f a c t , a p a r t from A^, t h e s e a r e t h e opening PC's of t h e f i r s t cadenza ( c f . b a r s 5-6 where A b e g i n s the cadenza). I t s d i s j u n c t s t r u c t u r e , however, d e n i e s i t t h e e x p l i c i t l i n e a r d i r e c t i v e q u a l i t y of p r e c e d i n g cadenzas, and t h e r e s t s which frame i t ^ i s o l a t e i t from s u r r o u n d i n g p h r a s e s . For t h e s e r e a s o n s i t may be c o n s i d e r e d a s e p a r a t e e n t i t y — a " d i v i d e r " — r a t h e r than an i n t e g r a l p a r t o f t h e phrase which precedes i t (as w i t h p r e v i o u s c a d e n z a s ) . The second phrase o f t h e ' b ' - s e c t i o n c o n t a i n s no such s u b d i v i s i o n s but, r a t h e r , i s one c o n t i n u o u s g e s t u r e c u l m i n a t i n g a t t h e end o f bar 15. F a c t o r s o f d o u b l i n g , c o l o r a t i o n , t e x t u r a l - d e n s i t y , r e g i s t e r , r h y t h m i c d e s i g n , and p i t c h o r g a n i z a t i o n ( a l l of which a r e d i s c u s s e d l a t e r ) ^The " r e s t " which f o l l o w s t h e b r i e f fragment i s a c t u a l l y i n t h e form of a b r e a t h mark (') o f which L i g e t i s t a t e s t h a t i t s d u r a t i o n i s t o be no more than a s i x t e e n t h - r e s t (*f ) . See Ten Pieces, p. 34. A sense of t e x t u r a l p r o g r e s s i o n might be c o n s i d e r e d t o a r i s e from t h e i n c r e a s i n g "urgency" o f t h e p h r a s e s ( i . e . , t h e tendency from a t e x t u r e o f m u l t i - f r a g m e n t e d p h r a s e s t o one of c o n t i n u i t y ) . 167 c o n t r i b u t e to the c h a r a c t e r i z a t i o n of the D-> i n bar 15 as a culmination p o i n t . The f i n a l cadenza i s t h e r e f o r e not considered i n t e g r a l to the second phrase but, r a t h e r , as a " p o s t - c a d e n t i a l extension." The phrases of the 'a'- s e c t i o n , then, are c o n s i s t e n t i n t h e i r s t r u c t u r e : three d i s j u n c t fragments plus an in t e g r a t e d cadenza. Those of the 'b'-section are co n s i s t e n t n e i t h e r among themselves nor w i t h those of the opening; r a t h e r , they are comprised of two and f i n a l l y one fragment, each without an int e g r a t e d cadenza. One common d e t a i l of t e x t u r a l design, however, concerns the employment of doublings and c o l o r a t i o n s . In the f i r s t phrase of each s e c t i o n semitone and whole-tone c o l o r a t i o n s f i g u r e most f r e q u e n t l y , whereas the second phrase of each i s marked by the use of octave doublings. These two modes of t e x t u r a l i n t e r a c t i o n are r e s p o n s i b l e f o r p a r t i c u l a r q u a l i t i e s of progression, to be d i s c l o s e d next. T e x t u r a l Progression as Manifest i n Density and S p a t i a l F l u c t u a t i o n s Because interdependent doublings and c o l o r a t i o n s are the on l y two modes of i n t e r a c t i o n between the bassoon and other instruments, they a l s o represent the only means of t e x t u r a l t h i c k e n i n g . Semitone and whole-tone c o l o r a t i o n s i n f l u e n c e s m a l l - s c a l e s p a t i a l f l u c t u a t i o n and, w i t h octave and unison doublings, a f f e c t the f l u c t u a t i o n of instrumentation-density (or simply the number of instruments sounding at any given time). Octave doublings themselves may be heard to a f f e c t o v e r a l l t e x t u r a l space, a more g l o b a l c o n s i d e r a t i o n . T e x t u r a l - d e n s i t y and t e x t u r a l space w i l l now be discussed i n greater d e t a i l . Textural-dens i t y R e f e r r i n g again to Example 68, instances of c o l o r a t i o n are bracketed (!) and the number of members i n each v e r t i c a l i t y c i r c l e d . 168 N o t i c e i n ph r a s e I o f t h e ' a ' - s e c t i o n t h a t c o l o r a t i o n s a r t i c u l a t e r e g i s t r a l l y h i g h e s t p o i n t s of t h e fragments, t h e f i r s t and l a s t h a v i n g t h r e e members and t h e m i d d l e ones, o n l y two.^ Phrase I I i s s i m i l a r i n t h a t h i g h p o i n t s a r e a c c e n t e d by c o l o r a t i o n s , each of which has two members. Phrase I of the ' b ' - s e c t i o n e x h i b i t s a mode of p r o g r e s s i o n i n i t s e x c l u s i v e use o f c o l o r a t i o n s . . S p e c i f i c a l l y , each of t h e f i r s t f o u r i n s t a n c e s c o n t a i n s two members ( i . e . , d i s t i n c t p i t c h e s ) w h i l e the c o l o r a t i o n marking the end of t h e phrase c o n t a i n s f o u r , t h e l a r g e s t g number heard i n t h e p i e c e . I n c o n s i d e r a t i o n of t h e a f o r e m e n t i o n e d i n s t a n c e s of c o l o r a t i o n , a l a r g e - s c a l e p r o g r e s s i o n towards p o i n t s of g r e a t e r d e n s i t y may be d i s c e r n e d . System (a) o f Example 69 i s a g r a p h i c r e p r e s e n t a t i o n of f l u c t u a t i n g c o l o r a t i o n - d e n s i t y (one mode of t e x t u r a l -d e n s i t y ) as d e f i n e d above, t h e g e n e r a l p r o g r e s s i v e d i r e c t i o n b e i n g d e p i c t e d by the arrow above t h e graph. Other modes of t e x t u r a l - d e n s i t y i n c l u d e f l u c t u a t i o n s i n t h e number of i n s t r u m e n t s i n v o l v e d i n o c c u r r e n c e s o f u n i s o n and o c t a v e d o u b l i n g . These a r e i n d i c a t e d on systems (b) and ( c ) , r e s p e c t i v e l y , on Example 69, the former p e a k i n g on t h e f o u r - p a r t u n i s o n on D~* i n bar 15. System (d) i l l u s t r a t e s i n s t r u m e n t a t i o n - d e n s i t y f l u c t u a t i o n , r e f e r r e d t o e a r l i e r . The c u l m i n a t i o n p o i n t h e r e i s a l s o i n measure 15. ^The number of members i n a g i v e n c o l o r a t i o n i n c l u d e s t h e bassoon p i t c h i t s e l f , g N o t i c e a l s o t h a t t h e end of phrase I i n t h e ' a ' - s e c t i o n i s a r t i c u l a t e d by a c o l o r a t i o n of t h r e e members, t h e l a r g e s t number he a r d to t h a t p o i n t . The harmonic q u a l i t y of t h e s e two v e r t i c a l i t i e s i s o f s i g n i f i c a n c e and w i l l be d i s c l o s e d l a t e r i n t h e c h a p t e r . 169 Example 69. Four modes o f t e x t u r a l - d e n s i t y f l u c t u a t i o n . instrumentation-density (octave) doubling-density (unison) doubling-density colorat ion-densi ty M M M i l l M i l l 1 1 1 1 1 / / \ 1 \ < J S \ 2. % — < 1 <, — » \ 4_ —< ( ^ —4 t / t x i - f -\ I \ \ l A Z. ^ \ , < • w p. Jo rt cn o co D" O (T> o CO 3 o o I—1 X) o rt- cu n rt n> o cn 3 J HI 4m -4 4W 4U • r a t e Ii-•4* •!1 7 \ IK. 5 171 T e x t u r a l space With r e f e r e n c e t o Example 68 once a g a i n (p. 165), t h e p i t c h c o n t e n t of each f o r m a l s e c t i o n i s "boxed" i n t o t h r e e groups ( t h e ' b ' - s e c t i o n 9 f e a t u r i n g a f o u r t h box a t the v e r y end). These r e p r e s e n t " s p a t i a l f i e l d s , " the temporal spans of which a r e r o u g h l y c o i n c i d e n t w i t h f o r m a l s u b d i v i s i o n s , e.g., phrases, cadenzas, e t c . Two d e t a i l s i n connect ion. ;with f l u c t u a t i o n s i n : t e x t u r a l space w i t h i n t h e ' a ' - s e c t i o n a r e noteworthy. F i r s t , t h e lower p i t c h boundary of t h e f i r s t two s p a t i a l f i e l d s i s B ^ l and, were i t not f o r o c t a v e d o u b l i n g s i n t h e second phrase, t h e upper boundary would i n c r e a s e by o n l y one semitone, e.g., from G//4 to A 4 . The o c t a v e d o u b l i n g s , however, extend t h e upper e x t r e m i t y to F#-* and i n an important sense p r o v i d e r e g i s t r a l p r e p a r a t i o n f o r t h e cadenza which f o l l o w s . Second, as c l e a r l y i n d i c a t e d on t h e graph, t h e o v e r a l l d i r e c t i o n o f r e g i s t r a l space (not j u s t r e g i s t e r ) i s one of a s c e n t . For example, not o n l y i s t h e end o f t h e 'a'-s e c t i o n i n a h i g h e r r e g i s t e r than i t s b e g i n n i n g , but the s p a t i a l f i e l d i s i t s e l f h i g h e r , e.g., compare B ^ - A ^ 4 i n t h e opening to A 4 - E ^ i n t h e f i n a l , cadenza. T h i s extreme s p a t i a l t r a v e r s a l , w i t h o u t r e t u r n to t h e opening r e g i s t e r , i s i t s e l f a f a c t o r of " i n c o m p l e t i o n " — a r e g i s t r a l l y a r t i c u l a t e d " h a l f - c a d e n c e . " A l t h o u g h o c t a v e d o u b l i n g s do not p r o v i d e r e g i s t r a l p r e p a r a t i o n f o r t h e f i n a l cadenza i n th e ' b ' - s e c t i o n , a s i m i l a r p a t t e r n o f ' s p a t i a l e x pansion and a s c e n t i s n e v e r t h e l e s s apparent. Here, t h e s p a t i a l boundary i s expanded i n b o t h d i r e c t i o n s i n t h e second f i e l d and i s f o l l o w e d by a c o n s i d e r a b l y narrower f i e l d as d e f i n e d by t h e c a d e n z a — a f i e l d which l i e s i n t h e 9 " S p a t i a l f i e l d s " a r e r e g i s t r a l spaces d e f i n e d by p i t c h e x t r e m i t i e s of p a r t i c u l a r f o r m a l s e c t i o n s o r , i n t h i s case, s u b d i v i s i o n s of such s e c t i o n s . 172 uppermost r e g i s t e r l i k e t h a t o f t h e f i n a l cadenza o f t h e ' a ' - s e c t i o n . ^ The o v e r a l l d i r e c t i o n of r e g i s t r a l space i s a g a i n one of a s c e n t . Two a d d i t i o n a l d e t a i l s r e g a r d i n g t e x t u r a l space i n t h e ' b ' - s e c t i o n a r e worth n o t i n g . One i s t h e minimal, y e t important e x p a n s i o n i n o v e r a l l space from t h e 'a' to 'b'"1 ^ s e c t i o n . The d o t t e d l i n e — c o n n e c t i n g t h e m i d d l e s p a t i a l f i e l d s of each s e c t i o n e x h i b i t s t h i s a s c e n t from F#-* t o A//^  ( t h e lower boundary r e m a i n i n g B^) . The o t h e r i s a s u b t l e r e c o l l e c t i o n o f t h e o p e n i n g r e g i s t e r e f f e c t e d by t h e bassoon's f i n a 1 C# 2 ( t h e f o u r t h ' s p a t i a l box i n t h e ' b ' - s e c t i o n ) . A l t h o u g h t h e r e l a t i v e l y s t a t i c s p a t i a l f i e l d and abrupt t e r m i n a t i o n of t h e f i n a l cadenza may be viewed as f a c t o r s o f "openness," t h i s b r i e f r e g i s t r a l a l l u s i o n would seem to denote c l o s u r e w i t h i n t h e r e a l m o f t e x t u r a l space and r e g i s t r a l traversal."''"'' Summary D i s j u n c t fragments i n t h e bassoon accompanied by s p o r a d i c o c t a v e and u n i s o n d o u b l i n g s , and semitone and whole-tone c o l o r a t i o n s i n t h e r e m a i n i n g i n s t r u m e n t s were s a i d to d e f i n e one t e x t u r a l element i n t h e t e n t h p i e c e . Conjunct, c a d e n z a - l i k e passages (without d o u b l i n g s and c o l o r a t i o n s ) and extended p e r i o d s o f s i l e n c e were no t e d as b e i n g two a d d i t i o n a l t e x t u r a l arrangements. C o l o r a t i o n - d e n s i t y , as w e l l a s ^ t h a t of u n i s o n and o c t a v e d o u b l i n g , were s a i d to d e f i n e s p e c i f i c i m o d e s of t e x t u r a l - d e n s i t y r e v e a l i n g p r o g r e s s i v e i n t e n s i f i c a t i o n towards s p e c i f i c p o i n t s i n t h e p i e c e . ^ C o n c e r n i n g t h e s e two cadenzas, i t i s i n t e r e s t i n g t h a t t h e p a t t e r n of s p a t i a l d e f i n i t i o n i n measures 9-11 i s one o f t a p e r e d c o n t r a c t i o n , w h i l e t h a t of b a r s 16-19 i s e x t r e m e l y s t a t i c . A l t h o u g h g e n e r a l l y apparent on t h e graph, t h e r h y t h m i c a c t i v i t y of t h e s e cadenzas w i l l l a t e r be shown to complement t h e s e p a t t e r n s . o f s p a t i a l f l u c t u a t i o n . ^ I n terms of l i n e a r p i t c h o r g a n i z a t i o n , a d d i t i o n a l r e i n f o r c e m e n t f o r t h e a s s e r t i o n o f openness i s o f f e r e d ; d e t a i l s appear l a t e r i n t h e c h a p t e r . 173 Instrumentation-density, a f o u r t h mode, was s a i d to take i n t o account a l l types of instrument i n t e r a c t i o n be i t i n the form of doubling or c o l o r a t i o n . A climax on i n measure 15 was noted w i t h respect to t h i s aspect of t e x t u r a l - d e n s i t y . F i n a l l y , t e x t u r a l space, a f f e c t e d by octave doublings i n p a r t i c u l a r , was a l s o shown to r e v e a l patterns of d i r e c t i o n and expansion throughout the piece. P r i n c i p l e s of Rhythmic and M e t r i c Design In viewing the rhythmic and metric design of piece No. 10 three p r i n c i p l e s w i l l be discussed: the f u n c t i o n of notated b a r l i n e s and t h e i r r o l e i n a r r i v a l point d e f i n i t i o n , impulse-number proportions of phrase fragments, and d i r e c t e d patterns of impulse-density f l u c t u a t i o n . In c o n s i d e r i n g the f i r s t of these, i t has been asse r t e d throughout t h i s paper that notated b a r l i n e s are l a r g e l y f o r ease of r e a d i n g — a convenience of n o t a t i o n a l o r g a n i z a t i o n r a t h e r than an i n d i c a t o r of accent-defined m e t r i c u n i t s . I t was a l s o noted i n Chapter I I that notated b a r l i n e s i n s o l o i s t i c pieces of the quintet o c c a s i o n a l l y appear to be placed i n order to mark 12 s p e c i f i c a r r i v a l p o i n t s . The tenth piece i s c o n s i s t e n t w i t h the f i r s t of these a s s e r t i o n s ; i t a l s o f e a t u r e s a c l e a r l y f e l t a r r i v a l p o i n t , but one which i s independent of the demarcation of notated b a r l i n e s . The D^  on the f i n a l sixteenth-note of measure 15 i s the j u n c t u r e i n question and i s , as noted e a r l i e r , the climax point f o r (unison) doubling-density (e.g., the f o u r - p a r t unison) and instrumentation-density (e.g., a l l f i v e instruments sound at once). As w i l l be explained l a t e r , l i n e a r c o n t i n u i t i e s a l s o culminate at t h i s point and i m p l i c a t i o n s of PC c e n t r i c i t y (on D) are r e a l i z e d here. I t i s c l e a r l y (and audibly) the " s t r u c t u r a l " a r r i v a l point of the 12 In these i n s t a n c e s , "downbeats" were defined as to parameters other than accent-delineated metric patterns. 174 e n t i r e p i e c e and, y e t , t h e b a r l i n e i s i n d i c a t e d j u s t a f t e r i t . The c l a r i n e t p o r t i o n of t h e cadenza commencing i n bar 16 has t h e e f f e c t o f an " a f t e r b e a t " r e l a t i v e t o t h e p r e c e d i n g , h i g h l y exposed a r r i v a l on D-*. Given t h i s a p p a r e n t l y c o n t r a d i c t o r y b a r l i n e ( a l t h o u g h i t i s n o t p e r c e p t i b l e as such) t h e performer, may t r e a t t h e a r r i v a l on D d i f f e r e n t l y from a s i t u a t i o n where t h e downbeat o c c u r s i n a c c o r d a n c e w i t h t h e c o n v e n t i o n a l a s s o c i a t i o n , t h a t i s , immediately a f t e r t h e b a r l i n e . While a p r e c i s e c h a r a c t e r i z a t i o n o f such a " t r e a t m e n t " i s d i f f i c u l t , a f e e l i n g of " i n c o m p l e t e n e s s " or " i n c o n c l u s i v e n e s s " i s l i k e l y t o accompany t h e a r r i v a l on D — a f e e l i n g which t h e performer may, i n f a c t , convey to the l i s t e n e r . 13 The r e s u l t i n g t e n s i o n i s d i s s i p a t e d , a l t h o u g h n o t c o m p l e t e l y , i n t h e e n s u i n g cadenza. Impulse-number p r o p o r t i o n s of phrase fragments i s the second p r i n c i p l e o f r h y t h m i c d e s i g n to be d i s c u s s e d and, i n t h a t a l l i n s t r u m e n t i n t e r a c t i o n i s i n t h e form o f i n t e r d e p e n d e n t d o u b l i n g and c o l o r a t i o n , t h e r h y t h m i c p a c i n g of t h e p i e c e i s e s s e n t i a l l y d i c t a t e d by t h a t of t h e bassoon p a r t i t s e l f . Example 70 c o n s i s t s of an i m p u l s e - d e n s i t y graph w i t h impulse-number p r o p o r t i o n s o £ phrase segments i n d i c a t e d above the graph, and two l e v e l s of p r o g r e s s i o n and r e c e s s i o n d e p i c t e d below. Regarding impulse-number p r o p o r t i o n s ( i . e . , t h e t o t a l number of impulses 14 and " a c t i v e " b e a t s i n each segment), d i s j u n c t p o r t i o n s o f t h e ' a ' - s e c t i o n 13 The r h y t h m i c " s t e a d i n e s s " o f t h e cadenza ( t o be commented on l a t e r ) and abrupt t e r m i n a t i o n of a c t i v i t y ( a l l u d e d to e a r l i e r ) r e s u l t i n t h e r e t e n t i o n o f a c e r t a i n degree of i n t e n s i t y . My own v i e w i s t h a t o n l y a f t e r t h e p i e c e i s a c t u a l l y f i n i s h e d i s t h e i n t e n s i t y f u l l y d i s s i p a t e d . 14 The l a r g e u n i t s of s i l e n c e have n o t been i n c l u d e d i n t h e impulse c a l c u l a t i o n of a c t i v e b e a t s . A l s o , because o f the r h y t h m i c i n t e r d e p e n d e n c e of the d o u b l i n g s and c o l o r a t i o n s , t h e y have not been counted as s e p a r a t e i m p u l s e s . 175 Example 70. Impulse-number p r o p o r t i o n s of phrase fragments and i m p u l s e - d e n s i t y graph. 176 177 and t h e f i r s t cadenza (measures 5-6) a r e r e l a t i v e l y b a l a n c e d . T h e s i x a c t i v e b e a t s of t h e f i r s t phrase, however, occur o v e r seventeen b e a t s of a c t u a l time, t h e t h r e e d i s j u n c t fragments b e i n g s e p a r a t e d by l a r g e p e r i o d s of s i l e n c e . A " t e n t a t i v e " q u a l i t y r e s u l t s — o n e which i s r e p l a c e d by a sense of d r i v e and urgency i n subsequent phrases where d i s j u n c t fragments a r e s e p a r a t e d by a s i x t e e n t h - r e s t a t most. These two t e n d e n c i e s a r e r e i n f o r c e d by t h e r h y t h m i c s t r u c t u r e o f each s e c t i o n ' s f i n a l cadenza. In b a r s 8-11, f o r example, a s t e a d y d e c l i n e i n r h y t h m i c a c t i v i t y c r e a t e s a " h e s i t a n t " ambiance, r e i n f o r c e d by the seemingly " r e l u c t a n t " p i t c h d e p a r t u r e to i n bar 11 ( p i c c o l o ) . ^ The ' b ' - s e c t i o n ' s cadenza, on t h e o t h e r hand, e x h i b i t s a s t e a d y r h y t h m i c d r i v e matching t h a t o f t h e p r e c e d i n g two p h r a s e s . The extended l e n g t h s of t h e cadenzas i n measures '7-11 and 16-22 ( i . e . , "extended" r e l a t i v e to t h e d i s j u n c t p o r t i o n s and cadenza i n b a r s 5-6) may be viewed as f u n c t i o n a l n e c e s s i t i e s . The " p r e s s i n g f o r w a r d " o f t h e ' a ' - s e c t i o n ' s second phrase g e n e r a t e s c o n s i d e r a b l y more momentum than i t s f i r s t p h rase and t h e r e f o r e r e q u i r e s a g r e a t e r "wind-down" p e r i o d f o r t h e d i s s i p a t i o n o f energy. In a d d i t i o n t o t h i s , i t not o n l y c o n c l u d e s t h e second phrase but p u n c t u a t e s t h e end o f t h e ' a ' - s e c t i o n as a whole. Conc e r n i n g t h e f i n a l cadenza o f t h e p i e c e , t h e c o n t i n u a t i o n of r h y t h m i c a c t i v i t y i n bar 16 and s u s t a i n e d c o n n e c t i n g bar 15 to 16 a r e f a c t o r s which suggest t h a t i t o p e r a t e s w i t h i n o r at t h e l e v e l of t h e "''"'Regarding t h e cadenza i n b a r s 8-11, t h e bassoon p o r t i o n ( c u r i o u s l y t h a t which i s r h y t h m i c a l l y i d e n t i c a l to t h e f i r s t cadenza, i . e . , | | | n | F^ | | s | | ] | | | | | 3I J ) i s a l s o r o u g h l y b a l a n c e d w i t h t h e o t h e r phrase p o r t i o n s . 16 T h i s p a r t i c u l a r p i t c h d e p a r t u r e marks an important p o i n t i n t h e s t r u c t u r e o f l i n e a r p i t c h o r g a n i z a t i o n , one which w i l l be exposed l a t e r i n the c h a p t e r . 178 ' b ' - s e c t i o n . On t h e o t h e r hand, i t s " p o s t - c a d e n t i a l " q u a l i t y n o t e d e a r l i e r , and extended l e n g t h (e.g., l o n g e r than t h e p r e c e d i n g p o r t i o n of t h e 'b'-s e c t i o n ) suggest t h a t i t a l s o o p e r a t e s a t a h i g h e r l e v e l , p u n c t u a t i n g t h e end of t h e p i e c e as a whole. The i n a c t i v i t y o f b a r s 19-21 may be heard as a ( p a r t i a l ) "wind-down" p e r i o d f o r t h e r h y t h m i c energy of t h e opening of t h e cadenza, the ' b ' - s e c t i o n , and on a s t i l l l a r g e r s c a l e , f o r t h e e n t i r e p i e c e . In c o n s i d e r a t i o n o f t h e i m p u l s e - d e n s i t y graph, t h e a p p a r e n t l y " b a l a n c e d " p hrase fragments d i s c u s s e d above ( i . e . , b a l a n c e d i n r e l a t i v e numbers of i m p u l s e s , i r r e s p e c t i v e o f r h y t h m i c c o n f i g u r a t i o n s ) r e v e a l p r o g r e s s i v e and r e c e s s i v e t e n d e n c i e s a l r e a d y a l l u d e d t o . As suggested i n l e v e l (a) below t h e graph i n Example 70, phrase fragments of t h e ' a ' - s e c t i o n e x h i b i t b r i e f r h y t h m i c p r o g r e s s i o n s , growing i n i n t e n s i t y and c u l m i n a t i n g a t the b e g i n n i n g o f t h e cadenza i n measures 7-8. The cadenza then e f f e c t s a d e f i n i t e r h y t h m i c r e c e s s i o n to bar 11. The ' b ' - s e c t i o n as d e p i c t e d i n l e v e l (a) r e v e a l s l i t t l e i n t h e way of r h y t h m i c p r o g r e s s i o n ; a s l i g h t i n t e n s i f i c a t i o n towards t h e a r r i v a l on D a t t h e end of bar 15 may, however, be d i s c e r n e d . L e v e l (b) i l l u s t r a t e s o v e r a l l p a t t e r n s of r h y t h m i c d i r e c t i o n , t h e ' a ' - s e c t i o n r e v e a l i n g a p r o g r e s s i v e u n i t f o l l o w e d by a r e c e s s i v e one, and t h e ' b ' - s e c t i o n e x h i b i t i n g a r e l a t i v e l y c o n s i s t e n t l e v e l of a c t i v i t y , t h e r e c e s s i o n o f which o c c u r s i m p l i c a t i v e l y t h r o u g h t h e i n a c t i v i t y of b a r s 19-21. Summary A l t h o u g h b a r l i n e - s u g g e s t e d downbeats ( l i k e t h o s e found i n o t h e r s o l o i s t i c p i e c e s ) a r e e s s e n t i a l l y n o n - e x i s t e n t i n t h e t e n t h p i e c e , t h e i n bar 15 emerges as a s t r u c t u r a l a r r i v a l p o i n t exposed t h r o u g h t e x t u r a l -d e n s i t y . An a p p a r e n t l y c o n t r a d i c t o r y b a r l i n e was n o t e d at t h i s p o i n t . In 179 a d d i t i o n t o t h i s a s p e c t o f rhythm, impulse-number p r o p o r t i o n s of p hrase fragments were found to be a p p r o x i m a t e l y b a l a n c e d , and t h e i r r h y t h m i c c o n f i g u r a t i o n s , d i r e c t e d . Regarding the l a t t e r , t h e ' a ' - s e c t i o n was d e p i c t e d as a r h y t h m i c p r o g r e s s i o n f o l l o w e d by a r e c e s s i o n , w h i l e the ' b ' - s e c t i o n e x h i b i t e d a r e l a t i v e l y s t e a d y l e v e l of a c t i v i t y , t h e "wind-down" p e r i o d o f which o c c u r s i n th e i n a c t i v i t y of t h e f i n a l measures. Modes of P i t c h O r g a n i z a t i o n L i n e a r D e t a i l s In p r e v i o u s c h a p t e r s we have o b s e r v e d l i n e a r e v e n t s s t r u c t u r e d i n a number o f d i f f e r e n t ways. In No. 2, f o r example, p i t c h e x t r e m i t i e s of s u c c e s s i v e a r p e g g i a t i o n s were found to r e v e a l s p e c i f i c l i n e a r i z a t i o n s w h i l e i n No. 4, two-note o s c i l l a t i o n s e x h i b i t e d a comparable s i g n i f i c a n c e . Other f a c t o r s such as dynamic exposure (No. 7 ) , and u n i s o n t r a n s f e r (No. 3) were a l s o shown t o g e n e r a t e s t e p w i s e l i n e a r c o n n e c t i o n s of r e l a t i v e s i g n i f i c a n c e . And i n No. 1, o u t e r - v o i c e p r o l o n g a t i o n and l a t e r a l v o i c e c r o s s i n g p r o v i d e d support f o r t h e maintenance o f p i t c h e x t r e m i t i e s i n a complete f o r m a l s e c t i o n t h u s r e v e a l i n g an a s p e c t of l a r g e - s c a l e p i t c h o r g a n i z a t i o n . Because of the t e x t u r a l primacy of t h e h i g h l y d i s j u n c t bassoon p a r t and s u b o r d i n a t e r o l e o f t h e o t h e r i n s t r u m e n t s , t h i s s t u d y of l i n e a r o r g a n i z a t i o n i n t h e t e n t h p i e c e w i l l f o c u s on r e g i s t r a l c o n n e c t i o n s i n t h e bassoon p a r t i t s e l f . A second mode o f l i n e a r o r g a n i z a t i o n , PC u n f o l d i n g , w i l l t a k e i n t o account semitone and whole-tone c o l o r a t i o n s p r o v i d e d by t h e oboe, c l a r i n e t , and horn. L i n e a r r e g i s t r a l c o n n e c t i o n s In t h e l i g h t of t h e bassoon's h i g h l y d i s j u n c t s t r u c t u r e , a l l u d e d to 180 above, i t may r e a d i l y be perceived as " m u l t i - v o i c e d . " ^ S p e c i f i c a l l y , p i t c h e s may be heard to form stepwise c o n t i n u i t i e s u n f o l d i n g i n four r e g i s t e r s simultaneously: i , and i v , • ^  . The j u s t i f i c a t i o n f o r these r e g i s t r a l designations i n v o l v e s m o t i v i c c o n s i d e r a t i o n s — a n aspect to be explained more f u l l y l a t e r i n the chapter. I t s r o l e i n r e g i s t r a l d e f i n i t i o n , however, i s i l l u s t r a t e d i n the f i r s t eight notes of the bassoon part as shown i n Example 71. The top s t a f f c o n s i s t s of the p i t c h e s as they occur i n the score; each of the lower staves r e v e a l s a four-note motive, the lowest p i t c h of each i n i t i a t e s one of the four r e g i s t e r s noted above. Example 71. M o t i v i c d e f i n i t i o n of r e g i s t e r s i and i i . The same four-note motive i n the next octave ( i . e . , B ^ to D^4) occurs over a much longer span, but f a i l s to continue to D 4 at any point ^ I n t h i s sense l i n e a r o r g a n i z a t i o n here i s not completely u n l i k e that found i n the second and f o u r t h p i e c e s . 181 18 i n the piece. R e g i s t e r i i i t h e r e f o r e c o n s i s t s of only the four-note motive i t s e l f . The r e g i s t r a l l y " i s o l a t e d " E^ 4 then i n i t i a t e s r e g i s t e r i v (T 19 which continues up to E J by measure 11. The reader i s now r e f e r r e d to Example 72 i n which a l l of the bassoon pi t c h e s are i n d i c a t e d on the bottom four staves of system (a) (corresponding to the four r e g i s t e r s defined above). The top two staves show the doublings and c o l o r a t i o n s provided by the other instruments. (The l a t t e r are stemmed down to the appropriate bassoon notes.) System (b) shows the r e l a t i v e l y foreground l e v e l of p i t c h o r g a n i z a t i o n i n which the f u n c t i o n s of a l l p i t c h e s i n the bassoon part are designated. ( N o t a t i o n a l symbols are i n d i c a t e d to the l e f t of Example 72.) While l i n e a r progressions and prolongations on systems (b) and (c) are s t r a i g h t f o r w a r d , s e v e r a l f a c t o r s of p i t c h exposure are noteworthy. For example, c e r t a i n rhythmic d e t a i l s serve to h i g h l i g h t s t r u c t u r a l p i t c h e s of l i n e a r progressions, p a r t i c u l a r l y the ascending f o u r t h , E^ 4 to A^ 4 (bars 3-5); here, each p i t c h of the ascent i s preceded by a r e s t . In the case of A^ 4 a delay of progression replaces the r e s t . I t s approach, i n f a c t , i s r h y t h m i c a l l y s i m i l a r to that of F# 4 i n bar 3 ( c f . " f j ^ and | | | | | ). 3 3 In a d d i t i o n to t h i s rhythmic d e t a i l and the more obvious d i s j u n c t approach and r e g i s t r a l exposure, three of the four p i t c h e s are punctuated by a c o l o r a t i o n i n one of the remaining instruments. (The harmonic i m p l i c a t i o n s ^ I n r e g i s t e r s i and i i the four-note motive continues up to D 2 and and e v e n t u a l l y up to A 2 and A^, r e s p e c t i v e l y . The d e n i a l of D 4 m r e g i s t e r i i i i s the main f a c t o r of separation between r e g i s t e r s i i i and i v . The PC D, i n f a c t , w i l l be shown to have s t r u c t u r a l s i g n i f i c a n c e i n t h i s piece as i t d i d i n Nos. 1, 4, 5, and 6. 19 be: While the bassoon extends up to E^-5 o n l y , the p i c c o l o notes i n bars 10 and 11 are considered to f u n c t i o n i n the l i n e a r connection and r e g i s t r a l extension up to E^; they are thus a c o n t i n u a t i o n of the bassoon's cadenza, not simply doublings or c o l o r a t i o n s . 182 Example 72. F i r s t and second l e v e l s of l i n e a r p i t c h s t r u c t u r e . primary linear progression (see text for criteria of "primary" designation) = less exposed linear progression prolongation of a particular pitch (neighbours stemmed to beam, embellishing patterns to slur) pitch in parentheses is "relocated" for interpretation of a linear progression "secondary" prolongation (see text for criteria of "secondary" designation) denotes "reinterpretation" of the second pitch (see text for details) 184 of t h e s e c o l o r a t i o n s w i l l be c o n s i d e r e d l a t e r . ) Each of t h r e e o t h e r s t r u c t u r a l p i t c h e s i n t h i s r e g i s t e r i s approached by a r e s t : t h e r e -e s t a b l i s h e d A ^ i n bar 7 (which proceeds almost immediately t o A^) , A ^ which b e g i n s t h e ' b ' - s e c t i o n (preceded by t h e generalpause of bar 12), and A^ two b e a t s l a t e r ( t h i s p i t c h i n i t i a t i n g t h e a s c e n d i n g f o u r t h t o i n measure 15). With r e f e r e n c e to system ( c ) , t h r e e d e t a i l s a r e noteworthy. F i r s t , t h e i n i t i a l a s c e n d i n g p r o g r e s s i o n , E ^ t o A ^ , i s c o u n t e r b a l a n c e d i n t h e ' b ' - s e c t i o n w i t h t h e descent from A ^ to ^ (measures 13-15). The e v e n t u a l c o n t i n u a t i o n o f t h e i n i t i a l a s c e n t up to E^ i s a l s o m i r r o r e d , t h i s time i n t h e f i n a l cadenza's r e i t e r a t i o n o f E \ A second d e t a i l c o n c e r n s t h e c o n t i n u a t i o n up to E^ j u s t mentioned and i n v o l v e s t h e "wave-s l u r " ( " " " ~ N s « * ' ) . At t h e second l e v e l £i.e., system ( c ) ] , t h e r e - e s t a b l i s h e d A ^ (bar 7) i s r e i n t e r p r e t e d ^ and e n h a r m o n i c a l l y n o t a t e d (as G#) to d e p i c t i t s s t a t u s as a p a s s i n g - t o n e t o A^. The same s i t u a t i o n a r i s e s i n b a r s 10-11 . 21 where t h e r e i t e r a t e d E -> i s u l t i m a t e l y r e i n t e r p r e t e d and e n h a r m o n i c a l l y n o t a t e d (as D#) to suggest i t s p a s s i n g - t o n e q u a l i t y t o E^. Through t h i s h i g h e r - l e v e l p a t t e r n o f r e i n t e r p r e t a t i o n b r i e f p r o g r e s s i o n s a r e connected to form a more comprehensive l i n e a r event. The t h i r d d e t a i l of s i g n i f i c a n c e i n t h e l i n e a r p i t c h s t r u c t u r e p e r t a i n s t o t h e apparent tendency towards t h e PC D. The i n i t i a l f o u r - n o t e motive, B^-B-C-D^, f o r example, e x h i b i t s i n c l i n a t i o n t o D, r e a l i z e d i n 20 That i s , i t i s r e i n t e r p r e t e d from i t s i n i t i a l o c c u r r e n c e where i t f u n c t i o n s as a g o a l o f motion. 21 \lK The i n i t i a l E9-3 a l s o s t a n d s as a l o c a l a r r i v a l p o i n t , i . e . , t h e g o a l o f motion o f t h e a s c e n t from A^ i n bar 7. 1 8 5 o 2 2 r e g i s t e r i i where D J i s reached i n bar 3 and prolonged u n t i l bar 1 5 . In r e g i s t e r s i and i i i , however, the motive c o n t i n u a l l y f a l l s short of i t s r e s p e c t i v e D, hence the passing-tone designation of C# 4 and C#2 i n measures 1 5 and 2 1 r e s p e c t i v e l y £see system ( c ) ] . Systems (a) and (b) of Example 7 3 represent t h i r d and f o u r t h l e v e l s of l i n e a r s t r u c t u r e . Each r e v e a l s the f i v e e s s e n t i a l l i n e a r progressions i n the piece, the highest, most encompassing l e v e l o m i t t i n g the i n i t i a l octave ascent from E^ 4 to E^ 5 ancl f o u r t h progression, E^ 4 to A'' 4 to E^ 4. In short, E^ 5 a n a ; E^-are considered j o i n t l y as an incomplete major-minor 2 3 IF upper neighbour to (to which i t moves i n bar 1 5 ) . E' 4 and E 4 , a l s o an incomplete major-minor upper neighbour, do not however.move to D4. Concerning r e g i s t e r s i , i i , and i i i — p r e d o m i n a n t l y u n f o l d i n g s of the f o u r -note motive, B^-B-C-D^—only i n r e g i s t e r i i i s the motive continued to D; the others, as noted above, are l e f t "hanging." One f i n a l aspect of l i n e a r p i t c h o r g a n i z a t i o n concerns m o t i v i c s t r u c t u r e , a l r e a d y discussed to some extent. Example 7 4 i l l u s t r a t e s occurrences of the four-note motive (the notes of which are beamed) i n r e g i s t e r s i , i i , and i i i . Apart from overlapping occurrences of the p a t t e r n i n r e g i s t e r i , i t i s i n t e r e s t i n g to note the i n t e r a c t i o n between m o t i v i c s t r u c t u r e s as such, and " a n t i c i p a t e d c l o s u r e " on the PC D (a tendency inherent i n the motive i t s e l f ) . In r e g i s t e r i i i the second of 2 2 System (b) r e v e a l s the s t r u c t u r a l d e t a i l s of the prolongation: upper neighbour (bars 3 - 5 ) , e m b e l l i s h i n g p a t t e r n (bars 6 - 7 ) , and f i n a l l y a descending l i n e a r approach from A^ (bars 1 3 - 1 5 ) . 2 3 As was noted e a r l i e r , t h i s c u l m i n a t i o n point i s a l s o the climax of instrumentation-density ( i . e . , i t i s the o n l y point where a l l f i v e instruments sound at once) and (unison) doubling-density ( i . e . , i t i s the o n l y PC doubled i n four p a r t s ) . The C / /5 which accompanies i t w i l l be deal t w i t h i n the s e c t i o n on harmonic d e t a i l s . 186 Example 73. T h i r d and f o u r t h l e v e l s of l i n e a r p i t c h s t r u c t u r e . mm. 1 3 7 8 11 13 15 16-18 21 immuri 00 188 Example 74. M o t i v i c o r g a n i z a t i o n i n r e g i s t e r s i , i i , and i i i . two o c c u r r e n c e s of t h e m o t i v e i s complete i n a m o t i v i c sense (e.g., i t c o n t a i n s no B^) and a l s o i n terms of PC c l o s u r e (e.g., i t does not c o n t i n u e to D). R e g i s t e r i i i s unique i n t h a t t h e motive o c c u r s o n l y once and does extend to D 3 whereupon t h e l a t t e r i s p r o l o n g e d ; i t i s t h e r e f o r e complete i n b o t h r e s p e c t s . F i n a l l y , r e g i s t e r i , m o t i v i c a l l y t h e most a c t i v e , i s " c l o s e d " w i t h r e s p e c t to m o t i v i c s t r u c t u r e ( t h e f i n a l C# b e i n g the f o u r t h PC of t h e p a t t e r n ) but open i n terms of PC c l o s u r e ( i . e . , i n t h e sense of a D - c e n t r i c i t y ) . PC u n f o l d i n g Apart from modes of l i n e a r i z a t i o n i n v o l v i n g p i t c h and/or PC c o n n e c t i o n s , p a t t e r n s of PC u n f o l d i n g — s p e c i f i c a l l y , t w e l v e - n o t e o r d e r i n g s — were a l s o noted i n Chapter I I . W h i l e such p a t t e r n s a r e not as c o n s i s t e n t l y a p p l i e d i n t h e t e n t h p i e c e as, say, t h e f i f t h , No. 10 does e x h i b i t a p a r t i c u l a r mode of PC u n f o l d i n g . Example 75 c o n s i s t s o f t h r e e s t a v e s 189 24 r e p r e s e n t i n g c o l o r a t i o n PC's, bassoon PC's, and t o t a l PC c o n t e n t . Segments c o r r e s p o n d i n g to d i s j u n c t fragments, cadenzas, e t c . , e s t a b l i s h e d e a r l i e r , a r e numbered f o r ease of r e f e r e n c e . One immediate o b s e r v a t i o n o f importance c o n c e r n s t h e c h r o m a t i c or 25 n e a r - c h r o m a t i c t o t a l PC c o n t e n t i n each segment. O f t e n t h e PC c o n t e n t of a whole fragment u n f o l d s ( i n t h e p i e c e ) i n a c h r o m a t i c or n e a r - c h r o m a t i c f a s h i o n , i n which case t h e "normal form" o r d e r i n g of t o t a l c o n t e n t ( i . e . , t h e t h i r d s t a f f o f Example 75) resembles t h a t o f t h e bassoon p a r t and c o l o r a t i o n s ( i . e . , t h e top two s t a v e s o f Example 75). Segments 1, 4, 5, 8, 9, and 13 r e v e a l t h i s r e l a t i o n s h i p . O t h e r s e x h i b i t s e v e r a l s m a l l e r 2 6 c h r o m a t i c " s u b s e t s " which, when c o n s i d e r e d j o i n t l y and o r g a n i z e d i n t o normal form, a g a i n g i v e r i s e t o c h r o m a t i c p a t t e r n s , e.g., segments 2, 6, 10, 11, and 12. The p a t t e r n s of u n f o l d i n g i n segments 3 and 7 r e v e a l l i t t l e i n t h e way of s t e p w i s e PC c o n n e c t i o n s , y e t t h e normal form o r d e r i n g of t h e i r r e s p e c t i v e t o t a l c o n t e n t s s t i l l d i s p l a y a n e a r - c h r o m a t i c PC l i n e a r i z a t i o n . 24 Concerning t h e t h i r d s t a f f , t o t a l PC c o n t e n t of each segment i s a r r a n g e d i n "normal form" i n t h e d i r e c t i o n i n d i c a t i v e o f t h e a c t u a l p i t c h u n f o l d i n g i n t h e music. That i s , i n a l l segments but nos. 4, 9, 11, and 13 PC's a r e o r d e r e d i n an a s c e n d i n g p a t t e r n w i t h t h e s m a l l e s t i n t e r v a l s to t h e l e f t . The o t h e r f o u r segments a r e " r e v e r s e d " v e r s i o n s of t h e normal form o r d e r i n g , i . e . , d e s c e n d i n g from l e f t t o r i g h t w i t h t h e s m a l l e s t i n t e r v a l s t o t h e r i g h t , a g a i n a r r a n g e d to r e f l e c t t h e d i r e c t i o n o f u n f o l d i n g i n t h e a c t u a l music. 25 Segments w i t h more than seven PC's w i l l n a t u r a l l y r e v e a l s t e p w i s e o r d e r i n g s . S m a l l e r s e t s , however, s t i l l e x h i b i t p r e d o m i n a n t l y c h r o m a t i c u n f o l d i n g s r a t h e r than c o l l e c t i o n s i n v o l v i n g numerous whole-tones and s m a l l l e a p s . 2 6 A " s u b s e t " i n t h i s c o n t e x t r e f e r s t o a group of p i t c h e s ( w i t h i n a segment) which u n f o l d i n a c h r o m a t i c f a s h i o n i n t h e p i e c e . I n segment No. 2 f o r example, two s u b s e t s may be d i s c e r n e d : D^^ down c h r o m a t i c a l l y t o A ^ S and up to F#3 ( t h e F b e i n g a n o t e of c o l o r a t i o n ) . (See s t a v e s i and i i . ) When t h e s e two s u b s e t s a r e c o n j o i n e d and a r r a n g e d i n t o normal form, a l l PC's except G a r e p r e s e n t . 190 Example 75. PC c o n t e n t o f f o r m a l segments. \9\ m e a s u r e : 1 s e g m e n t : 1 ' a ' - s e c t i o n -d is junc t f r a g m e n t s c a d e n z a phrase I 1 d i s j u n c t f ragments phrase I I c a d e n z a b ' - s e c t i o n ^ d i s j u n c t f r a g m e n t s - ^ p h r a s e I p h r a s e d i v i d e r d i s j . f r . p h r a s e H c a d e n z a i • co lorat ion p-c 's ii = bsn . p - c ' s iii= t o t a l p - c c o n t e n t 192 In a d d i t i o n to the c h a r a c t e r i s t i c of chromatic o r d e r i n g , PC content i s i t s e l f an important aspect of l i n e a r o r g a n i z a t i o n . I t i s , i n f a c t , r e s p o n s i b l e f o r s p e c i f i c r e l a t i o n s h i p s between contiguous and non-contiguous s e g m e n t s — r e l a t i o n s h i p s such as expansion, i n c l u s i o n , o v e r l a p p i n g , and twelve-note aggregate completion. Segment no. 1, f o r example, i s embedded in t o the expanded no. 2, the l a t t e r c o n t a i n i n g a l l PC's except G. While the normal form ordering of the t h i r d segment overlaps that of the second (e.g., F and F#), the f i r s t a r t i c u l a t e d PC i n no. 3 ( i . e . , i n the a c t u a l music) i s G, thus completing the twelve-note aggregate i n i t i a t e d i n no. 2. (The square bracket from no. 2 to no. 3 i n Example 75 i l l u s t r a t e s t h i s completion.) Segment no. 3 omits A and A#, A being the f i r s t and highest p i t c h of no. 4, and A//, the lowest. Segment no. 4 a l s o contains a l l PC's except one, t h i s time G#. I n t e r e s t i n g l y G# i n no. 3 i s the r e g i s t r a l 27 high point of the i n i t i a l ascending f o u r t h progression exposed e a r l i e r . The second phrase of the 'a'-section opens w i t h a t r a n s p o s i t i o n of •T+3 j -the f i r s t segment of phrase I : e.g., m* x 1 15" Segments 5 and 6 overlap and j o i n t l y i n c l u d e a l l PC's except A* and C— the f i r s t two a r t i c u l a t e d i n segment no. 7. This second overlapping completion of the t o t a l aggregate i s a l s o i n d i c a t e d i n Example 75 by a square bracket. Each phrase of the 'a'-section e x h i b i t s a near-completion of the twelve-note aggregate i n i t s opening two segments. The missing  p i t c h ( e s ) i s (are) furnis h e d by the " a r t i c u l a t e d " opening of the t h i r d  segment i n each case ( i . e . , nos. 3 and 7 r e s p e c t i v e l y ) . Phrase I of the 'b'-section opens i n a s i m i l a r f a s h i o n to that of The s t r u c t u r a l value of A^ i n segment no. 3 warrants i t s omission i n no. 4 and j u s t i f i e s negation of A i n no. 3. (The r e g i s t r a l connection to A, remember, occurs i n bar 7, not w i t h the A of segment no. 4.) ' 193 the 'a'-section. That i s , i t s f i r s t segment i s embedded i n t o i t s second, the l a t t e r c o n s i s t i n g of a l l PC's except one. The missing D#, although not the f i r s t a r t i c u l a t e d PC of segment no. 11, i s the lowest i n the 2 8 normal form o r d e r i n g . An overlapping twelve-note completion may once again be noted, as i n d i c a t e d i n Example 75. The second phrase of the 'b'-section was s t a t e d e a r l i e r to be uniquely constructed of one continuous d i s j u n c t fragment. I t i s a l s o u n p a r a l l e l e d i n terms of i t s PC content as i t i s the only s i n g l e segment which contains a l l twelve. This sense of completion i s complemented by the culmination of t e x t u r a l  and l i n e a r progressions, s p e c i f i c a l l y on the f i n a l of the segment (as noted e a r l i e r ) . One f i n a l r e l a t i o n s h i p i s noteworthy.. I t concerns the bassoon part i n segments 11 and 13 and, s p e c i f i c a l l y i t s i n c l i n a t i o n towards the PC D i n each case. Segment no. 11 (the phrase d i v i d e r ) stops short on the upper neighbour E^, while no. 13 sounds e s s e n t i a l l y the same PC's but s u b s t i t u t e s the lower neighbour C# f o r E^. The two segments a l s o d i f f e r i n that no. 13 contains the u l t i m a t e " r e s o l u t i o n -note," D, provided by the p i c c o l o . In t h i s sense—one purely of PC content, i r r e s p e c t i v e of the a c t u a l order of a r t i c u l a t i o n — s e g m e n t no. 13 might be viewed as " c l o s e d " r e l a t i v e to no. 11. Summary Because of the d i s j u n c t d i s p o s i t i o n of the bassoon p a r t , r e g i s t r a l l i n e a r connections were found to be of s i g n i f i c a n c e i n the o r g a n i z a t i o n of p i t c h content i n t h i s piece. Four r e g i s t e r s were e s t a b l i s h e d , e s s e n t i a l l y through m o t i v i c consistency ( i . e . , the four-note motive B^-B-C-D^), i n 28 The s i g n i f i c a n c e of t h i s completion l i e s i n the f a c t that the composed or d e r i n g c l o s e l y resembles that of the "normal form," and the D# i n i t i a t e s the second "subset" of the segment. 194 which f i v e p r i m a r y p r o g r e s s i o n s were exposed. A tendency towards t h e PC D, i n h e r e n t i n t h e f o u r - n o t e motive i t s e l f , was r e v e a l e d i n the p r i m a r y p r o g r e s s i o n s thus r e i t e r a t i n g a D - c e n t r i c i t y w i t n e s s e d i n p r e v i o u s p i e c e s (e.g., Nos. 1, 4, 5, and 6 ) . These p r i m a r y p r o g r e s s i o n s a r e E^-VE->, as an inco m p l e t e major-minor upper n e i g h b o u r t o D^; E^4/g4^ a s a n i n c o m p l e t e major-minor upper n e i g h b o u r to D 4 ( t h e l a t t e r n ever o c c u r r i n g but r a t h e r i m p l i e d ) ; B^3 t o C/P, s u g g e s t i n g motion towards D 4 which, a g a i n , never a c t u a l l y o c c u r s ; B^ 2 t o C//^  and up to D^; and B ^ t o C//2 t e n d i n g towards, but f a l l i n g s h o r t o f , D 2. Segments of p h r a s e s d e f i n e d e a r l i e r were s t u d i e d here f o r t h e i r PC cont e n t ( i n c l u d i n g t h a t of c o l o r a t i o n s a l s o ) , and p a t t e r n s o f u n f o l d i n g were found t o r e v e a l c h r o m a t i c and n e a r - c h r o m a t i c c o l l e c t i o n s . R e l a t i o n -s h i p s between segments, w i t h r e s p e c t to t w e l v e - n o t e a g g r e g a t e c o m p l e t i o n , were a l s o found to be of s i g n i f i c a n c e i n t h e p i e c e . Harmonic D e t a i l s In t h a t c o l o r a t i o n and d o u b l i n g a r e t h e o n l y forms o f in s t r u m e n t i n t e r a c t i o n i n t h e p i e c e , t h e y a l s o r e p r e s e n t t h e o n l y i n s t a n c e s of harmonic u n i t s — i . e . , v e r t i c a l i t i e s w i t h s p e c i f i c i n t e r v a l c o n t e n t . Consonance-dissonance q u a l i t y o f c o l o r a t i o n s w i l l be examined f i r s t , w i t h a d i s c u s s i o n o f t h e i r s p e c i f i c placement and con t e n t t o f o l l o w . A s t u d y of the v a r i o u s d o u b l i n g s and t h e i r placement w i l l c o n c l u d e t h e s e c t i o n . Consonance-dissonance q u a l i t y of c o l o r a t i o n s The f i v e s i m u l t a n e i t i e s used i n the p i e c e i n o r d e r o f t h e most consonant to most d i s s o n a n t ( e x p l a i n e d below) a r e [ 0 , 2 ] , [ o , l ] , [ 0 , 1 , 3 ] , [ o , l , 2 ] , and [ o , l , 2 , 4 ] . Semitone and whole-tone c o n t e n t , as w e l l as t h e number o f members i n each v e r t i c a l i t y a r e f a c t o r s i n the c l a s s i f i c a t i o n o f 195 harmonic q u a l i t y . For example, [ 0 , 2 ] i s the most consonant (and t h e r e f o r e has a C-D f a c t o r of 1) because i t i s the only v e r t i c a l i t y without a semitone. The most dissonant harmony i s [o,1,2,4] (with a f a c t o r of 5) because i t has the greatest number of members and two semitones. The v e r t i c a l i t y [o,l] i s the second most consonant because i t i s the only other set w i t h two elements; i t has a C-D f a c t o r of 2 . Between [ o , l , 3 ] | and [ 0 , 1 , 2 ] , the former i s more consonant (with a f a c t o r of 3 ) as i t contains only one semitone compared to the l a t t e r ' s two ( t h e r e f o r e having a f a c t o r of 4). Example 76 i l l u s t r a t e s a l l instances of instrument i n t e r a c t i o n be they doublings or c o l o r a t i o n s . The aforementioned " s e t - t y p e s " w i t h t h e i r corresponding C-D f a c t o r s are i n d i c a t e d below the v a r i o u s instances of c o l o r a t i o n . R e f e r r i n g to Example 76, one p a r t i c u l a r observation concerning consonance-dissonance f l u c t u a t i o n i s noteworthy. Phrase I of the 'a'-s e c t i o n e x h i b i t s a s h i f t from r e l a t i v e consonance ( i . e . , f a c t o r s 3 , 1, and 2 ) to dissonance ( i . e . , f a c t o r 4 ) . The three-note s o n o r i t y i n measure 5, i n f a c t , occurs only once and i s the most dissonant found i n the 'a'-s e c t i o n . Phrase I I leans towards the consonant side w i t h harmonies of f a c t o r s 1 and 2 . The 'b'-section r e v e a l s a s i m i l a r p a t t e r n : phrase I p i c k s up where the 'a'-section l e f t o f f — i . e . , w i t h r e l a t i v e consonance— and moves to the most dissonant v e r t i c a l i t y i n the piece i n bar 14. Phrase I I d i s p l a y s sets of f a c t o r s 1 and 2 not u n l i k e the second phrase of the 'a'-s e c t i o n . In both s e c t i o n s , then, a consonance dissonance consonance p a t t e r n emerges, w i t h the peak of dissonance o c c u r r i n g at or near the end of the f i r s t phrase of each. The r e t u r n to r e l a t i v e l y consonant s o n o r i t i e s i n the second phrase of each s e c t i o n may be heard as r e s o l u t i v e . In a sense t h i s aspect of "consequence" c o n t r a d i c t s other 196 Example 76. Consonance-dissonance f a c t o r s of c o l o r a t i o n v e r t i c a l i t i e s . 197 'a'-section measure nos.: c o l o r a t i o n p i t c h e s : bassoon p i t c h e s : set-types: C-D f a c t o r s : doublings: phrase I phrase I I i r [0,1,3] [0,2][0,l] [0,1,2] 3 1 2 4 [0,2] [0,1] 1 2 two-part unison/ three cons. notes two-three-part o c t . and u n i s • / three cons, notes [0,1] 2 2 oct./ three-part u n i s . / three-part one octaves/ one unison/ note two cons. note f o u r cons, notes notes b - s e c t i o n measure nos.: c o l o r a t i o n p i t c h e s : bassoon p i t c h e s : set-types: C-D f a c t o r s : doublings: 13 [0,1] 2 phrase I phrase I I 14 i r 15 a—1 j 1 1 rHH 1 n. , * M •a -/•— 1 ft- ^ / w m ^ s [0,1][0,1] [0,2] [0,1,2,4] 2 2 1 5 u n i s . / two-part one u n i s . / note one note u n i s . and oct./two cons, notes two-three-part o c t . / three cons, notes [0,l][0,2] [0,l] 2 1 2 two-part f o u r - p a r t u n i s . / unis./one two cons. note notes 198 f a c t o r s o f "openness" a t t h e end o f t h e ' a ' - s e c t i o n ( e . g . , f a c t o r s such as r e g i s t r a l a s c e n t and " h e s i t a n t " - p i t c h d e p a r t u r e from t o E 5 ) , w h i l e r e i n f o r c i n g t h e f e e l i n g of " c l o s u r e " on t h e i n bar 15 [ e f f e c t e d by t h e c u l m i n a t i o n of i n s t r u m e n t a t i o n - d e n s i t y and (un i s o n ) d o u b l i n g - d e n s i t y , as w e l l as t w e l v e - n o t e a g g r e g a t e c o m p l e t i o n and l i n e a r p i t c h c o n n e c t i o n ] . S p e c i f i c placement and cont e n t o f c o l o r a t i o n s Many c o l o r a t i o n s would appear t o be s t r a t e g i c a l l y p l a c e d ; some punctuate s t r u c t u r a l p o i n t s i n r e g i s t r a l l i n e a r p r o g r e s s i o n s d e f i n e d and i l l u s t r a t e d e a r l i e r , w h i l e o t h e r s a r t i c u l a t e t h e ends of f o r m a l segments (e . g . , p h rases or f r a g m e n t s ) . The f i r s t c o l o r a t i o n i n t h e p i e c e , f o r i n s t a n c e , harmonizes t h e f i n a l p i t c h of t h e bassoon's opening d i s j u n c t fragment, i . e . , t h e f o u r - n o t e m o t i v e , B -B-C - D , i l l u s t r a t e d e a r l i e r . C u r i o u s l y , one o f t h e c o l o r a t i o n p i t c h e s i s D ^ , t h e a s s e r t e d " a r r i v a l -p o i n t - p i t c h " of t h e motive i n r e g i s t e r i i (measure 3, bassoon). I n t h i s sense the c o l o r a t i o n i s an " a n t i c i p a t i o n " o f t h e s t r u c t u r a l D3 a p p e a r i n g l a t e r i n t h e bassoon. The r e m a i n i n g c o l o r a t i o n s i n t h e f i r s t p h r ase harmonize s t r u c t u r a l p i t c h e s i n t h e i n i t i a l a s c e n d i n g f o u r t h -L 7 Li 29 p r o g r e s s i o n , E t o A 4 (as no t e d e a r l i e r ) . The f i n a l p i t c h of the f i r s t fragment i n phrase I I , l i k e t h a t of phrase I , i s marked by a c o l o r a t i o n ( a l t h o u g h t h e harmonic q u a l i t y i s 30 d i f f e r e n t ) . The l a s t two c o l o r a t i o n s i n t h e ' a ' - s e c t i o n harmonize t h e 29 b A I t i s t h e a r r i v a l p o i n t o f t h i s p r o g r e s s i o n , A i n bar 5, which has t h e C-D f a c t o r 4 h a r m o n i z a t i o n , t h e most d i s s o n a n t of t h e ' a ' - s e c t i o n . I t s a r t i c u l a t i o n i s h i g h l y a c c e n t e d on t h e one hand, but somewhat " d i s g u i s e d " by t h e d i s s o n a n t harmony on the o t h e r . 30 These two fragments, each t e r m i n a t e d w i t h a c o l o r a t i o n , a r e t r a n s p o s i t i o n a l l y r e l a t e d as e x p l a i n e d e a r l i e r . The p a r a l l e l i s m o f t h e two p h rases i n t h e ' a ' - s e c t i o n , a l s o n o t e d e a r l i e r , i s h e i g h t e n e d by t h i s r e l a t i o n s h i p . 199 r e - e s t a b l i s h e d A^ 4 (measure 7) of t h e a s c e n d i n g p r o g r e s s i o n i n r e g i s t e r i v and t h e A 4 (measure 7) to which i t u l t i m a t e l y moves. N o t i c e t h a t , w h i l e each of t h e s e two s t r u c t u r a l p i t c h e s i s c o l o r e d by a lower h a l f -s t e p , A i s harmonized d i f f e r e n t l y here from measure 5 (where i t s lower h a l f and whole-step sound). The c o l o r a t i o n s o f A ^ 4 and F#4 i n measure 13 a r e noteworthy as t h e s e p a r t i c u l a r p i t c h e s i n i t i a t e t h e " c o u n t e r b a l a n c i n g " d e s c e n d i n g f o u r t h - p r o g r e s s i o n , A^ 4 t o E ^ 4 , i l l u s t r a t e d e a r l i e r . A l t h o u g h A i s harmonized d i f f e r e n t l y here from t h e opening a s c e n t , i t s c o l o r a t i o n tone c o n c u r s w i t h t h a t o f t h e A^ 4 j u s t mentioned, i . e . , G. F# 4 i s , however, harmonized as i n bar 3, w i t h F 4 . The next two v e r t i c a l i t i e s i n phrase I of the ' b ' - s e c t i o n a r t i c u l a t e p o i n t s of l e s s e r importance i n the l i n e a r s t r u c t u r e . B^ o f bar 13, f o r example, i n i t i a t e s t h e second f o u r - n o t e motive i n r e g i s t e r i i i , w h i l e t h e c o l o r e d E 4 o f bar 14 i s another of the p i t c h e s i n t h e d e s c e n d i n g f o u r t h , A^ 4 to E^^. Two of t h e r e m a i n i n g v e r t i c a l i t i e s a r e worthy o f mention: f i r s t , t h e c o l o r a t i o n o f t h e bassoon's A^ i n measure 14 p u n c t u a t e s t h e end of 31 phrase I w i t h t h e most d i s s o n a n t s o n o r i t y of t h e p i e c e . The second i n v o l v e s t h e D^/C#^ v e r t i c a l dyad i n measure 15. The c e n t r i c i t y of t h e PC D and, more s p e c i f i c a l l y , the p i t c h have a l r e a d y been n o t e d . W h i l e the d i s s o n a n t C// i n t e n s i f i e s t h e a r r i v a l on D, i t a l s o t e n ds t o s l i g h t l y 3 2 " b l u r " the l a t t e r . The f o u r - p a r t u n i s o n d o u b l i n g o f and subsequent 31 T h i s p o i n t , as i n d i c a t e d e a r l i e r , i s analogous to t h e c l o s e o f p h r a s e I i n t h e ' a ' - s e c t i o n where C-D f a c t o r 4 ( t h e most d i s s o n a n t t o t h a t p o i n t ) i s found. 32 I t i s i n t e r e s t i n g to compare the d i s p o s i t i o n of p i t c h e s i n t h i s f i n a l c o l o r a t i o n t o those of t h e f i r s t one i n bar .1. In t h e e a r l i e r i n s t a n c e t h e ( c o l o r a t i o n ) was n o t e d as an a n t i c i p a t i o n o f t h e bassoon's s t r u c t u r a l two b a r s l a t e r . I n t h e f i n a l c o l o r a t i o n , i s t h e main n o t e and C//^  i s the c o l o r a t i o n p i t c h ; t h e two PC's have e s s e n t i a l l y t r a d e d f u n c t i o n s . 200 s u s t a i n i n g of i n the p i c c o l o , however, confirm i t s r o l e as a.point of 33 p i t c h c l o s u r e . S p e c i f i c placement of octave and unison doublings Octave and unison doublings were discussed e a r l i e r i n the l i g h t of t h e i r c o n t r i b u t i o n to the f l u c t u a t i o n of t e x t u r a l - d e n s i t y . As i n many instances of c o l o r a t i o n , however, these doublings may a l s o be viewed i n c e r t a i n cases as f a c t o r s of i n t e n s i f i c a t i o n . Three such p o i n t s e x i s t i n the 'a'-section. The f i r s t i s i n measure 5 where the l a s t three notes of the d i s j u n c t p o r t i o n of phrase I ( l e a d i n g i n t o the cadenza) are doubled 34 i n unison. The second instance accompanies the opening three notes of phrase I I . These i n t u r n lead i n t o the f o u r t h and f i n a l note of the fragment which, as stated e a r l i e r , i s colored by a semitone. Perhaps the most emphatic instance, however, i s that which occurs i n measure 7. The four notes culminating on the s t r u c t u r a l A 4 are doubled i n unison by the oboe and c l a r i n e t . (This p a r t i c u l a r A 4 i s s t r u c t u r a l as i t i s the immediate goal of the i n i t i a l ascending f o u r t h - p r o g r e s s i o n , E^ 4 to A^ 4, and on a l a r g e r s c a l e , the t r i t o n e d i v i d e r of the octave-progression, b 4 b E ^ to E*5.) The unison doubling ( f o u r - p a r t ) of i n bar 15 i s the most s t r a t e g i c doubling i n the 'b'-section; as noted e a r l i e r , i t s r e a l s i g n i f i c a n c e l i e s i n i t s placement as a peak w i t h i n the progression of (unison) doubling-density. 33 9 The bassoon's f i n a l C# , however, may be heard as a s u b t l e "reminder " of C//5 which accompanies i n bar 15. The f i r s t note of the three i s the A 4 goal of the i n i t i a l ascending f o u r t h - p r o g r e s s i o n , a l s o colored as noted e a r l i e r . And the f i n a l note i s D3, the prolonged a r r i v a l point of the four-note motive i n r e g i s t e r i i , a l s o discussed i n the previous s e c t i o n . 201 Summary In d e a l i n g w i t h the harmonic s t r u c t u r e of t h i s piece consonance-dissonance f a c t o r s (based on semitone and whole-tone content, and the c a r d i n a l i t y of the v a r i o u s v e r t i c a l i t i e s ) were e s t a b l i s h e d f o r the instances of c o l o r a t i o n used throughout. Each s e c t i o n e x h i b i t e d p r o g r e s s i v e l y more dissonant s t r u c t u r e s towards the end of i t s f i r s t phrase, followed by more consonant s o n o r i t i e s i n i t s second. The most dissonant s o n o r i t y of the piece was found i n the ' b ' - s e c t i o n , thereby r e v e a l i n g one element of o v e r a l l harmonic d i r e c t i o n from the 'a' to 'b'-section. Instances of c o l o r a t i o n were f r e q u e n t l y found to h i g h l i g h t s t r u c t u r a l p i t c h e s i n r e g i s t r a l l i n e a r progressions ( p a r t i c u l a r l y those i n the upper-most r e g i s t e r ) , and other important j u n c t u r e s such as phrase beginnings and endings. Octave and unison doublings were a l s o found to i n t e n s i f y s t r a t e g i c p o i n t s i n the p i e c e , the of bar 15 being the most s i g n i f i c a n t of such p o i n t s . Connective Factors Between the  N i n t h and Tenth Pieces Four f a c t o r s point to a p o s s i b l e r e l a t i o n s h i p between the n i n t h and tenth p i e c e s . The f i r s t of these concerns i n d i c a t i o n s i n the score at the 35 end of the n i n t h piece. Such i n d i c a t i o n s i n c l u d e "break o f f suddenly" (as though a c o n t i n u a t i o n were forthcoming), silenzio assoluto (suggesting an "expectant" q u a l i t y ), senza diminuendo (thus d e f e r r i n g a f e e l i n g of c l o s u r e ) , and attacca ( d i r e c t i n g an immediate c o n t i n u a t i o n ) . 36 The second f a c t o r i n v o l v e s the f i r s t three PC's of piece No. 9. 35 L i g e t i , Ten Pieces, p. 33. 36 The whole piece, remember, c o n s i s t s of only nine PC's i n an ordered u n f o l d i n g . 202 S p e c i f i c a l l y , t h e opening s u s t a i n e d and r e i t e r a t e d and subsequent E and D a r e PC's of p r i m a r y importance i n t h e l i n e a r s t r u c t u r e of t h e t e n t h p i e c e ( E ^ and E b e i n g c o n s i d e r e d j o i n t l y as an i n c o m p l e t e major-minor upper n e i g h b o u r t o th e main a r r i v a l p o i n t D). The l i n e a r s t r u c t u r e of t h e e n t i r e n i n t h p i e c e and one p a r t i c u l a r r e g i s t r a l p r o g r e s s i o n i n t h e t e n t h would appear to be r e l a t e d , t h i s b e i n g t h e t h i r d f a c t o r o f c o n n e c t i o n between t h e two. As s t a t e d e a r l i e r , t h e n i n t h p i e c e i s comprised of a n i n e - n o t e u n f o l d i n g . As i t t u r n s out, t h i s u n f o l d i n g e s s e n t i a l l y o u t l i n e s an a s c e n d i n g p r o g r e s s i o n from to A^6 ( t h i s r e g i s t e r b e i n g i n t h e extreme upper range of t h e i n s t r u m e n t s i n v o l v e d ) . PC's E^ and A^ a r e i n t e r e s t i n g l y a l s o t h e e x t r e m i t i e s of t h e a s c e n d i n g f o u r t h - p r o g r e s s i o n i n r e g i s t e r i v o f t h e t e n t h p i e c e (measures 37 3-5). T h i s r e l a t i o n s h i p i s summarized i n Example 77. Example 77. L i n e a r p r o g r e s s i o n r e l a t i o n s h i p between t h e n i n t h and t e n t h p i e c e s . F i n a l l y , i n t h e l i g h t of t h e p a t t e r n o f PC u n f o l d i n g i n p i e c e No. 9 ( d i s c u s s e d i n Chapter I I ) and t h e concept of t w e l v e - n o t e aggregate c o m p l e t i o n n o t e d between c e r t a i n v c o n t i g u o u s segments of No. 10, a 37 The i n t e n s i t y o f No. 9, r e s u l t i n g from the upper range of the i n s t r u m e n t s , i s matched i n the t e n t h p i e c e as t h e p r o g r e s s i o n i n q u e s t i o n i s at t h e top o f t h e bassoon's range. 203 p a r t i c u l a r l y s t r o n g c o n n e c t i o n may be d i s c e r n e d between the two p i e c e s . As noted i n Example 78, i f t h e descending PC l i n e i n No. 9 i s extended i t g e n e r a t e s t h e t h r e e PC's absent from t h e p i e c e — c u r i o u s l y , t h o s e found a t t h e b e g i n n i n g of No. 10. T h i s l a r g e - s c a l e i n s t a n c e o f t w e l v e - n o t e aggregate c o m p l e t i o n p r o v i d e s an important bond between t h e two p i e c e s ; i n a d d i t i o n , i t a n t i c i p a t e s t h e use of inter-segment c o m p l e t i o n w i t h i n t h e t e n t h p i e c e i t s e l f . Example 78. Twelve-note aggregate c o m p l e t i o n from t h e n i n t h t o t h e t e n t h p i e c e . Summary A number o f f a c t o r s have been c i t e d above as p o i n t i n g to a c o n n e c t i o n o r r e l a t i o n s h i p between t h e n i n t h and t e n t h p i e c e s . Notes i n th e s c o r e a t t h e end of No. 9 were s a i d t o imply a l a c k of c o m p l e t i o n and a need to c o n t i n u e immediately, w h i l e u n d e r l y i n g d e t a i l s of PC u n f o l d i n g ( e .g., E^-E-D and the p r o g r e s s i o n from E^ 7 to A^) were found to p r o v i d e an a s s o c i a t i o n between the two p i e c e s . And f i n a l l y , an important c o n n e c t i o n was a l s o r e v e a l e d i n t h e t w e l v e - n o t e a g g r e g a t e c o m p l e t i o n a t t h e b e g i n n i n g o f t h e t e n t h p i e c e , t h e f i r s t n i n e PC's h a v i n g u n f o l d e d i n No. 9. 204 Summary The f o r e g o i n g a n a l y s i s of t h e t e n t h p i e c e has i n c l u d e d independent e x a m i n a t i o n s of form d e l i n e a t i n g f a c t o r s , t e x t u r a l s t r u c t u r e , r h y t h m i c and m e t r i c d e s i g n , and p i t c h o r g a n i z a t i o n . A s s o c i a t i o n s between parameters have been i n d i c a t e d where a p p l i c a b l e . W h i l e concepts such as r e g i s t r a l l i n e a r c o n n e c t i o n s and consonance-dissonance q u a l i t y were i n t r o d u c e d i n p r e v i o u s c h a p t e r s ( a l b e i t under c o n s i d e r a b l y d i f f e r e n t c i r c u m s t a n c e s ) , p r o g r e s s i v e t e n d e n c i e s i n t e x t u r a l space and modes of t e x t u r a l - d e n s i t y , as w e l l as impulse-number p r o p o r t i o n s o f p h r a s e segments a r e a s p e c t s s p e c i f i c to t h e a n a l y s i s of t h e t e n t h p i e c e . R e l a t i o n s h i p s between t h e n i n t h and t e n t h p i e c e s were a l s o d i s c u s s e d , t h e r e b y a d d i n g a n o t h e r subgroup t o t h e l i s t o f t h o s e p r e v i o u s l y d e f i n e d . CHAPTER V CONCLUSION In s e e k i n g an u n d e r s t a n d i n g of the m u s i c a l language of Gyorgy L i g e t i ' s Ten Pieces for Wind Quintet, t h e f o r e g o i n g study has p r e s e n t e d i n d i v i d u a l e x a m i n a t i o n s of m u s i c a l parameters such as form, t e x t u r e , rhythm and meter, and p i t c h . W h i l e the a u d i t o r y e x p e r i e n c e of t h i s (or any) music i n v o l v e s s i m u l t a n e o u s c o n s i d e r a t i o n of a l l m u s i c a l parameters, v i e w i n g them i n i s o l a t i o n f o r t h e purposes of a n a l y s i s a l l o w s s p e c i f i c d e t a i l s of t h e i r i n d i v i d u a l s t r u c t u r e s to be a s s e r t a i n e d b e f o r e a t t e m p t i n g an u n d e r s t a n d i n g of the i n t r i c a c i e s of t h e i r i n t e r a c t i o n . Chapter I I f o c u s s e d on c e r t a i n p r i n c i p l e s (some g e n e r a l , o t h e r s more s p e c i f i c ) w i t h i n t h e v a r i o u s m u s i c a l parameters and e x e m p l i f i e d them i n e x c e r p t s from the second to n i n t h p i e c e s i n t h e q u i n t e t . T h i s p r o v i d e d a b a s i s f o r t h e d e t a i l e d a n a l y s e s of p i e c e s 1 and 10 ( i n C h a p t e r s I I I and I V ) . I n t h e s e p a r t i c u l a r s t u d i e s , m u s i c a l parameters ( e . g . , form, t e x t u r e , e t c . ) were a l s o t r e a t e d s e p a r a t e l y , but i n d e a l i n g w i t h the two p i e c e s as complete e n t i t i e s — i . e . , l o o k i n g a t them on a more g l o b a l l e v e l — i n s t a n c e s of i n t e r a c t i o n between parameters were i l l u s t r a t e d , thus p r o v i d i n g a more comprehensive view of the o v e r a l l m u s i c a l s t r u c t u r e i n each c a s e . The q u i n t e t was suggested i n Chapter I to be r e p r e s e n t a t i v e of L i g e t i ' s works s i n c e t h e m i d d l e s i x t i e s , i l l u s t r a t i n g many c o m p o s i t i o n a l p r o c e d u r e s i n a medium c o n s i d e r a b l y more "compact" than t h a t of most of h i s o t h e r works. The f a c t i s t h a t L i g e t i ' s own c h a r a c t e r i z a t i o n of h i s m u s i c a l language i n t h i s p e r i o d i s a c c u r a t e l y r e p r e s e n t e d i n t h e q u i n t e t . He speaks 205 206 of h i s music ( s i n c e the m i d d l e s i x t i e s ) as h a v i n g "no t o n a l c e n t r e s " on t h e one hand, but not t r e a t i n g a l l t w e l v e n o t e s " e q u a l l y " on t h e o t h e r . * W h i l e t o n a l c e n t r e s , as such, may not be i n o p e r a t i o n i n t h e q u i n t e t , p i e c e s 5, 6, and e s p e c i a l l y 10, r e v e a l e d a s t r o n g i n c l i n a t i o n towards t h e PC D, r e f e r r e d to as a " D - c e n t r i c i t y . " L i n e a r d i r e c t e d n e s s , i n s t r u m e n t a l d o u b l i n g , and d u r a t i o n a l exposure a r e some of the f a c t o r s s u g g e s t i n g such an i n c l i n a t i o n t o , and r e i n f o r c e m e n t o f , t h a t p a r t i c u l a r PC. I n t h e f i r s t p i e c e , PC c e n t r i c i t y appeared to i n v o l v e b o t h D and C, t h e s e b e i n g t h e p i t c h e x t r e m i t i e s of the ' a ' - s e c t i o n , m a i n t a i n e d t h r o u g h o u t e r - v o i c e p r o l o n g a t i o n and l a t e r a l v o i c e c r o s s i n g . The ' b ' - s e c t i o n a l s o r e v e a l e d l i n e a r d i r e c t e d -ness to and C^, t h e f i n a l p i t c h e s of the p i e c e . L i g e t i a l s o comments ( i n c o n n e c t i o n w i t h h i s works from t h e m i d d l e s i x t i e s ) t h a t c e r t a i n "arrangements" o f i n t e r v a l s " d e t e r m i n e t h e c o u r s e of 2 the music and the development o f the form." The q u i n t e t f u r n i s h e s numerous i n s t a n c e s o f t h i s as i n t h e t h i r d p i e c e , f o r example, where v e r t i c a l complexes were shown to grow p r o g r e s s i v e l y more d i s s o n a n t ( a c c o r d i n g to the a s s e r t e d c r i t e r i a of harmonic q u a l i t y ) toward t h e c l i m a x , a f t e r which a t r e n d towards i n c r e a s e d consonance was d i s c e r n e d . (See Examples 44 and 45.) A l s o , v e r t i c a l arrangements o f i n t e r v a l s were shown to be a f a c t o r of f o r m a l segmentation i n t h e f i f t h p i e c e ; of t h e f o u r s e c t i o n s , t h e f i r s t and t h i r d were noted as b e i n g r e l a t i v e l y r e s t r i c t e d i n o v e r a l l t e x t u r a l space (and, hence, v e r t i c a l i n t e r v a l l i c d i s p o s i t i o n ) , w h i l e t h e second and f o u r t h s e c t i o n s were shown t o be r e g i s t r a l l y d i s p e r s e d . And f i n a l l y , p i e c e No. 1 was d e f i n e d as to t h e f l u c t u a t i o n i n harmonic q u a l i t y t h r o u g h a d e r i v e d system of con s o n a n c e - d i s s o n a n c e c l a s s i f i c a t i o n ; v e r t i c a l i t i e s w i t h s p e c i f i c ''"Ligeti, l i n e r n o t e s f o r Melodien. 2Ibid. 207 C-D (consonance-dissonance) f a c t o r s were shown to p l a y a v i t a l r o l e i n t h e maintenance o f p i t c h e x t r e m i t i e s i n t h e ' a ' - s e c t i o n . (See Example 64.) The harmonic s t r u c t u r e of the f i r s t p i e c e ' s ' a ' - s e c t i o n a l s o i l l u s t r a t e s 3 L i g e t i ' s concept of "h a r m o n i c - m u s i c a l f l o w , " i n which i n t e r v a l c o m b i n a t i o n s merge s l o w l y i n t o one another r a t h e r than change a b r u p t l y . L i g e t i f u r t h e r d e f i n e s h i s music from the m i d d l e s i x t i e s as u t i l i z i n g m i c r o p o l y p h o n i c t e x t u r e s i n which l i n e s a r e more d i r e c t e d and r e t a i n a 4 c e r t a i n degree of independence w i t h i n the " o v e r r i d i n g c o n t r a p u n t a l network." A g a i n , p i e c e s 1 and 3 come to mind. In t h e l a t t e r , two suggested t e c h n i q u e s — u n i s o n t r a n s f e r and p i t c h i n t e r c h a n g e — w e r e s a i d t o c r e a t e l i n e a r c o n t i n u i t i e s w i t h i n an o v e r a l l t e x t u r e o f complex polyphony. Regarding t h e f i r s t p i e c e , o u t e r - v o i c e p r o l o n g a t i o n s and l a t e r a l v o i c e - c r o s s i n g e v e n t s , noted e a r l i e r , emerge as independent l i n e a r s t r u c t u r e s u n d e r l y i n g t h e web-l i k e i n t e r w e a v i n g of i n s t r u m e n t a l p a r t s . W h i l e many of t h e t e c h n i q u e s o u t l i n e d above a r e r e p r e s e n t a t i v e of e a r l i e r works t y p i f i e d by Atmospheres ( i n a d d i t i o n to r e p r e s e n t i n g L i g e t i ' : s music of t h e m i d d l e s i x t i e s ) , t h e s t y l e of Apparitions and Aventures—i.e., r a p i d s u c c e s s i o n s of d i s p a r a t e m u s i c a l i d e a s — w a s a l s o seen t o s u r f a c e i n the q u i n t e t , p a r t i c u l a r l y i n the s i x t h and e i g h t h p i e c e s . The q u i n t e t , then, can be viewed as r e p r e s e n t a t i v e of L i g e t i ' s c o m p o s i t i o n a l s t y l e i n the m i d d l e s i x t i e s ; i n a d d i t i o n , i t may be seen t o expose r e f i n e m e n t s of e a r l i e r t e c h n i q u e s and d e v i c e s . The e x p l i c a t i o n , i l l u s t r a t i o n , and d e t a i l e d a n a l y s i s of t h e s e c o n c e p t s ^ - i n r e l a t i v e i s o l a t i o n (as i n Chapter I I ) , and i n more extended a p p l i c a t i o n s (as i n Chap t e r s I I I and I V ) — a i m s t o e s t a b l i s h a fundamental working knowledge o f L i g e t i ' s 3 Ibid. 4 Ibid. 208 m u s i c a l language i n t h e Ten Pieces for Wind Quintet. WORKS CITED Books and P e r i o d i c a l s B e r r y , W a l l a c e . Structural Functions in Music. Englewood C l i f f s : P r e n t i c e - H a l l , I n c . , 1976. C l i f t o n , Thomas. Music as Heard. New Haven: Y a l e U n i v e r s i t y P r e s s , 1983. Cone, Edward. " A n a l y s i s Today." The Musical Quarterly ( A p r i l 1960): 172-188. L i g e t i , Gyorgy. Quoted i n Ove N o r d w a l l , l i n e r n o t e s f o r Musica ricercata (1951-53), on Duo Pohjola. Grammofonfirma BIS 18, r e c o r d e d i n W. Germany, 1974. . L i n e r n o t e s f o r Ligeti: Melodien for Orchestra. Decca H e a d l i n e , Head 12, 1976. No r d w a l l , Ove. " L i g e t i , Gyorgy." The New Grove Dictionary of Music and Musicians. E d i t e d by S t a n l e y S a d i e . London:' M a c m i l l a n P u b l i s h e r s L i m i t e d , 1980. V o l . 10, pp. 853-856.' Music L i g e t i , Gyorgy. Apparitions. Wien: U n i v e r s a l E d i t i o n , c l 9 6 4 Atmospheres. Wien:. " U n i v e r s a l , , E d i t i o n , c l 9 6 3 . . . Aventures. F r a n k f u r t : C.'F. P e t e r s Music P u b l i s h e r s , c l 9 6 4 . Double Concerto. Mainz: B. S c h o t t ' s Soehne, e l 9 7 4 . Requiem. F r a n k f u r t : C. F. P e t e r s Music P u b l i s h e r s , c l 9 6 6 Ten Pieces for Wind Quintet. Mainz: B. S c h o t t ' s Soehne,ccl969. Volumina. F r a n k f u r t : C. F. P e t e r s Music P u b l i s h e r s , c l 9 6 7 . 209 SELECTED BIBLIOGRAPHY Beyer, W. H. "Compositional P r i n c i p l e s i n Three Works of Gyorgy L i g e t i . " D.M.A. D i s s e r t a t i o n , U n i v e r s i t y of Washington, 1975. G r i f f i t h s , P a u l . Modern Music: The avant garde since 1945. New York: George B r a z i l l e r , Inc., 1981. L i c h t e n f e l d , Monika. "Gyorgy L i g e t i oder das Ende der s e r i e l l e n Musik." Melos 39 (1972): 74-80. . L i n e r notes f o r Ligeti: Zehn Stucke fur Blaserquintett. Wergo 60059, 1.97.0. "Zehn'Stucke f u r B l a s e r q u i n t e t t von Gyorgy L i g e t i . " Melos 39 (1972): 326-333. L i g e t i , Gyorgy. "Metamorphosis of Musi c a l Form." Die Reihe 1 (1965): 5-19. Nordwall, Ove. "Two Hungarians Abroad." Tempo 88 (Spring 1969): 22-25. P l a i s t o w , Stephen. " L i g e t i ' s Recent Music." Musical Times 115 (May 1974): 379-81. R o l l i n , R. L. "The Genesis of the Technique of Canonic Sound Mass i n L i g e t i ' s Lontano." Indiana Theory Review 2 (1979): 22-33. The Process of Te x t u r a l Change and the Org a n i z a t i o n of P i t c h i n L i g e t i ' s Lontano." D.M.A. D i s s e r t a t i o n , C o r n e l l U n i v e r s i t y , 1973. Salmenhaara, E. Das musikalische Material und seine Behandlung in den Werken "Apparitions," "Atmospheres," "Aventures," und "Requiem" von Gyorgy Ligeti. Regensburg: Gustav Bosse V e r l a g , 1969. Yannay, Y. "Towards an Open-Ended Method of A n a l y s i s of Contemporary Music: A Study of Selected Works by Edgard Varese and Gyorgy L i g e t i . " D.M.A. D i s s e r t a t i o n , U n i v e r s i t y of I l l i n o i s , 1974. 210 

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}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            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:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0095760/manifest

Comment

Related Items