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Aspects of pitch and pitch-class organization in Nikolai Roslavets's Trois compositions pour piano McIsaac, David William 1986

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ASPECTS OF PITCH AND PITCH-CLASS ORGANIZATION IN NIKOLAI ROSLAVETS'S TROIS COMPOS IT IONS POOR PIANO (1914) By DAVID WILLIAM MCISAAC A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS MUSIC THEORY i n THE FACULTY OF GRADUATE STUDIES (Department o-f Music) We accept t h i s thes'i /S as con-forming to the. -required standard THE UNIVERSITY OF BRITISH COLUMBIA J u l y 1986 © David W i l l i a m McIsaac, 1986 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis f o r scholarly purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Music .  The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date J u l y , 1986 DE-6 rvR-n i i ABSTRACT N i k o l a i A n d r e e v i c h R o s l a v e t s (1881-1944) i s a u n i q u e f i g u r e i n R u s s i a n a v a n t - g a r d e m u s i c a l d e v e l o p m e n t s o-f t h i s c e n t u r y . H i s s y s t e m o f t o n a l o r g a n i z a t i o n , . s i m i l a r t o S c r i a b i n ' s r e l i a n c e on a c e n t r a l c h o r d a l complex . . . was b a s e d on c h o r d s o f s i x t o e i g h t o r more t o n e s , u s e d . . . as s u b s t i t u t e s f o r t h e f u n c t i o n a l r e l a t i o n s h i p s o f c l a s s i c a l t o n a l i t y , w h ich he d i d n o t r e j e c t b u t r a t h e r t r i e d t o e xpand. T h e s e " s y n t h e t i c c h o r d s " o f s p e c i f i c and i n v a r i a b l e i n t e r v a l l i e s t r u c t u r e c o u l d be t r a n s p o s e d not o n l y t o t h e s e v e n p i t c h e s o f t h e c l a s s i c a l d i a t o n i c s c a l e , b u t a l s o t o a l l t w e l v e d e g r e e s o f t h e c h r o m a t i c s c a l e . T h r o u g h s y s t e m a t i c a p p l i c a t i o n o f s u c h t r a n s -p o s i t i o n s , R o s l a v e t s ' s c o m p o s i t i o n s r e v e a l e d e l e m e n t s s i m i l a r t o d o d e c a p h o n i c s e r i a l t h i n k i n g as e a r l y as 1914-15. . . . ( D e t l e f Gojowy, " H a l f Time f o r N i k o l a i R o s l a v e t s , " i n Russian and Soviet Musics Essays for Boris Sctowarz , 212. ) Trois Compositions pour piano (1914) e x h i b i t s u c h c h a r a c -t e r i s t i c s . Gojowy *s Neue sov/jetische Musi A der 20er Jahret and G e orge P e r l e ' s Serial Composition and Atonality b o t h i n c l u d e l i m i t e d r e f e r e n c e s t o Trois Compositions as w e l l a s g e n e r a l com-men t a r y about R o s l a v e t s ' s c o m p o s i t i o n a l t e c h n i q u e s . However, d e t a i l e d s t u d i e s o f p i t c h and p i t c h - c l a s s (PC) o r g a n i z a t i o n i n m u s i c by t h i s l i t t l e - k n o w n composer a r e l a c k i n g . P r o c e e d i n g •from t h e a n a l y s e s of Gojowy and P e r l e , t h e p r e s e n t t h e s i s exam-i n e s c e r t a i n a s p e c t s o f R o s l a v e t s ' s " s y n t h e t i c c h o r d " s y s t e m ( d e s i g n a t e d i n t h e t h e s i s a s t h e i n t e r v a l - c 1 a s s complex o r ICC s y s t e m ) i n Trois Compositions, i n c l u d i n g : (1) PC c o n t e n t s o f h a r m o n i e s i n t h e p i e c e s - - c o n t e n t s b a s e d on t r a n s p o s i t i o n - 1 e v e l s ( T - l e v e l s ) of ICCs a s s o c i a t e d w i t h t h e p i e c e s — a n d v a r i a n c e s t h e r e o f , some of w h i c h a r e r e l a t e d t o t h e f o r m s of t h e p i e c e s ; i i i (2) h a r m o n i c s u c c e s s i o n s and a s s o c i a t e d T - l e v e l s s (3) r h y t h m i c a s p e c t s o f t h e s e T - l e v e l s and t h e i r s u c c e s s i o n s , w h i c h i n d i c a t e a b a s i s o-f h i e r a r c h y o f T - l e v e l s s ( 4 ) c h a r a c t e r i s t i c s o f T - l e v e l s u c c e s s i o n s as t o PC c o n t e n t , and PC i n v a r i a n c e and p i t c h c o n t i -n u i t y i n v o l v i n g a d j a c e n t T - l e v e l s , p a r t i c u l a r l y T - l e v e l s r e l a t e d by i n t e r v a l - c 1 a s s (IC) 3s and (5) p a t t e r n s o f l i n e a r and v e r t i -c a l o r d e r i n g o f PCs a s t o t h e i r i n c l u s i o n i n p a r t i c u l a r T - l e v -e l s . T h e s e a r e d i s c u s s e d i n C h a p t e r Two, f o l l o w i n g an i n t r o d u c -t i o n t o R o s l a v e t s and h i s m u s i c i n C h a p t e r One. In c o n s i d e r a t i o n o f R o s l a v e t s ' s p o s i t i o n as a p o s t - R o m a n t i c composer, o t h e r c o m p o s i t i o n a l t e c h n i q u e s and t e n d e n c i e s e v i d e n t i n Trois Compositions a r e i n v e s t i g a t e d i n t h e t h e s i s . C h a p t e r T h r e e i n v o l v e s an e x a m i n a t i o n o f t o n a l i t y i n t h e t h r e e p i e c e s , w h i l e C h a p t e r F o u r i n v o l v e s a s t u d y o f o c t a t o n i c i s m and s e r i a l -ism, some c h a r a c t e r i s t i c s o f w hich a r e t o be f o u n d i n Trois Compositions. i v TABLE OF CONTENTS Abstract • ••• i i L i s t o-f Examples and Figures v i i Acknowledgements xi Chapter One: Introduction ......1 Biographical Information. ......1 Aspects o-f Roslavets's Compositional Style and Techn i que •• 4 Notes 10 Chapter Two: The Interval-C1 ass Complex in Trots Compos i t ions. 15 Introduction and Terminology.. .15 The ICC in Trois Compos f t ions. 22 ICC of " I " 22 ICC Of " I I " 30 ICC of " I I I " 34 Harmonic Successions and Successions o-f Transposition-Levels 44 Transpositional Relationships o-f Adjacent T-Levels 44 Transpositional Cycles o+ T-Levels...............46 " I " 47 " I I " . . 51 " I I I " 52 T-Level Occurrences and Their Rhythmic C h a r a c t e r i s t i c s : Towards a Hierarchy o-f T-l e v e l s 54 Harmonic Rhythm o-f " I " 55 Harmonic Rhythm o-f " I I " 57 Harmonic Rhythm o-f " I I I " 59 Hierarchy o-f T-Levels .62 T-Level Occurrences and Their Relationships to Form: " I " 64 "I I " 65 " I I I " 66 Recurrent Harmonic Successions 67 C h a r a c t e r i s t i c s o-f T-Level Occurrences as to PC Content 71 PC Invariance and Pitch Continuity 71 PC Invariance in IC-3-Related T-Levels.. 85 V Element Occurrence and Ordering in Trois Compos i t i ons ........91 Linear Element Occurrence and Ordering: " I " 91 " I I " .93 "111 "... 93 Element occurrence in bass l i n e s 95 V e r t i c a l Element Occurrence and Ordering in Individual Harmonies: " I " 95 " I I " 99 " I I I " lOl " I " , " I I " , and " I I I " as a whole 104 V e r t i c a l Element Adjacencies 105 Conclusion 113 Notes 117 Chapter Three: Tonality in Trois Compositions .125 Introduction 125 Tonality in " I " 127 Surface Tonal Features 127 Midd1eground/Background Linear Structures o-f " I " 131 I n i t i a t i n g s i n g l e - p i t c h exposure. 131 Linear structures in " I " 134 Melodic fragments 136 Bass-line l i n e a r structures 137 Middleground/BacWground Harmonic Structures of " I " 139 Tonality in " I I " 140 Surface Tonal Features .140 Midd1eground/Background Linear Structures of " I I " 146 Diminished-seventh li n e a r structures in mm. 6-9. 146 Mi dd1eground/Background Harmonic Structures of " I I " 150 Tonality in " I I I " 151 Surface Tonal Features 151 Midd1eground/Background Linear Structures of " I I I " . . . 154 Midd1eground/Background Harmonic Structures of " I I I " 157 Conclusion 159 Notes 161 v i Chapter Four: Other Systems o-f Pitch-Class Organization in Trois Compositions 165 S e r i a l PC Organization .168 S e r i a l Ordering of T-Levels and o-f PCs in T-Levels 170 S e r i a l Ordering o-f Melodic Pitches 172 Notes 175 Chapter Five: Conclusion 178 The ICC System 178 Tonality, Octatonicism, and S e r i a l ism. 180 Implications o-f " I I I " Concerning Matters o-f S t y l e and Large-Scale Form.. 181 Selected Bibliography... 183 Appendix A: Chronological L i s t o-f Works by Roslavets 185 L i s t o-f Works by Genre 191 Appendix B: T-Level I d e n t i t i e s o-f Individual Harmonies in " I " , Measures 6-8 196 GDjowy's Analysis o-f T-Levels in " I I I " 198 An A n a l y t i c a l A l t e r n a t i v e : A Single ICC •for " I " , " I I " , and " I I I " 201 Prolongation o-f T-Levels.. 202 v i i LIST OF EXAMPLES AND FIGURES Example 2-1. Pitch c o l l e c t i o n s in " I " , m. 1, and corresponding PCC T-le v e l s 17 Example 2-2. Transposable PCCs o-f " I " , " I I " , and " I I I " , as i l l u s t r a t e d by Perle, with numbering o-f PCs added 19 Example 2-3. ICC o-f " I " , with T-level successions 23 Example 2-4. PC c o l l e c t i o n o-f m. 13 in " I" 26 Example 2-5. Expanded ICC and T - l e v e l s in mm. 6-8 28 Example 2-6. Expanded ICC at T-0 and i t s r e l a t i o n s h i p to other PC c o l l e c t i o n s in " I " and "I I " 29 Example 2-7. ICC o-f " I I " , with PCs p a r t i t i o n e d into harmonies .31 Example 2-8. The ICCs o-f " I I I " 35 Example 2-9. Musical orthography o-f the ICC o-f " I I I " 41 Example 2-10. PC c o l l e c t i o n s , m. 3 41 Example 2-11. Element "3" in mm. 3-4 42 Example 2-12. T-O c o l l e c t i o n , m. 12, as an inversion o-f ICC at T-0 .43 Figure 2-1. Transpositional r e l a t i o n s h i p s between successive T - l e v e l s in " I " , " I I " , and " I I I " 45 Figure 2-2. T-level successions o-f " I " and the IC cycles 48 Figure 2-3. T-level successions o-f " I I " and the i n t e r v a l 5 cycle 51 Figure 2-4. T-level successions o-f " I I I " and the IC cycles 52 Example 2-13. Harmonic rhythm and -form o-f " I " 55 Example 2-14. Harmonic rhythm and -form o-f " I I " ...58 Example 2-15. Harmonic rhythm and -form o-f " I I I " 60 v i i i Figure 2-5. Hierarchy o-f T-le v e l s based on -frequency o-f occurrence and t o t a l time-spans.... 62 Figure 2-6. Recurring T-level successions in Trois Compos i t i ons. 68 Example 2-16. Invariant PCs o-f I C - i - to IC-6-related T - l e v e l s 72 Example 2-17. PC invariance and p i t c h continuity in T-level successions of Trois Compositions .76 Example 2-18. PC invariance in IC-3-related T-level f a m i l i e s . . . . . 87 Figure 2-7. Successions of T-level f a m i l i e s 88 Example 2-19. Primary melody of ' " I " 91 Example 2-20. Primary melody of " I I " . . 93 Example 2-21. Primary melody of " I I I " 94 Example 2-22. Harmonies of " I " with pitches represented by element numbers. 96 Figure 2-8. Element occurrences in v e r t i c a l p o s i t i o n s of the harmonies of " I " 98 Example 2-23. Harmonies of " I I " with pitches represented by element numbers. lOO Example 2-24. Harmonies of " I I I " with pitches represented by element numbers 102 Figure 2-9. V e r t i c a l element occurrence in ranges of p o s i t i o n s in Trois Compositions. 105 Example 2-25. S i m i l a r i t i e s o-f harmonies in " I " (with pitches represented by element numbers)....... 106 Example 2-26. S i m i l a r i t i e s of harmonies in " I I " (with pitches represented by element numbers) 108 Example 2-27. S i m i l a r i t i e s of harmonies in " I I I " (with pitches represented by element numbers).......111 Example 2-28. S i m i l a r i t i e s of v e r t i c a l element orderings of harmonies in " I and " I I I " 113 Example 3-1. ICC T - l e v e l s T-0, T - l i , and T-4 in " I " 127 ix Example 3-2. Surface structures and progressions o-f Eb, D, and G t o n a l i t i e s in " I" 128 Example 3-3. Tritone sequences o-f mm. 6-8 and th e i r tonal implications.... 130 Example 3-4. I n i t i a t i n g s i n g l e pitches in " I " . 132 Example 3-5. Linear structures in " I " .134 Example 3-6. Melodic -fragments o-f mm. 1-5 and 10-13 o-f " I " 136 Example 3-7. The PC progression G-G*t/Ab in mm. 6-8. . . . . . 137 Example 3-8. Bass-line structures o-f " I " 138 Example 3-9. Midd1eground/background harmonic structure o-f " I " 140 Example 3-10. ICC o-f " I I " and i t s resemblance to F 141 Example 3-11. T-O harmonies in mm. 13, 1, and 10-12. .... 142 Example 3-12. Surface tonal -features in " I I " 143 Example 3-13. Harmonies o-f mm. 6-9 and the i r tonal imp 1 i cat ions.... 145 Example 3-14. Eb in mm. 3-5 145 Example 3-15. Arpeggiated diminished-seventh harmonies in the primary melody o-f mm. 6-9 147 Example 3-16. Midd1eground/background linear structures o-f " I I " 149 Example 3-17. Midd1eground/background harmonic structures o-f " I I " 150 Example 3-18. The ICC o-f " I I I " 151 Example 3-19. Surface tonal structures in " I I I " 152 Example 3-20. IC-5-related PC successions in mm. 3-7 of " I I I " 153 Example 3-21. Midd1eground/background linear structures of " I I I " 154 Example 3-22. F#/Gb and the lin e a r structures of "III"..155 Example 3-23. Bass-line structure in " I I I " 156 X Example 3-24. Midd1eground/background harmonic structures o-f " I I I " 158 Example 4-1. ICCs o-f Trois Compositions compared with octatonic col l e c t i o n s 166 Figure 4-1. S e r i a l ordering o-f T- l e v e l s in Troi s Compositions .170 Example 4-2. S e r i a l ordering o-f primary melody and bass-line PCs 172 Example 6-1. C o l l e c t i o n s in mm. 6-8 and the most simi lar T-levels 196 Figure 6-1. T-level successions in " I I I " , as given in Gojowy's a n a l y s i s . . . . . . . 199 Figure 6-2. ICCs "a" and "d" in " I I I " 200 Example 6-2. Prolonged T-l e v e l s in T r o i s Compositions... 203 ACKNOWLEDGEMENTS I wish to extend my appreciation to the -following people: Prof. Wallace Berry, my thesis advisor, -for his guidance, valu-able c r i t i c i s m s , and encouragement; Prof. William Benjamin, with whom I f i r s t began the thesis research, for his help and contin-uing i n t e r e s t ; Prof. John Roeder, for reading the the s i s and giving valuable c r i t i c i s m s ; Dr. Detlef Gojowy, for providing i n -formation on current research into Roslavets; p i a n i s t Sarah Rothenberg of New York, who graciously provided me with a tape recording of a concert at New York's The Kitchen which featured premiere performances of works by Roslavets, including T r o i s Compositions pour piano, with Ms. Rothenberg, v i o l i n i s t Guillermo Figueroa, and c e l l i s t Jerry Grossman; Prof. Marketa Goetz-Stankiewicz, for her assistance with German t r a n s l a t i o n s ; Prof. Barbara Heldt, for her assistance with t r a n s l i t e r a t i o n s of Russian names; s t a f f members of the Music Library and Inter-l i b r a r y Loan Service; and family and fr i e n d s in Vancouver and Ontario, f o r t h e i r help and encouragement. F i n a l l y , I would e s p e c i a l l y l i k e to thank my wife Francine, whose assistance and loving support have helped me to complete the t h e s i s . Excerpts from the score are used with the permission of Music Associates of America, representatives for Boe1ke-Bomart, Inc., copyright owners of Trois Compositions. 1 CHAPTER ONE INTRODUCTION At the beginning of t h i s century, Russian art was in the vanguard of European development and i t continued to be so well into the Soviet period. The S t a l i n i z a t i o n of Soviet music and the subsequent i n -sistence on a national and popular symphonic s t y l e have served to obscure the work and the very e x i s t -ence of an important and o r i g i n a l group of Russian composers active in the f i r s t quarter of the century, including the remarkable Nikolay Rosslavetz [Nikolai Roslavets] (1881-1944), who anticipated aspects of twelve-tone music. . . . 1 Although, from an h i s t o r i c a l perspective, Roslavets may be described as a "minor experimentator," he i s , nonetheless, one of the more s i g n i f i c a n t but little-known f i g u r e s of avant-garde music in Russia during the f i r s t three decades of t h i s century. Biographical Information" Born in the Chernigov region of the Ukraine, January 5, 1881, Roslavets came from a ru r a l background. Saminsky finds i "curious" that Roslavets, a sophisticated musician and thinker, "should be a peasant pur sang, his parents being former s e r f s and he himself a shepherd boy up to the age of twelve.""* Roslavets was i n i t i a l l y self-taught in music. He himself i n d i -cates that his musical talent appeared around the age of seven or eight, and was manifested under the influence of his uncle, with whom he studied the v i o l i n . Later, Roslavets had lessons in Konotop, and eventually was admitted to the music classes of 2 A. M. Abaza, in Kursk, where he studied the v i o l i n , elementary theory, and harmony. 0 From 1902 to 1912 he was a student at the Moscow Conserva-tory, studying v i o l i n with Jan Hrimaly CIvan Grzhimali (1844-1915)3, counterpoint, fugue, and -form with Alexander A. I l ' i n s k i i (1859-1920); and composition and orchestration with Sergei N. Vasilenko (1872-1956). He graduated in 1912 with a s i l v e r medal for his cantata Heaven and Earth, based on the text by Byron. There are indic a t i o n s o-f his r a d i c a l views while he was a student at the Conservatory."* However, there seems to be l i t t l e information a v a i l a b l e concerning the composer's post-Conservatory l i f e and musical a c t i v i t i e s up to the early 1920s. What i s known about t h i s period, l a r g e l y through his autobio-graphical a r t i c l e , i s his development of a new system of tonal organization. 5' In 1922, he was the temporary d i r e c t o r of the Khar'kov Con-servatory.* He then worked on the e d i t o r i a l s t a f f of the Moscow State Music Publishing House, notably as the editor of and con-t r i b u t o r to the Marxist and progressive p e r i o d i c a l Muzykal'nara Aul'tura (1924). (Only three issues of the journal were pub-lished.) Roslavets was generally quite active in the 1920s as a c r i t i c and writer on music, venting "his r a d i c a l ideas in v a r i -ous essays in the mid-twenties, . . . [which] earned him the en-mity of v i r t u a l l y everybody except a small group of extreme mod-e r n i s t s , " T One group with which he came into c o n f l i c t was the more conventionally oriented Association of P r o l e t a r i a n Musi-cians Clater, Russian Association of P r o l e t a r i a n Musicians, or 3 RAPM3, which "reproached him -for his bourgeois ideology."*-0 U n t i l 1929, he was a board member of the modernist Association •for Contemporary Music, the Soviet association c l o s e l y linked with ICSM. In 1928-29, ACM was reorganized as the All-Russian Society -for Contemporary Music, but i t ceased to e x i s t by 1931. 1 1 In the l a t t e r half o-f the 1920s, the limited response to his works, and pressure -from RAPM and Soviet a u t h o r i t i e s led him to abandon his avant-garde s t y l e of composition -for a more acceptable tonal s t y l e . Roslavets p u b l i c l y confessed h i s p r e v i -ous errors ( i . e . , "his modernist s t y l e and h i s avoidance of the emotional") in 1930 in the Proletarian Musician LProletarsk i i Muzykant, journal of RAPM 3. 1 2 Roslavets "then accepted an i n v i t a t i o n to Tashkent t i n Uz-bekistan, a region of the Soviet Union] where he switched to folk music in Uzbek s t y l e and composed the f i r s t national Uzbek opera. A l l music d i c t i o n a r i e s published in the West speculate that Roslavetz was banished from Moscow and that he disappeared without trace in the wake of the p o l i t i c a l purges of the 1930s. Perhaps he moved to Tashkent to escape p o l i t i c a l r e p r i s a l s . " 1 " More recently however, Gojowy has provided little-known informa-tion about Roslavets and his a c t i v i t i e s a f t e r the 1920s, dismis-sing rumours about Roslavets's e x i l e to and death in S i b e r i a that arose as a consequence of his "non-person" status under the c u l t u r a l p o l i c i e s of S t a l i n and Zhdanov. 1 4 Roslavets went to Uzbekistan in 1931, where he became one of the f i r s t Russian musicians to contribute to the development of musical cultu r e in Middle Asia. He was di r e c t o r of the Radio Center of the Uzbek So-v i e t Republic and conductor of the Uzbek Music The-ater. He composed music based on [Uzbek] national 4 melodies and rhythms. His b a l l e t Pakhta ["Cotton peasant"], dedicated to the struggle for independence o-f the cotton industry in the USSR, and his symphony, "Soviet Uzbekistan," composed -for the 15th anniversa-ry o-f the October Revolution, were performed with great success under his baton. He was awarded an honorary diploma by the government of the Uzbek Republie. In November 1933, he returned to Moscow as a producer f o r the All-Union Radio Committee (1933-35) and as d i r e c t o r of the All-Russian Concert Associa-tion ( u n t i l 1939); from 1936, he served as head of the section of s c i e n t i f i c c o l l a b o r a t o r s in the trade union RABIS. He taught composition in the Musical Po1ytechnical School, lectured to m i l i t a r y band d i -rectors, and continued to compose. During these years he wrote important t h e o r e t i c a l works, such as "Counterpoint" and "Fugue," which remain unpublished. Although he was s e r i o u s l y i l l during the Second World War, he became intensely involved in the general struggle and composed p a t r i o t i c songs dedicated to the defenders of his country. . . . ie» Roslavets died in Moscow, August 23, 1944. Aspects of Roslavets's Compositional S t y l e and Technique Roslavets's student compositions and e a r l i e r chamber works were influenced by French impressionism. 1"* But soon a f t e r the completion of his studies, his s t y l e changed. In the 1910s, Roslavets developed a s e r i e s of harmonic p r i n c i p l e s of a new to-n a l i t y , applicable to his music. He indicates having a vague notion of these p r i n c i p l e s , even f i n d i n g them to be evident in hi s student compositions of 1909-1911. In early 1913, he com-posed the f i r s t works, a v i o l i n sonata and some songs, which manifested his own i n d i v i d u a l ,compositional techniques, and for the next six years, u n t i l 1919, he continued to develop these t e c h n i q u e s . 1 7 Gojowy c i t e s the songs Volkovo kladbishche (text by Burliuk) and Vy nosits liubov' (Bo1'shakov), both from the end of 1913, as pieces in which Roslavets "achieved a new har-5 manic ordering which w'as nat diatonic and which he referred to as the synthetic chord t e c h n i q u e . " 1 0 These chords, the basis of the harmonic organization in his music, consist of six to eight and more pitches, are transposable to a l l twelve chromatic lev-e l s , and can include t e r t i a n chords o-f conventional t o n a l i t y . Such "synthetic" chords are used not only -for c o l o u r i s t i c pur-poses but, more importantly, to sub s t i t u t e for conventional ton-al structures. Although the p r i n c i p l e o-f c l a s s i c a l t o n a l i t y i s absent -from Roslavets's works up to the time of h i s autobio-graphical a r t i c l e (1924), " t o n a l i t y as a concept of harmonic unity e x i s t s unchanged and appears in the form o-f the aforemen-tioned synthetic chords. . . . " 1» These chords can be expressed v e r t i c a l l y or h o r i z o n t a l l y , and involve some rules of voice-l e a d i n g . 2 0 In addition, p r i n c i p l e s of "a new polyphony," and "new rhythmic forms" were developed, so that, by the end of 1919, he came to a f u l l e r awareness of a l l these p r i n c i p l e s as elements of a "new system of sound organization." This system, in h i s opinion, was "destined to ul t i m a t e l y replace that of the obsolete c l a s s i c a l system . . . and to lay a firm foundation un-der the i n t u i t i v e (in f a c t , only anarchistic) compositional methods with which the majority of contemporary composers opera-teCdl. . . In general, Roslavets's music i s characterized by a number of d i f f e r e n t influences and trends. The noted Russian musicolo-g i s t , Boris Asafiev, discusses one of these: Somewhat apart, in view of i t s sharp antagonism to contemporary currents, stood the output of Roslavetz. . . . As i s demonstrated by the f i r s t v i o -l i n sonata (1913), and then by a number of other 6 works, Roslavetz already then set up, in a f a r - s i g h t -ed and daring manner, the problem o-f constructivism that we are at present so much concerned with. It was necessary to speak o-f his works at that time us-ing a terminology that has now become elementary, as: the organizational p r i n c i p l e , a s t r i c t l y constructive system, and a business-like accuracy in mastering the material. Roslavetz was, and has remained quite aloof from modernism. Though he used a d i f f e r e n t type of material, Roslavetz fundamentally sought the same as Schoenberg --the precise laws of a severe logic of sounds. Roslavetz r e a l i z e d that true c l a s s i c i s m does not l i e in safeguarding the methods of the "old men" and not in a s t y l i z a t i o n of modern music with t h e i r methods and by using archaic material, but that the question i s of elaborating a s t r i c t system of sound-organiza-ti o n , whence w i l l n a t u r a l l y -follow c l a s s i c a l l y per-f e c t compositions, through a formation of new materi-a l . 2 2 "Constructivism" was a Russian a r t i s t i c and a r c h i t e c t u r a l movement that was f i r s t influenced by Cubism and Futurism and i s gener-a l l y considered to have been i n i t i a t e d in 1913 with the "painting r e l i e f s " — a b s t r a c t geometric construc-t i o n s — of Vladimir Tat 1in. Antoine Pevsner and Naum Gabo joined T a t l i n and his followers in Moscow, and upon publ i c a t i o n of t h e i r j o i n t l y written Realist Manifesto in 1920 they became the spokesmen of the movement. It i s from the manifesto that the name Constructivism was derived; one of the d i r e c t i v e s was "to construct" a r t . Because of t h e i r admiration for machines and technology, Functionalism, and modern i n d u s t r i a l materials such as p l a s t i c , s t e e l , and glass, they were also c a l l e d a r t i s t - e n g i n e e r s . Soviet opposition to the C o n s t r u e t i v i s t s ' aesthetic radicalism resulted in the group's d i s p e r s i o n . 2 3 Roslavets's development of a new system of p i t c h and p i t c h -c l a s s organization, and the "anti-emotionalism and formalism" 2"* that characterized his work, would seem to represent in part a musical manifestation of c o n s t r u c t i v i s m . 2 0 Just as s i g n i f i c a n t are references in a number of sources to the composer as a "Russian Schoenberg" and as a "Scriabin-i s t . " Roslavets denies that his system i s influenced by 7 Scr i a b i n , or by Schoenberg, although he admits "Skryabin (in a musical-formal respect, but in no wise i d e o l o g i c a l l y . . .) i s of course -far nearer to me than Schoenberg, whose work, I con-fess, I have got to know only comparatively r e c e n t l y . " 2 * There are in f a c t i n d i c a t i o n s of limited contact between Sc r i a b i n and Roslavets: N. A. Roslavets i s regarded as a strong follower of S c r i a b i n . . . . Indeed, he [Roslavets] considered Scriabin as his most important teacher. Apart from the f a c t that Roslavets frequently submitted his works to S c r i a b i n , there was no d i r e c t contact be-tween the two. It i s known that Scriabin considered Roslavets's atonal works favourably, p a r t i c u l a r l y the f i r s t Sonata f o r V i o l i n and Piano (1913). During t h i s period, Roslavets formulated his ideas in the t h e o r e t i c a l work Navaya si sterna organ i zac i i zvuMov CA New System of Sound Organization], Roslavets here based his theory on the works of Scriabin; likewise t h i s thesis also contains consideration of the works of A. Schoenberg. Roslavets observed with S c r i a b i n c e r t a i n sound complexes and described them as "syn-t h e t i c chords." This theory of "sound complexes" found t h e i r p r a c t i c a l a p p l i c a t i o n in a s e r i e s of sym-phonic and chamber music works by Roslavets of the period from 1919 to 1924.^ However, according to Schwarz, Roslavets's V i o l i n Sonata (1913) was the f i r s t atonal work by a Russian composer, and his S t r i n g Quartet No. 3 of 1920 employed a "tone row" t e c h n i q u e . 2 8 In f a c t , there are a number of s i m i l a r i t i e s between the composi-t i o n a l technique of Roslavets with that of Schoenberg: [Roslavets] developed the ["synthetic chord"] technique in piano miniatures, so that by 1915 i t had become a 12-note system, embracing concepts of 12-note s e r i a l ism and mirror symmetry. In the V i o l i n Concerto (1925) he added the p r i n c i p l e of complemen-tary p i t c h - c l a s s groups which together form 12-note sets. His s e n s i t i v e , consistent 12-note writing has many s i m i l a r i t i e s with that of Schoenberg, whose work, however, Roslavets did not encounter u n t i l 1923. Roslavets's works "found only limited response. Even-3 t u a l l y , he seemed to relent in h i s d o c t r i n a i r e approach." 3 0 Roslavets's s t y l e changed to a more accessible tonal s t y l e . Roslavyets's CRoslavets's] Marxism and his asso-c i a t i o n with communistic theories and p r a c t i c e could not f a i l to a f f e c t his compositions. He considered i t his duty to come out as composer of revolutionary music. Beginning with 1913, revolutionary music in Russia was created in bulk and poorly, and in accor-dance with s p e c i f i c a t i o n s and requests from the res-pective organisations. Roslavyets was the f i r s t "convinced" composer of music for the p r o l e t a r i a t . He set himself the task of e r a d i c a t i n g the d i l e t t a n -tism from composition of t h i s kind and t h e i r i n v a r i -ably poor s t y l e and taste, usually derived from the repertory of the operetta and " l i g h t " music. Even for the p r o l e t a r i a t Roslavyets endeavoured to write masterly and complex music. But in s p i t e of his theoretic premises that the most complex music i s within the grasp of the workingman, i f i t but "orga-nises tonal matter" well, Roslavyets f i n a l l y had to make a number of concessions, and his revolutionary compositions, written for workmen's clubs, d i f f e r strongly in s t y l e from his "serious" compositions. Everything i s simpler, more p r i m i t i v e and h i s usual complex musical language (the modernistic one) gives way to a p l a i n e r one. As an intermediate essay, Roslavyets wrote several songs to revolutionary texts by present-day Russian poets and some of bygone years, preserving his s t y l e i n t a c t . Such are Songs of the Labouring Professions, and The Songs of the Pevolutionr two volumes which cannot be denied t h e i r s t r u c t u r a l musical m e r i t s . " 1 Roslavets's s t y l e in the cantata October (1924) was described as "somewhat too sentimental" and "reminiscent of Strauss and Wagner. " 3 S B Schwarz mentions that, in the 1930s, Roslavets wrote l i g h t e r theatre music, as well as compositions based on -folk, e s p e c i a l l y Uzbek, m u s i c . 3 3 In addition, Roslavets wrote a g i t a -tion-propaganda music, and, as suggested by Gojowy*s recent l i s t i n g s of pieces by the composer (see Appendix A), c l a s s i c a l tonal compositions in the 1930s and 1940s.3"* Considering these observations, one might t e n t a t i v e l y 9 i d e n t i f y four periods in Roslavets's compositional career, namely: (1) an early, student period, up to 1912; (2) 1912-1919, a post-Conservatory or development period in which his compositional technique was developing; (3) 1919-1925, a mature period that includes both polyphonic s t y l e s (involving linear expressions of tone complexes) and, e s p e c i a l l y towards 1925, more Romantic s t y l e s (e.g., use of T r i s t a n harmonies); 3* and (4) 1925-1944, a period of tonal compositions, including the writing of agitation-propaganda songs and music based on f o l k songs. Trois Compositions pour piano (1914) represents the compos-er's development of compositional technique in the second, post-Conservatory phase of his career. Roslavets developed his syn-t h e t i c chord technique in piano miniatures, such as Trois Compo-sitionsi in f a c t , the f i r s t two pieces of the set involve a s t r i c t a p p l i c a t i o n of the technique whereby one "synthetic chord" or p i t c h - c l a s s complex (PCC) determines the harmonic structures of a piece. Moreover, such pieces, e s p e c i a l l y those composed towards 1915, e x h i b i t c e r t a i n features of twelve-tone ser i a l i s m . 3 d Gojowy's Neue sowjetiscfte Musi A der 20er Ja/>re, and his numerous a r t i c l e s on Russian musical developments, including those dealing s p e c i f i c a l l y with R o s l a v e t s , 3 " present the most detailed published studies of the composer's l i f e and works to date; the former includes an analysis of Trois Compositions. George Perle's b r i e f a n a l y t i c a l discussion of the three pieces in Serial Composition and Atonality represents one of the f i r s t English-language analyses of Roslavets's music. 3 0 IO Although Gojowy and Perle together identi-fy such aspects o-f Trois Compositions as PCCs associated with the pieces, transpo-s i t i o n l e v e l s o-f these PCCs (which -form the bases o-f harmonic u n i t s ) , and general c h a r a c t e r i s t i c s of Roslavets's s t y l e , few d e t a i l s concerning p i t c h - c l a s s (PC) and p i t c h organization in the pieces are provided. Hence, the primary objective of the present t h e s i s i s a comprehensive invest i g a t i o n of PC and pitch organization, beyond what has been treated elsewhere. Chapter Two w i l l deal e x c l u s i v e l y with the "synthetic chord" technique, presenting the observations of Gojowy and Perle as a basis for further a n a l y t i c a l studies. Harmonic successions, t h e i r PC content, and the ordering of PCs within individual "synthetic chords" w i l l also be examined in some d e t a i l . Chapter Three w i l l deal with t o n a l i t y as that concept applies to Roslavets's organization of PCs and pitches, and Chapter Four w i l l treat aspects of octatonic and s e r i a l organization that apply to the music. Notes 1. E r i c Salzman, Twentieth-Century Music: An Introduction, 2nd ed. (Englewood C l i f f s , New Jersey: P r e n t i c e - H a l l , 1974), 27-28. S i m i l a r l y , Jim Samson indicates the s i g n i f i c a n c e of Roslavets: "The importance of Russia as a centre f o r progres-si v e thinking in the a r t s at the turn of the century has only recently been f u l l y appreciated. . . . The atonal V i o l i n Sonata and p r o t o - s e r i a l Three Piano Pieces of Rosslavetz [Roslavets], both dating from 1913-14, and the mechanistic compositions of Mossolov CMosolov] and Desschevov CDeshevovl in the twenties help to place in some sort of perspective the second decade achievements of Stravinsky and Prokofiev. (Jim Samson, Music in Transition: A Study of Tonal Expansion and Atonality, 1900-1920 [London: J. M. Dent and Son, 19773, 73-74.) 2. The d e s c r i p t i o n of "minor experimentator" i s found in Boris Schwarz, Music and Musical Life in Soviet Pussia: Enlarged 11 Edition 1917-1981, 2nd, enlarged ed. (Bloomington, Indiana: Indiana University Press, 1983), 9 (hereafter cited as Mus. Soviet Puss i a) . 3. Information in t h i s chapter on Roslavets i s taken from the following authors (see bibliography -for additional informa-t i o n ) : Nikolai Roslavets, Detlef Gojowy, Lazare Saminsky, and Leonid L. Sabaneyeff CSabaneev]. Encyclopaedic sources include: New Grove Dictionary of Music and Musicians, 6th ed., s.v. "Roslavets" (hereafter cited as Grove, 6th ed.)J Die Musik in Geschichte und Gegenwart, s.v. "Ros1awetz" (hereafter cited as MGG); Das Grosse Lexikon der Musik, s.v. "Ross1awetz"i and Baker's Biographical Dictionary of Musicians, 7th ed., s.v. "Roslavetz". 4. Lazare Saminsky, Music of Our Day: Essentials and Prophecies (New York: International Publishers, 19275 New York: Da Capo, 1975), 264. Concerning the date of b i r t h , some sources indicate the Julian calendar date ( i . e . , December 24, 1880). Curiously, Das Grosse lexikon der Musik indicates January 4, 1881 (December 23, 1880, Julian calendar) as the date of b i r t h . {Das Grosse Lexikon der Musik, s.v. "Ross 1 a w e t z ) Roslavets mentions that he was born in the v i l l a g e of Dushatino, and later-lived and worked in Konotop, both communities in the former gov-ernment d i s t r i c t of Chernigov in the Ukraine. (Roslavets, "Nik. A. Roslavets o sebe i svoern tvorchestve," CNik. A. Roslavets on Himself and His Work], Sovremennaia muzyka CContemporary Music], 5 C1924]: 132-133 Ctrans. in Gojowy, Neue sowjetische Musik der 20er Jahre (Laaber: Laaber-Ver1ag, 1980), 395; hereafter cited as "Ros1avets"-NsM.]) Apparently, Dushatino was renamed Surazh, now part of the Briansk Oblast [region!, based on information in Piemann Musiklexikon: £rganzungsband, 1975 ed., s.v. "Ross 1awets", and in Das Grosse Lex ik on der Musik, s.v. "Rosslawets". 5. Roslavets, "Ros1avets"-NsM, 395. 6. Saminsky echoes Roslavets in indicating that, "while at the conservatory he [Roslavets] was d i s l i k e d for radicalism ." and that once he -finished his studies, he " r i d himself of the conservatory prescriptions very quickly." (Saminsky, Music of Our Day, 264; see also Roslavets, "RosIavets"-NsM, 396.) 7. Roslavets, "Ros1avets"-NsM, 396-393. 8. Gojowy's indication that a c e l l o sonata was composed in Khar'kov, in March of 1921, suggests that Roslavets was l i v i n g in or near the town before his directorship. (Gojowy, "Nikolaj Andreevic Roslavec, ein f rCiher 2w6 1 f tonkompon i st, " Die Musik-forschung, 22/1 [January-March 19691: 37.) Interestingly, one source provides information on the founding in 1922 of a school of composers at the Khar'kov Musical Institute (later the con-servatory) by S. Bogatiryov, although there i s no mention of Roslavets. (Grove, 6th ed., s.v. "Khar'kov".) 12 9. Schwarz, Mus. Soviet Russia, 86. Among his accomplish-ments was the f i r s t Russian introduction to Schoenberg's Pierrot Luna ire. ("Lunnly P'yero Arnol'da Shyonberga," K novim beregam 3 [19233: 28; reference in S w e , 6th ed. , s.v. "Roslavets".) 10. Grove, i b i d . 11. "[The3 ACM's journal Sovremennaia Muzyka ceased p u b l i -cation in March 1929, followed in 1930 by the demise of the ex-ce l l e n t monthly Muzykal'noye Obrazovanie which had represented the independent musical i n t e l l i g e n t s i a and the conservatory c i r c l e s . Only the brash voice of Pro letarsk i i fiuzyk ant [journal of RAPM3 was l e f t , pretending to speak for a l l the musicians. In the meantime, many important members had abandoned the ACM, among them Miaskovsky, and the organization simply ceased to function even pr i o r to i t s dissolution in 1931." (Schwarz, Mus. Soviet Russia, 58-59.) 12. Percy A. Scholes, ed., The Oxford Companion to Music, 9th ed. (New York, Toronto: Oxford University Press, 1955), 895. Roslavets, in his autobiographical a r t i c l e ("Roslavets"-NsM, 398), argued his aesthetical position using "a Marxist defence of an aesthetic of musical positivism, which opposed the idea of an objectively definable emotional quality and which saw the creative act as a moment of the human intellect's highest exertion, looking forward to the subconscious being realized in the form of the conscious and to music based on a new fixed system of tone organization." (Gojowy, Grove, 6th ed., s.v. "Roslavets".) 13. Schwarz, Mus. Soviet Russia, 86. There are no indica-tions in the l i t e r a t u r e to date that Roslavets in fact wrote an opera, much less the f i r s t national Uzbek opera. Curiously, his former composition and orchestration teacher, Sergei Vasilenko, in collaboration with Uzbek composer M. Ashrafi, i s credited with t h i s accomplishment: "In 1938 he [vasilenko] worked in Tashkent on the f i r s t Uzbek opera, Burian [The Snowstorm3." (Grove, 6th ed., s.v. "Vasilenko.") 14. One such "unconfirmed report" about the death of Roslavets in Sib e r i a i s given in MGG, s.v. "Rosiawetz". 15. Gojowy, "Half Time for Nikolai Roslavets (1881-1944): A Non-Love Story with a Post-Romantic Composer," Russian and Soviet Music: Essays for Boris Schwarz, ed. Malcolm Hamrick Brown (Ann Arbor, Michigan: University Microfilms International Research Press, 1984), 215-216; quotation from In the World of Music [V mire muzyki3, (Moscow, 1981): 5. Gojowy also refers to another source concerning the a c t i v i t i e s of Roslavets in the 1930s. iMuzyka I'naia entsiklopediia, [Moscow, 19783, s.v. "Roslavets" [vol. 4, col s . 711-7123.) 16. Grove, 6th ed., s.v. "Roslavets". Interestingly, 13 Montagu Montagu-Nathan states that Roslavets had been " i n f l u -enced a l i t t l e by Rebikof. . . . " (Montagu Montagu-Nathan, Con-temporary Russian Composers [London: Cecil Palmer and Hayward, 1917; Westport, Connecticut: Greenwood, 19703, 315.) Vladimir Ivanovich Rebikov (1866-1920), Russian composer, developed a s t y l e o-f composition that employed the whole-tone scale and augmented t r i a d , and "claimed p r i o r i t y in t h i s respect over Debussy and other European composers." (Baker's Biographical Dictionary of Musicians, 7th.ed., s.v. "Rebikov".) This "earned him a reputation as the -finest Russian impressionist, and he also became known as the -father o-f Russian modernism." (Grove, 6th ed., s.v. "Rebikov".) 17. Roslavets, "Ros1avets"-NsM, 396-398. 18. Grove, 6th ed., s.v. "Roslavets". 19. Roslavets, "Roslavet5"-/Vs/>i 396-397. The reference to "pitch" i s c l a r i f i e d in Chapter Two with discussion of the term "pitch-class" (PC). 20. Ibid., 397. Saminsky states: "From his harmonic foun-dation he evolved several years ago a peculiar system of voice leading and a new polyphony which led to his tonal organiza-tion." (Saminsky, Music of Our Day, 265.) 21. Roslavets, "Ros 1 avets "-/V^ /9, 397. 22. Boris Asafiev, Russian Music from the Beg inn ing of the Nineteenth Century, trans. Alfred J. Swan (Ann Arbor, Michigan:. J. W. Edwards, 1953): 262. 23. The New Encyclopaedia Britannica, 15th ed., s.v. "Constructivism". Interestingly, M. Montagu-Nathan indicates Roslavets's interest in a r t i s t i c aspects associated with the movement: "Roslavets i s a v e r s a t i l e composer and evidently a man of cultivated tastes and wide sympathies. . . . As to exter-nal symptoms i t i s worthy of mention that Roslavets a f f e c t s c o l -oured ink, a circumstance which w i l l have some significance for students.of latter-day tendencies; more s t r i k i n g than t h i s are the Cubist designs which adorn the covers of some of his pieces." (Montagu Montagu-Nathan, Contemporary Russian Composers, 315.) 24. Leonid Sabaneyeff [Sabaneevl, Modern Russian Composers, trans. Judah Jaffe (New York: International Publishers, 1927; Da Capo, 1975), 203. 25. The "fad of such c o n s t r u c t i v i s t music became very popu-lar in the later 1920s, but none was as highly acclaimed as Mosolov's Iron Foundry, c a l l e d a mighty hymn to machine work by one Soviet c r i t i c , a symbol of the enthusiasm of S o c i a l i s t i n -d u s t r i a l i z a t i o n . " (Schwarz, Mus. Soviet Russia, 85; quotation from Is tori a Muzyki Narodov SSSR, [Moscow, 1966 3, vo l . 1, p. 14 169.) Gerald Abraham likewise refers to Roslavets as an anti-romantic c o n s t r u c t i v i s t . (Abraham, "The Reaction Against Roman-ticism: 1890-1914," New Ox ford History of Music, ed. Martin Cooper [Toronto: Oxford University Press, 19743, v o l . 10, p. 137. ) 26. Abraham, i b i d . 27. Michael Goldstein, "Skrjabin und die Skrjabinisten. Das Schaffen Skrjabins und seiner Nachfo1ger—Induktion und Deduktion," Musik Konxepte 32/33. A left sand r Skrjabin und die Skrjabinisten, ed. Heinz-Klaus Metzger and Rainer Riehn, trans, of a r t i c l e from Russian to German by P. Ruhl (Munich: Edition Text + K r i t i k , 1983), vol. 32-33 (September 1983): 181 (my t r a n s l a t i o n ) . Goldstein also includes a short analysis of Roslavets's Uetre nalet i te (1913; text by A. Blok) on p. 188. Other sources indicate Roslavets's association with Scriabin; for example, S i g f r i e d S c h i b l i includes Roslavets in "a close c i r c l e of S c r i a b i n i s t s . " (Sigfried S c h i b l i , Alexander Skrjabin und seine Musik. Grenxuberschreitungen eines prometheischen Geistes. [Munich, Zurich: R. Piper and Co. Verlag, 19833, 348; my translation.) 28. Schwarz, Mus. Soviet Russia, 86. 29. Grove, 6th ed., s.v. "Roslavets". 30. Schwarz, Mus. Soviet Russia, 86. 31. Sabaneev, Modern Russian Composers, 206-207. 32. Schwarz, Mus. Soviet Russia, 86; quotation from E. Braudo, fl/'e Musik, 20/7 (April 1928): S3. Although Schwarz in-dicates 1927 as the date for October, i t was actually composed in 1924. 33. Schwarz, /?us. Soviet Russia, 86. 34. Gojowy, "Half Time," 217-219. 35. Gojowy states: "Around 1920 (Third Quartet, Medita-tion), he again changes from the polyphony and contrapuntal forms to a milder Tristan harmony with the V i o l i n Concerto (1925)." (Gojowy, Neue sowjetische Musik, 985 my translation.) 36. Grove, 6th ed., s.v. "Roslavets"; Gojowy, Neue sowjetische Musik, 138. 37. Gojowy, "Roslavec," Die Musikforschung, 22/1 (1969): 22-38, and "Half Time," 211-220. 38. George Perle, Serial Composition and Atonality, 4th rev. ed. (Berkeley, Los Angeles: University of C a l i f o r n i a Press, 1977), 43-44. I 5" CHAPTER TWO THE INTERVAL-CLASS COMPLEX IN TROIS COMPOSITIONS I n t r o d u c t i o n and T e r m i n o l o g y As t h e a n a l y s e s by D e t l e f Gojowy and G e o r g e P e r l e a r e p i o n e e r i n g s t u d i e s o-f t h e work a-f R o s l a v e t s , we t u r n i n i t i a l l y t o them -for p r e l i m i n a r y i n s i g h t s i n t o Trois Compositions, w i t h w h i c h t h e y b o t h d e a l . The c o m p o s i t i o n a l s y s t e m o-f most e a r l y w o r k s by R o s l a v e t s i s b a s e d on t h e p r i n c i p l e o-f t r a n s p o s a b l e t o n e c o m p l e x e s i n s c a l e -form t h a t r e p r e s e n t t h e e n -t i r e t o n e c o l l e c t i o n i n a g i v e n t i m e - s p a n . A g i v e n t o n e complex d e t e r m i n e s w h i c h t o n e need o r need n o t s o u n d , a l t h o u g h n o t i n w h i c h o r d e r , o c -t a v e , o r m o t i v e . W i t h i n t h e c h r o m a t i c s c a l e , t h e r e a r e e l e v e n p o s s i b l e t r a n s p o s i t i o n l e v e l s -for e v e r y p o s s i b l e c o m p l e x . T h i s s y s t e m was n o t i n v e n t e d and u t i l i z e d e x c l u -s i v e l y by N. A. R o s l a v e t s , b u t i n d e e d , i-f one b e -l i e v e s h i s own t e s t i m o n y , was d e v e l o p e d i n d e p e n d e n t l y o-f S c r i a b i n ' s s i m i l a r s y s t e m . 1 More r e c e n t l y , Gojowy s t a t e s : [ R o s l a v e t s ' s s y s t e m ] was b a s e d on c h o r d s o-f s i x t o e i g h t o r more t o n e s , u s e d . . . a s s u b s t i t u t e s -for t h e - f u n c t i o n a l r e l a t i o n s h i p s o-f c l a s s i c a l t o n a l i t y , w h i c h he d i d n o t r e j e c t b u t t r i e d t o e x p a n d . T h e s e " s y n t h e t i c c h o r d s " o-f s p e c i f i c and i n v a r i a b l e i n t e r -v a l l i e s t r u c t u r e c o u l d be t r a n s p o s e d . . . t o a l l t w e l v e d e g r e e s o-f t h e c h r o m a t i c s c a l e . . . . t i n ] t h e t o n e c o m p l e x , a s u s e d by S c r i a b i n and R o s l a v e t s , t h e o r d e r o-f i t s e l e m e n t s r e m a i n s -f r e e ; t h e c o m p l e x i s d e - f i n e d o n l y b y i t s i n t e r v a l l i c s t r u c t u r e . 2 More s p e c i f i c a l l y , G o j o w y ' s a n a l y s i s i d e n t i f i e s t h e " t r a n s p o s -a b l e t o n e c o m p l e x e s " a s s o c i a t e d w i t h t h e t h r e e p i e c e s , and t h e t r a n s p o s i t i o n l e v e l s ( T - l e v e l s ) o f e a c h c o m p l e x f r o m w h i c h p i t c h 16 c o l l e c t i o n s in the respective pieces are derived. Perle's study in Serial Composition and Atonali ty includes a l i s t i n g in musical notation of the "sets" or transposable tone complexes associated with each piece, an analysis o-f the PC con-tent o-f a short excerpt o-f " I I I " and i d e n t i f i c a t i o n of tone com-plex T-levels, and a b r i e f d e s c r i p t i o n of the s a l i e n t points of Ros1avets's compositional technique, part of which i s quoted below: In his Trois Compositions for piano, Roslavetz employs an independent set for each move-ment. . . . As in Scriabin's works, the set functions simultaneously as scale and chord. Transpositions are used much more f r e e l y , p i v o t a l connections being employed, in general, merely as a means of immediate assoc i at i on. 3 To begin, some c l a r i f i c a t i o n and additional terminology i s required to f a c i l i t a t e further a n a l y s i s . The "transposable tone complex," an important aspect of pit c h and p i t c h - c l a s s (PC) or-ganization in Roslavets's music, i s designated by the d i f f e r e n t authors as "synthetic chord" (Roslavets), "Tonkomplex" (Gojowy), and "set" . (Per le) . S p e c i f i c a l l y , i t involves a c o l l e c t i o n of pit c h - c l a s s e s (PCs) and hence i s more accurately termed a "pi t c h - c l a s s complex" (PCC).° To understand how PCCs are trans-posed and employed in the music, Ex. 2-la i l l u s t r a t e s m. 1 of " I " , with the pitches segmented into c o l l e c t i o n s . These c o l l e c -t i ons can be t e n t a t i v e l y designated as harmonies, given the s i -multaneous occurrences of pitches involved and generally v e r t i -cal o r i e n t a t i o n of pitches in most collections.'* In Ex. 2-lb, the p i t c h - c l a s s e s (PCs) represented in the c o l l e c t i o n s of Ex. 2-la are ordered to i l l u s t r a t e s i m i l a r i t y of PC c o l l e c t i o n s 17 v through tr a n s p o s i t i o n . Each ordered PC i s numbered according to the PC i n t e r v a l i t -forms with the -fi r s t PC o-f the c o l l e c t i o n . Example 2-1. Pitch c o l l e c t i o n s in " I " , m. 1, and corresponding PCC T- l e v e l s . (a)Pitch c o l l e c t i o n s in " I " , m. 1: (b) T-O T-3 T-10 0 1 3 4 6 8 910 0 1 3 4 6 8 9 0 1 3 4 6 8 9 INTERVAL VECTOR: 14 S 6 S 3 31 13 3 3 4 4 21 13 3 3 4 4 2) Segmentation o-f pitches into c o l l e c t i o n s in order to iden-t i f y the PCC T-levels, as shown in Ex. 2-1, i s p a r t i a l l y indica-ted in Gojowy's analysis o-f Trois Compositions which includes the successions o-f PCC T-levels (and measure i n d i c a t i o n s ) . Moreover, both Perle and Gojowy indicate the transposable PCCs associated with each piece.'' But, segmentation o-f pitches into c o l l e c t i o n s i s a r e l a t i v e l y simple matter anyhow, given the gen-e r a l l y homophonic texture o+ the pieces, with many o-f the c o l -l e c t i o n s appearing as si m u l t a n e i t i e s or recognizable arpeggia-tions thereof. More importantly however, the time-spans and temporal placements of the pit c h c o l l e c t i o n s generally coincide 18 with the notated meter, in the sense that the i n i t i a l attack-points of many harmonies correspond to the b a r l i n e or to conven-t i o n a l time-points o-f metric subdivision within the bar (e.g., in 4/4 meter, time-spans i n i t i a t e d on the second, t h i r d , or fourth "beats")." In Ex. 2-lb, the -fi r s t harmony in m. 1 o-f " I " i s designated as T-O because i t i s the -fi r s t o-f the piece, the -fi r s t T-level o-f the PCC. More importantly, i t i s a r e f e r e n t i a l harmony in the sense that, as l a t e r analyses w i l l show, t h i s PC c o l l e c t i o n begins and ends the piece (as do the i n i t i a l PC c o l l e c t i o n s of "I I " and " I I I " , r e s p e c t i v e l y ) , and, of any T-level of the PCC of " I " , i t occurs most frequently and has the greatest t o t a l time-span . Also in Ex. 2-lb, the l i s t i n g of ordered PCs of each c o l -l e c t i o n in m. 1, with PCs numbered according to the PC i n t e r v a l they -form with the f i r s t PC of each scale, i l l u s t r a t e s how the second and t h i r d harmonies of m. 1 are transpositional1y related to the f i r s t , in terms of PC content, with one minor exception ( i . e . , C in T-0 not being transposed in T-3 and T-10). In addi-t i o n , the i n t e r v a l vectors" of the three harmonies are i n d i c a -ted, to i l l u s t r a t e that T-O i s s i m i l a r to a limited extent in i n t e r v a l - c l a s s ( I C ) 1 0 content to T-3 and to T-10, while T-3 and T-10 have the same IC content. The p a r t i c u l a r ordering of T-O PCs, s t a r t i n g with D, i s based in part on Perle's presentation of PCCs for each piece (each at T-O), shown in Ex. 2-2 with ordered PCs numbered as in Ex. 2-lb. 19 Example 2-2. Transposable PCCs of " I " , " I I " , and " I I I " , as i l l u s t r a t e d by Perle, with numbering o-f PCs added. PCC OF T, T-0: 0 1 P C C O F •ii*, T - O : V 0 (1) P C C O F -in-, T - O : 0 1 3 4 8 9 (101 3 4 8 9 11 3 4 8 (9) (10) tin The bracketed PCs in each ordered c o l l e c t i o n represent those PCs or transpositions thereof not appearing with every T-l e v e l , an issue which w i l l be -further investigated in the -fol-lowing section o-f t h i s chapter. Given that the PCCs of " I " and " I I I " are in the prime -form, when one excludes -from considera-t i o n the variant PCs, and given the s i m i l a r i t i e s o-f the three transposable PCCs, D i s the -first PC o-f the ordered PCC at T-0 for " I " , and likewise C#/Db i s the f i r s t f o r the PCC of " I I " , and G f o r the PCC of " I I I " . Based on the PC numbering scheme i l l u s t r a t e d in Exx. 2-1 and 2-2, 1 1 any PC in a given T-level is designated with a number, an "element" number, in order to show i t s r e l a t i o n s h i p s to the other PCs of that T - l e v e l . One PC in nearly every T-level occurrence ( i . e . , c o l l e c t i o n in the music) w i l l be designated with element number "O", although t h i s does not imply any greater s i g n i f i c a n c e to t h i s PC.*-2 Given that 20 c e r t a i n elements do not appear in the PCCs (at T-O) as shown in Ex. 2-2, these w i l l l i k e l y not be represented in the p i t c h c o l -l e c t i o n s of the pieces. O-f course, a PC which i s a given e l e -ment in one T-level cannot be the same element in another T-1eve1. Because the PCC as Roslavets uses i t has a " s p e c i f i c and i n v a r i a b l e i n t e r v a l l i e structure" which can "be transposed . . . to a l l twelve degrees of the chromatic s c a l e , " 4 3 such a PCC w i l l be referred to in the t h e s i s as an interval-c1 ass complex (ICC). Such an ICC consists of an ensemble of ICs spanning the c o n s t i t -uent PCs (as shown in Ex. 2-1 with the i n t e r v a l vector). For purposes of c l a s s i f i c a t i o n , component PCs are abstracted as an ascending scale. The IC r e l a t i o n s h i p s between PCs of a PCC nec-e s s a r i l y remain the same when those PCs are assigned r e g i s t r a l and temporal i d e n t i t i e s in the music. A given ICC i s transposable in the sense that the PCs that co n s t i t u t e i t are transposable. In other words, an ICC may be r e a l i z e d by various PCCs. (It i s understood that the operation of transposition does not apply to i n t e r v a l s or ICs.) T - l e v e l s are designated "T-x", "x" representing the number of semitones of transposition above the T-level of the r e f e r e n t i a l PCC that begins and ends a given piece (T-O). Hence, the T-level i s a simple way of i n d i c a t i n g a harmony's PC content independent of s p e c i f i c temporal and r e g i s t r a l l o c a t i o n . With some exceptions, most i f not a l l of a given T-level*s PCs appear in any given harmony in Trois Compositions. The temporal and r e g i s t r a l or-dering of elements can and usually does vary with every harmony 21 or T - l e v e l . The designation in t h i s thesis o-f a T-level in a given measure i s used to refer to the PC c o l l e c t i o n o-f that T-level or harmony. It i s often not necessary to be concerned with the temporal and r e g i s t r a l configurations of PCs. This chapter w i l l provide more insight into Roslavets's ICC system, incorporating the a n a l y t i c a l observations of Gojowy and Perle as a basis for further d e t a i l e d examination of composi-t i o n a l technique in the pieces. The f i r s t part of t h i s chapter examines the ICCs of the three pieces and how the harmonic units are derived from these ICCs. The second part investigates har-monic successions and T-level occurrences, while the f i n a l sec-tions deal with T - l e v e l s as to PC content, and v e r t i c a l and l i n -ear element ordering within i n d i v i d u a l harmonies and in element successions involving adjacent harmonies. 22 The ICC in Trot's Compositions Gojowy indicates that two o-f these three pieces are each based on a s i n g l e transposable PCC that we consider to be a s i n g l e ICC. The observations o-f Gojowy and Perle generally con-cur, with some minor exceptions. We can c l a r i f y the organiza-t i o n o-f the PC material in a l l three pieces by segmenting each piece into PC c o l l e c t i o n s . ICC o-f " I " Perle and Gojowy c i t e the same PC c o l l e c t i o n as the basis -for the harmonies o-f " I " , except that Perle includes the brack-eted variant element "10" ( i . e . , C in T-O, as represented in Ex. 2-2). The bracketed PCs in Perle's ICCs are those elements not appearing with every T-level occurrence. He indicates that "Cvlariants o-f the set are more or less c o n s i s t e n t l y employed. These are derived not through the chromatic i n f l e c t i o n of set-elements, as in Scriabin's Seventh Sonata, but through the sys-tematic omission of c e r t a i n components of the basic forma-t i o n . " 1 0 The ICC of " I " i s presented in Ex. 2-3a, and the segmenta-tio n of pitches into ICC T-levels (in scale form, with T-levels indicated) in Ex. 2-3b.1«* 23 Example 2-3. ICC of* " I " , with T-level successions. (a)T-O PCCs o-f the ICC o-f " I " : n [no E L E M E N T : 0 1 3 4 6 8 9 1 0 0 (b)Pltches o-f " I " segmented into PCCs at various T - l e v e l s : M E A S U R E : ( 1 ) P I T C H E S : 121 A 2 S C A L A R R E P R E S E N T A T I O N O F P C C : T - L E V E L : O 3 10 24 Example 2-3b continued. (41 (31 (61 25 Example 2-3b continued. (10,111 (12) [131 ¥-*f-—STV-• 6 1 , Vr'*" r -• — r~7zb* ffr*-— Some harmonies contain pitches which cannot be understood as part o-f the PCC Gojowy describes: C5 (m. 1, T-O); B4 (m. 4, T - i i ) ; B5 (m. 7, T - l l ) ; and Eb4 (m. 7, T - l l ) . Perle's variant element "IO" (C) in h i s version o-f the T-O PCC accounts -for a l l but the last o-f these anomalous pitches, Eb4 being element "2" which i s not -found with any other T-level in " I " . The element "10" PCs in question have a subsidiary or elaborative function, although element "2" (Eb) i s a s i g n i f i c a n t bass-line p i t c h . On the other hand, the locations of c o l l e c t i o n s containing variant elements have a c e r t a i n formal s i g n i f i c a n c e : T-O (m. 1) and T-11 (an exact t r a n s p o s i t i o n of the T-O harmony, m. 4) i n i t i a t e the f i r s t and second phrases of the piece, r e s p e c t i v e l y ; and T-11 (m. 7, d i f f e r e n t temporal-registral configuration of pitches to the previous T - l l ) precedes the time-span with the p i t c h -c1imax of the piece (G#6). Another problematic PC c o l l e c t i o n i s that of m. 13. Gojowy i d e n t i f i e s i t as T-O; in f a c t , the PC content i s nearly i d e n t i -cal to T-O, except that G appears instead of Gb. Perle speaks 26 of the p i t c h material as being derived -from "transpositions o-f the set [complex] that are c l o s e l y related in p i t c h content to the o r i g i n a l statement o-f the s e t . " 1 5 * It i s p o s s i b l e to i d e n t i -fy the c o l l e c t i o n as the ICC at T-9 as well as at T-0, since six o-f seven PCs belonging to either T - l e v e l . One p l a u s i b l e expla-nation involves i t s connective function with " I I " : the PC c o l -l e c t i o n in m. 13 i s i d e n t i c a l to the PCC of " I I " at T-10 (Ex. 2-4) . Example 2-4. PC c o l l e c t i o n of m. 13 in " I " . ICC of " I " at T-O: ICC of " I " at T-9: PC Content of m. 13: oM4 ICC of " I I " at T-10: T-level i d e n t i f i c a t i o n in mm. 6-8 i s problematic because of fewer PCs per c o l l e c t i o n and because more than one T-level can be adduced to explain the PC content of each c o l l e c t i o n . Gojowy*s analysis of T-level succession (Ex. 2-3b) explains 27 these in d i v i d u a l c o l l e c t i o n s as " d i f f e r e n t , i r r e g u l a r s c a l e -e x c e r p t s , " 1 0 excerpts of the ICC at some T - l e v e l . Perle does not discuss these measures s p e c i f i c a l l y . Example 2-5 i l l u s -t r a t e s that each of the complete PC c o l l e c t i o n s of the second halves of mm. 6 and 7, and of m. 8, are derived from an expanded version of the basic ICC, which d i f f e r s from the above-mentioned expanded ICC r e a l i z e d in mm. 1, 4, and 7. Example 2-5, s t a f f (a), i l l u s t r a t e s the PC content of the individual harmonies, while s t a f f (b) shows these PCs combined into larger c o l l e c t i o n s ( i . e . , T-levels of the expanded ICC), both in scale form. These are compared with s i m i l a r T - l e v e l s of the basic ICC of " I " on s t a f f (c). 28 Example 2-5. Expanded ICC and T - l e v e l s in mm. 6-8. 161 (SECOND HALF) (7) (SECOND HALF) UIPC CONTENT (b)EXPANDED ICC AI T-0 ...AT T-2 (c)BASIC ICC AT T-0 ...AT T-2 ...T-2 .AT T-9 (81 (a)PC CONTENT ^ 1 il 1 Jl f*'\ (b)EXPANDED ICC AT T-7 • j ) , * J » > ' W IcIBASIC ICC AT T-7 ...AT T-2 2 ^ The expanded PCCs are t r a n s p o s i t i o n a l l y related, with the expanded PCC o-f m. 7, second h a l f , T-2 o-f the expanded PCC o-f m. 6, second h a l f , and the expanded PCC of m. 8 T-7 of the expanded PCC of m. 6. The temporal-registral configuration of pitches in these three time-spans r e f l e c t s t h i s T-O,T-2,T-7 tran s p o s i t i o n a l r e l a t i o n s h i p of the expanded PCC (Ex. 2-3, mm. 6-8). The ex-panded T-0 (m. 6) c l o s e l y resembles the basic ICC of " I " both at T-O and T-7, the expanded T-2 (m. 7) the basic ICC at T-2 and T-9, and the expanded T-7 (m. 8) the basic ICC at T-7 and T-2, with only a -few PCs d i f f e r i n g in each case. Moreover, there are s i m i l a r i t i e s in PC and element content between the expanded ICC, the basic ICC, the PC c o l l e c t i o n in m. 13, and the ICC of " I I " (Ex. 2-6). Example 2-6. Expanded ICC at T-0 and i t s r e l a t i o n s h i p to other PC c o l l e c t i o n s in " I " and " I I " . I C C O F T A T T - 0 : 7 E X P A N D E D I C C A T T - 0 : 9 \}0\o • I " , T - 0 ( H . 1 3 1 / M P , T - 1 0 I C C O F *ir A T T - I : UnilUe the harmonies of mm. 1-5 and 10-13, where a l l PCs of a given T-level are v e r t i c a l i z e d or v e r t i c a l l y oriented in a si n g l e harmonic unit, the expanded PCCs of mm. 6-8 are p a r t i a l l y subdivided into subset c o l l e c t i o n s or, more s p e c i f i c a l l y , subset harmonies. The subdivided PCs form more than one harmonic unit, each with i t s PCs v e r t i c a l l y oriented. Individual subset harmo-nies have PCs that d i f f e r with those of other subset harmonies and other PCs that are invariant; hence, the designation "par-t i a l l y subdivided." This represents a step towards the complete l i n e a r i z a t i o n or l i n e a r presentation of a T-level's PCs, in the 30 sense that a T - l e v e l ' s PCs can be subdivided into more and more subset c o l l e c t i o n s to the point where the subsets are a c t u a l l y i n d i v i d u a l PCs. Such l i n e a r i z a t i o n characterizes later works by Roslavets, although the i n i t i a l T -levels o-f mm. 6 and 7 ( T - l l ) in " I " are l i n e a r i z e d , as i s T - l l (m. 7) o-f " I I I " . (The t e r t i a n harmonies, implied by the successions o-f pitches in these l i n -earized T-levels, are examined in Chapter Three.) Such T-level subdivision, as well as differences in chord structure and tex-ture, d i s t i n g u i s h mm. 6-8 as a formal unit. S i m i l a r l y , there are subdivisions of T-levels into subset c o l l e c t i o n s in mm. 6-8 of " I I " (T-2, T-10, and T-8), and m. 4 of " I I I " (T-7, T-O, and T-5). Thus a l l such T-level subdivision occurs in middle, de-velopmental sections of the pieces. In contrast with " I " and " I I " , there i s a greater tendency towards these harmonic subsets and l i n e a r i z a t i o n s in " I I I " , with the texture being less homo-phonic and more contrapuntal. These d i s t i n c t i v e features of " I I I " are examined la t e r in t h i s chapter. ICC of " I I " As in " I " , one ICC i s the basis of a l l harmonic and melodic structures in " I I " . 1 " * Example 2-7a shows the r e f e r e n t i a l PCC which r e a l i z e s the ICC of " I I " , and Ex. 2-7b, based on Gojowy's a n a l y s i s , 2 0 shows the piece's PCs segmented into T - l e v e l s . 31 Example 2-7. The ICC of " I I " , and PCs partitioned into harmonies. (a)ICC of " I I " : o o E L E M E N T : 0 1 3 4 6 8 9 1 1 0 <b)"II" segmented into PCCs at various T - l e v e l s : 1 2 1 ( 3 1 M E A S U R E : I D P I T C H E S 2 5t hi i . W v—i *p-J u. 4 3 2 = 2 : -r S C A L A R P R E S E N T A T I O N O F P C C S T - L E V E L : O 3 _L 8 1 I 1 0 I Z Z Z E 1 3 3 1 4 1 \ ± h i 5£ i^j 1*. X» 1 * s -9—r w — w 3 a—TT^* 1 0 3 rtT L hf^r i__Jr<,Jy«__.. 7T yjarr*^ A'?-32 33 Gojowy shows no variant element in his -form o-f the ICC, but Perle includes a variant element "1" ( i . e . , not part o-f the re-f e r e n t i a l PCC), bracketed in Ex. 2-7a. Element "1" only occurs in mm. 6-8 in the bass-line in p a r t i a l arpegg i at i ons o-f the T-2 (m. 6), T-10 (m. 7), and T-8 (m. 8) harmonies, r e s p e c t i v e l y . 2 1 The occurrence o-f T-levels with element "1" in mm. 6-8 o-f " I I " , in the middle development section o-f a r e c a p i t u l a t i v e ternary •form, i s s i m i l a r to the use o-f expanded ICCs in mm. 6-8 o-f " I " , and contributes to the -formal r o l e o-f these measures. Unlike variant element "10" in " I " , however, variant element "1" in "I I " i s not associated with less s i g n i f i c a n t functions in the melodic-harmonic structures. It plays an important r o l e in a conventional tonal i n t e r p r e t a t i o n of the harmonic structures, a topic to be treated more f u l l y in Chapter T h r e e . 2 2 The ICCs of " I " and " I I " are quite s i m i l a r . Gojowy notes that the PCs of the ICCs of " I " and " I I " are inversional1y re-l a t e d . 2 3 In f a c t , the T-le v e l s of " I I " could be redesignated as T-levels of the PCC of " I " i t s e l f , with the i n i t i a l PCC of " I I " as T - l l of the PCC of " I " . However, the above-mentioned variant elements in the PCCs of " I " and " I I " make i t d i f f i c u l t to ex-p l a i n PC organization in " I " and " I I " in terms of a s i n g l e ICC. 34 ICC of " I I I " Unlike " I " and " I I " , which have a limited number of v a r i -ations o-f t h e i r respective ICCs, " I I I " apparently has seven v a r i a t i o n s o-f i t s ICC i-f we -follow the segmentation of pitches suggested by Gojowy's presentation of T-level successions. 2"* Example 2-8a presents these v a r i a t i o n s at T-0, each l a b e l l e d with a lower case l e t t e r . To the r i g h t of these PC c o l l e c t i o n s i s a l i s t of T - l e v e l s of these v a r i a t i o n s , with the indic a t i o n s of measures in which they appear. Those v a r i a t i o n s with l e t t e r s "a" to "d" correspond to Gojowy's four ICCs for the piece. In-cluded with these i s Perle's "set" with bracketed variant e l e -ments "9", "10", and "11". Example 2-8b i l l u s t r a t e s the segmen-tat i o n of pitches into PC c o l l e c t i o n s , s i m i l a r to the analyses of Exx. 2-3b and 2-7b. 35 Example 2-8. The ICCs o-f " I I I " . (a)Seven variant ICCs, with T - l e v e l s and locations; Gojowy's -four ICCs (a, b, c, d) and Perle's s i n g l e ICC with variant elements: ELEMENTS: 0 1 2 3 4 6 8 9 10 11 60J0VY a a: T-O.T-5 (N. 1) T-S (N. 12) b: T-l.T-4 (N. 3) W.T-0 (N. 4) c: T-8.T-3.T-7, T-10 (N. 2) T-l l (N. 7) T-2 (NN. 8, 10-lD I T-5.T-0, T-4.T-7 (N. 13) T-0 (NN. 14-15) i: T-8 (NN. 3-6) T-6 (H. 8); T-9 (N. 9) e: T-l IN. 3) PERLE mJOLm f. T-5 «N. 4) L . L . Iv l i L,, 9: T-0 (N. 12) f f = 36 Example 2-8 continued. (b)"111" segmented into PC c o l l e c t i o n s : ( 2 1 M E A S U R E : [ 1 1 P I T C H E S 3 I 1 3E 5? S C A L A R P R E S E N T A T I O N O F PCCs T - L E V E L : 0 S I 8 JUL. ( 2 ) ( 3 1 [ 4 1 HP 33 J i s 10 I I I 1 J 4 " - i ' 7 37 38 The differences between the ICCs c i t e d by Gojowy and Perle r e f l e c t the i nc 1 us i veness o-f t h e i r respective ICCs. While Gojowy uses -four ICCs (with no variant PCs) to account -for the most -frequently occurring c o l l e c t i o n s or th e i r transpositions, Perle has only one ICC with three variant PCs. Although Gojowy's ICCs and T-l e v e l s account -for the PC con-tent o-f most harmonies in " I I I " , the concept o-f -four d i f f e r e n t ICCs employed in " I I I " i s problematic. Why should the f i n a l piece of t h i s set be deemed so r a d i c a l l y d i f f e r e n t from " I " and " I I " in terms of compositional technique that i t should embrace four ICCs, e s p e c i a l l y in l i g h t of i t s smaller dimensions? More-over, the perception of four d i s t i n c t harmonies based on these four d i f f e r e n t ICCs would be u n l i k e l y . Perhaps the strongest indicator for the use of one ICC i s the rather unique musical orthography of the ICC of " I I I " ( i . e . , the mixture of sharps and f l a t s as accidentals in the scalar presentation of the ICC PCs, and PC i n t e r v a l s formed), and the consistency with which pitches of i n d i v i d u a l c o l l e c t i o n s in the music conform to i n t e r v a l l i e r e l a t i o n s h i p s suggested by the ICC PCs (Fig. 2 - 1 ) . 2 0 39 Example 2-9. Musical orthography o f the ICC o-f "III" (a)ICC at T-0: T-0 LEVEL PCs: 6 - 61 - Bb - B - Db - DI - <E - F - Gb) - 6 ELEMENT: 0 1 3 4 6 8 9 10 11 0 PC INTERVALS 1 2 1 2 2 1 1 1 1 i CNRONATIC SENITONE (AUGMENTED PRIME) DIATONIC SENITONES (NINOR 2NDS) DOUBLY AU6NENTED PRIME DIMINISHED 3RD CHROMATIC SENITONE DIMINISHED 3RD CHROMATIC SEMITONE (b)T-levels in "III": MEASURE: 111 T-LEVEL: O [2] C2) 7 10 131 1 (3) ( 3 ) 4 141 7 (3) (3) (3) 40 Example 2-9 continued. (41 (5-6) [71 [8) 5 8 11 2 ii) $ ~ — ^ — L T n y-n+v0 ' v > ^ " — — -(81 [?] [10-111 6 9 2 [121 5 t r i a l As'*'*** , , L j l j i i *v*— [121 [131 0 5 0 4 0) (131 (14-151 7 0 Note: Boxed pitches are those elements (e.g., "9", "10", "11") not occurring with every T-level, and bracketed in Perle's "set". Elements missing from a T-level are indicated by a gap in the scale and a bracketed element number above the s t a f f . Pitches that are added to the T-level are included in the scale with brackets. F i n a l l y , pitches that are enharmonical1y named in the music, as to the ICC at T-O, are included in the scale with the name (based oh the ICC) above or below as a bracketed s o l i d notehead. Thus the musical orthography strongly suggests that a single ICC i s the source for the PC c o l l e c t i o n s of " I I I " . (Hence, Gojowy's observations to the contrary are discussed in Appendix B.) Some variations shown in Ex. 2-8a cannot be ade-quately explained as forms of any of the suggested ICCs. For example, the i n i t i a l c o l l e c t i o n of m. 3 (T-l) includes elements "11" (G) and "3" (B)j Gojowy designates this PCC as "irregular." 41 These additional elements can be thought o-f as belonging to the second T-1 harmony in m. 3 (Ex. 2-10). Example 2-10. PC c o l l e c t i o n s , m. 3. T-1 T-1 T-4 This second T-1 c o l l e c t i o n o-f m. 3 i s tranposed at T-4 (m. 3), and T-7 and T-O (m. 4). Perle in -fact c i t e s these PC c o l -l e c t i o n s as evidence that Roslavets c o n s i s t e n t l y omits s p e c i f i c elements (in t h i s case, elements "3" and "11") to produce v a r i -ant T - l e v e l s . * * Similar to the omitted B (element "3") of the second T-1 harmony, m. 3, and i t s occurrence in the preceding (T-1) harmony, element "3" PCs, omitted from T-4 (D, m. 3), T-7 (F, m. 4), and T-O (Bb, m. 4), are found in preceding harmonies (Ex. 2-11) 42 Example 2-11. Element "3" in mm. 3-4. As indicated e a r l i e r , the texture o-f m. 4 i s strongly remi-niscent o-f mm. 6-8 in " I " where the three T-levels (T-O, T-2, and T-7), embodying a multiple transposition o-f a melodic-har-monic -figure, are each subdivided into three separate "subset" harmonies. F i n a l l y , Ex. 2-12 demonstrates that the second PC c o l l e c -t i o n o-f ro. 12 (T-O) i s a modified inversion of that of T-0. 43 Example 2-12. T-0 c o l l e c t i o n , m. 12, as an inversion of ICC at T-O. PCs: Db - Eb - 6b - 6 - Bbb - Bb - B - Db I N T E R V A L * . 2 3 1 2 1 1 2 PCs: I N T E R V A L : I C C A T T - 0 Ob - 0 1 - E - F - 6 - 6 1 - Bb - B - Db 2 1 1 2 1 2 1 2 Ultimately, the ICC indicated by Perle proves to be most useful as the unbracketed elements occur in at least 80% of the T-le v e l s o-f " I I I " , and the bracketed elements less often. E l e -ment "2" occurs only once and i s l o g i c a l l y not included in the PCC, although element "11" might as well have been excluded too as i t occurs only twice in the e n t i r e piece. Two-thirds of occurrences of these variant elements in " I I I " are decorative or otherwise s t r u c t u r a l l y less s i g n i f i c a n t pitches ( i . e . , occurring as inner-voice pitches, and/or having short durations). Hence, there i s a r e l a t i o n s h i p , although not altogether consistent, between element occurrence and the func-tion or r e l a t i v e s t r u c t u r a l importance of the variant element. With the ICCs established, the groundwork has been l a i d for the subsequent discussion of harmonic successions and the asso-ciated T - l e v e l s . 2 3 * 44 Harmonic Successions and Successions of Transposition-Levels The study of harmonic successions in Trois Compos it i ons i n -volves, to a large extent, the study o-f successions o-f T- l e v e l s . As has been explained, the PC content o-f a s i n g l e harmony in a given piece i s , with some exceptions, ultimately based on the PC content o-f one T-level o-f the ICC associated with that piece. This study w i l l i n i t i a l l y be concerned with t r a n s p o s i t i o n a l re-lat i o n s h i p s o-f adjacent T - l e v e l s in a harmonic succession, and tran s p o s i t i o n a l cycles which -form the basis o-f many such adja-cencies in Trois Compositions. This section and the one suc-ceeding i t w i l l t e n t a t i v e l y e s t a b l i s h which T-levels are harmon-i c a l l y s i g n i f i c a n t in the pieces. Transpositional Relationships o-f Adjacent T-Levels One o-f the c h a r a c t e r i s t i c s o-f harmonic successions in Trois Compositions involves the t r a n s p o s i t i o n a l r e l a t i o n s h i p s o-f adja-cent T-levels and the -frequencies o-f occurrence o-f such r e l a -tionships (Fig. 2 - 1 ) . 45 Figure 2-1 Transpositional r e l a t i o n s h i p s between successive T - l e v e l s in " I " , " I I " , and " I I I " . (a)T-levels and IC r e l a t i o n s h i p s : •r M E A S U R E : I 5 6 8 1 0 T - L E V E L : 0 - 3 - 1 0 1 - 4 7 - 1 0 - 4 1 1 - 9 - 2 5 1 1 - 0 1 1 - 2 7 3 - 6 P C I N T E R V A L S : 3 7 3 3 3 3 6 7 1 0 5 3 6 1 1 1 3 5 8 3 I C : 3 5 3 3 3 3 6 5 2 5 3 6 1 1 3 5 4 3 1 0 1 1 1 2 1 3 6 - 3 - 6 - 9 - 4 - 9 0 9 3 7 5 3 3 3 5 5 3 •IV M E A S U R E : 1 2 3 4 5 6 7 8 9 T - L E V E L : 0 - 5 8 - 1 1 0 - 3 1 0 - 3 6 - 9 2 - 5 1 0 - 3 8 - 1 1 - 4 7 P C I N T E R V A L S : 5 3 5 9 5 7 5 3 3 5 3 5 5 5 3 5 3 I C : 5 3 5 3 5 5 5 3 3 5 3 5 5 5 3 5 3 9 1 0 1 1 1 2 1 3 - 1 4 7 0 - 5 0 - 5 0 0 5 5 7 5 7 0 5 5 5 5 5 0 •ur M E A S U R E : 1 2 3 4 5 , 6 7 8 9 1 0 , 1 1 T - L E V E L : 0 - 5 8 - 3 - 7 - 1 0 1 - 1 - 4 7 - 0 - 5 8 1 1 2 - 6 9 2 P C I N T E R V A L S : 5 3 7 4 3 3 0 3 3 5 5 3 3 3 4 3 5 I C : 5 3 5 4 3 3 0 3 3 5 5 3 3 3 4 3 5 1 0 , 1 1 1 2 1 3 1 4 , 1 5 2 - 5 - 0 5 - 0 - 4 - 7 0 3 7 5 7 4 3 5 3 5 5 3 4 3 5 46 Figure 2-1 continued. (b)Frequencies of occurrence of PC i n t e r v a l and IC r e l a t i o n s h i p s between adjacent T - l e v e l s in " I " , " I I " , and " I I I " : P C I N T E R V A L : l l l l O 3 9 4 8 5 7 6 • I " : 1 1 1 1 1 1 1 3 3 2 •ir: 6 1 li 2 • I I P : 1 1 3 6 3 T O T A L : I l l 2 8 2 3 1 2 0 8 2 I C : l 2 3 4 5 6 • P : 2 l 1 2 1 6 2 • I P : 7 1 3 • H P : 1 1 3 9 T O T A L : 2 l 3 0 4 2 8 2 The IC r e l a t i o n s h i p s o-f adjacent T-levels occurring most -frequently are ICs 3 and 5, which Gojowy i d e n t i f i e s as charac-t e r i s t i c o-f many harmonic successions in Roslavets's works. In the succession o-f t r a n s p o s i t i o n a l l e v e l s , d e f i n i t e r e g u l a r i t i e s can be observed. The chromatic progression i s d e f i n i t e l y avoided, but, on the other hand, progressions by minor t h i r d s are frequent, as are those by fourths and f i f t h s . 2 0 Transpositional Cycles of T-Levels Not only are adjacent T-levels usually related by IC 3 or 5, but there often appears a succession of several T - l e v e l s in which adjacent T - l e v e l s are related e x c l u s i v e l y by one of these ICs, frequently ascending. For example, in " I " , mm. 1-3 (see F i g . 2 - l a ), the T-level succession T-IO,T-1,T-4,T-7,T-10 exclu-s i v e l y involves an ascending IC 3. Where T-x i s followed by T-x+3, T-x+6, T-x+9, T-x+O, and so on (e.g., T-10, T-1, T-4, T-7, T-10), such a succession w i l l be termed a T-level cycle, 47 s p e c i f i c a l l y a PC-interval 3 cycle (or int e r v a l 3 c y c l e ) . There are in f a c t three i n t e r v a l 3 cycl e s : T-O, T-3, T-6, and T-9 (cycle 3-0)5 T - l , T-4, T-7, and T-10 (cycle 3-1)5 and T-2, T-5, T-8, and T - l l (cycle 3-2). The i n t e r v a l 5 cycle involves: T-O, T-5, T-10, T-3, T-8, T - l , T-6, T - i l , T-4, T-9, T-2, and T-7. Such cycles of T-lev e l s are the basis of harmonic succes-sions in the p i e c e s . 2 " Oftentimes, however, only a few T-lev e l s o-f a cycl e are used be-fore a transference to another cy c l e or components thereof. In some instances, a s i n g l e T-level of one cycle i s interpolated with T-l e v e l s of another c y c l e . Moreover, a T-level of a cycle ( e s p e c i a l l y an i n t e r v a l 3 cycle) may occur out of order with respect to other members of the cyc l e . "I". Figure 2-2a presents the T-level successions- of " I " , i l l u s t r a t i n g the T-level components belonging to each i n t e r v a l 3 cycle, while F i g . 2-2b i l l u s t r a t e s the r e l a t i o n s h i p of these cycles to the i n t e r v a l 5 cyc l e . 48 Figure 2-2. T-level successions of " I " and IC c y c l e s . (a)Interval 3 cycles and T - l e v e l s belonging to each, with underlying balanced pattern o-f succession: M E A S U R E 1 2 3 4 T - L E V E L C Y C L E S 3 - 0 : 0 - - 3 9 3 - 1 : 1 0 - - 1 - 4 - 7 - - 1 0 - - 4 5 6 7 8 1 0 , 1 1 1 2 1 3 3 - 2 : 3 - - 6 - - 3 - 6 - - 9 . . . 9 - - 0 7 4 1 1 . . . 2 — 5 — — 2 3-o: « « 3 - 1 : I H I I H I I I I H I H I I 3 - 2 : H H i m i l l H . . . f W * t H...IIHIHI...HW 3 - 0 . 3 - 0 3 - 1 . .3-1 3 - 2 . (b)Ascending i n t e r v a l 5 c y c l e o-f T - l e v e l s , with T - l e v e l s "I " derived -from t h i s c y c l e and the i n t e r v a l 3 cycles (indicated in brackets on the le-ft): I N T E R V A L 5 C Y C L E * . 0 - 5 - 1 0 - 3 - 8 - 1 - 6 - 1 1 - 4 - 9 - 2 - 7 - 0 - 5 - 1 0 - 3 - 8 - 1 - 6 - 1 1 - 4 - 9 - 2 - 7 - 0 M E A S U R E : 1 T - L E V E L : 0 -( 3 - 0 ) M E A S U R E : I . . ! 2 T - L E V E L : I O 1 4 -(3-1) M E A S U R E : 3 T - L E V E L : 4 (3-D : • M E A S U R E : 4 . . : T - L E V E L : 11--(3-2) M E A S U R E : T - L E V E L : ( I N T E R V A L 5 ) M E A S U R E : t n 10-11 12 T - L E V E L : ( 0 - 3 1 . . . 3 6 9 (3-0) : -10 - 2 — 5 - 5 -6 - 1 1 -7 - 1 1 — 8 - 2 - 7 N E A S U R E : T - L E V E L : 12.: 4 -1 3 - 0 49 Note: The T-level succession o-f " I " i s indicated by following the horizontal dash l i n e from l e f t to right and continuing on the following l i n e . In F i g . 2-2a, T-level successions are shown with components of the i n t e r v a l 3 cycles on separate l i n e s . The transference from one i n t e r v a l 3 c y c l e to another i s apparently based on a "balanced" (rather than a purely symmetrical) pattern of cycle appearance. The progression from cyc l e 3-0 (m. 1) to 3-1 (mm. 1-3) to 3-2 (mm. 4-7) and f i n a l l y back to 3-0 (mm. 10-13) i s not f u l l y balanced unless one i n t e r p r e t s T-7 (m. 8) and T-4 (m. 12) as references to the 3-1 c y c l e , of which these two T - l e v e l s are components. This 3-1 c y c l e occurs before the f i n a l 3-0 cycle (mm. 10-13). Such a progression of i n t e r v a l 3 T-level cycles i s then the underlying balanced structure upon which the harmonic organization of " I " i s based in part. The 3-0 c y c l e (with com-ponents in mm. 1 and 10-13) acts as the framework fo r the T-level successions of the piece, with the i n i t i a l T-0,T-3 succes-sion (m. 1) being completed in mm. 10-13 (the r e c a p i t u l a t i o n ) with T-3,T-6,T-9,T-O. The two other i n t e r v a l 3 cycles, 3-1 and 3-2, involve most of the other T - l e v e l s , and are in some degree associated with the piece's development. The central 3-2 cycle (mm. 4-7) coincides with the approximate midpoint of " I " . The three i n t e r v a l 3 cycles are components of the i n t e r v a l 5 c y c l e whereby each in t e r v a l 3 c y c l e T-level (e.g., T-O, T-3, T-6, and T-9 of the 3-0 cycle) appears at a regular i n t e r v a l in the i n t e r v a l 5 cycle; in other words, every t h i r d component (see the top of F i g . 2-2b). One can thus r e l a t e the i n t e r v a l 3 cycles, whose components are i s o l a t e d on separate l i n e s in F i g . 50 2-2b, to the a l l - i n c l u s i v e i n t e r v a l 5 c y c l e . The i n t e r v a l 5 c y c l e apparently controls the sequence o-f T-levels or, more spe-c i f i c a l l y , the transference from one i n t e r v a l 3 c y c l e to anoth-er. The i n t e r v a l 5 cycle, in conjunction with the i n t e r v a l 3 cycles, i s also the basis for some incompatible i n t e r p o l a t i o n s (e.g., T-9, m. 4, and T-4, m. 12, among others). The i n i t i a l T-0,T-3 (cycle 3-0, m. 1) t r a n s f e r s to the 3-1 c y c l e (mm. 1-3) by moving one T-level back on the i n t e r v a l 5 c y c l e (T-3 to T-10, m. 1). (Note the v e r t i c a l dotted l i n e in F i g . 2-2b connecting the T-level ending one horizontal l i n e to that beginning another horizontal l i n e . For ease of viewing, additional v e r t i c a l dotted l i n e s beginning at the top of F i g . 2-2b connect the i n t e r v a l 5 cycle to the aforementioned interpo-lated T-levels.) Once the 3-1 c y c l e i s completed with T-4 (m. 3), there i s a transference to the 3-2 c y c l e (mm. 4-7), also by moving back one T-level on the i n t e r v a l 5 cycle. S i m i l a r l y , the i n t e r p o l a t i n g T-4 level in m. 12 ( i . e . , component of the 3-1 cycle interpolated in the 3-0 cycle of mm. 10-13) i s derived from the i n t e r v a l 5 cycle through a reversal in d i r e c t i o n in the c y c l e ' s order. Another interpolated T - l e v e l , T-9 in m. 4 ( i . e . , component of the 3-0 c y c l e interpolated in the 3-2 cycle of mm. 4-7), i s likewise explained by a s i m i l a r procedure. In other words, such transferences and i n t e r p o l a t i o n s involve i n t e r v a l 7 r e l a t i o n s h i p s between the T-levels in question. The other s i g -n i f i c a n t T-level succession not explained by i n t e r v a l 3 cycles, the T-0,T-2,T-7 sequence (mm. 6-8), i s based in part on a rota-tion of the T-2,T-7,T-O portion of the i n t e r v a l 5 c y c l e . 51 In conclusion, the i n t e r v a l 5 c y c l e - - i n conjunction with the i n t e r v a l 3 eyeles--would appear to be the basis of most successions in " I " , e s p e c i a l l y the aspects o-f transference and i n t e r p o l a t i on. "II". The T-level successions o-f " I I " are based on the i n -ter v a l 5 cy c l e . Figure 2-3 shows the cycle i s modified, how-ever, because c e r t a i n T-levels are omitted, and inserted e l s e -where in the piece. These transferred T-level successions are la b e l l e d as A, B, C, and D in F i g . 2-3. Figure 2-3. T-level successions of " I I " and the i n t e r v a l 5 eyele. M E A S U R E : 1 2 3 -4 5 6 7 8 9 10-13 T - L E V E L : 0--5 8-1--10--3--6 -9 . -2-5-10-3--8-11--4-7--0-5-0 Ca • a • Ba ••••aaaa Da a a a Aa a a a I N T E R V A L A . . . C . . . 0 . . . . 5 0--5--10--3--8--1 -6--11--4--9-2 - 7 - 0 C Y C L E : B T-level succession C (T-10,T-3) and D (T-li,T-4) involve i n t e r v a l 5 c y c l e components out of sequence. 3 0 Successions B (T-5,T-10,T-3,T-8, mm. 6-8) and A (T-O,T-5, mm. 10-12) are reca-p i t u l a t i o n s of e a r l i e r successions; A r e c a p i t u l a t e s the i n i t i a l succession of " I I " following the completion of the i n t e r v a l 5 cycle. B would also seem to have some formal s i g n i f i c a n c e as i t occurs in the development, beginning with the harmony associated with the melodic climax point of the piece. 52 "III". Figure 2-4 presents the T-level successions of "I I I " and the T-level cycles that are components thereof. Figure 2-4. T-level successions o-f " I I I " and the T-level eye 1es. (a)Surface successions: M E A S U R E : 1 3 4 5-6 7 8 9 1 0 - 1 1 1 2 1 3 T - L E V E L : 0 - - 5 - - 8 — 3 - - 7 - - 1 0 — I ~ 4 — 7 — o ~ 5 — 8 — 1 1 — 2 - 1 6 - 9 ) - 2 5- io) -5 C Y C L E S : 1 I ( ) ( ) . T 3 - 1 * * 3 - 2 I N T E R V A L 5 M E A S U R E : 8 9 10-11 T - L E V E L : 2—6—9—2 1 1 1 1 1 1 1 1 1 1 M E A S U R E : 12 13 : : : 14-15 T - L E V E L : 5--0--5-0-4--7-0 (b) Under 1 y i ng symmetrical T-level structure o-f " I I I " : M E A S U R E : 1 2 3 4 5 , 6 7 8 9 1 0 1 2 1 3 1 4 T - L E V E L : 0 - 5 8 - 3 - 7 - 1 0 1 - 4 7 - 0 - 5 8 1 1 2 - 6 9 2 5 - 0 5 - 0 - 4 - 7 0 0 ( 5 ) 7 7 - 0 - 5 5 ( 7 ) 0 3 - 1 I N T E R V A L 5 3 - 2 The T-level successions o-f mm. 2, S-iO, and 13-15 (shown on the l e f t side of F i g . 2-4a) are related in part through transpo-s i t i o n as the dotted v e r t i c a l l i n e s suggest. Harmonic-melodic f i g u r a t i o n s in mm. 1-2 are transposed with modifications in mm. 12-13, while the f i n a l two phrases (mm. 8-11 and 12-15) cadence on transpositions of the same arpeggiated f i g u r a t i o n . The other T-level successions involve cycles 3-1 (mm. 2-4) and 3-2 (mm. 4-13), connected in m. 4 by an in t e r v a l 5 cycle segment (T-7,T-O, T-5). The complete 3-0 cycl e does not occur in adjacent T-le v e l s as do the other IC-3 cycl e s . In a sense, cycles i n i t i a t e d by T-7 in mm. 2-4 and T-5 in 53 mm. 4-13 involve prolongations o-f these T-levels. In t h i s con-text, prolongation r e f e r s to a s i t u a t i o n whereby a T-level i s r e i t e r a t e d , with a limited number of other T - l e v e l s between the i n i t i a l occurrence and the r e i t e r a t i o n . Invariance of the r e i t -erated T-level's PCs through the intervening T-1eve 1(s)--espe-c i a l l y in the form of p i t c h c o n t i n u i t y — f a c i l i t a t e s the percep-tion of T-level prolongation. P a r t i c u l a r l y when the intervening T-l e v e l s are related to the r e i t e r a t e d T-level and to each other by ICs 3 or 5, there i s a greater incidence of PC invariance. Such PC invariance in IC-3-related T - l e v e l s or, more s p e c i f i c a l -l y , in T - l e v e l s of an i n t e r v a l 3 c y c l e , w i l l be examined in a l a t e r section of t h i s chapter; a discussion of prolongation i s to be found in Appendix B. Hence, there i s a simpler symmetrical structure involving T-O, T-5, and T-7 underlying the T-level successions (Fig. 2-4b). T-5 and T-7 are symmetrically related to T-O ( i . e . , i n t e r v a l 5 above and below). Because of t h i s symmetrical structure, m. 4 i s an apparent foc a l point of the piece. Surface features such as the octave ascent in the melody and inner voices contribute to t h i s mea-sure's s i g n i f i c a n c e . S i m i l a r l y , mm. 6-8 in " I " appear to be a f o c a l point of that piece, aside from melodic, harmonic, rhyth-mic, t e x t u r a l , and formal reasons. The harmonic successions of " I " , l i k e those of " I I I " , are generally based on i n t e r v a l 3 T-level cycles with the exception of mm. 6-8, where the i n t e r v a l 5 cycle segment ( i . e . , T-O,T-2,T-7) occurs. The fact that T-O follows, rather than precedes, T-2,T-7 in the i n t e r v a l 5 cycle does not diminish the s i g n i f i c a n c e of the cycle's appearance. 54 Moreover, both mm. 6-8 in " I " and m. 4 in " I I I " involve the sub-d i v i s i o n o-f T-level PCs o-f three successive T - l e v e l s each into three d i s t i n c t , subset harmonies, with the multiple transposi-t i o n o-f the i n i t i a l three-harmony -figuration in each case. This s i m i l a r i t y also rein-forces the o v e r a l l s i m i l a r i t i e s of these measures and t h e i r -function in the respective pieces. Based on t h i s preliminary study o-f harmonic and T-level successions, one can say that " I I " and e s p e c i a l l y " I I I " involve a t i g h t e r control o-f harmonic organization than " I " because o-f t h i s greater r e l i a n c e on in t e r v a l 3 and 5 cycles as bases -for successions. This l i m i t a t i o n o-f harmonic successions to c e r t a i n -formulae i s a d i s t i n c t i v e c h a r a c t e r i s t i c o-f Roslavets's composi-t i o n a l t e c hnique. 3 1 T-Level Occurrences and Their Rhythmic C h a r a c t e r i s t i c s : Towards a Hierarchy o-f T-levels The a n a l y t i c a l examples indicate that c e r t a i n T-levels oc-cur more frequently than others. This suggests that c e r t a i n T-le v e l s are more s i g n i f i c a n t in the harmonic structure of the pieces, so that there i s in fact a hierarchy of T - l e v e l s . Such a hierarchy might be based not only on T-level frequency of oc-currence but also on the t o t a l time-spans a l l o t e d to individual T- l e v e l s throughout each piece, and on the location of T-levels in r e l a t i o n s h i p to formally s i g n i f i c a n t time-points. This h i e r -archy i t s e l f suggests a form of t o n a l i t y since t o n a l i t y involves in part "the h i e r a r c h i c ordering of PC f a c t o r s " whereby "pitch content i s perceived as f u n c t i o n a l l y related to a s p e c i f i c 55 p i t c h - c l a s s or p i'tch-c 1 ass-comp lex of r e s o l u t i o n . " 3 2 These dif-ferent aspects of T-level occurrence, which e s s e n t i a l l y concern T-level rhythmic c h a r a c t e r i s t i c s , are examined in t h i s section to i n f e r such a hierarchy of T-l e v e l s . To begin, the harmonic rhythm of T-levels in the three pieces i s i n d i v i d u a l l y analyzed. Harmonic rhythm of "Z". Example 2-13a presents the harmon-i c rhythms of T-lev e l s in " I " with the time-spans of each T-level indicated by durational notation independent of p i t c h . A chart i n d i c a t i n g the form of " I " i s also included (Ex. 2-13b), for the purpose of analyzing T-level location in r e l a t i o n to formally important time-points. Example 2-13. Harmonic rhythm and form of " I " . (a)Harmonic rhythm of " I " : M E A S U R E : 1 2 3 4 5 6 7 T - L E V E L : 0 3 10 1 4 7 10 4 11 9 2 5 11 0 11 2 D U R A T I O N O F T - L E V E L : V\- J J iU li •>) R H Y T H M O F S U B S E T H A R M O N Y : M E A S U R E : 8 9 10 11 12 13 T - L E V E L : 7 3 6 3 6 9 4 9 0 (J- c) 3 J < J J 0 J J J . P 56 (b)Form of " I " (modified r e c a p i t u l a t i v e ternary form) : C A3: expos i t i on mm. 1-3 1st phrase m. 1 tc3 m. 2 Cc3 mm. 1 and 2 (Cc3-extension) have 4 modifications of i n i t i a l motive, m. 1 m. 3 Cd3..... cadence (with e l i s i o n , into m. 4) mm. 4-5 2nd phrase m. 4 [ c * 1 . . . . i n i t i a l f i g u r a t i o n transposition of i n i t i a l f i g u r a t i o n , m. 1, followed by r e p e t i t i o n of another modifica-tion (arpeggiations) of i n i t i a l mot i ve m. 5 Ce3 ..... cadence (with e l i s i o n , into m. 6); 3-2 T-level cycle components in mm. 4-7 might suggest mm. 4-5 as beginning of development CB3: development/new material mm. 6-9 3rd phrase m. 6 Cf-g3 m. 7 C f * - g ' 3 . i n i t i a l f i g u r a t i o n , m. 6, repeated with modifications in m. 7 m. 8 Cg"3....modified transposition of Cg3, m. 6 in mm. 7 and 8; abrupt cadence, m. 9 with rest CA'3: modified r e c a p i t u l a t i o n mm. 10-13 4th phrase m. 10 Cc"3 m. 11 Cc"3...mm. 10-11 modified (arpeggiated) transposition of m. 2 f i g u r a t i o n s m. 12 C c " 3 . .modif led Cc"3 m. 13 Cc""3..cadence; mm. 10-13 have limited s i m i l a r i t i e s with mm. 1-3 In mm. 3-4 and 8-9 (Ex. 2-13a), there are bracketed rhythms above the s t a f f that indicate the time-spans of harmonies ( i . e . , T-4 and T-7, respectively) including r e s t s which follow. Par-t i a l l y because of the i r r e g u l a r i t y produced in the harmonic rhythm by such rests and the sense of deceleration, the T-4 and T-7 harmonies (mm. 3-4 and 8-9 respectively) delineate phrases. 57 The harmonic rhythms o-f T-level successions in " I " play an important r o l e in del i n e a t i n g form. For one thing, variances in the time-spans o-f harmonies concur with apparent -formal d i v i -sions. In mm. 1-5 (the i n i t i a l "A" section of the ternary form), the most common and shortest time-span of the indi v i d u a l harmonies i s the quarter value, with longer h a l f - and dotted-half values found at phrase beginnings and in m. 5, the f i n a l measure of t h i s section. Measures 10-13 are s i m i l a r , with quar-ter-value harmonic rhythm and the dotted-half-value in m. 13. In contrast, the harmonic rhythm of mm. 6-9 i s more complex. If one defines the harmony in terms of the T-levels (both basic and expanded), the most common and shortest T-level time-span of mm. 6-9 i s the dotted-eighth value. This indicates a deceleration in the harmonic rhythm between mm. 1-5 and mm. 6-9, and a conse-quent acceleration (mm. 6-9 to mm. 10-13). On the other hand, i f the rhythm of the subset harmonies i s taken into considera-t i o n , then the most common and shortest T-level time-span of mm. 6-9 i s the eighth-value, which indicates an acceleration and consequent deceleration involving mm. 1-5, 6-9, and 10-13, res-p e c t i v e l y . However one perceives harmonic rhythm in mm. 6-9, the acceleration and/or deceleration concurs with changes in other musical parameters (e.g., the compound rhythm, and meter) in these measures. Har-monic r-hythm in "II". Example 2-14 presents the harmon-ic rhythm and form of " I I " . 58 Example 2-14. Harmonic rhythm and -form o-f "II <a)Harmonic rhythm o-f " I I " : M E A S U R E : 1 2 3,4 5 6 7 8 T - L E V E L : O 5 8 I 10 3 6 9 2 5 10 3 8 11 4 D U R A T I O N O F T - L E V E L : X4. M E A S U R E : 9 10 11 12 13 T - L E V E L : 7 0 5 0 5 0 0 1 4 3 J < * ) J J J J J (b)Form o-f " I I " ( r e c a p i t u l a t i v e ternary -form): CAD: exposition mm. 1-5 1st phrase mm. 1-2 Cc3 mm. 3-5 Cc'3..two-pitch motive with arpeggiated harmony repeated in mm. 1-45 2nd sub-phrase unit Cc'3 has repeated T-level succession (T-10,T-3, mm. 3-4), extended by r e p e t i t i o n o-f m. 4, melodic f i g u r e in m. 5; continu-ation into CB3 without cadence (un-less in m. 6, T-2,T-5) CB3 development/new material mm. 6-9 2nd phrase m. 6 Cd3 m. 7 Cd'3 mm. 8-9 C d " 3 .. cadence- 1 i ke -figuration with simul-t a n e i t i e s repeated in transposition in mm. 6-85 extension with cadence in mm. 8-9 59 Example 2-14b continued. CA'3 r e c a p i t u l a t i o n mm. 10-14 3rd phrase mm. 10-12 Cc3.m. 1 progression repeated m. 13 Cd"' 3 ... transposed simultaneity -from CB3 •for -final cadence chord What d i f f e r e n t i a t e s " I I " from " I " and " I I I " , among other things, i s the r e g u l a r i t y of harmonic change through much of the piece, namely the common quarter-value time-span of most harmo-nies. The only i r r e g u l a r i t i e s occur in mm. 9 and 11-14 (Ex. 2-14) because of rests following the harmonies, again interpreted as s i l e n c e s through which harmonic perceptions continue. In these measures, rhythmic deceleration, a factor in cadence, r e s u l t s . Unlike the diffe r e n c e in the harmonic rhythm of mm. 6-9 in " I " ( i . e . , another indicator of the ternary form), the harmonic rhythm of " I I " i s generally regular and thus not a facto r in the perception of the formal d i s t i n c t i o n of mm. 6-9. Harmonic rhythm of "III". Example 2-15 presents the harmonic rhythm and form of " I I I " . 60 Example 2-15. Harmonic rhythm and form of " I I I " . (a)Harmonic rhythm, with time-spans of harmonies given below: M E A S U R E . ' 1 2 3 4 5 6 7 T - L E V E L : O S 8 3 7 1 0 1 4 7 0 3 8 11 D U R A T I O N O F T - L E V E L S ! j j J ; 1 « ~ - - - - - - - ^ j ; ^ TIM-SMNS:U> 5 6 4 2 4 2 10 2 4 3 5 19 17 M E A S U R E : 8 9 10 11 12 T - L E V E L : 2 6 9 2 5 13 0 5 0 4 7 14 I S 6 J. J. J* 5J. JNJ- W 7 7 6 6 c/ 12 19 5 6 4 2 4 2 13 <b)Form of " I I I " : CA3: exposition mm. 1-2 1st phrase m. 1 C c 3 m. 2 Cd3 continuation into m. 3, with no cadence mm. 3-6 2nd phrase (continua- m. 3 Ce3 i n i t i a l f i g u r a t i o n has limited t i o n of s i m i l a r i t i e s with i n i t i a l f i g -exposition uration, m. 1 with new m. 4 Cf3 climaxing action, c o n s i s t i n g material) of two-fold modified transpo-s i t i o n of three-harmony f i g -urat i on mm. 5-6 Cg3 ......highpoint or cadence of c l i -maxing action of m. 4 m. 7 Ch3 bridge to "B" 61 Example 2-15 continued. CB3: development/new material mm. 8-11 3rd phrase m. 8 C i 3 m. 9 C i ' 3 . modified r e p e t i t i o n of 2nd f i g u r a t i o n , m. 8 mm. 10-11 Cj3 .... cadence CA'3: modified r e c a p i t u l a t i o n mm. 12-15 4th phrase m. 12 Cc'3 modified transposition of m. 1 m. 13 Cd'3 modified transposition of m. 2 mm. 14-15 [ j ' ] . . . t r a n s p o s i t i o n of mm. 10-11 The harmonic rhythm in " I I I " varies constantly, in contrast to the consistent harmonic rhythm of " I " and " I I " . Moreover, the i n i t i a l time-points of some harmonies do not coincide with the notated b a r l i n e , examples of such being T-O <m. 1), T-5 (m. 4), T - l l (m. 7), T-5 (m. 12), and T-O (m. 14). Up to m. 5 there are r e l a t i v e l y short harmonic durations, except for T - l <m. 3), which i s s i g n i f i c a n t as i t coincides with an apparent phrase beginning. Measures 5-7 represent a r e l a -t i v e l y sudden deceleration in the harmonic rhythm, a f t e r which there i s some degree of acceleration with m. 8, and another pe-riod of deceleration with mm. 9 - l i . The r e c a p i t u l a t i o n (mm. 12-13) represents an acceleration, with shorter harmonic durations, followed by a f i n a l deceleration at the cadence (mm. 14-15). There are c e r t a i n r e l a t i o n s h i p s between harmonic rhythm and form in " I I I " . Some s i n g l e T-levels of longer duration coincide with, or occur in close proximity to, cadences or formally im-portant time-points: T-8 (mm. 5-6)5 T - l l (m. 7), a melodic "bridge" to the resumption of harmonic a c t i v i t y in m. 85 T-2 62 (mm. 10-11), preceding the modified r e c a p i t u l a t i o n of mm. 1-2 in mm. 12-13; and T-O (mm. 14-15), the f i n a l measures and exact tran s p o s i t i o n of T-2 harmony (mm. 10-11). The longer durations, and the sense of deceleration produced thereby, contribute to the e f f e c t of cadence. Int e r e s t i n g l y , each of the four afore-mentioned time-spans i s approximately nine eighth values in durat i on. Hierarchy of T-l e v e l s Figure 2-5 presents a hierarchy of T-levels in the i n d i v i d -ual pieces and in Trois Compositions as a whole, based on f r e -quency of occurrence and t o t a l time-spans. In F i g . 2-5c, the T-level h ierarchies for the in d i v i d u a l pieces (Fig. 2-5a and 2-5b) are combined by a v e r a g i n g . 3 3 Figure 2-5. Hierarchy of T-levels based on frequency of occurrence and t o t a l time-spans. (a)Hierarchy of T-l e v e l s from most s i g n i f i c a n t to least based on frequency of occurrence'. DESCENDING HIERARCHIC ORDER, LEFT TO RIGHT "I " : 0 2 / 3 / 4 / 7 / 9 / 1 1 6/10 (1 / Si NO 8) •II": 0 5 3/10 8 ( 1 / 2 / 4 / 6 / 7 / 9 / 1 1 ) • I i r : 0 3 7 2 / 4 / 8 (1 / 3 / 6 / 9 / 10 / 11) T - ' I i r : 0 5 3/7 2 / 4 / 10 9 / 11 6/8 1 63 Figure 2-5 continued. (b) Hierarchy o-f T - l e v e l s based on t o t a l time-spans: •I': 0 11 4/7 3 / 5 / 9 2 6/ 10 1 •II": 0 5 3/ 10 8 7 1 / 2 / 4 / 6 / 9 / 11 •III': 0 8 2 / 5 11 9 1 / 7 4 / 6 3 / 10 •r-'III": 0 5 11 2 8 7 9 3 4 10 1/6 (c) Hierarchy o-f T - l e v e l s based on combination o-f (a) and (b), above: • I " : 0 11 4/7 3/9 2 3 6/10 1 •11". 0 5 3/ 10 8 7 1 / 2 / 4 / 6 / 9 / 11 • I i r : 0 5 8 2 7 4 11 9 1 6 3 / 10 • I ' - ' I i r : 0 3 7 2 3 / 11 4 8 / 9 10 1 6 Note: In (a), T - l e v e l s indicated in brackets are those that occur only once. The solidus separates two or more T-le v e l s which are determined to have the same degree o-f s i g n i f i c a n c e , based on -frequency o-f occurrence and t o t a l time-span. T-O i s most important in a l l three pieces, based on occur-rence and t o t a l time-span, and because i t i s the -first and -final T-level o-f the i n d i v i d u a l pieces. This strongly suggests that i t functions as a r e f e r e n t i a l sonority, or "tonic," in each piece. In " I I " and " I I I " , and o v e r a l l in the pieces, T-5 i s the second most important T - l e v e l , while in " I " , T - l l i s the most important T-level a f t e r T-O. While T-5 and T - l l frequently oc-cur with T-O in T-level successions in the respective pieces at formally s i g n i f i c a n t time-points, i t i s d i f f i c u l t to make analo-gies with conventional t o n a l i t y and i t s hierarchy of chords, es-p e c i a l l y tonic and dominant chords. Perhaps the function of T-5 and T - l l with respect to T-O i s best described as a u x i l i a r y , es-64 p e c i a l l y when the former occur between r e i t e r a t i o n s of T-0. Certain conventional tonal implications of these T-level h i e r a r -chies are, however, explored in Chapter Three. T-levels that are s i g n i f i c a n t due to t h e i r roles in s p e c i f -ic IC cycles are also s i g n i f i c a n t in the hierarchies i l l u s t r a t e d in F i g . 2-5. For example, in " I " , T - l l (m. 4) i s the i n i t i a l 3-2 cycl e T - l e v e l , and T-3 <m. IO) i n i t i a t e s the resumption of the 3-0 cycle. In " I I " , T-10 and T-3, which occur in mm. 3, 4, and 7, are the f i r s t T - l e v e l s out of the int e r v a l 5 cyc l e . In "I I I " , T-0, T-5, and T-7 are important in the underlying symmet-r i c a l structure which i s centered at m. 4. T-level s i g n i f i c a n c e , besides being determined by frequency of occurrence and t o t a l time-span, i s also suggested by occur-rence in r e l a t i o n to formally important time-points. On occa-sion, the r e i t e r a t i o n of a p a r t i c u l a r T-level w i l l coincide with another formally important time-point. Such T-level occurrences at formally important time-points are examined below in the i n -div i d u a l pieces. T-level Occurrences and Their Relationships to Form "I". In addition to reasons c i t e d above, T-0 i s more s i g -n i f i c a n t because of i t s occurrences in the f i r s t and f i n a l f o r -mal sections, which help to delineate the r e c a p i t u l a t i v e ternary form of " I " . Perle notes the r e l a t i o n s h i p of T-level recurrence to form: "The larger formal implications of co n t r o l l e d transpo-s i t i o n a l r e l a t i o n s are r e a l i z e d to a limited extent in • the derivation of the concluding bars of the f i r s t piece from trans-65 pos i t i o n s o-f the set that are c l o s e l y related in PC content to the o r i g i n a l statement o-f the set." 3'* In addition, T-O occurs in m. 6, at the approximate midpoint o-f " I " . T - l l i n i t i a t e s the second phrase (mm. 4-5) with an exact p i t c h transposition o-f the T-0 harmony (m. 1), and i n i t i a t e s the middle section (m. 6), and recurs within i t (m. 7). 3* 3 1 Interest-ingly, the T-11,T-0,T-11 succession (mm. 6-7), employing the two most s i g n i f i c a n t T-levels in " I " , occurs in the middle -formal section, and strongly implies two conventional t o n a l i t i e s , which are discussed in more d e t a i l in Chapter Three. T-4, T-5, and T-7 are used to terminate the - f i r s t , second, and t h i r d phrases, r e s p e c t i v e l y . T-3, which succeeds T-0 (m. 1), i n i t i a t e s the r e c a p i t u l a t i o n and recurs in i t , in m. 11. Other T-levels which recur in s i m i l a r s i t u a t i o n s are T-2 (mm. 4 and 7), as part o-f cadential harmonic successions, and T-4 (mm. 2 and 12), decorating or connecting more important T-levels in c y c l i c progressions. Hence, T-O, T - l l , and, to a lesser extent, T-3, T-4, T-5, and T-7 can be considered to be the most s i g n i f i -cant T-levels in " I " both because of t h e i r positions within the T-level hierarchies (Fig. 2-5) and because of t h e i r locations in r e l a t i o n to the piece's form. "II". There are a few points of interest concerning the re l a t i o n s h i p of T-levels to form. F i r s t , the T-0,T-5 succession (mm. 1 and 10-12) i s one indicator of the r e c a p i t u l a t i v e ternary form. Interestingly, the only other occurrence of T-5 takes place in m. 6 (T-2,T-5), the f i r s t measure of the middle sec-66 ti o n , with the T-2 sonority containing the highest melodic pitch o-f the piece. Another succession o-f intere s t i s T-10,T-3 (mm. 3, 4, and 7), occurring in both the -first and middle -formal sec-tions, although neither T-level occurs elsewhere in " I I " . Sur-face -features o-f the three occurrences betray no s i m i l a r i t y (other than the PC content o-f the harmonies), so that there i s no r e a d i l y perceivable connection between the two formal sec-tions due to t h i s recurrence. F i n a l l y , the only occurrence of T-7 (m. 9) concludes the middle section (mm. 6-9), l i k e that of " I " (T-7, m. 8), and precedes the r e c a p i t u l a t i o n (mm. 10-13) and i t s T-O,T-5,T-O successions. 3* "Ill". T-O and T-5, which appear together in a number of harmonic successions in " I I I " , occur at formally important time-points: m. 1, the f i r s t succession; m. 4, a f o c a l point in the f i r s t part of " I I I " , preceding the harmonic "repose" of mm. 5-7; and mm. 12-13, the modified r e c a p i t u l a t i o n of mm. 1-2. The co-incidence of these T-l e v e l s with such time-points i s quite simi-lar to that in " I I " , where T-O,T-5 begins the piece and i s used in the r e c a p i t u l a t i o n . (Of course, there are the formal imp l i -cations of T-O's appearance as the f i r s t and f i n a l T-level of " I I I " , which Perle has noted.) 3 5" Associated with recurrences of the T-O,T-5 T-level succes-sion are three other T-l e v e l s : T-4, T-7, and T-8. T-O,T-5,T-8 occurs in both mm. 1-2 and 4-6, the beginning and end of the f i r s t formal section. T-4,T-7,T-O occurs in mm. 3-4, in connec-tion with the approach to the harmonic repose of mm. 5-7, and 67 also occurs in mm. 13-15, the f i n a l cadence. T-4, T-7, and T-8 function as T-levels either following or preceding T-O and/or T-5, generally with adjacent T-levels related by ICs 3 or 5. One other T-level of s i g n i f i c a n c e i s T-2, which i n i t i a t e s and concludes the f i r s t phrase of section "B" (mm. 8-11) of the t e r -nary form of " I I I " . In general, T - l e v e l s that are more s i g n i f i c a n t , based on the hierarchies presented in F i g . 2-5, usually appear at formal-ly important time-points. Recurrent Harmonic Successions Components of the three i n t e r v a l 3 cycles and the int e r v a l 5 cyc l e of T-level successions recur, some with more frequency than others, and some in two or three pieces (Fig. 2-6). 68 Figure 2-6. Recurring T-level successions in Trots Compos ttions. (a)Frequent 1y occurring T-level successions, with the number of occurrences: T-O,T-5 T-4,T-7 T-5,T-O T-2,T-5 T-3,T-6 T-5,T-8 T-6,T-9 T-7,T-O T-9,T-2 T-10.T-3 4 4 3 3 3 3 3 3 3 (b)Multiple T-level successions: Pi ece T-1 eve 1 successions T-O,T-5,T-8 T-O,T-5,T-O T-5,T-O,T-5 T-4,T-7,T-O T-4,T-7,T-O,T-5 IC success i ons 5-3 5-5-5-5 5-5-5 3-5 3-5-5 T-IO,T-l,T-4,T-7 3-3-3 3-3 " I I " "III " I I " " I I I " " I I " " I I I " II " III " Measure 1-2 1-2 4-5 10-12 12- 13 8-10 3-4 13- 15 8-10 3-4 T-l,T-4 2 T-9, T-2, T-5 5-3 II J II 4-5 T-3,T-10 2 "I I " 5-6 T-7,T-10 2 "I I I " 9-12 T-8 , T - l l 2 T-10,T-1 2 T-6, T-9, T-2,T-5 3-5-3 "I I " 5-6 T- l l , T - 2 2 " I I I " 8-12 II J II "III II J II " I I " 1- 3 2- 4 10-12 4-5 (c)Recurring T-level successions o+ two and more T-leveli M J II MEASURE: 1 2 3 4 3 6 7 8 10,11 12 13 T-LEVEL: 0—3—10 1-4 7-10-4 11-9-2 5 11-0 11-2 7 3-6 9 - 4 - 9 0 RECURRENT * * • * i ( )—• SUCCESSIONS: * — * MEASURE: 1 2 3,4 3 6 7 8 9 10,11 12 13 T-LEVEL: 0-5 8-1 10-3 6-9 2-5 10-3 8--11-4 7 0-5 0 0 RECURRENT * 1 t * * * SUCCESSIONS: t—• * * *—I I * * * 69 Figure 2-6c continued. " I l l l l M E A S U R E : T - L E « E L : R E C U R R E N T 1 2 3 4 5,6 7 8 9 10 12 13 14 0-5 8—3—7—10 1-4 7-0-5 8 11 2-6 9 2 5-0 5-0-4-7 0 J . J J J - * t f f - * S U C C E S S I O N S : i i f—f f { ) — f Note: Recurring T-level successions are indicated above using "* with "*" denoting f i r s t and l a s t s o n o r i t i e s of the re-curring successions. "#- ( ) indicates an interpolated T-l e v e l , not part of the recurring succession. In t h i s f i g u r e , recurring two-T-level successions are only indicated when they are not part of multiple T-level successions. Based on F i g . 2-6a, only 44 of the 144 possible T-level successions involving d i f f e r e n t combinations of two T-levels are u t i l i z e d in the three pieces (16 recurrent successions and 28 non-recurrent). Some of these frequently occurring two-T-level successions are components of multiple T-level successions (Fig. 2-6b), a l l of which have adjacent T - l e v e l s related by ICs 3 or 5. Figure 2-6c i l l u s t r a t e s the recurrent T-level successions. Some successions, by v i r t u e of t h e i r recurrences at formal-ly important time-points, have c e r t a i n r e l a t i o n s h i p s to the forms of " I " , " I I " , and " I I I " . The succession T-0,T-5,T-8 be-gins " I I " and " I I I " and occurs in mm. 4-6 of " I I I " at the con-junction of the i n t e r v a l 5 and the 3-2 cycles (mm. 4-7). Suc-cession T-7,T-O,T-5 occurs both in " I I " (mm. 9-10) and " I I I " (m. 4), although the occurrences d i f f e r in function. S i m i l a r i l y , another c y c l i c succession, T-3,T-6,T-9, occurs in " I " (mm. 10-12) and " I I " (mm. 4-5), with each occurrence having a d i f f e r e n t formal function. As noted e a r l i e r , the c y c l i c succession 3-1 occurs in the f i r s t phrases of " I " (mm. 1-3) and " I I I " (mm. 2-70 4 ) . The s u c c e s s i o n T-9 ,Y-2,T-5 ("I", mm. 4-5) and i t s v a r i a n t T-6,T-9,T-2,T-5 ("II", mm. 5-6, and " I I I " , mm. 8-12) r e c u r , co-i n c i d i n g with important j u n c t u r e s : i n " I " , at the cadence of the -form's "A" s e c t i o n ! i n " I I " , l i n k i n g the "A" s e c t i o n , mm. 1-5, t o the middle "B" s e c t i o n ; and i n " I I I " , l i n k i n g the - f i r s t phrase and cadence o-f the "B" s e c t i o n with the r e c a p i t u l a t i o n i n m. 12. F i n a l l y , t h e r e i s the a l t e r n a t i o n o-f two T - l e v e l s i n -v o l v e d i n the s u c c e s s i o n T-O,T-5,T-0,T-5 which o c c u r s i n " I I " , mm. 10-14, and " I I I " , mm. 12-13 (mm. 12-15, i-f i n t e r p o l a t e d l e v -e l s are d i s c o u n t e d ) , both o-f which are c o n c l u d i n g s u c c e s s i o n s . Those i n t e r p o l a t e d l e v e l s , T-4,T-7 with T-O -following, p r e v i o u s -l y o c c u r r e d i n mm. 3-4 o-f " I I I " and i n " I I " , mm. 8-10 ( i . e . , T-4,T-7,T-O,T-5). To complete t h i s study o-f the ICC system and the T - l e v e l s u c c e s s i o n s u n d e r l y i n g the harmonic p r o g r e s s i o n s , the next s e c -t i o n s o-f t h i s c h a p t e r w i l l examine T - l e v e l s u c c e s s i o n s as to PC c o n t e n t , and element o c c u r r e n c e and o r d e r i n g , r e s p e c t i v e l y . 71 C h a r a c t e r i s t i c s o-f T-Level Successions as to PC Content PC Invariance and Pitch Continuity With six or more PCs per T - l e v e l , there are a number o-f i n -variant PCs in most T-level successions, and a number o-f these invariant PCs involve p i t c h continuity, that i s , PC invariance in the same r e g i s t e r . The number o-f invariants in a PCC and a transposition o-f i t depends on the t o t a l IC content o-f the PCC, as indicated by the i n t e r v a l vector. Quite simply, with the i n -t e r v a l vector o-f the ICC o-f " I " < not including element "10") be-ing C3 3 5 4 4 23, there are three invariants between T-levels related by IC 1, three between IC-2-related T - l e v e l s , -five be-tween IC-3-related T - l e v e l s , -four between IC-4-related T-levels, and -four between IC-5-related T - l e v e l s . In the case o-f IC-6-related T-levels, the i n t e r v a l vector number -for IC 6 (in t h i s case, two) must be m u l t i p l i e d by two in order to determine the number o-f invariant PCs. 3" Such invariance and continuity can a f f e c t one's perception of s i m i l a r i t i e s and differences in har-monic progression. PC invariance and p i t c h continuity are examined in Exx. 2-16 and 2-17. In Ex. 2-16, PCs of T - l e v e l s of the three pieces, in scale form, are compared on the basis of T-level IC r e l a t i o n -ships to i l l u s t r a t e differences in the numbers of invariant PCs. Boxes highlight these invariant PCs. Variant elements in each T-level are bracketed, with the implication that t h e i r absence in c e r t a i n harmonic successions in the music w i l l mean possibly fewer invariant PCs in those successions. •" 72 Example 2-16. Invariant PCs o-f IC-1- to IC-6-re 1 ated T-level< •r T-0 I T-0 L-I/L,,\ n a n I I I * t«i nj 1 — hn * 1« 1-1 l_m J t f —ILK- _ i 1 /* * yo ELEMENT NUMBERS: 0 1 4 T-l 9 10 ELENENT NUMBERS: 0 3 T-0 8 9 0 3 6 8 10 T-2 bo ft? " 10 0 1 4 6 8 T-0 0 1 3 4 6 9 T-3 9 10 0 1 3 6 0 1 T-4 8 10 8 9 T-0 4 6 0 1 3 T-5 J2ZE 6 8 9 10 0 1 3 4 T-0 jzzz 0 3 4 6 9 10 T-6 rr-\o ^0 A 6 9 10 0 3 4 73 Example 2-16 c o n t i n u e d . •II' T-O T-O 0 1 4 T - l 0 1 3 4 T-4 11 0 3 T-O 8 9 11 0 T-O d h H <>0 P 0 1 3 6 8 11 T - 2 0 1 4 6 8 9 1 1 T - 3 11 0 1 4 6 9 11 0 1 3 4 6 T-O T-O H P -n & m 0 3 4 6 9 11 T - 3 0 3 6 9 T-6 |HH|°(n) T ID 3sc 9 0 1 3 6 8 6 9 0 3 7 4 Example 2-16 continued. • n r T-0 T-0 0 1 4 9 10 11 T-1 0 1 3 4 8 10 T-4 11 0 3 8 9 10 T-0 8 9 11 0 4 6 T-0 0 1 3 6 8 10 11 T-2 0 1 3 4 6 8 9 11 T-5 IT 10 11 0 1 4 6 8 9 8 10 11 0 1 3 4 6 T-0 T-0 a s •55 0 1 3 4 6 9 11 T-3 0 3 4 6 9 10 T-6 9 10 0 1 3 6 8 6 9 10 0 3 4 75 There may be as few as two and as many as seven PCs common to adjacent harmonies. I C - l - r e l a t e d T-levels in " I " and "I I " (which occur very infrequently) usually have only four common PCs, while IC-3- and IC-5-related T-levels (which occur most frequently in a l l three pieces) have f i v e to seven invariant PCs. Example 2-17 i l l u s t r a t e s PC invariance and p i t c h continuity in the harmonic successions of the pieces. These harmonic suc-cessions are shown on the f i r s t of three systems, with p i t c h c o n t i n u i t y highlighted in the second, and PC invariance ( i n v o l -ving d i f f e r e n t r e g i s t e r s ) i s o l a t e d in the t h i r d , with l i n e s con-necting the invariant PCs. A pair of numbers (the f i r s t un-bracketed, the second bracketed) for every succession indicates the t o t a l number of invariant PCs and pit c h c o n t i n u i t i e s , res-pect i v e l y . Following the systems i l l u s t r a t i n g PC invariance and pitch c o n t i n u i t y in a given piece, a graph—based on information pre-sented in the s y s t e m s — v i s u a l l y i l l u s t r a t e s the degree of chang-ing PC content in each succession, with the height of the s o l i d l i n e i n d i c a t i n g the number of invariant PCs in each succession. An elevation in the l i n e indicates less s i m i l a r i t y because of fewer invariant PCs. In order to account for pit c h continuity, an additional h a l f - u n i t value i s assigned to such pitches, based on one unit value per invariant PC as indicated on the l e f t side of the graphs. Dash l i n e s in the graphs i l l u s t r a t e p i t c h c o n t i -nu i ty. 76 Example 2-17. PC invariance and p i t c h continuity in T - l e v e l successions p+ Trois Compositions. •r M E A S U R E : 1 1 1 1 2 1 1 3 1 T - L E V E L : O 3 io l 4 7 io P I T C H C O L L E C T I O N S : F "rw— - t o — ^ — HO JN JO THW— %S—b P I T C H C O N T I N U I T Y : b,-* J i t — -V P C I N V A R I A N C E ( W I T H O U T P I T C H C O N T I N U I T Y ) : 3 ( 4 ) 4 ( 1 ) 5 ( 1 ) 5 ( 1 1 5 ( 2 ) 5 ( 2 ) 2(1) 3(1) 4(2) 4(3) 4(2) 3(1) 4(2) 4(1) 78 Example 2-17 continued. [81 [10,111 (121 (131 « 7 3 6 9 4 9 0 1 ^ tf/ = i -K » ^ M — ^ ^8 | Sf ^ . re mso=a»=l o — j? i s a i — • • t |0— — j \ ° 1 i>8 ! / ! r t 1 ¥ — " \<r te' 'o ' ^ " " o " 4(1) 3(1) 3(2) 5(2) 3(1) 4(2) 4(2) 6(3) Graph o-f changing PC content in " I " : NUMBER OF INVARIANT PCs , 1 1 1 'I 1 I ^ r J U " I j i • T-: 0 3 10 1 4 7 10 4 11 9 2 3 11 0 11 2 7 3 6 9 4 9 0 N.: 1 2 3 4 3 6 7 8 10,11 12 13 0 1 2 3 4 5 6 7 79 80 E x a m p l e 2 - 1 7 c o n t i n u e d . (41 [SI (6) ' 3(01 5(4) S(l) 5(2) 5(2) 5(2) 3(2) 5(1) 4(2) 5(3) 4(2) 4(0) 4(0) 8(1) 81 Example 2-17 continued. Graph of changing PC content in " I I " : NUMBER OF INVARIANT PCs Li T-: 0 3 8 1 10 3 10 3 6 9 2 5 10 3 8 11 4 7 0 5 0 0 N.: 1 2 3 4 5 6 7 8 9 10,11 12 13 " I I I " 5(0) 4(1) 3(2) 3(0) 3(0) 3(0) 7(1) 82 Example 2-17 c o n t i n u e d . [31 1 4 [41 7 0 5 13,61 8 in (71 11 [81 2 J W i^H fci hi} fr* -43—- k g — ^ tg. fry i ftojft i * — —*a_hP 1 A ° 5HF- ^ 1 w°te 1 BO ha ^ , t.n Jt.fl fro — to '* y ^ i < » — 2 =*e— -Jol ... 0„_^O i i — I :—1 410) 413) 313) 3(3) 3(0) 3(0) 3(2) 191 9 [10,111 2 1121 3 7^* »? JFfr Iff tey t [131 3 J2S-0 3(2) 3(1) 4(3) 3(3) 4(1) 312) 3(2) 83 Example 2-17 continued. 3(0) 3(1) 3(2) Graph of changing PC content in " I I I " NUMBER OF INVARIANT PCs 0-1-2-3-4-5-6- -» • I-: 0 5 8 3 7 10 1 4 7 0 5 8 11 2 6 9 2 5 0 5 0 4 7 0 N.: 1 2 3 4 . 5 7 8 9 10 12 13 14 In " I " and " I I " , IC-3-related T-levels generally have f i v e invariant PCs, while IC-5-related T-levels have -four} in " I I I " , there are on average four, and three invariant PCs, respective-ly- IC-1-, 2-, 4-, and 6-related T - l e v e l s which occur i n f r e -84 quently in a l l three pieces generally have fewer invariant PCs ( i . e . , usually between three and -four PCs) . When one compares the t o t a l number o-f successions in each piece and the t o t a l num-ber o-f invariant PCs, there are -fewer invariant PCs in " I I I " -for the number of harmonic successions, compared with " I " and " I I " . (There are in t o t a l s l i g h t l y more invariant PCs in successions in " I I " than in "I".) In other words, successions of " I I I " ex-h i b i t a greater degree of harmonic change, based on PC i n v a r i -ance. This i s due in part to the frequent occurrence of PCCs with few or no variant elements. Moreover, PC invariance has c e r t a i n , a l b e i t l i m i t e d , i m p l i -cations for the forms of the pieces. In the f i r s t and f i n a l phrases of " I " (mm. 1-3 and 10-13, r e s p e c t i v e l y ) , there i s more PC invariance and pit c h c o n t i n u i t y than in mm. 6-8 (including progressions T - 5 , T - l l tmm. 5-6] and T-7,T-3 [mm. 8-10]). In mm. 1-4 and 9-13 of " I I " , there i s less PC invariance and pit c h con-t i n u i t y than the middle section. In " I I I " , mm. 1, 2 (from T-lO), 3, and 8-12 (the t h i r d phrase) have more PC invariance and pitc h continuity than mm. 2, 4-8 (development), and 12-15 (reca-p i tu1 at i on) . An equally important factor in the perception of s i m i l a r i t y in two harmonies i s the extent of pit c h continuity. Even with invariant PCs in a succession, i t i s d i f f i c u l t to perceive simi-l a r i t y in the two harmonies with l i t t l e or no pitch continuity, as i s the case with most harmonic successions in Trois Composi-tions. In going from " I " to " I I I " , there i s an increasing ten-dency for harmonic successions with no pitch continuity ( i . e . , 85 -from 11% to 33% of successions). Like PC invariance, p i t c h c o n t i n u i t y has some implications for form. In " I " , successions T-O,T-3 (m. 1), T-10,T-4 (m. 3), and T-9,T-O (mm. 12-13), with at least three p i t c h c o n t i n u i t i e s each, occur at the beginning or at cadences. Successions T-4, T - l l (mm. 3-4) and T - 5 , T - l l (mm. 5-6), with no p i t c h continuity and fewer invariant PCs than preceding successions, span adja-cent formal sections. In " I I " , successions T-6,T-9 (m. 4) and T-4,T-7 (mm. 8-9), with at least three p i t c h c o n t i n u i t i e s each, immediately precede new formal sections. In " I I I " , successions T-4,T-7,T-O,T-5 (mm. 3-4, with the climaxing action of the f i r s t s ection, mm. 1-7) and T-9,T-2,T-5 (mm. 9-12, t h i r d phrase ca-dence and link to the recapit u l a t i o n ) have at least three p i t c h c o n t i n u i t i e s in each component succession, although PC i n v a r i -ance i s less in mm. 4-8. S t r u c t u r a l l y s i g n i f i c a n t p i t c h c o n t i -n u i t i e s include: C4 and Ftt/Gb4 ("I", m. 3), D4 ("I", mm. 12-13), E2,3 ("II", mm. 8-9), and Attl ("III", mm. 7-8), a l l of which occur at cadences. 3" PC Invariance in IC-3-Related T-Levels The greater number of invariant PCs in T-levels related by IC 3, the basis of in t e r v a l 3 cycles which govern many T-level successions in the three pieces, supports the concept of T-level f a m i l i e s based on T-le v e l s comprising the interval 3 cycles (e.g., T-O, T-3, T-6, and T-9 of the 3-0 cycle comprising the 3-0 T-level family).-* 0 In f a c t , there may be some basis for the notion of "modulation" from one T-level family (or component T-86 level thereof) to another. In a given T-level family (in " I " and " I I " at l e a s t ) , there i s an invariant PC c o l l e c t i o n forming a conventional diminished-seventh chord ( i . e . , three superim-posed IC 3 i n t e r v a l s , elements "0", "3", "6", and "9" of each T - l e v e l ) , t h i s c o l l e c t i o n being invariant to the four T-levels of the family. In " I I I " , element "9" does not c o n s i s t e n t l y oc-cur with every T - l e v e l ; hence only three PCs of the invariant diminished-seventh PC c o l l e c t i o n of a family occur with any given T-level of the family. PC invariance in T-level f a m i l i e s in a l l three pieces i s i l l u s t r a t e d in Ex. 2-18. In Ex. 2-18a, which presents T - l e v e l s T-0, T-3, T-6, and T-9 (T-level family 3-0) of " I " , " I I " , and " I I I " , four invariant PCs in each T-level of a family ( i . e . , the diminished-seventh chord) are highlighted with s o l i d v e r t i c a l l i n e s , and indicated in Ex. 2-18b by open noteheads in a scalar presentation of T-level family invariant PCs. Those four PCs occurring in at least two of the four T-levels, referred to as "quasi-invariant PCs," are highlighted in Ex. 2-18b with s o l i d noteheads. The other four PCs in a family occur with only one T - l e v e l , and possibly two, i f variant elements are employed. The invariant and quasi-invariant PCs of T-level f a m i l i e s 3-1 (T-1, T-4, T-7, and T-10) and 3-2 (T-2, T-5, T-8, and T - l l ) in the three pieces are also i l l u s t r a t e d in Ex. 2-18b. Interest-ingly, the PC c o l l e c t i o n s shown in Ex. 2-18b are octatonic c o l -1 ec t i ons. "*x 87 Example 2-18. PC invariance in IC-3-related T-level -families. (a)T-O, T-3, T-6, and T-9 in " I " , "II", and "III": ' I I ' • I I I ' T-O ,-3 I T-6 "1* bo loi £21 T-9 bo Wi ^ 4 3iS te 315 (b) Co 1 1 ect i ons o-f invariant and quasi-invariant PCs o-f T-level -families 3-0, 3-1, and 3-2: T-LEVEL FAMILY 3-0: T-LEVEL FAMILY 3-1: T- l T-4 zz 2Z T- 7 E&,fr« T-10 T-LEVEL FAMILY 3-2: T-2 T-5 T-8 T-U in S3 Figure 2-7 presents the successions o-f T-level -families in the three pieces, based on the T- l e v e l s , and tables o-f T-level •family occurrences and t o t a l time-spans. Figure 2-7. Successions o-f T-level -families. M j M M E A S U R E : 1 2 3 4 5 6 7 8 T - L E V E L : 0 - 3 - 1 0 1-4 7 - 1 0 - 4 1 1 - 9 - 2 5 11 - 0 11-2 7 T - L E V E L F A M I L Y : 3-0/1/2: 0 1 2—0—2 0—2 1 M E A S U R E : T - L E V E L : 3-0/1/2: 1 0 , 1 1 1 2 3 - 6 9 - 4 - 9 0 I I 0 1—0— 1 1 3 I T - L E V E L F A M I L Y : O C C U R R E N C E S : T O T A L T I N E - S P A N S I 8 T H V A L U E S ) : 3 - 0 3 - 1 3 - 2 7 5 5 2 8 1 8 3 0 "II M E A S U R E : 1 2 3 , 4 5 6 7 8 9 1 0 , 1 1 1 2 T - L E V E L : 0 - 5 8 - 1 1 0 - 3 6 - 9 2 - 5 1 0 - 3 8 - 1 1 - 4 7 0 - 5 0 3-0/1/2: 0—2- 1 - - - 1 - - - 0 — - 2 — 1 — 0 - - 2 — 1 0 — 2 -- 0 T - L E V E L F A N I L Y : 3 - 0 3 - 1 3 - 2 O C C U R R E N C E S : 7 4 5 T O T A L T I N E - S P A N S : 2 9 1 3 1 8 39 Figure 2-7 continued. " I l l " MEASURE: 1 2 3 4 5 7 8 9 10 12 T-LEVEl: 0 - 5 8 - 3 - 7 - 1 0 1 - 4 7 - 0 - 5 8 11 2 6 9 2 5 0 3-0/1/2: 0—2——0—1 0—2 0 2 0 M E A S U R E : 13 14 I T - L E V E L F A M I L Y : 3-0 3-1 3-2 T - L E V E L : 5 - 0 - 4 - 7 0 1 O C C U R R E N C E S : 6 2 4 I T O T A L T I N E - S P A N S 26.5 15 42.5 3-0/1/2: 2—0—1 0 I There are no cle a r consistencies in the locations and func-tions of the invariant diminished-seventh PCs of each T-level family, although with " I " there i s a tendency for these PCs to be exposed in some sense ( i . e . , location in the outer voices, or exposure through temporal i s o l a t i o n ) . Such inconsistency cannot be explained by tonal procedures, such as resolutions of the two tr i t o n e s comprising the invariant diminished-seventh structures ( i . e . , outward or inward semitonal r e s o l u t i o n ) . Nor are there apparent consistencies in the locations and functions of the quasi-invariant PCs. In general, F i g . 2-7 i l l u s t r a t e s the fact that 3-0 and 3-2 family T-levels each tend to occur more frequently and have to-ta l time-spans greater than 3-1 family T - l e v e l s . Perle indicates that p i v o t a l connections between harmonies in Trois Compositions are generally used "merely as a means of immediate association.""* 2 This i s generally true when "pivot" is defined as a pit c h continuity in adjacent harmonies, since such pivot pitches generally e x i s t between only two adjacent harmonies in Trois Compositions. On average, there i s one pit c h 90 con t i n u i t y per succession, although there i s constant f l u c t u a -tion in the number o-f such pivot pitches with each succession. When "pivot" i s understood more broadly as any invariant PC in adjacent harmonies, then there are more pivots as Ex. 2-17 has shown. The above-mentioned diminished-seventh -formations common to IC-3-related T-level f a m i l i e s represent a more s p e c i f i c type of pivot reminiscent of Scriabin's Seventh Sonata., as analyzed by Perle. Another p i v o t a l formation i s the "diminished-seventh" chord, comprising the only notes common to a l l four members of the tr a n s p o s i t i o n a l complex [ i . e . , the set at T-0, T-3, T-6, and T-93. . . . Of importance in i t s connection with larger formal e l e -ments i s the group of notes comprising the t r i t o n e r e l a t i o n s h i p s within the set, the invariance of which at the transposition of a t r i t o n e r e s u l t s in a s i x -note segment common to any two sets a t r i t o n e apart."*»= While there i s , on average, one pi t c h c ontinuity per suc-cession, approximately 76% of such pivot pitches of Trois Com-positions (79% in " I " , 77% in " I I " , and 73% in "III") are invar-iant diminished-seventh PCs of the T-level family to which e i -<• ther T-level of the given succession belongs. 91 Element Occurrence and Ordering in Trois Compositions Besides the study o-f T-level successions as to PC contents, there i s the matter o-f v e r t i c a l and linear element occurrence and ordering, both within i n d i v i d u a l harmonies and between adja-cent harmonies.'*'* Although Gojowy observes that only PC content o-f harmonically or l i n e a r l y disposed c o l l e c t i o n s (and not order-ing or r e g i s t r a l location) i s determined by the ICC system,'**9 there are i d e n t i f i a b l e , though l i m i t e d , patterns of element oc-currence and ordering which w i l l now be examined. Linear Element Occurrence and Ordering " I " . Example 2-19 presents the pitches of the primary mel-ody of " I " , with corresponding element numbers. Example 2-19. Primary melody of '" I' MEASURE! 1 T-LEVEU 0 10 I 2 I 1 13 |4 I 7 10 4 | 11 I 3 I 9 2 | 5 | o Q ELEMENT* I I I I I NUMBERS! 3 8 10 9 8 3 4 I 3 8 3 4 I 3 0 6 I 3 8 10 3 0 I 0 I 9 2 Example 2 - 1 9 continued. M. | 6 T- 111 I 7 I 11 fee. •# -4n g ^ b n i ^ L ~ — 1 ,i " Q—& 1 7 i n O J L , \ u,\ 5*^ VW<>.9 -TJ r * " n r, o 1—"— NO.| 8 4 6 0 9 3 1 10 9 8 3 I 8 4 6 0 9 10 3 1 10 9 8 5 | N. | 8 T- I 7 I 10,11 | 12 | 13 1 3 6 | 9 4 9 | 0 E> Q\uW) \b0 I - t — NO.| 3 1 10 9 8 3 | 3 8 3 4 | 3 8 3 I 3 | Elements " 3 " , " 8 " , and " O " (in descending order o-f occur-rence) are used more -frequently in the primary melody, pa r t i c u -l a r l y in mm. 1 - 5 and 1 0 - 1 3 . Where there are two or more primary melody pitches per harmony, one -finds that " 3 " and, to a lesser extent, " 1 " , " 8 " , and " 9 " occur -frequently as i n i t i a l melodic elements. - In most cases, these elements represent the t e x t u r a l -ly isolated i n i t i a l pitches o-f harmonies. Where there i s only one melody p i t c h per harmony, elements " 3 " and " O " -frequently occur. Hence r element " 3 " would seem to be l i m i t e d l y associated with t h i s i n i t i a t i n g -function. Elements " O " , " 4 " , and " 8 " -fre-quently succeed " 3 " in the primary melody. Element " O " also oc-curs in c e r t a i n cadences ( i . e . , T - 5 , m. 5 ; T - O , m. 1 3 ; and T - 1 0 , m. 3 ) . 93 "II". Example 2-20 presents pitches o-f the primary melody of " I I " , with corresponding element numbers. Example 2-20. Primary melody o-f " I I " K . | 1 12 | 3 I 4 I 5 I 6 T - | 0 3 18 1 | 10 3 I 10 3 | 6 9 | 2 I 7 5 |10 18 | 3 18 11 4 | NO.I 11 8 | 8 4 | 8 4 I 11 9 | 3 3 I 3 0 11 1 3 0 11 | 3 0 11 31 H. I 9 I 10-11 I 12 I 13 I T - | 7 L 0 5 I 0 | 0 1 N0.| 9 | 11 8 1 11 I 11 I Elements "11", "3", and "8" occur most -frequently in the primary melody, with element "11" the most s i g n i f i c a n t o-f these as i t i s the i n i t i a l element o-f the piece and o-f the recapitula-t i o n , and also the -final element. Moreover, the -final T-level (T-O, m. 13) i s transposed in m. 6 (T-5, which succeeds f-2 and i t s p i t c h c l imax), m. 7 (T-3), and m. 8-.(T-ll), with el ement "11" retained in the primary melody in each case. However, there i s no a s s o c i a t i o n with -function, as with element "3" in " I " . There are no apparent patterns o-f element ordering within the primary melody. "III". Example 2-21 presents pitches pf the primary melody of "III",, with corresponding element numbers. 94 Example 2-21. Primary melody o-f " I I I " . 1 2 | 3 5 | 8 3 7 10 I 1 I 4 1 4 | 7 MM 3 9 10 6 8 9 | 0 4 4 3 1 3 11 9 10 9 10 10 I 10 0 1 N. | 4 T- | 0 I 5-6 I 8 I 7 I 11 *\&9*<>"'' :  N0.| 10 0 1 10 0 (8) I 6 (3) 10 I 8 3 0 1 4 6 13) 8 0 1 4 1 H. I 8 I 9 | 10-11 I 12 T- | 2 6 | 9 | 2 1 3 I 13 | 14-15 I 1 5 0 4 7 1 0 I fee 3p MO.I U) 8 0 8 0 | 8 | 3 1 0 | 3 9 10 4 6 I 0 4 4 3 I 3 1 0 Although elements "O", "3", "4", and "IO" occur more f r e -quently and have the greatest t o t a l time-spans, there i s no ap-parent consistency in element recurrence or ordering. there are a number of element sequences that do recur, such as: »3»_»9»_ "10" in mm. 1 and 125 "O"-"4"-"4"-"3" in mm. 2 and 13; and "10"-" 0 " - " l " in m. 4. A l l three involve the transposition of harmon-ic-melodic f i g u r e s , while sequences «3»-»9"-"10" <m. 1) and "3"-" l l " - " 9 " - " 1 0 " (m. 3) involve no such r e p e t i t i o n . Certain e l e -ment recurrences suggest a limited form of element c o n t r o l : element "10" in m. 1, in m. 3 as a lo c a l melodic goal, in m. 4 as an i n i t i a l element, and in mm. 5-6 as a melodic goal; and the 95 a l t e r n a t i o n o-f "8" and "O" in mm. 7-11. In the three pieces, elements "3", "0", and "8" occur most •frequently in the primary melody. Element occurrence in bass lines. In the bass l i n e s , "1", "O", and "6" in " I " , "4" and "6" in " I I " , and "1" and "6" in " I I I " occur most -frequently. In general, "1" and "6" occur most •frequently in the bass l i n e s o-f the three pieces. Analyses o-f l i n e a r element successions involving adjacent harmonies reveal no consistent p r i n c i p l e s o-f o r d e r i n g . 4 1 9 V e r t i c a l Element Occurrence and Ordering in Individual Harmonies Limited patterns o-f v e r t i c a l element occurrence and order-ing are, to some extent, s i g n i f i c a n t despite any inconsisten-c i es. "I". Example 2-22a i l l u s t r a t e s the PCs o-f the ICC at T-O, with Ex. 2-22b presenting the v e r t i c a l i z e d harmonies o-f " I " in sta-f-f notation and, below t h i s , with pitches represented by ap-propriate element numbers. In the case o-f two or more primary melody pitches per harmony, the representative elements are s t a -ted both l i n e a r l y ( i . e . , on one l i n e usually with dashes sepa-r a t i n g element numbers) and v e r t i c a l l y . Brackets and a s t e r i s k s highlight these v e r t i c a l i z e d melody pitches. Melody pitches in the score have stems that are connected to beams. 96 E x a m p l e 2-22. H a r m o n i e s o f " I " w i t h p i t c h e s r e p r e s e n t e d by e l e m e n t numbers. ( a ) P C s o-f ICC AT T-O: L„ ho ^ E L E M E N T S : o 10 ( b ) V e r t i c a l i z e d T - l e v e l s , w i t h r e p r e s e n t a t i v e e l e m e n t numbers: "it ^ kg AN —^ gg-frg f V E R T I C A L P O S I T I O N 8 I §(10) 1 1 1 *(10> • 1 7 1 i(8) §8 0 1 4 0 1 9 6 0 1 i(8) «3 to 1 6 1 *3-8-10 3 8 1 *3 8 1 8 4 9 1 H-8-10 9 6 1 5 I 0 0 «(4) 1 0 *(4) 1 *3 M •6 1 0 1 9 1 4 1 9 V) 13-4 1 9 #3-4 1 0 8 1 1 9 0 3 1 3 1 4 i 9 1 *8 1 1 4 3 4 1 4 4 8 1 2 1 1 1 1 1 1 9 1 1 9 3 1 1 8 4 1 1 1 6 4 6 1 6 6 1 6 1 8 1 6 6 1 1 1 1 1 1 1 T - L E V E L : I 0 3 10 1 1 4 1 7 10 4 1 11 9 2 1 M E A S U R E : I 1 1 2 1 3 1 4 1 Jfre-\fnO P 8 1 1 I H0- 1 7 1 0 1 *9- 1 *9- 1 6 | 6 • • ' 1 *0- 4 11 10 | *0- 4 11 10 I 3 1 4 M l *8- 10 3 4 | *8- 10 3 4 1 4 1 1 * 1 *6- •13) *(10) »I8) | H- i(3) U10) *(8) | 3 | 8 4 | «4" *3-l *10-9 *8-3 | *4- *3-i *10-9 *8-5 | 2 1 3 1 1 (3) 11) (3) (3) I (3) (4) (1) (3) (3) | 1 1 9 (9-3-8) I 1,3 0,1 1,3 1,3 1 1,3-2,4 0,1 1,3 1,3 1 1 1 1 1 T - 1 3 1 11 0 1 11 2 1 N . | 3 1 6 1 7 1 97 Example 2-22 continued, 7 1 1 *3 9 1 8 •8 8 1 •0 1 4 1 4 11 10 | 0 •14) 1 •3 3 •3 1 6 1 SI 10 S 4 | 9 •3-4 1 0 0 0 1 3 1 4 1 •(3) •(10) •(8) | 18 1 1 9 9 9 1 1 1 3 1 •3-1 •10-9 •8-3 | 6 8 1 6 6 6 1 9 1 2 1 (0) (1) (3) | 1 6 1 1 4 1 1 8 1 1 1 11,0 0,1 1,3 1 4 0 1 4 1 4 1 3 1 1 1 1 1 1 T- 1 7 1 3 6 1 9 4 9 1 0 1 N. 1 8 1 10,11 1 12 1 13 1 Note: Asterisks (*) indicate primary melody elements, while "+" (m. 4, T-9 and T-2) indicates a s i m p l i f i c a t i o n in the represen-tati o n of these s o n o r i t i e s whereby melody elements "3" and "0", respectively, doubled one octave below, are deleted in order to show the seven-element sonority. "++" (m. 5, T-5) shows an a l -ternate way o-f regarding the lower pitches o-f T-5 harmony, as melodic approach pitches to Eb4. In Ex. 2-22 and those to -follow, the lowest v e r t i c a l posi-tion in a chord ( i . e . , the lowest pitch) i s designated "position one," the next lowest p o s i t i o n " p o s i t i o n two," and so on. Hence, the f i r s t harmony of " I " (Ex. 2-22) has element "6" in p o s i t i o n one, "1" in p o s i t i o n two, "4" in three, "9" in four, and so on. Because seven-PC harmonies consistently appear, es-p e c i a l l y in mm. 1-5 and 10-13, c e r t a i n patterns of element oc-currence in the in d i v i d u a l v e r t i c a l positions can be observed, as i l l u s t r a t e d in Figure 2-8. 98 Figure 2-8. Element occurrences in v e r t i c a l p o s i t i o n s of the harmonies o-f " I " . (a) Most -frequent element occurrences in positions in " I " : 7: 6: 5: 4: 3: 2: 1: E1ements 0,*8 9 3 4 *0 4 *9 3,8 *4 6 *1 *3 1 *6 1 8,9 0,4 (b)Most frequent element occurrences in p o s i t i o n ranges in " I " : P o s i t i o n | Elements ranges I 4- 8: 1-3: 5- 8: i-3 : I 0, 3 8, 9 4, IO I 1 4 6 3 I I I I O I I 1 3 3 4 8 4,6,9 9 8 Note: In proceeding -from l e f t to r i g h t in F i g . 2-8a and 2-8b, there i s a descending order o-f element frequency in a p o s i t i o n or p o s i t i o n range. A comma between two elements (e.g., 0,4) indicates that elements "O" and "4" occur the same number of times in a c e r t a i n p o s i t i o n . "#" indicates the most frequent occurrences of an element in any p o s i t i o n . Patterns of v e r t i c a l element occurrence in ranges of v e r t i -cal p o s i tions (Fig. 2-Sb) have elements "1", and, to a lesser extent, "3", "4", and "6" as occurring frequently in the lower po s i t i o n s of harmonies, while elements "0", and, to a lesser ex-tent, "3", "4", "8", and "9" occur more frequently in the upper posi t ions. However, as shown in Figure 2-Sa, a d i f f e r e n t element i s generally the most frequently occurring in each v e r t i c a l posi-t i o n , except for p o s i t i o n s one and two, in both of which element "1" i s most frequent. If we su b s t i t u t e the next most frequent element, "6", f o r "1" in p o s i t i o n one, we obtain a " r e f e r e n t i a l " harmony -for " I " , in the sense that i t r e f l e c t s the average reg-i s t r a l d i s t r i b u t i o n of the elements of the PCC. That i s , many 99 o-f the harmonies in " I " , e s p e c i a l l y in mm. 1-5 and 10-13, are v a r i a t i o n s o-f t h i s " re-f erent i al " structure. It c o n s i s t s o-f e l e -ments »6•,-',l,'-"4,,-"9,,-•,0"-"3"-,,8,, , ordered -from lowest to high-est in r e g i s t e r . When we su b s t i t u t e T-O PCs -for these elements, t h i s " r e f e r e n t i a l " harmony i s Ab-Eb-Gb-Cb-D-F-Bb, the -first ver-t i c a l i t y o-f " I " . In other words, the -first v e r t i c a l i t y o-f " I " establishes a normative r e g i s t r a l d i s t r i b u t i o n o-f elements o-f the PCC, a d i s t r i b u t i o n which i s maintained, s t a t i s t i c a l l y , throughout " I " . This s t a t i s t i c a l uniformity i s not maintained in mm. 6-8 due to the use o-f the expanded ICC, and the textural d i fferences. "II". The patterns o-f v e r t i c a l element occurrence are i l -lustrated in Ex. 2-23. lOO Example 2-23. Harmonies o-f " I I " with pitches represented by element numbers. (a)PCs o-f the ICC at T-O: E L E M E N T S : o 1 bo 9 11 ( b ) V e r t i c a l i z e d T - l e v e l s , with representative element numbers: V E R T I C A L 8 1 1 i 1 1 1 3 1 P O S I T I O N 7 1 1 1 8 1 8 4 1 8 « 1 1 1 9 1 «3 t3 | 1 1 U 1 6 1 8 1 1 1 1 1 1 1 I 1 1 9 1 3 4 | 9 6 | 1 1 8 8 8 | 3 1 0 9 1 6 6 1 9 3 1 9 1 1 I 6 1 1 | 8 3 0 0 1 4 1 0 6 1 4 0 I 6 1 1 18 3 I 1 1 8 1 0 1 1 9 6 1 3 1 6 4 1 0 8 | 0 6 10 6 1 4 0 | 4 6 3 1 2 1 4 0 1 3 9 1 3 8 16 8 1 0 9 | 9 4 9 1 11 9 3 1 9 3 1 4 0 14 0 1 8 4 | 6 t l t4 1 t4 I 1 1 1 I I I • 1 T - L E V E L 1 0 3 1 8 1 I 1 0 3 1 1 0 3 1 6 9 | 1 0 3 1 M E A S U R E 1 1 1 2 1 3 14 1 5 | 6 1 i t IS 5E r fe—I ^ E ho. 3 7 * JZL ~0~ — 7 1 3 0 1 1 1 3 0 1 1 3 1 9 1 1 1 8 1 U 1 1 1 1 6 1 1 1 8 8 1 1 1 8 8 8 1 3 1 8 U 1 8 1 8 1 5 1 8 3 0 1 8 3 0 6 1 0 1 3 9 1 9 1 0 1 4 1 0 1 1 6 1 0 1 1 6 4 1 6 1 0 6 1 0 1 6 1 3 1 4 3 1 4 3 0 1 4 1 9 3 1 9 1 3 1 2 1 9 9 1 9 9 9 1 1 1 1 4 0 1 4 1 9 1 1 1 6 t l t4 t4 | 6 t l t4 t4 t i l | t8 | 6 4 1 6 1 t4 | 1 1 - 1 1 1 1 1 T - 1 1 0 3 1 8 4 1 7 1 0 51 0 1 01 N . 1 7 1 8 1 9 1 1 0 - 1 1 I 1 2 I 1 3 I l O l Note: Asterisks (#) indicate deleted doublings o-f primary melo-dy and bass elements, s i m p l i f i c a t i o n s of harmonies in order to show the seven-element sonority. "+" (m. 6) indicates a modifi-cation of the T-2 harmony, with a l l elements including "1" in the v e r t i c a l representation. Unlike the harmonies of " I " , those of " I I " always have the primary melody element in the uppermost v e r t i c a l p o s i t i o n . With regard to element occurrence in ranges of p o s i t i o n s (lower three p o s i t i o n s and the upper four, as suggested by the d u p l e - t r i p l e polyrhythmic f i g u r e s of mm. 1-5 and 10-13), elements "4" and, to a lesser extent, "9", "6", and "O" (F, Bb, G and Ctt, respective-ly)** 5* occur frequently in the lower three positions while "8", "11", and "3" (A, C, and E, respectively) occur frequently in the upper four p o s i t i o n s . As with " I " , a " r e f e r e n t i a l " harmony of " I I " can be derived from the frequently occurring elements (from lowest to highest, » 4 . . _ M 9 » _ . , 3 . . _ » 6 . . _ . . o n _ n 8 » _ n X 1 n ) _ Like the " r e f e r e n t i a l " harmony of " I " , t h i s structure a c t u a l l y occurs in " I I " , in mm. 13 (T-O), 6 (T-5), 7 (T-3), and 8 ( T - l l ) . "III''. Because of the v a r i a b l e texture of " I I I " , in the number of elements per harmony, and in the contrapuntal inner voice fragments, the harmonic structures are not consistent. However, Ex. 2-24 attempts to interpret the music s i m i l a r to Exx. 2-22 and 2-23. Elements within one T-level or harmony that can be interpreted as melodic ( e s p e c i a l l y those separated by a semitone or tone from adjacent elements) are included in Ex. 2-24 with the adjacent element(s) in one p o s i t i o n , but these are also v e r t i c a l i z e d so that only one element occurs in one p o s i -102 t i on, Example 2-24, Harmonies o+ "III element numbers. with pitches represented by (a)PCs o-f the ICC at T-0: ELERENTS: bo \\o bo X o n o 10 11 ( b ) V e r t i c a l i z e d T - l e v e l s , with representative element numbers VERTICAL 10 POSITION 9 | T-LEVEL MEASURE 103 Example 2-24 continued. l i p 3g i iZ2I -*e- 2 10 1 H O - 0 | 1 1 9 1 8 1 1 1 8 1 0—1 I 1 §3- 3 1 71 I10--0--1 —10—0—1- 9 1 3 1 *8- 0 1 61 8--6 8-6 4 | 8 1 #4- 4 1 *8--0- -8 S I 0--1--0 0 - 1 - 0 10 I 4 1 §0-1- 1 1 3 8 0 4 1 9 8-9 9 9 tt 1 0 1 *6— 8- | 0 4 6 3 1 4 - 4 — 3 1 •10 1 *0- l - | 6 3 4 2 1 10 8 10 1 •6-10 | 1 4 6 3 1 1 8 10 8 I 1 1 M l 1-1 1 1 1 T- 1 7 0 3 1 8 1 11 1 2 M. 1 4 1 3-6 1 7 1 8 io i i 9 1 I 8 1 I 71 M I «8 6 | 8 | 0 S | 3 | 3 4 1 4 | 6 3 1 6 | 10 2 | 10 | 4-II I 1 T - 1 6 | 9 • . 1 8 1 9 I I » I I I M - 6 | I I *3-9~10 11 I I M 1 8 I * 3 ~ l - 0 | I *1 I -3 1 4 I 1-0-11 I I I 2 I *10 I *9 I 4 0 8 6 1 I I I S 4 3 0 8 6 11 2 I I 8 4 | tO 1 6 | 8 6 »3 I 13--1-I tO M *4 0 | t l I 4 1 3 8 1 4 I 1 6 0 1 | 6 I I I 5 0 4 7 | 0 I 10-11 I 12 13 I 14-13 104 A study of element occurrence in lower and upper ranges o-f po s i t i o n s reveals a tendency -for elements "1", "4", and "6" (G#, B, and Db) to appear more -frequently in lower v e r t i c a l p o s i -tions, and "0", "3", and "8" <G, Bb, and Dt*) in the upper p o s i -tions. This pattern o-f occurrence i s s i m i l a r to that o-f " I" . *»s Elements "2", "5", "9", "10", and "11" do not appear as con s i s t e n t l y as elements "0", "1", "3", "4", "6", and "8", the invariant or unbracketed elements o-f the ICC. Patterns of e l e -ment occurrence in individual p o s i t i o n s are such that often two and more elements are strongly represented in one p o s i t i o n ; hence, there i s no cle a r " r e f e r e n t i a l " harmony. "I", "II", and "III'' as a whole. There are no apparent consistencies in v e r t i c a l element location and occurrence in the three pieces as a whole. As suggested by the " r e f e r e n t i a l " har-monies of " I " (elements "6"-"1"-"4"-"9"-"0"-"3"-"8", lowest to highest r e g i s t e r s ) and " I I " ("4"-"9"-"3"-"6"-"0"-"8"-"11"), ver-t i c a l element d i s t r i b u t i o n s in harmonies of the two pieces tend to be quite d i f f e r e n t . With " I I I " , there i s no " r e f e r e n t i a l " harmony, although a few harmonies bear some resemblance to those of " I " . Figure 2-9 i l l u s t r a t e s limited tendencies in ranges of v e r t i c a l element p o s i t i o n s in the three pieces as a whole. 105 Figure 2-9. V e r t i c a l element occurrence in ranges o+ pos i t i o n s in Trois Compos i t i ons. Groups o-f vert i c al pos i t ions: 4- 7 1-3 5- 7 1-4 Frequently occurring elements (descending order o-f frequency; elements with fewer occurrences in brackets): O, 3, 8, 9 4, 1, 6 8, 3, O 6, 4, 1, 0 (4, 9, 11) (8, 0, 9) (4, 9, 11) (8, 9, 3) Elements "1", "4", and "6" (Eb, Gb, and Ab) tend to occur in the lower three or four v e r t i c a l p o s itions while "0", "3", "8", and "9" <D, F, Bb, and Cb) tend to occur in upper v e r t i c a l posi t ions. V e r t i c a l Element Adjacencies Element adjacencies, which are independent of v e r t i c a l po-s i t i o n , likewise have no consistencies i n d i c a t i v e of delibe r a t e PC c o n t r o l . There are however a few i d e n t i f i a b l e adjacencies (e.g., elements-pairs, and e1ement-trichords) occurring with enough frequency to be of i n t e r e s t . What i s p a r t i c u l a r l y note-worthy i s the fac t that the v e r t i c a l element orderings of many of the harmonies in each of the pieces ( e s p e c i a l l y in " I " and "II") appear to be derived from a limited number of v e r t i c a l element structures in the respective pieces. Derivation i s p r i -marily through rearrangements of element-pairs and -tr i c h o r d s , and inversions of elements within these p a i r s and tri c h o r d s . This would suggest that elements, and not just PCs, are an im-portant determinant in v e r t i c a l element ordering. Example 2-25 i l l u s t r a t e s such a process of der i v a t i o n with the harmonies of 106 Example 2-25. S i m i l a r i t i e s o-f harmonies in " I " (with pitches represented by element numbers). I 10 I 8 I I » I I 4 I 1 I 6 I I 0 0 4 1 1 8 8 8 3 | 8 T-LEVEL | 0,11 7 3, 9 4 3 I 3 I 0 I 9 I I 4 I 1 I 6 I I 0 io I 3 0 | 0 9 I 9 8 I I 4 1 I 1 6 I 6 1 I 0 MEASURE | 1,4 3 1,12 12 10,11 | 1 1 2 2 | 1 I 8 I 3 I I 0 I 9 I I 4 I 1 I 6 I 0 I 0 I 1 a? £3£ te l I 3 I 9 I (3) I 1 I 0 I 4 I 8 1 6 I T-LEVEL | 9 MEASURE | 4 0 0 0 1 6 6 6 | 9 9 0 0 | 3 4 9 9 4 1 8 3 3 3 1 1 0 8 I 1 8 9 14 8 4 4 3 | 1 6 1 1 8 16 0 I 2 2 3 1(0) 6 4 4 5 1(1) 10,11 6 I 4 | I 0 I 4 8 | 10 I 3 3 | (1) 9 I 1 11 10 3 4 10 9 3 0 1 1 I I 11 10 | 0, 2 3 4 10 3 1 0 6,7 I 6, 7 1 11 7 8 11 10 5 4 10 9 1 0 107 Note: In t h i s and following Examples dealing with v e r t i c a l e l e -ment adjacencies, gaps in the v e r t i c a l presentations of elements are for the purpose of h i g h l i g h t i n g v e r t i c a l l y adjacent elements used in other harmonies. T-O (m. 1) i s restated f o r purposes of compar i son. Many of the harmonies are c l e a r l y derived from T-0, m. 1, which explains the resemblance between the " r e f e r e n t i a l " harmony and the T-O harmony of m. 1. However, the derivation of some harmonies require explanation. T - l (m. 2) i s the same as T-O (m. 1) except for an exchange of "4" and "8". T-10 <m. 3) i s s i m i l a r to T-O (m. 1) i f the uppermost elements "6" and "4" are rotated to the bottom of the harmony, while T-4 (m. 3) i s l i k e -wise s i m i l a r i f "3" and "8" are rotated to the top of the har-mony. T-9 (m. 4) r e s u l t s in a harmony s i m i l a r to T-O <m. 1) i f interpolated elements are removed. In other words, "8" and "0" (upper p o s i t i o n elements) are interpolated with »6"-"4"-"l" to produce "6"-"8"-"4"-"0"-"1", with «9»-»3» in the upper two p o s i -tions. Likewise, T-6 (mm. 10-11) involves a s i m i l a r a l t e r n a t i o n of elements. Although T-2 (m. 4) and T-5 (m. 5) do not r e a d i l y resemble element formations of other harmonies, T-2 i s derived from T-5, with the v e r t i c a l rearrangement of element-pairs and an e1ement-trichord. The harmonies of mm. 6-8 do not appear to have been derived from other harmonies in the piece, but these measures comprise a d i s t i n c t formal section with d i f f e r e n t har-monic structures based on an expanded ICC. However, one harmony which has limited s i m i l a r i t i e s to the f i n a l harmonies of mm. 6, 7, and 8 i s T-O (m. 13), which shares elements "1", "3", "4", and "8" with t h i s f i n a l harmony. Similar methods of element reordering are used to i l l u -108 s t r a t e the deri v a t i o n of some harmonies in " I I " (Ex. 2-26). Example 2-26. S i m i l a r i t i e s o-f harmonies in " I I " (with pitch* represented by element numbers). I I I 11 11 I 8 8 I 3 3 I 0 0 I 3 11 8 0 11 4 9 6--1--4 11 I 11 8 I 8 11 8 3 9 9 3 11 9 6 3 0 4 8 11 9 6 0 3 4 10 T-LEVEL | 0 0 2,10,8 3,3,11,0 | 0 3 3 MEASURE | 1 10-12 6, 7,8 6,7,8,13 I 1 1 10,11 3 109 Example 2-26 continued. I 11 8 8 I 8 11 4 11 T-LEVEL | 0 MEASURE | 1 11 6 0 8 1 9 9 3 8 1 2 2 4 11 9 8 3 3 1 0 11 0 3 1 3 11 I 8 I 1 61 0 I 6 I I 3 1 11 3 3 0 11 8 3 8 11 0 9 | 3 6 9 4 1 4 4 6—1—4 I 3 | 10 10 10 7 1 3 4 7 110 Example 2-26 continued. I 3 £ 3 * i i f c 1 11 3 1 11 11 1 1 4 3 3 | 3 6 1 8 9 3 1 1 11 9 6 | 9 8 1 3 8 8 1 1 6 U 1 6 0 11 1 3 0 1 1 6 I 1 0 6 1 1 0 11 8 | 11 6 8 1 0 6 4 6 1 1 8 4 0 | 4 3 0 1 6 4 0 3 1 1 9 1 4 1 1 9 0 9 | 0 9 1 11 9 9 1 1 3 8 4 | 8 4 4 1 9 8 11 4 1 1 1 1 1 1 6 9 | 6 11 9 1 0 7 4 11 1 1 2 3 3 | 3 8 3 | 10 9 8 8 1 The ascending order o-f elements in T - l <m. 2; p a r t i c u l a r l y elements " 9 " - "8 " - "0" - " 6" - " 11 " ) would seem to be derived -from the extraction -from T-5 <m. 1) o* every second element in an ascend-ing order. This process o-f extraction includes r o t a t i o n through the element order, in the sense that once the uppermost element or next to uppermost element o-f the harmony's ascending order has been used, one proceeds to the next-lowest or lowest ele-ment, re s p e c t i v e l y , o-f the harmony to extract the next element in the order. S i m i l a r l y , the descending order o-f T - l l ' s <m. 8) lower elements <i.e., "O"-"6"-"3"-"9"-"4") are used to derive every second element o-f T-4's <m. 8) ascending order o-f ele-ments. T-7 (m. 9) then involves a p a r t i a l l y symmetrical reor-I l l der ing o-f T-4's (m. 8) elements. Unlike those o-f " I " and " I I " , many o-f the harmonies o-f " I I I " are not c l e a r l y derived -from element reorderings o-f other harmonies. Example 2-27 i l l u s t r a t e s those harmonies with s i m i l a r i t i e s in v e r t i c a l element adjacency. Example 2-27. S i m i l a r i t i e s in the harmonies o-f " I I I " (with pitches represented by element numbers). I 4 1 I 1 0 4 8 1 6 3 8 4 18 0 8 0 1 4 1 3 3 1 3 8 1 6 13 8 0 8 1 1 6 0 1 1 8 0 6 3 | 0 3 3 3 1 6 8 1 1 4 6 1 3 4 | 0 4 4 0 16 6 10 1 1 3 8 1 6 1 4 1 3 8 14 10 4 4 1 8 0 6 0 1 1 6 0 1 1 1 1 1 6 1 1 1 1 8 3 7 10 I 5 0 4 7 | 2 6 9 2,0 1 2 2 2 2 1 13 13 13 13 | 8 8 9 10,14 112 Example 2-27 continued. 1 3 0 8| 0 6 1 4 3 1 4 81 1 1 8 8 0 | 4 3 1 1 8 1 3 1 1 3 4 0 1 1 4 3 3 1 1 8 1 6 0 1 0 6 1 8 6 8 1 1 0 4 6 1 1 1 1 1 3 3 1 1 10 6 10 I 6 0 1 3 4 1 8 4 1 4 0 1 1 1 6 10 4 I 3 4 1 8 I 1 1 3 1 6 8 4 1 1 1 1 H 8 1 1 0 6 1 6 0 1 0 1 6 1 1 1 1 1 1 1 T-LEVEL | 8 6 91 8 3 1 3 0 1 7 4 1 10 7 0 i MEASURE | 3-6 8 9 1 2 13 I 2 13 I 2 13 I 2 13 14 1 In general, the v e r t i c a l element orderings o-f harmonies in "III" are such that -fewer chords are derived -from preceding chords. This constrasts to some degree with the harmonies o-f " I " , many.o-f which are derived in some recognizable extent -from preceding harmonies, p a r t i c u l a r l y T-O, m. 1. In -fact, there are c e r t a i n s i m i l a r i t i e s between the chord structures o-f " I " and " I I I " , because o-f the common element content ( i . e . , »0"-"l"-"3"-"4"-"6"-"8") o-f t h e i r respective ICCs, as shown in Ex. 2-28. As many o-f the harmonies in " I " are derived -from T-O (m. 1) , t h i s w i l l be the only harmony o-f " I " c i t e d in the comparison with structures o-f " I I I " . 113 Example 2-2S. S i m i l a r i t i e s in v e r t i c a l element orderings of harmonies in " I " and " I I I " . T-LEVEL MEASURE 1 8 1 1 1 (0) 1 1 1 10 (8) 1 1 3 1 8 (6) 1 10 0 1 9 11 1 3 0 3 (4) 1 3 9 8 1 4 10 1 0 8 8 3 1 8 8 3 1 3 9 1 9 3 0 0 1 1 4 6 1 1 8 1 4 1 4 6 1 4 6 4 1 8 1 1 1 4 1 4 1 6 0 10 I 6 0 1 6 6 6 1 1 0 1 1 1 0 6 1 1 1 1 0 2,0 0 2 1 10 1 6 1 6 1 1 1 10,14 13 8 1 2 3 8 1 10,11 3 1 1 3 3 3 1 3 3 3 1 1 3 Such v e r t i c a l adjacencies and derivations o-f harmonies by element reorderings o-f preceding harmonies may well be t y p i c a l o-f Ros 1 avets's music. Cone 1us i on Having examined the ICC system in Trois Compositions and c h a r a c t e r i s t i c s that pertain to i t s a p p l i c a t i o n in the music, we should summarize some of the important points raised in t h i s chapter. Each piece's harmonic organization i s based in part on the ICC associated with the given piece, the ICC whose PC content i s transposed to produce the PC c o l l e c t i o n s comprising a piece, usually expressed harmonically but at times l i n e a r l y . Although there i s a basic ICC -for each piece, and each PC c o l l e c t i o n rep-resents a transposition o-f that basic ICC, there are v a r i a t i o n s in element content. I n t e r e s t i n g l y , though the PC content o-f the three basic ICCs d i f f e r s , there are important s i m i l a r i t i e s in element contents <i.e., elements "O", "3", "4", "6", and "8", 114 with "1" and "9" in two of the three ICCs). In each piece, one T-level (T-O) acts as a r e f e r e n t i a l son-o r i t y -for the given piece, in the sense that the sonority begins and concludes the piece and i s most s i g n i f i c a n t in that respect and as to frequent occurrence, greater t o t a l time-span through the piece, and coincidence with formally important time-points. T- l e v e l s can in f a c t be hierarchized, based on these c r i t e r i a , i n d i c a t i n g the s i g n i f i c a n c e of each in a given piece. Each piece has a d i f f e r e n t hierarchy of T - l e v e l s , although T-0, T-5, T-3, and T-8 are s i g n i f i c a n t T - l e v e l s in the three pieces as a who 1e. Harmonic successions generally involve IC-3- and IC-5-rela-ted T-levels, and frequently employ two, three, and four compon-ent T-levels of an ascending i n t e r v a l 3 or 5 cycle, or combina-tions thereof. E s p e c i a l l y in " I " and " I I I " , three or four T-l e v e l s of an i n t e r v a l 3 T-level family in c y c l i c order (e.g., with the 3-0 cycle, T-O,T-3,T-6,T-9) are employed before pro-ceeding to another i n t e r v a l 3 c y c l e or component(s) thereof. However, a number of the transferences from one i n t e r v a l 3 T-level family lor component) to another involve IC-5-related T-l e v e l s . In f a c t , in " I I " , as opposed to " I " and " I I I " , the harmonic succession i s based on a reordered i n t e r v a l 5 cycle. PC invariance in a l l four (or even three or two) T-levels of a family of IC-3-related T - l e v e l s and transferences from one family (or component) to another may be viewed as analogous to the PC c o l l e c t i o n of a tonal key and modulations between such keys. 115 Studies of PC and element occurrence, ordering, and a s s o c i -ation, within i n d i v i d u a l PC c o l l e c t i o n s and involving adjacent c o l l e c t i o n s , show no r e a d i l y apparent consistencies i n d i c a t i v e 0- f d e l i b e r a t e control o-f PC organization. Because most harmonic successions involve IC-3- or IC-5-related T-levels, there are usually three or -four invariant PCs in a given succession, while only one o-f these invariant PCs involves pitch c o n t i n u i t y . IC-1- , -2-, -4-, and -6-related T-levels, which occur infrequently in a l l three pieces, have fewer invariant PCs. Pitches tend to proceed by IC-1 and -2, somewhat less by IC-3 and -4, and much less by IC-5, and -6, to those pitches of succeeding harmonies in the same voice or v e r t i c a l p o s i t i o n , with no apparent, con-s i s t e n t l y applied p r i n c i p l e s of voice-1eading or p i t c h succes-s i on. Elements "3", "0", and "8" tend to occur most frequently in the primary melodies of the three pieces, with "3" in " I " (as to i t s occurrence as i n i t i a l element of most T-levels) and "11" in " I I " having added s i g n i f i c a n c e . Elements "1" and "6" occur most frequently in the bass-lines of the three p i e c e s . 4 - In general however, few apparent consistencies in element ordering are found in the melodies and bass-lines of " I I " and even moreso in " I I I " . Some s i g n i f i c a n t patterns of v e r t i c a l element occurrence, ordering, and association are to be found, e s p e c i a l l y in " I " and " I I " . In the three pieces as a whole, elements "1", "4", and "6" tend to occur in the lower r e g i s t e r , "0", "3", "8", and "9" in the upper. "Re f e r e n t i a l " harmonies of " I " and " I I " consist 116 of the most frequently occurring element in p a r t i c u l a r v e r t i c a l placements. Many harmonies in " I " and " I I " represent modifica-tions of the respective " r e f e r e n t i a l " harmonies. The study of v e r t i c a l element adjacencies ( i . e . , element-pairs and - t r i -chords), and the derivations of element orderings of many harmo-nies from those of a few, bear t h i s out to some extent. Such derivations are through the following means: rearrangements of element-pairs and -t r i c h o r d s ; inversions of elements within these p a i r s and tri c h o r d s ; rotations upward and/or downward; the deri v a t i o n of alternate elements of one chord (in one d i r e c t i o n or another) to produce the element ordering of another; and sym-metrical reorderings of elements. This suggests that elements, and not just PCs, are a determinant in v e r t i c a l ordering. Many of the harmonies in f a c t involve some recognizable, minimal modification of the element ordering of others. With " I " and " I I " , there i s a c e r t a i n homogeneity of element order in the harmonies, much less true of " I I I " . In general, there are c e r t a i n s t y l i s t i c c h a r a c t e r i s t i c s that d i f f e r e n t i a t e " I " and " I I " from " I I I " , the more s a l i e n t of these being: (1) the PC contents and ICAs of the ICCs, and the use of more variant T-levels in " I I I " , i n d i c a t i v e of fre e r ap-p l i c a t i o n s of the ICC system in the la s t piece; (2) the greater f l e x i b i l i t y in harmonic rhythm in " I I I " , s p e c i f i c a l l y the i n -consistency in T-level time-spans, compared with the harmonic rhythms of " I " and " I I " ; (3) the more pervasive use of complete, uninterrupted ascending i n t e r v a l 3 cycles of T-le v e l s in " I I I " as compared with " I " ; (4) fewer i d e n t i f i a b l e patterns of PC and 117 element occurrence, ordering, and association in " I I I " , due in part to the variances in texture, and the tendencies toward l i n -ear, contrapuntal a c t i v i t y ; and <5) fewer, overtly tonal struc-tures and procedures in " I I I " , which i s made evident in Chapter Three. However, there are ce r t a i n s i m i l a r i t i e s between " I " and "I I I " that perhaps suggest a r e c a p i t u l a t i v e ternary structure r e l a t i n g the three pieces as a set. Such a structure in -fact imitates the r e c a p i t u l a t i v e ternary -form o-f each piece. These s i m i l a r i t i e s are: (1) the use o-f complete i n t e r v a l 3 cycles o-f T-leve l s in " I " and " I I I " , as opposed to the use o-f the int e r v a l 5 cycle which characterizes " I I " ; (2) both " I " and " I I I " have portions o-f t h e i r development sections (mm. 6-8, and m. 4, res-p e c t i v e l y ) , employing successions -from the in t e r v a l 5 cycle; (3) the general i r r e g u l a r i t y o-f the harmonic rhythm, as opposed to that o-f " I I " ; (4) the tendency to have elements "1", "4", and "6" in the lower range o-f v e r t i c a l p o s itions, with "0", "3", "8", and "9" in the upper range; and (5) the procedure o-f sub-d i v i d i n g PC contents o-f a T-level to produce contrasting harmon-ic content in mm. 6-8 o-f " I " ( s p e c i f i c a l l y , T-O, T-2, and T-7) and m. 4 o-f " I I I " (T-7, T-O, and T-5). Notes 1. Gojowy, Meue sowjetische Musik, 138 (my t r a n s l a t i o n ) . 2. Gojowy, "Hal-f Time," 212. 3. Perle, Serial Composition, 43. 4. Gojowy, Neue sowjetische Musik, 138. 118 5. Wallace Berry de-fines a p i t c h - c l a s s (PC) as "pitch inde-pendent o-f s p e c i f i c r e g i s t r a l occurrence" and pitch-class-com-plex (PCC) as "a complex o-f such pitches g e n e r i c a l l y under-stood." (Wallace Berry, Structural Functions in Music CEnglewood Cli-f-fs, New Jersey: P r e n t i c e - H a l l , 19763, 27n. ) 6. Although the PCs o-f a T-level can be expressed l i n e a r l y in the music, as they are to some degree in " I " ( T - l l , mm. 6 and 7) and " I I I " ( T - l l , m. 7), a T-level in Trois Compositions usu-a l l y occurs in the music as a s i n g l e harmonic unit with c e r t a i n melodic components ( i . e . , pitches o-f the primary melody, bass l i n e , or inner melodies). "Primary melody" r e f e r s to a li n e a r p i t c h c o n t i n u i t y usually -found in the upper voice of a piece, although i t may appear for a time elsewhere in the texture. Such a placement in the uppermost part of the texture, in con-t r a s t to other li n e a r p i t c h c o n t i n u i t i e s found in inner voices or those forming a bass l i n e , focuses one's attention on i t ; hence the primacy of t h i s melody. The "bass l i n e " i s the se-quence of pitches formed by the lowest pitches of harmonies, usually one for each harmony. 7. Perle, Serial Composition, 43; Gojowy, Neue sowjetische Musik, 138-141. However, Gojowy does not apparently explain the method of segmentation into p i t c h c o l l e c t i o n s used to a r r i v e at these T-level successions. In Gojowy's notational system, which i s used for his charts that i d e n t i f y the ICCs and t h e i r PC con-tents in musical excerpts, the twelve-PC system ( i . e . , PCs of a chromatic scale beginning with C) i s used. PCs of the ICC, in ascending scale form, are represented by X's, while those PCs not of the ICC are represented by O's. Hence, the ICC of " I " i s represented by the following: 0-0-X-X-O-X-X-O-X-O-X-X. Gojowy also represents t h i s ICC with a short-hand designation XII=1,2, 5,8,IO, where an ICC based on a 12-PC system (XII) lacks e l e -ments 1(C), 2(C#/Db>, 5(E), 8(G), and 10(A). In notating the ICC T-levels, Gojowy uses a designation very s i m i l a r to that used by Perle; namely, "TI" to represent the i n i t i a l appearance of the PCC in the piece, "T2" as t h i s PCC transposed up a semi-tone, and so on. In my study, as in Perle's, the i n i t i a l PCC w i l l be referred to as the "T-O" l e v e l . 3. More s p e c i f i c guidelines of segmentation should be es-tablished. One p r i n c i p l e i s to i s o l a t e s i m u l t a n e i t i e s and de-l i n e a t e p i t c h c o l l e c t i o n s using time-points where there are i n -terruptions in p i t c h a c t i v i t y in a l l voices or parts. In other words, one groups together into s i n g l e c o l l e c t i o n s those pitches whose time-spans overlap. While not p r o h i b i t i n g the inclusion of s i n g l e pitches into two adjacent T-levels, t h i s i n i t i a l p r i n -c i p l e makes that less l i k e l y while allowing most pitches that are temporally associated to be included in the same c o l l e c t i o n . Then, and e s p e c i a l l y when there i s consistency in the number of PCs per c o l l e c t i o n , these segmented c o l l e c t i o n s are examined for PC and IC s i m i l a r i t i e s . Combining smaller c o l l e c t i o n s into l a r -ger ones or d i v i d i n g c o l l e c t i o n s into subsets in order to main-119 tain consistency of c o l l e c t i o n s i z e , i s another p r i n c i p l e in de-termining the derivation of harmonies from ICCs in Roslavets's music. There are a few exceptions to the above-mentioned guide-l i n e s of PC segmentation. In m. 3, the three harmonies (T-7, T-lO, and T-4) would otherwise be considered as one, because of the sustained C4 and the guidelines i n d i c a t i n g that overlapping pitches are included in a s i n g l e ICC T - l e v e l . The consistent occurrence of s i x to eight PCs per harmony, often as simultanei-t i e s , i s the c r i t e r i o n for designating three harmonies in m. 3. Although the second halves of mm. 6 and 7, and m. 8, would ap-pear to represent a s i t u a t i o n s i m i l a r to that of m. 3 (whereby these time-spans, despite the t r i l l s , are segmented into three harmonies), a d i f f e r e n t approach i s employed in assessing the segmenting of these time-spans, as discussed l a t e r in t h i s sec-t i o n of Chapter Two. 9. Alle n Forte, The Structure of Atonal Music (New Haven, Connecticut: Yale University Press, 1973), 13f. 10. Berry defines an i n t e r v a l c l a s s (IC) as including "any given i n t e r v a l within the octave together with i t s inversion (complement) and a l l compound extensions (expansions by one or more octaves) of the given i n t e r v a l or i t s inversion. If enhar-monically equivalent forms are considered of the same c l a s s , there are six i n t e r v a l classes (the unison excluded). . . . " (Berry, Structural Functions, 193n.) 11. To r e i t e r a t e , each ordered PC i s numbered according to the PC i n t e r v a l i t forms with the f i r s t PC of the c o l l e c t i o n . 12. Elements ( i . e . , the PCs in s p e c i f i c p o s i t i o n s within the ICC scale form) have numbers in quotation marks (e.g., "0") in the text of the t h e s i s to d i s t i n g u i s h these from other arabic numbers. Again, element "O" in an ICC or i t s T-level would rep-resent the " f i r s t " PC although " f i r s t " does not imply primacy or importance as of the f i r s t degree of a tonal scale. 13. Gojowy, "Half Time," 212. Elsewhere, Gojowy r e f e r s to "scale-defined tone-complexes", with s p e c i f i c i n t e r v a l l i c r e l a -tionships between the component PCs. (Gojowy, Neue sowjetische Musik, 138.) 14. Perle, Serial Composition, 43. 15. Ibid., 44. 16. See fn. 8 f o r p r i n c i p l e s underlying segmentation of pitches into PC c o l l e c t i o n s . 17. Perle, Serial Composition, 43. 18. In thinking ahead to the discussion of " I I I " and to Gojowy's analysis of ICC structure (he i d e n t i f i e s four s i m i l a r but individual ICCs), one wonders why he indicates that four 120 ICCs are operative in " I I I " while only one i s operative in " I " , t h i s despite the f a c t that the o r i g i n a l ICC of " I " does not eas-i l y explain the PC c o l l e c t i o n s of mm. 6-8. Another approach to T-level i d e n t i t y in mm. 6-8 i s to base each of the three harmo-nies in the three aforementioned time-spans on an ICC T-level most c l o s e l y resembling the PC content of the harmony in ques-t i o n . This i s examined in more d e t a i l in Appendix B. 19. Gojowy, Neue sowjetisc/?e Musik, 138-139. 20. Ibid., 139. 21. Int e r e s t i n g l y , in Gojowy*s l i s t i n g of T-level succes-sions, there i s an "X" in m. 7 which i s l i k e l y meant to desig-nate the T-level with element "1" although t h i s p a r t i c u l a r v a r i -ation also occurs in mm. 6 and 8 (which have no "x" in Gojowy's 1i st i ng) . 22. That i s , element "1" pitches occur a perfect fourth (IC-5) below the i n i t i a l bass p i t c h , as the f i f t h of the minor-minor-seventh chord that c o n s t i t u t e s the lower component of these harmonies. In a sense, element "1" has strong tonal im-p1icat ion. 23. Gojowy, Neue sowjetische Musik, 139. 24. Ibid., 141. 25. Perle, Serial Compos i t i on, 43-44. A recent a r t i c l e by Perle prompted an examination of " I I I " in terms of i t s musical orthography. (Perle, "Scriabin's Se1f-Analyses," Music Analysis, 3/2 CJuly 19843: 101-124? e s p e c i a l l y 107, l l O - l i l . ) Such con-stancy in the i n t e r v a l s formed between ordered (scale form) PCs of T - l e v e l s in " I I I " undoubtedly led Perle to suggest the use by Roslavets of a s i n g l e ICC. Quite l i k e l y although unsubstanti-ated i s the f a c t that Roslavets may have been influenced by S c r i a b i n in t h i s regard. Although the ICC of " I I I " i s noted be-cause of i t s d i f f e r e n t PC i n t e r v a l pattern, those of " I " and " I I " are s i m i l a r in the sense that the respective T-l e v e l s con-s i s t e n t l y r e f l e c t the PC i n t e r v a l pattern of the p a r t i c u l a r piece's ICC. 26. Perle indicates the p r a c t i c e of element omission but the i l l u s t r a t i o n of the ICC or "set" of " I I I " f a i l s to bracket PC Bb ( i . e . , element "3" in ICC at T-O) as such a variant e l e -ment. (Perle, Serial Composition, 43-44.) 27. Another approach to T-level i d e n t i t y in the three pieces, given the s i m i l a r i t i e s of the three ICCs, i s to have one si n g l e ICC for a l l three pieces. This i s b r i e f l y examined in Appendix B. 28. Gojowy, Neue sowjetische Musik, 140 (my t r a n s l a t i o n ) . 121 29. Later studies of PC invariance in IC-3-related T - l e v e l s w i l l group such T-le v e l s into T-level -families ( i . e . , with T-level -family 3-0 including T-0, T-3, T-6, and T-9, and 3-1 and 3-2 -families including T-levels corresponding to those in the 3-1 and 3-2 cycles, r e s p e c t i v e l y ) . 30. The reasons -for these displacements would seem to be related to the tonal aspects o-f the piece, which w i l l be dealt with in Chapter Three. The T-10,T-3 succession, r e i t e r a t e d in mm. 3-4 (which in itsel-f i s s i g n i f i c a n t ) , has an Eb-major t r i a d PC component which i s generally invariant through these mea-sures. The T - l l , T - 4 succession (m. 8) s i m i l a r l y has an E-major PC component which i s invariant in mm. 8-9. Both o-f these t r i -ads have important s t r u c t u r a l implications -for and r e l a t i o n s h i p s with the apparent " t o n a l i t y " o-f " I I " , F major. 31. If T-level designations were altered so as to r e f l e c t the use of one ICC for a l l three pieces, there would be no con-nections between the c y c l i c T-level successions of the three pieces, in terms of some structure involving a l l three. Such T-level successions appear to be independent of one another. 32. Berry, Structural functions, 27. 33. This i s done in order to provide a more r e a l i s t i c e v a l -uation of T-level s i g n i f i c a n c e in the event that a T-level oc-curs frequently but has r e l a t i v e l y short time-spans, or with the opposite s i t u a t i o n . 34. Perle, Serial Composition, 43. 35. I n t e r e s t i n g l y , T - l l in " I " (mm. 6 and 7) and in " I I I " (m. 7) both involve l i n e a r i z a t i o n s of the T-level PCs. 36. Both T-5 and T-7, IC-5-related to T-O, have a somewhat symmetrical or "opposing" r e l a t i o n s h i p . The tonal analogies as-sociated with T-O (tonic?), T-5 (subdominant?) and T-7 (domin-ant?) w i l l be examined in Chapter Three. 37. Perle, Serial Composition, 43. 38. Allen Forte, The Structure of Atonal Music, 29f., e s p e c i a l l y 31-32. 39. PC invariance and p i t c h continuity as pertaining to prolonged T-l e v e l s i s discussed in Appendix B. 40. T-levels T-1, T-4, T-7, and T-10 are part of T-level family 3 - l j T - l e v e l s T-2, T-5, T-8, and T - l l , part of T-level family 3-2. 41. With T-level f a m i l i e s of " I " and " I I I " , these invariant and "quasi-invariant" PCs form octatonic 1-2 ( i . e . , semitone-tone) c o l l e c t i o n s while such a PC c o l l e c t i o n derived from T-122 level -families o-f " I I " -forms an octatonic 2-1 ( i . e . , tone-semi-tone) c o l l e c t i o n . In a recent a r t i c l e on the development of oc-tatonicism in Russian and non-Russian music, Richard Taruskin has some i n t e r e s t i n g observations concerning the octatonic c o l -l e c t i o n in the music o-f Scriabin that have some implications -for the music o-f Roslavets. He states that in "the music of his CScriabin'sl l a s t period, . . . the octatonic c o l l e c t i o n does not interact with diatonic harmony or emphasize t r i a d i c cog-nates. . . . Rather, in a work l i k e the Sixth Sonata, Op. 62 (1911-12) . . . the three octatonic sets act as r e f e r e n t i a l c o l -l e c t i o n s , -functionally akin to keys in the t r a d i t i o n a l sense. . . . A sense o-f tonal motion i s achieved by modulations from one octatonic grouping to another. That t h i s was a con-scious technique based on t r a d i t i o n a l tonal procedures i s made clear by the f a c t that a S c r i a b i n essay in octatonicism, what-ever the vagaries along the way, w i l l always end in the same oc-tatonic key as i t began. That S c r i a b i n conceptualized the octa-tonic c o l l e c t i o n as a pair of i n t e r c a l a t e d diminished-seventh c o l l e c t i o n s . . . i s revealed by his note s p e l l i n g . . . . " (Richard Taruskin, "Chernomor to Kashchei: Harmonic Sorcery; or, Stravinsky's 'Angle'," Journal of the American Musicological Society, 38/1 CSpring 19853: p. 99, fn. 47). In the case of the three individual pieces by Roslavets, the three octatonic c o l -l e c t i o n s are derived from the invariant and "quasi-invariant" PCs of 3-0, 3-1, and 3-2 T-level f a m i l i e s , r e s p e c t i v e l y . More-over, transference from one octatonic c o l l e c t i o n to another, or, in other words, from one T-level family to another, whether a T-level family i s represented by one or by more T-lev e l s (as i s the case with the three pieces, where s e r i e s of T - l e v e l s ascend-ing by IC 3 are common). With regard to the f i n a l cadence, Roslavets not only concludes with the same T-level family with which the piece begins, but ends with the same T - l e v e l . Of course, s i m i l a r i t i e s in the usage of octatonic techniques by S c r i a b i n and Roslavets may be limited because of such things as the PCs in a T-level family which occur with only one T - l e v e l . (There i s no r e a d i l y apparent pattern to the location or func-t i o n of these "non-octatonic" PCs in Trois Compositions. Hence, the octatonic system as applied to the pieces i s primarily theo-r e t i c a l in nature, and i s not indicated in PC events.) There are s i t u a t i o n s in the three pieces (as w i l l be demonstrated in the discussion of t o n a l i t y in Chapter Three) where t e r t i a n tonal structures and tonal procedures are employed, which d i f f e r from Scriabin's p r a c t i c e of non-interaction between the octatonic c o l l e c t i o n and tonal structures. Yet, despite such di f f e r e n c e s in the form of octatonicism in the music of Roslavets, there may be some basis for the a p p l i c a t i o n of octatonic theory and struc-tures to the music of Roslavets, i f not to the three pieces. In Chapter Three, there i s some additional discussion of octatoni-cism in the three pieces. 42. Perle, Serial Composition, 43. 43. Perle, Serial Composition, 41-42. Excerpts of the Sev-enth Sonata (pp. 42-43) i l l u s t r a t e such PC invariance in "sets" 123 (T-levels) a t r i t o n e apart. Jim Samson challenges some o-f these observations when he states: "In Serial Composition and Atonal-ity, George Perle has drawn attention to p i v o t a l segments Dther than the 7/3 unit which create l i n k s between transpositions, no-tably the diminished seventh and the segment superimposing two minor t h i r d s a perfect -fourth apart. Undoubtedly Skryabin made use of such p i v o t a l segments as a means of l i n k i n g and even (oc-c a s i o n a l l y ) combining transpositions, but I have found no e v i -dence to support Perle's claim [excluded in the above quotation] that there i s a "closed system of transpositions" based on these segments. The choice of transpositions in the seventh sonata has been governed by the t r i t o n e link and by the work's quasi-tonal structure, not mentioned by Perle." (Samson, Music in Transition, 209). In f a c t , in Trois Compositions, the frequent use of IC-3-related T-levels as the basis for harmonic succes-sions (often proceeding through three or more T-le v e l s of a T-level cycle [e.g., " I " , mm. 1-3, T-10,T-i,T-4,T-7,T-103), in combination with the i n t e r v a l 5 cy c l e , indicates a limited sys-tem of t r a n s p o s i t i o n . With regard to the term "pivot", another i n t e r p r e t a t i o n might include a s i n g l e , " i n i t i a t i n g " p i t c h which precedes other PCs of a given harmony. This occurs frequently with the harmonies of " I " and " I I I " . Such a p i t c h would be p i v -otal i f i t (or rather the PC) were common to the harmony preced-ing i t as well as i t s own harmony. Of those adjacent harmonies with s i n g l e , i n i t i a t i n g pitches in " I " , 71% have an i n i t i a t i n g p i t c h which i s p i v o t a l (65% when one includes a l l adjacencies of harmonies), while 60% of adjacent harmonies with s i n g l e , i n i t i -a ting pitches in " I I I " have an i n i t i a t i n g p i t c h (56% including a l l adjacent harmonies. Hence, there i s no strong tendency for such i n i t i a t i n g pitches to act as p i v o t s . 44. To r e i t e r a t e and c l a r i f y , "element" represents the po-s i t i o n of a PC within an ordered c o l l e c t i o n of P C s — i n t h i s the-s i s , a s c a l e — w i t h the element numbered according to the PC i n -terval i t forms with the f i r s t PC of the c o l l e c t i o n . The f i r s t PC of each PCC of the three pieces i s determined by using the prime forms of the PCCs of " I " and " I I I " , as they are most simi-lar when one excludes from consideration the variant PCs as shown in Perle's a n a l y s i s . (Perle, Serial Composition, 43.) The prime form of the PCC of " I " has elements "0", "1", "3", "4", "6", "8", and "9" (Forte set 7-32), while that of " I I I " has e l e -ments "0", "1", "3", "4", "6", and "8" (Forte set 6-Z24). (The numbering should not be confused with Forte's integer notation, where PC C i s 0, Ctt/Db i s 1, and so on.) While the prime form of the PCC of " I I " d i f f e r s from those of " I " and " I I I " , there are c e r t a i n s i m i l a r i t i e s between the ICCs of the three pieces (as i l l u s t r a t e d in Ex. 2-2). Hence, D, the f i r s t PC of the or-dered PCC at T-0 for " I " , i s element "0", Ctt/Db i s element "0" in the PCC of " I I " at T-0, and G i s element "O" in the PCC of " I I I " at T-0. Again, the designation element "0" does not nec-e s s a r i l y imply primacy of the PC represented by "0" in r e l a t i o n to the other PCs of the T - l e v e l . In f a c t , i t may be rather d i f -f i c u l t for the l i s t e n e r to r e l a t e each PC to the "0" PC. How-ever, as w i l l be noted in the discussion of " I " , element "3" has 124 a limited form o-f primacy, given i t s -frequent occurrence as the i n i t i a l element o-f many T-levels. 45. Gojowy, Neue sovtjetische Musik, 133. 46. Element successions in harmonic successions with the same T-level sequences were examined, whether the PC content and o v e r a l l sequence o-f PCs was s i m i l a r ( i . e . , a s i n g l e ICC being used -for a l l three pieces) or not ( i . e . , i n d i vidual ICCs used •for the pieces). Harmonic sequences whose T-lev e l s were related by the same IC value (e.g., IC-3-related T-levels, such as T-O, T-3, T-l,T-4, and so on) and those that were not, thus a l l T-level successions, were investigated -for consistencies in e l e -ment successions. Even element successions involving the same v e r t i c a l p o s itions ( i . e . , successions o-f elements in p o s i t i o n one, two, three, and so on) o-f adjacent harmonies were evalu-ated. It appears that there are no consistencies i n d i c a t i v e o-f p r i n c i p l e s o-f element ordering. Temporal ordering o-f elements not necessarily in the same melody or l i n e , p a r t i c u l a r l y e l e -ments that are i s o l a t e d or exposed (e.g., through s i n g l e pitch attacks, or being outer elements o-f simultaneities) were exam-ined -for any patterns o-f ordering, revealing no consistent p r i n -c i p1es. 47. Similar references to PCs in t h i s study w i l l assume the use o-f PCs o-f the ICC at T-O ( i . e . , the ICC o-f the piece being examined, or o-f " I " i-f no reference to a piece i s made). 48. In a discussion o+ chord structures in Roslavets'5 music, Gojowy indicates that the t r i t o n e i s -frequently -found, while the perfect -fourth i s infrequently used, and the minor second generally avoided. IC 1 usually appears as a major sev-enth or minor ninth. Gojowy provides one example from " I " (m. 6) where IC l s (in the form of minor ninths) are resolved to more consonant i n t e r v a l s . (Gojowy, Neue savjjetische Musik, 196-197. ) 49. Although not discussed in Chapter Three, the tonal im-p l i c a t i o n s of v e r t i c a l element occurrences are noteworthy. E l e -ments "O", "3", and "8" form the dominant chord of the minor to-n a l i t y suggested by the PCs of any of the three ICCs. (The PCs of the ICC of " I I " a c t u a l l y suggest D minor and F major.) For example, elements "O", "3", and "8" (PCs D, F, and Bb) of the ICC of " I " at T-O form the dominant of Eb minor, the t o n a l i t y suggested by the ICC PCs. In " I I " , elements "8" and "11", which frequently occur as uppermost pitches, are the mediant and domi-nant PCs of the major t o n a l i t y that the ICC of " I I " suggests. Elements "1" and "6" occurring frequently in the bass-lines are the tonic and subdominant PCs of the minor t o n a l i t i e s which the ICCs suggest. I 3-D CHAPTER THREE TONALITY IN TROIS COMPOSITIONS Introduction Roslavets suggests that c l a s s i c a l t o n a l i t y i s completely absent in his works up to 1924, although " t o n a l i t y as a concept o-f harmonic unity" e x i s t s in the form of the "synthetic chords." 1 [Roslavets's system] was based on [synthetic] chords . . . used . . . as sub s t i t u t e s -for the -functional r e l a t i o n s h i p s o-f c l a s s i c a l t o n a l i t y , which he did not r e j e c t but rather t r i e d to expand. . . . Composition based on the manipulation o-f tone complexes [ i . e . , the synthetic chords] may at times approach the tech-nique o-f twelve-tone writing. . . . This, however, occurs -fortuitously, not out o-f necessity. The meth-od may also generate other structures unrelated to twelve-tone procedures [ i . e . , tonal structures3. 2 5 The s i g n i f i c a n c e o-f Roslavets's compositional technique i s noted by Goj owy: This system o-f transposing tone-complexes i s to be observed p r i n c i p a l l y in the composers of the Mos-cow region. However, one need not regard t h i s neces-s a r i l y as as a revolutionary r e v i v a l of composition: Roslavets regards his system not so much as the means of emancipation from t r a d i t i o n as an instrument for imposing order in opposition to the present impres-sion istic-ex pressionistic tonal anarchy, which guides music to a dead-end.9 Chapters Three and Four explore structures and procedures of other systems of PC organization in Trois Compositions. Of p a r t i c u l a r i n t e r e s t are tonal, actatonic, and dodecaphonic ser-i a l ordering procedures. I n i t i a l l y , we w i l l be concerned with t o n a l i ty. 126 Although t h i s present study centers primarily on more con-ventional tonal structures and procedures ( i . e . , c h a r a c t e r i s t i c o-f the "common p r a c t i c e period"), Roslavets* s ICC system may represent an expanded tonal system, in the sense o-f Wallace Berry's d e f i n i t i o n o-f tonality,** whereby these conventional ton-al structures and procedures are but one -facet o-f Roslavets's ICC system. The system has an apparent hierarchy o-f T-levels, with T-O as a r e f e r e n t i a l harmony or "pitch-class-complex of r e s o l u t i o n , " " as well as procedures for harmonic succession ( i . e . , the use of cycles of T - l e v e l s in ICs 3 and 5). The h i e r -archy D f T - l e v e l s as well as c e r t a i n symmetrical c h a r a c t e r i s t i c s of T-level successions and of IC-3-related T-level f a m i l i e s sug-gest c e r t a i n mi dd 1 eground/background structures' 9 not unlike such large-scale structures in tonal compositions. It i s from the resources of t h i s expanded tonal system that Roslavets derives tonal structures and procedures. The nota-t i o n a l orthography f o r ICC PCs of " I " and " I I " in p a r t i c u l a r , the f a c t that a l l three pieces have ICCs resembling the minor scale, and the f a c t that c e r t a i n harmonic successions are based on IC-5-related T-level successions (which resemble tonic-sub-dominant or tonic-dominant progressions) indicate that the ICC system i s contingent in part on t r a d i t i o n a l tonal procedures. This study w i l l involve an examination of the i n d i v i d u a l pieces for surface and midd1eground/background tonal implications and t o n a l l y suggestive procedures. 127 Tonality in " I " Surface Tonal Features Perhaps the t o n a l i t i e s most c l e a r l y suggested in " I " are Eb, D, and G (generally minor mode). This i s not s u r p r i s i n g as the most -frequently occurring T - l e v e l s in " I • (T-O, T-11, and T-4) consist o-f PCs -forming these minor scales, respectively (Ex. 3-1). Example 3-1. ICC T - l e v e l s T-0, T - l l , and T-4 in " I " . T-0 (Eb MINOR) T - l l (D MINOR) T ^ 0 ° Note that two o-f the less s i g n i f i c a n t t o n a l i t i e s in " I " , F major and Bb major (mm. 7-8), are related to D minor and G mi-nor, respectively. Of course, not a l l harmonies suggesting the Eb, D, and G t o n a l i t i e s are nec e s s a r i l y derived from these re-spective T-levels, nor do these T-l e v e l s as they appear in the music necessarily suggest the respective t o n a l i t i e s . A T-level PC c o l l e c t i o n can suggest a number of d i f f e r e n t harmonic struc-tures, and a number of d i f f e r e n t t o n a l i t i e s . However, i t i s in-te r e s t i n g to note that the most s i g n i f i c a n t PCs of " I " (deter-mined by evaluating both frequency of occurrence and t o t a l time-128 spans of a l l occurrences o-f each PC) include tonic t r i a d PCs o-f these three t o n a l i t i e s . Example 3-2 provides a comprehensive analysis i l l u s t r a t i n g surface harmonic and melodic structures associated with these three t o n a l i t i e s . Example 3-2. Surface structures and progressions of Eb, D, and G t o n a l i t i e s in " I " . [11 [21 (31 (41 T-O T-4 T-4 T-ll HARMONIES (HARMONIC SUCCESSION) 129 Example 3-2 c o n t i n u e d . Ml [51 (6) 17] [81 <T-9> T-ll T-O T-ll ii I— v i i — I I--A6,bII Eb: v i i - - - 1 v i i - -——I v i i—I Bb: I F: vii 1——-[10-111 [121 [131 (T-3) (T-6) (T-9) T-4 (T-9) T-O 1 a 1 l o }o • • J \ ) " >-0 r -T P - ^ * • ' i x I - T W T \ ° [ " f T T »lft I I A: I vii7 c: I V I V OR 9: IV V/IV I V IV V/IV I v a: ii7 V7 Eb: I I I I To some degree, the t e m p o r a l - t e x t u r a l c o n - f i g u r a t i o n of har-monies p e r m i t s a t o n a l i n t e r p r e t a t i o n , as i n mm. 10-13. Even those s i m u l t a n e i t i e s with s i x and more PCs i m i t a t e t o n a l t e r t i a n s t r u c t u r e s by p l a c i n g apparent chord " r o o t s , " t h i r d s , f i f t h s , 130 and sevenths in the lower r e g i s t e r o-f the harmonies as well as in exposed upper voices. There-fore, they can be interpreted t o n a l l y , as Ex. 3-2 shows in mm. 1-8. Many o-f the PCs that are not part o-f these tonal t e r t i a n subsets can be perceived as ton al chord extensions ( i . e . , ninths, elevenths, thirteenths, or chromatic a l t e r a t i o n s thereof) although t h i s also depends upon v e r t i c a l configurations. In general, the tonal harmonic analy-s i s in Ex. 3-2 i s self-explanatory, with some exceptions. The succession from D minor to Eb that involves the entire ty of m. 6 i s re i t e r a t e d but reduced in the f i r s t half of m. 7 to a D minor-to-Eb major harmonic succession that precedes the v i i - I succession in F. Measure 8 involves a modified v i i - I sue cession in Bb. What i s i n t e r e s t i n g about the f i n a l three harmo nies of mm. 6 and 7 and of m. 8 are the t r i t o n e sequences and th e i r implications of the Eb, D, and G t o n a l i t i e s (Ex. 3-3). (Of course, not a l l pitches indicate these t o n a l i t i e s , as is suggested by the references to Eb in m. 6 and Bb in m. 8.) Example 3-3. Tritone sequences of mm. 6-8 and th e i r tonal implications. (61 (71 (81 Eb: I F: I— Bb: I 131 The -final harmony o-f " I " , T-O <m. 13), represents in part a combination of G minor and Eb t o n a l i t i e s . Although T-O i s asso-ciated with Eb minor, T-O in m. 13 has been modified by the re-placement o-f Gb with G. (The PC c o l l e c t i o n i s also T-10 o-f the ICC in " I I " , serving a connective -function between the two pieces.) An examination o-f middleground/background linear ( i . e . , primary melody- and bass-1ine-derived) structures, and midd1eground/background harmonic structures, w i l l -further i l l u -minate tonal implications in the piece, and in p a r t i c u l a r the interactions o-f these three t o n a l i t i e s as suggested by the T-O harmony o-f m. 13. M i dd 1 eground/Background Linear Structures o-f " I " Pitches comprising the outer voices of a texture are c r i t i -cal for perception, e s p e c i a l l y since the harmonies, comprising six and more d i f f e r e n t PCs (often with no octave doublings), produce a r e l a t i v e l y thick texture, and generally progress by step motion. While c e r t a i n linear structures or aspects thereof in the three pieces have tonal implications, there are others that do not. These are, nonetheless, discussed in t h i s Chapter because of t h e i r apparent s i g n i f i c a n c e . One important aspect of line a r structures in " I " i s that of i n i t i a t i n g s i n g l e - p i t c h exposure. I n i t i a t i n g s i n g l e - p i t c h exposure. The sequence of i n i t i a l , textura1ly-iso 1ated s i n g l e primary melody p i t c h e s 7 i s i l l u s t r a -ted in Ex. 3-4 with open noteheads on the f i r s t of two staves. 132 The second s t a f f involves a reductive analysis o-f t h i s sequence o-f i n i t i a t i n g pitches viewed as a background structure. Given the -frequency o-f IC 3 r e l a t i o n s h i p s between adjacent i n i t i a t i n g pitches, i t i s possible to perceive such adjacent pitches as dyads, with three or more successive pitches related by IC 3 as chords. An IC r e l a t i o n s h i p between two adjacent pitches other than IC 3 represents a "break," so to speak, with the second of these two pitches forming a dyad with a pitch following i t . Example 3-4. I n i t i a t i n g s i n g l e pitches in " I " . [11 (21 [31 [41 [51 T-0 T-3 T-10 T-1 T-4 T-7 T-10 T-4 T- l l T-9 T-2 T-5 1 .' : • X j ; >*:... i I I I \ - i i i i ; [61 (71 (81 (10,111 [121 [131 T-l l T-0 T-il T-2 T-7 T-3 T-6 T-9 T-0 133 In most cases the duration o-f an i n i t i a t i n g p i t c h equals or represents a s i g n i f i c a n t portion o-f the time-span o-f the harmony to which i t belongs. Hence, these pitches have a surface agogic value in addition to metric accent as a r e s u l t of coincidence with m e t r i c a l l y stronger time-points. Duration i s thus as im-portant a c h a r a c t e r i s t i c of these i n i t i a t i n g pitches as i s pre-cedence. Therefore, Eb4 (m. 5), although preceded by grace notes Fb3 and Bb3, i s thus considered a part of t h i s sequence of i n i t i a t i n g pitches. S i m i l a r l y , the t r i l l pitches of m. 8 as well as those f o l -lowing the i n i t i a l pitches of mm. 6 and 7 are deemed part of the sequence of i n i t i a t i n g pitches because of t h e i r durations, and because they represent a continuation of that sequence through a chromatic ascent from the i n i t i a l t r i l l pitches of mm. 6 and 7 (D4-E4). The t r i l l p i tch D4 (and not E4) i s the primary i n i t i a l p i t c h , given the i n i t i a l harmonies suggested in these measures. This sequence of i n i t i a t i n g pitches could be thought of as a "pitch axis", a s e r i e s of prominent pitches around which other pitches gravitate.* 3 In the reductive summary of Ex. 3-4, the sequence of prim-a r i l y IC 3 dyads, formed by pairs of these i n i t i a t i n g s i n g l e pitches, i s seen to form a structure i n d i c a t i v e of a large-scale plan of PC c o n t r o l . This s e r i e s of IC 3 dyads chromatically as-cends from D-F to F-Ab, with arpeggiations of diminished-seventh harmonies ( i . e . , mm. 1-3 and 7-13). However, there appears to be a b i f u r c a t i o n in t h i s structure in mm. 4-5 when the progres-sion from E-(G) can be perceived to descend as well, through Eb 134 to D. This alternate path i s represented in Ex. 3-4 with a dash-line beam in mm. 4-7. Linear structures in "I". Example 3-5 presents a more com-plete i l l u s t r a t i o n o-f linear structures in " I " . The sequence of pitches includes those extracted -from the primary melody, the bass l i n e , and those uppermost harmonic pitches (indicated in Ex. 3-5 with "X"s) that occur higher than current melody pitches. Primary melody pitches having durations longer than an eighth value are denoted with open noteheads while s h o r t e r - v a l -ued pitches are designated with s o l i d noteheads. Example 3-5. Linear structures in " I " . (11 (21 (31 (41 (31 (BIFURCATION IN LINEAR STRUCTURE) A\ u t—, b* \-> e—o_ fa, Arfa «— —W 11 4 v *'^ > n " i—m— & \>T -0 1 v—&- 9— 1 -**f> j -J-—V-n—£e—|— „ O— v- — — f r o - 1 i u 135 Example 3-5 continued. [6] 171 181 [10-111 • V - •jlo ' Vin? h a ^5— «#3toT <T/0 ' O — fen ± "—P fcs*-^ I a—: > =»— pbfl J t=r--/-a — * p — 1 [121 V [131 4 -4 J H - ^ H ————• ( f 0 0 -/=r* - V* •l. - -• -. — f There i s a middleground structure in mm. 1-6 involving both primary melody and bass-line pitches, with the PC 1ines—sugges-ted by successions o-f c e r t a i n prominent pitches"* — descending by ICs 1 and 2 ( i . e . , F4-E4-Eb4-D4 in the primary melody, and Ab2-G2-F2-Fb3-Eb4-D4) . D4 in -fact remains as an important s t r u c t u r -al p i t c h in mm. 6-13. In mm. 5-13, a middleground progression o-f G5-G86-G84-G4, involving both primary melody and upper r e g i s -ter pitches, i s apparent. A s i m i l a r structure involves bass pitches in mm. 6-13 ( i . e . , D4-G#3-A2-G#2-G2). Again, there i s an apparent descending tendency in the PC l i n e suggested by these pitches. 136 Melodic fragments. A d d i t i o n a l l y , there are c e r t a i n melodic fragments characterized by s i m i l a r successive IC sequences that suggest another dimension of underlying linear structure (Ex. 3-6) . Some o-f the pitches are notated an octave higher to show s i m i l a r i t i e s in IC sequence (numbers above the pi t c h e s ) . A l l noteheads are beamed together to i d e n t i f y melodic fragments, la b e l l e d with lower case l e t t e r s . Example 3-6. Melodic fragments of mm. 1-5 and 10-13 of " I " (11 (21 (21 [31 (41 (51 (101 (121 ••' "B" "o* *p' (TRANSPOSED) IC PATTERN ( ) 5—2—2—1—2—1—2 5—2—1—2 5 - 2 ~ 3 " 2 - 3 5 - 2 - 1 - 2 3E 11-21 (2-31 (4-51 (10-131 is-10] 3 There i s an antecedent-consequent r e l a t i o n s h i p between fragments m and nf and o and p in that consequent fragments n and p, transpositions of each other, cadence by step to f i n a l pitches of three quarter values in duration, while the antece-dent m and o fragments are characterized by larger i n t e r v a l s moving in disjunct motion. Hence, as there i s a connective PC 137 (F#) between -fragments m and n, so too there i s a connection be-tween -fragments o and p, a progression between the -final G o-f o and the i n i t i a l G** o-f p. This progression involves p i t c h a c t i v -i t y in mm. 6-8 (Ex. 3-7) . . • . -Example 3-7. The PC progression G-G*»/Ab in mm. 6-8. (61 (71 (8) (91 (101 (M. 5-10) * 7 — T -4* i* ft T *»*— *» f — » i 4 • ; Both G and G**/Ab are prolonged, in a sense, in mm. 6-8, thus emphasizing the G-to-G8/Ab progression in mm. 5-10. Stud-ies o-f PC -frequency and duration have indicated the general s i g -n i f i c a n c e o-f G and Gtt/Ab in " I " . In addition, there are tonal implications of t h i s G-Gtt/Ab succession -for Eb t o n a l i t y , which i s also prominent in these measures. In general, the -frequent occurrence o-f such melodic se-quences (IC 5 -followed by a s e r i e s o-f ICs 1 and/or 2), indicate such sequences are s i g n i f i c a n t in " I " , perhaps motivic. Bass-I ins l i n e a r structures. There are midd1eground/back-ground ind i c a t o r s of both Eb and G t o n a l i t i e s in the bass-1ine pitches (Ex. 3-8). 138 Example 3-8. Bass-line structure o+ " I " . <a)Eb t o n a l i t y : 111 121 (3) [41 [31 [61 17) ± 3! i—1 1— 1 *—1 4* 4-. V 3 «Kia-TPT. > i > ' — ' ^ tft-3-RBwrej> 77«— (81 [101 t i l l (121 [131 3 (b)Q t o n a l i t y : (11 (31 14) (31 (61 (71 (81 (10,111 (121 (131 2 g : V7 1 V-—bVI—V b l l 1 139 The r e i t e r a t e d A2-G*t/Ab2 (mm. 10-11), the Ab2-G2 succession (mm. 1-4), the prominence o-f D4 (mm. 6-7), and the -final G bass pit c h (mm. 12-13) might indicate a tendency towards G t o n a l i t y (Ex. 3-8b). In addition, the r e i t e r a t e d primary melody D4 in mm. 12-13 reinforces G. However, t r i t o n e s in the background structure suggest Eb t o n a l i t y in the f i n a l measures. Of course, Eb minor with Gb replaced by G i s suggested by T-O PCs (m. 13), t h i s harmony i n d i c a t i n g both G and Eb t o n a l i t i e s . Midd1eground/background harmonic structures of " I " Besides structures i n d i c a t i v e of Eb, G, and D t o n a l i t i e s , the most s i g n i f i c a n t T-levels of the piece as to frequency of occurrence and t o t a l time-spans ( i . e . , T-0, T - l l , T-4, T-3, T-9, and T - 7 ) , 1 0 and "balanced" occurrences of IC-3-related T-level f a m i l i e s ( i . e . , 3-0, 3-1, 3-2, 3-1, and 3 - 0 ) 1 1 would a l l be s i g -n i f i c a n t f a c t o r s of midd1eground/background structure of " I " (Ex. 3-9). 140 Example 3-9. Midd1eground/background harmonic structure of " I " . [11 (21 [31 (41 (31 (61 T-0 T-3 T-10 T-10 T-4 T-l l T-3 T-ll T-0 Tonality in " I I " Surface Tonal Features As in " I " , references to t o n a l i t y in " I I " are f l e e t i n g , ob-scured by non-diatonic PCs and the absence of t e r t i a n struc-tures. However, of a l l inferable tonal centers, F appears to be the most s i g n i f i c a n t . The ICC at T-0, although s i m i l a r to the D minor scale, a c t u a l l y resembles the r e l a t i v e F scale more close-l y : element "1" (D, T-O) i s a variant element, and because ele-ment "11" (C), the dominant degree of F, i s included in the ICC 141 of " I I " (Ex. 3-10). Indeed, the PC hierarchy o-f " I I " (based on PC occurrence and t o t a l time-spans) i s i n d i c a t i v e b-f F as the most s i g n i f i c a n t PCs are diatonic to F, with dominant, tonic, and subdominant PCs at the top of the hierarchy. Example 3-10. ICC of " I I " and i t s resemblance to F. ICC of "II" n o ELEMENTS 0 1 3 4 6 8 9 11 F SCALE 331 In some s i t u a t i o n s a v e r t i c a l harmony w i l l resemble the tonic chord of the major t o n a l i t y suggested by the harmony's T-l e v e l . t a T-0 i s the most s i g n i f i c a n t T-level in " I I " as indica-ted by a h i e r a r c h i z a t i o n of T - l e v e l s (based on T-level occur-rence and t o t a l time-spans). Other s i g n i f i c a n t T - l e v e l s (from greater to lesser) are T-5, T-3, T-IO, T-8, and T-7, with the other T-l e v e l s each occurring only once. The temporal-textural c h a r a c t e r i s t i c of T-0 (m. 13) i s such that i t suggests a I-V-I progression in F (Ex. 3-11)5 the Fs are doubled and r e i t e r a t e d . Although the t h i r d and f i f t h of the F chord ( i . e . , A5 and C6) are part of the T-0 simultaneity, the temporal and textural sep-aration of the simultaneity and i t s short duration make i t pos-s i b l e to perceive i t as a V7 chord in F situated between the 142 doubled F and*its recurrence (implied I ) . In comparison, other T-0 harmonies do not have such a temporal-textural configuration that - f a c i l i t a t e s the perception o-f F structures (Ex. 3-11). Example 3-11. T-0 harmonies in mm. 13, 1, and 10-12. (131 111 110-121 T-0 T-0 T-0 In some sense, the T-5 harmonies adjacent to those T-0 har-monies in mm. 10-12 suggest a u x i l i a r y harmonies since -five o-f the seven T-0 pitches proceed by step to those o-f T-5. Other tonal surface features are presented in Ex. 3-12. 143 Example 3-12. Sur-face tonal features in " I I " . t i l (21 (31 (41 (31 (61 T-0 T-3 T-10 T-3 T-10 T-3 T-6 T-2 T-5 HARMONIES Eb: I t b l l ) - — I - (bll)—-I Bb: viI7 I-V7-I 144 Example 3-12 continued. C71 T-10 T-3 [81 T-8 T- l l T-4 [91 T-7 (10-121 T-O T-5 5 113] T-O r + § V9 , T<"L. ^fec > I b# /I r* ,1,= l TV -9—9 ft: 3 T Ab: vi7—(VJ—I-V7-I E: vii7 I-V7-I F: I-V7-I The same textural-temporal configuration 0+ T-O (m. 13) characterizes T-5 (m. 6), T-3 (m. 7), and T - l l (m. 8), with each harmony suggesting a tonal t e r t i a n chord and conceivable local t o n a l i t y ( i . e . , Bb, Ab, and E, r e s p e c t i v e l y ) . The doubled E pitches (E2,E3) and the r e i t e r a t i o n s of Gtt and B (mm. 8-9: T - l l , T-4,T-7) prolong the E chord and t o n a l i t y . And with T-5 (m. 6) and T - l l (m. 8), immediately preceding chords rein-force the im-p l i e d t o n a l i t i e s (Bb and E, respectively) because lower pitches o-f the preceding T-2 and T-8 harmonies suggest dominant-func-ti o n i n g t e r t i a n chords (Ex. 3-13). 145 Example 3-13. Harmonies o-f mm. 6-9 and t h e i r tonal implications. 161 T-2 171 T-S T-10 (8) T-3 T-8 T-l l T-4 (91 T-7 5 I K ! > 9^1 l b / / ft* 2 f i » * 3 ^ 3! VP * 1 •6- + Bb: vii7 —I--V7--I E: vii7 I--V7--I »b: wl7 (V)-I--V?--I Another harmonic succession ( s i m i l a r to that o-f mm. 8-9) involving invariant PCs o-f tonal implication occurs in mm. 3-5 (Ex. 3-14). Example 3-14. Eb in mm. 3-5. (31 T-10 T-3 (41 T-10 T-3 (SI T-6 T-9 2 a 3 i 146 The emphasis on Eb i s due in part to the r e i t e r a t i o n of the T-10,T-3 s u c c e s s i o n . 1 3 Eb-triad PCs occur in the outer voices o-f the T-10 harmonies, and the E2 pitches (T-3) suggest an upper leading-tone to Dtt/Eb ( i . e . , b l l ) . Although most of the T-10 PCs are diatonic to Eb, the Eb-triad PCs, e s p e c i a l l y G and Bb (due in part to t h e i r v e r t i c a l configuration), are p a r t i a l l y ob-scured by these other PCs. Hence, i t may be more accurate to describe the occurrences of Eb pitches in the bass l i n e as Eb "roots" rather than s p e c i f i c a l l y describing the chords as Eb t r i ads. Midd1eground/background linear structures of " I I " Diminished-seventh structures in mm. 6-9. Certain middle-ground /background structures, l i n e a r and harmonic, imply t o n a l i -ty, e s p e c i a l l y F. An important component of the l i n e a r struc-tures in " I I " i s the segment in mm. 6-9. Between F6 (m. 6) and F5 (m. 9), two a l t e r n a t i n g diminished-seventh chords are formed by primary melody pitches, while a t h i r d diminished-seventh chord i s formed by bass-line pitches. In Ex. 3-15a, these pitches are highlighted by beams, while in Ex. 3-15b open note-heads comprise the diminished-seventh chord of which the melody pi t c h i s a component, s o l i d noteheads denoting components of the other diminished-seventh chords. For example, diminished-sev-enth chord C-D**/Eb-Ftt/Gb-A i s prominent in T-2 (m. 6) and T-8 (m. 8), whose melodic pitches form C-D#/Eb-F*»/Gb-A. Likewise, diminished-seventh chord D-F-Gtt-B i s prominent in T-10 (m. 7), and in T-4 and T-7 (mm. 8-9). Example 3-15c suggests the essen-147 t i a l chord progression governing the primary melody pitches o-f mm• 6 — 9• Example 3-15. Arpeggiated diminished-seventh harmonies in the primary melody o-f mm. 6-9. (a)Primary melody and bass-line pitches: (61 171 181 191 b I? r [ 0 -0—±7J Q - ? — <b) Dimi n i shed-seventh components o-f harmonies in mm. 6-9: T-2 T-5 T-10 T-3 T-8 T-ll T-4 T-7 <c)Background harmonic succession suggested by diminished-seventh chords -formed by melody pitches: 148 These melodic chords imply a harmonized "expansion" o-f the i n i t i a l F86-F6 melodic succession <m. 6) o-f t h i s section, an expansion involving a progression o-f two semitonally displaced diminished-seventh chords whose uppermost pitches are F# and F, resp e c t i v e l y . The C-D*t/Eb-F#/Gb-A diminished-seventh chord, -fir s t in t h i s middleground harmonic progression, i s in -fact a component o-f i n i t i a l harmonies in mm. 6 <T-2) and 8 (T-S), while the D-F-G#/Ab-B diminished-seventh chord (the consequent harmo-ny) i s a component o-f the -final harmonies in mm. 8-9 (T-4,T-7). The t h i r d d i m i n i shed-sevent h chord (C**/Db-E-G-A#/Bb) occurs in the bass l i n e o-f mm. 6-8. Also, note the coincidence between IC-6-related T- l e v e l s in mm. 6-9 (e.g., T-2 and T-3, T-5 and T - l l , T-IO and T-4) and the diminished-seventh chords (Ex. 3-15). The midd leground/background resolutions o-f s t r u c t u r a l as well as surface t r i t o n e s , some including the melody pitches o-f mm. 6-9, indicate the s i g n i f i c a n c e of ce r t a i n t o n a l i t i e s , espe-c i a l l y F. An analysis of lin e a r structures a r t i c u l a t e d by the primary melody and bass l i n e (Ex. 3-16) incorporates these pre-vious observations with a study of midd1eground/background tonal structures. 149 Example 3-16. Midd1eground/background linear structures of " I I " . HI 12) 131 [4] [51 [61 17) [81 191 [10-12) 113) The prominence o-f PCs F and C, the s t r u c t u r a l t r i t o n e reso-lutions suggested by the local tonal regions Bb (m. 6) and E (mm. 8-9), and "exposed" pitches 1* 1 strongly imply F. The Eb "root" (mm. 3-5), as well as outer-voice occurrences o+ Eb (e.g., mm. 6, 7, 8), act as a preparation -for the E-F s t r u c t u r a l resolut ion. ISO Mi dd 1 eground/background harmonic structures o-f " I I " Example 3-17 presents these structures. Example 3-17. Midd 1 eground/background harmonic structures o-f " I I " . t i l 121 13,41 151 [61 171 18) 19] [10-121 [13] T-: 0 5 10 3 2 5 10 3 8 11 4 7 -0 5 0 0 The i n t e r v a l 5 cy c l e o-f T-le v e l s underlying the harmonic sequence o-f " I I " would not i t s e l f suggest a m i dd 1 eground/background structure, were i t not -for cycle -fragments taken out o-f sequence and repeated, as well as the coincidence o-f c e r t a i n T - l e v e l s with -formally important t ime-points. 151 Tonality in " I I I " Surface Tonal Features Of the three pieces, " I I I " represents PC organization that i s the least tonal, p a r t i a l l y because of the infrequent use of c l e a r t e r t i a n tonal harmonies and tonal harmonic progressions. Even the notation of PCs of the ICC of " I I I " <i.e., s p e c i f i c a l l y the choice of accidentals used with the PCs), unlike those of the ICCs of " I " and " I I " , i s not r e a d i l y conducive to tonal i n -t e r p r e t a t i o n although the PCs of the ICC of " I I I " themselves do form a minor scale <Ex. 3-18). Example 3-18. The ICC of " I I I " . ICC of " I i r ELEMENTS 0 1 3 4 6 8 9 10 11 61/Ab MINOR SCALE Yet, despite the apparent tonal nature of the ICC, i t i s not c l e a r l y exploited as a "tonal" resource in " I I I " . 1 " * Example 3-19 shows a few surface features that do suggest tonal proce-dures and structures. 152 Example 3-19. Surface tonal structures in "III' (31 T-I HARMONIES (41 (5-61 T-5 T-8 171 T-l l (81 T-2 T-6 [91 (10-111 T-9 T-2 E fa 1 3/ 1/ FEATURES OF HARMONIES 1 ± TONAL 77 S1 C*a , * .JL*J!l^A _ _ _ _ i "si^ A : V - - - I g: v - i - i v — - V 7 - - I D: i—v F : I--V7 Eb: I ' . j . v7 1 Bb: v [121 T-5 T-O [131 T-3 T-O T-4 T-7 [14-151 T-O Db: I or Gb: V In mm. 3-7, there i s a s e r i e s o-f IC-5-related PCs with most o-f the component pitches approached (at times with i n t e r - r e g i s -t r a l connections) as tonics, by upper and lower semitonal 153 1 ead ing-tones suggestive o-f an augmented-sixth chord on the •flattened supertonic degree (Ex. 3-20). Long stems and beaming at the bottom o-f the system indicate these tonic pitches. To a limited extent, IC 3 and 4 dyads -formed between pitches o-f indi-vidual harmonies (isolated by brackets in Ex. 3-20, second sys-tem) suggest tonal chords in a " t o n i c i z i n g V-I" sequence; these tonal implications are indicated. Example 3-20. IC-5-related PC successions in mm. 3-7 o-f "III 131 (41 (5-61 171 (81 Fl B 0 6 C L-fJ il II—*Lil 1 1 - Jl 1 l 1 Only in such PC successions o-f mm. 5-7 are t o n a l i t i e s rep-resented with any c l a r i t y , either because o-f the PC successions or because PC configuration suggests t e r t i a n harmonies. 154 Midd leground/background l i n e a r structures o-f " I I I " Example 3-21 i l l u s t r a t e s the li n e a r structures o-f " I I I " . Example 3-21. Mi dd 1 eground/background linear structures o-f " I I I " . I l l , 121 131 [41 13-61 171 — ff— — 1 r *" — J tf—— -J- . 4 - — .4-[81 [91 [10-111 (121 [131 [14-151 (11 [31 [41 (5) [71 [81 [91 [101 [121 [141 — «! : — — y L . I — — = — ^ : M <X£-155 There i s a clear midd1eground/background linear structure involving a PC a s c e n t 1 " o-f primary melody pitches, including the r e g i s t r a l l y highest pitches in mm. 1-4. It continues to Cx4 (m. 7) and could be perceived to continue to Eb5 (m. 12). While such c o n t i n u i t i e s have no speci-f ic tonal i m p l i c a t i o n , 1 " they do a-f-fect one's perception o-f melodic motion and in t h i s sense e s t a b l i s h a perceptible path through the piece. A PC that occurs -frequently in the primary melody in close proximity to pitches o-f t h i s "ascending" s t r u c t u r a l l i n e i s F#/ Gb. Ftt/Gb may in fac t represent a secondary tonal center. This pattern o-f occurrence i s shown in Ex. 3-22, where the s t r u c t u r a l l i n e , represented by beamed pitches, are separated -from occur-rences o-f Ftt/Gb. Int e r e s t i n g l y , such exposed occurrences o-f F#/Gb do not occur a-fter m. 7, the apparent terminus o-f the "ascending" s t r u c t u r a l l i n e . Example 3-22. Ftt/Gb and the li n e a r structures o-f " I I I " . tl] (2) 131 141 15-61 17) (8) 191 HO) (121 (141 h— c 1/ -4 »< - - - -p -J—Mu— j— hi -in— it f = X* ^ — Kfr y+ \-» ' Fi/5t: I «7 156 A possible explanation o-f t h i s F#/Gb involves i n t e r p r e t i n g the -final T-O (mm. 14-15) as a dominant (<J) harmony o-f F4*/Gb, although the tonic harmony neither precedes nor -follows i t . It does however appear in the linear structure associated with the primary melody in mm. 1-7, with the recurrences o-f Ftt/Gb, and with the Att/Bb (t h i r d o-f the tonic triad) and Ctt/Db (-fi-fth) o-f the PC ascent o-f the s t r u c t u r a l l i n e (Ex. 3-22). Bass-line linear structures are shown in i s o l a t i o n in Ex. 3-23. Example 3-23. Bass-line structure in " I I I " . (11 (21 (31 (41 (5-61 [7] [8] (91 s k i - ) r — ^ - * » — * *'£ *> *t Bb: I-Eb: V-(10-111 [12] [131 [14-15] 3! Bb: IV Eb: I Cl/Db In mm. 12-15, the bass l i n e i s centered around and cadences on C*»/Db. A middleground progression of Eb2 (mm. 10-11) to Db2 (mm. 12-15), preceded by an enharmonically spelled, arpeggiated Bb t r i a d (suggestive of a V-I PC progression in Eb), l i n k s these two phrases. In mm. 1-7, however, the bass l i n e i s not as c l e a r l y defined as i t i s in mm. 8-15 (given the short duration 157 of many bass pitches), which complicates the derivation of a mi dd1eground/background structure. On the other hand, an essen-t i a l bass l i n e could be perceived to begin with G#2 (m. 1), as shown in Ex. 3-23. As a r e s u l t , i t may be possible to perceive mm. 12-15 as a "summary" of the PC events in mm. 1-11 because of the modified transposition of mm. 1-2 in mm. 12-13. Hence, the midd1eground/background bass-line structure would be reducible to c e r t a i n s a l i e n t PCs (Ex. 3-23, l a s t s t a f f ) . I n t e r e s t i n g l y , the ascending PC l i n e (Bb-Cx) e s s e n t i a l l y involves mm. 1-7, while the bass-line structure includes mm. 8-15, with m. 7 as an i n t e r - r e g i s t r a l bridge between the two s t r u c t u r a l l i n e s , involving a descending PC succession D (Cx4>, C (C3), and Bb (A#2). This indicates some formal d i s t i n c t i o n between mm. 1-7 and 8-15, highlighted by parametric changes such as reduced tempo and generally slower harmonic rhythm (especial-ly mm. 5-11), and the p a r t i a l t r ansposition of mm. 1-2's T-level succession in mm. 8-9. Midd1eground/background harmonic structures of " I I I " . The harmonies forming the middleground/background structures in " I I I " are shown in Ex. 3-24. harmon i c 158 Example 3-24. Midd1eground/background harmonic structures o-f " I I I " . [11 T-O (21 T-7 [4] T-7 T-O T-5 15,61 T-8 [81 T-2 [101 T-2 (121 T-5 h T-O (21 T-7 (41 T-7 T-O T-5 [121 [141 T-5 T-O 3 3 * — i i The underlying symmetrical structure based on c y c l i c suc-cessions o-f T - l e v e l s (indicated e a r l i e r in Chapter Two) -forms the main component o-f a midd leground/background structure, wh i 159 also includes cadential and other s t r u c t u r a l l y important harmo-nies not part o-f the cycles. 1 0 With -few exceptions however, none 0+ these s i g n i f i c a n t harmonies takes on e x p l i c i t l y tonal q u a l i t i e s , either in v e r t i c a l configuration or in harmonic suc-cession. As with the linear structures discussed above, there i s only a sense of proceeding to a following t o n a l i t y in a f l u c -tuant context, whether suggested by a s i n g l e PC or by a t e r t i a n harmony, with no apparent return to or emphasis of c e r t a i n har-monies, except for T-0 and, to a lesser extent, for T-5, T-8, T-2, T-7, and so on. In addition, there i s no recurrent PC c o l -l e c t i o n coincident with the recurring Ftt/Gb in mm. 1-7. As has been established in the previous analyses of the three pieces, " I I I " d i f f e r s from the other two pieces in i t s surface and midd1eground/background harmonic and melodic charac-t e r i s t i c s . " I l l " seems to represent the more mature, or experi-mental, of the three pieces, involving fewer obvious references to tonal harmonic structures and procedures while using more line a r structures in a more contrapuntal texture. Cone 1 us ion The three pieces exhibit some important features of conven-t i o n a l t o n a l i t y . From the ICCs which are the basis of each piece, tonal structures and procedures are derived and employed in the pieces, e s p e c i a l l y in " I " and " I I " . In f a c t , some char-a c t e r i s t i c s of the ICC system (e.g., the PC content of the ICCs) are evidently tonal, i n d i c a t i n g that the system i s contingent upon tonal procedures. However, tonal manifestation takes d i f -160 ferent -forms, and i s dependent upon c e r t a i n -features in the mu-s i c to highlight the tonal aspects. For one thing, given the s i x to eight (and more) d i f f e r e n t PCs per harmony, and the many non-diatonic PCs, i t i s often d i f f i c u l t to perceive tonal t e r -t i a n chords unless v e r t i c a l and r e g i s t r a l d i s t r i b u t i o n of PCs h i g h l i g h t s PCs of such chords. In addition, l i n e a r structures (both surface melodic features and midd1eground/background structures) need to adhere to c e r t a i n tonal conventions (e.g., dissonance r e s o l u t i o n , pitch successions such as ascending i n t e r v a l 5 cycles) and emphasize tonic and dominant PCs of given t o n a l i t i e s through PC r e i t e r a t i o n and agogic accentuation. In " I " , Eb, G, and D t o n a l i t i e s are most obvious and s i g -n i f i c a n t , suggested to some degree by clear t e r t i a n chord s t r u c -tures of these t o n a l i t i e s , by surface melodic features, and also by midd1eground/background linear structures. In " I I " , surface features do not as c l e a r l y imply the piece's p r i n c i p a l t o n a l i t y , F, with the exception of the f i n a l harmony. Likewise, other subordinate t o n a l i t i e s are implied by transpositions of the f i -nal harmony. The l i n e a r structures, both surface and middle-ground/background, are responsible for conveying the impression of F. In " I I I " , t o n a l i t y i s at best fluctuant. There are tem-porary i n d i c a t i o n s of c e r t a i n t o n a l i t i e s (e.g., A, D, and G, as-sociated with the i n t e r v a l 5 PC succession, mm. 5-7; C#/Db, mm. 12-15) but no recurring, c l e a r i n d i c a t i o n s of any t o n a l i t y . Un-l i k e the T-0 harmonies of " I " and " I I " that are not only r e f e r -e n t i a l s o n o r i t i e s in the sense of being h i e r a r c h i c a l l y important but also incorporate tonic t r i a d s of the respective t o n a l i t i e s , 161 the T-O harmony of " I I I " does not r e a d i l y suggest a tonic t r i a d •for any t o n a l i t y . 1 " C e r t a i n l y , tonal structures and procedures cannot be ad-duced to explain a l l PC occurrences and -functions. An inferred tonal system does, however, allow one to perceive musical motion and r e l a t i o n s h i p s between musical events with respect to ves-t i g e s of -familiar tonal procedures and structures. Notes 1. Roslavets, " R o s l a v e t s " - ^ , 397. 2. Gojowy, "Hal-f Time," 212. Elsewhere, Gojowy indicates the non-functional nature of harmonies in Roslavets's music, despite t h e i r correspondence to romantic chord structures. (Gojowy, Neue sowjetische Musik, 196.) 3. Gojowy, Neue sovijetische Musik, 146; my t r a n s l a t i o n . 4. Berry states: "Tonality may be thus broadly conceived as a formal system in which pitch content is perceived as func-tionally related to a specific pitch-class or pitch-class-complex of resolution, often preestab1ished and preconditioned, as a basis for structure at some understood level of perception. The tonal system c o n s i s t s of a hi e r a r c h i c ordering of PC fac-tors, with the tonic ( f i n a l , axis, center, etc.) the ultimate point of r e l a t i o n s h i p which tonal successions are contrived to "expect." . . . In more recent s t y l e s in which t o n a l i t y i s r e l e -vant a system may (but need not) consist of s p e c i f i c scalar f o r -mulations (PC c o l l e c t i o n s ) of these or other kinds, with deriva-t i v e melodic and harmonic configurations disposed in such a way as to express and give primacy to a p a r t i c u l a r "tonic" or, in fluctuant contexts, p a r t i c u l a r "tonics." Often such tonal con-tent i s reminiscent of conventions of the tonal period. (Berry, Structural Functions, 27-28.) 5. Ibid. 162 6. In t h i s t h e s i s , "middIeground/background" indicates some underlying or non-foreground aspect or structure. Although the combination o-f the two Schenkerian terms may be con-fusing and contradictory, and although the pieces are not tonal (hence, a rather loose a p p l i c a t i o n o-f the two Schenkerian concepts to the pieces), t h e i r use together i s apt, considering that there i s oftentimes more than one non-foreground l e v e l . Moreover, i t i s d i f f i c u l t to d i f f e r e n t i a t e the "middleground" from the "back-ground" in t h i s music; hence, the more general designation "midd1eground/background" to indicate any or a l l non-foreground structures or aspects, rather than one term or the other. 7. Exceptions to t h i s use of an i n i t i a t i n g s i n g l e - p i t c h exposure are: T-0, T-1, and T-0 harmonies (tin. 6), T-2, T-3, and T-2 (m. 7), and T-7, T-8, and T-7 (m. 8). S i g n i f i c a n t l y , these measures are a d i s t i n c t formal u n i t . 8. This i s s i m i l a r to the idea of pi t c h axis as expounded by Richard Chrisman in his Ph.D. d i s s e r t a t i o n "A Theory of Axis-T o n a l i t y for Twentieth-Century Music" (Ph.D. d i s s e r t a t i o n , Yale University, 1969), 22f. To quote Chrisman, a pi t c h axis i s "a l i n e or s e r i e s of points about which other p i t c h structures are arranged." This term i s , according to Chrisman, r e l a t i v e l y -free of associations with tonic-dominant t o n a l i t y and free of s p e c i f -ic functional associations (p. 22). Some of Chrisman's a n a l y t i -c a l processes (e.g., determining s i g n i f i c a n t PCs and T-levels through c a l c u l a t i o n of occurrences and t o t a l time-spans through a given piece) are employed in t h i s t h e s i s . 9. A PC l i n e i s a s e r i e s of successive PCs, in t h i s case representing actual pitches in the music, although the pitches are not located within one r e g i s t e r or octave, and need not be adjacent to each other. In " I " , the PC l i n e s have a descending tendency (e.g., the PC l i n e Ab-G-F-Fb-Eb-D, mm. 1-6, represent-ing bass p i t c h e s ) . A "prominent p i t c h " i s one that i s usually temporally and/or r e g i s t r a l l y i s o l a t e d (e.g., in the outer voices of the texture), often having metrical and/or agogic ac-centuation. In " I " , the si n g l e i n i t i a t i n g pitches are examples of prominent pitches. 10. The hierarchy of T-levels, in descending h i e r a r c h i c or-der, i s : 0, 11, 4, 3/9, 7, 2, 5, 6/10, 1. T-8 i s not used in " I " . 11. The 3-0 family of T-levels includes T-O, T-3, T-6, and T-9; 3-1 includes T-1, T-4, T-7, and T-10; and 3-2 includes T-2, T-5, T-8, and T - l l . 163 12. As stated e a r l i e r , two tonal t e r t i a n chord components as the lowest pitches and another component as the highest p i t c h would - f a c i l i t a t e tonal i n t e r p r e t a t i o n s o-f more complex harmon-ies. Such harmonies are: T-10, mm. 3-4 (Eb); T-5, m. 6 (Bb); T-3, m. 7 (Ab)5 T - l l , m. 8 (E); and T-0, m. 13 (F). 13. The PC content o-f T-10 corresponds to the Eb-major scale. This also suggests the reason why T-10 and T-3 were re-moved -from the i n t e r v a l 5 c y c l e that i s the basis o-f T-level successions in " I I " . 14. To r e i t e r a t e , "exposed" pitches refer to those that occur in outer voices of a homophonic texture, or that are rhythmically or temporally isolated in some manner. For ex-ample, A#/Bb in mm. 1, 4, 5, 8, and 10-12; and E in mm. 3, 4, and 5. 15. Interestingly, the PC content of the ICC of " I I I " does suggest a p o t e n t i a l approach to understanding PC organization. This involves subdividing the ICC into subsets, based on the accidentals of the PCs as notated. In other words, G, Bb, and Db (elements "O", "3", and "6", respectively) form one subset while Gtt, B, and D# (elements "1", "4", and "8", respectively) form another. In f a c t , the G-Bb-Db subset forms a v i i - i r e l a -tionship to the Gtt-B-Dtt subset, when one of the two i s enharmon-i c a l l y understood. There are some instances where two- and three-pitch subdivisions of harmonies, produced by temporal-textural configurations of pitches (such as dyads formed by sim-ultaneously attacked pitches), involve PCs of one subset or ano-ther. This p r i n c i p l e of PC location i s however not c o n s i s t e n t l y applied to a l l harmonies, nor i s the above-mentioned " v i i - i " r e l a t i o n s h i p exploited in the temporal-textural configurations of individual harmonies. 16. Ascending PC l i n e r e f e r s to a n o n - l i t e r a l ascent in the sense that there i s no constant ascent within one r e g i s t e r . In " I I I " , the PC ascent i s : Bb5-B5-C5/C6-C#4-Cx4. 17. Each two-pitch succession suggests a 1eading-tone-to-tonic succession. 18. To r e i t e r a t e , t h i s structure includes the T-7-centered cyc l e (3-1, mm. 2-4), T-O (m. 4), and the T-5-centered cycle (3-2, mm. 4-13), with an i n i t i a l T-0,T-5 succession (m. 1) and f i n a l T-7,T-0 succession (mm. 13-15). Both T-5 and T-7, IC-5-related to T-0, have a somewhat symmetrical or "opposing" r e l a t i o n s h i p . These T-levels T-O, T-5, and T-7 have associa-tions with t o n a l i t y at least on a s u p e r f i c i a l basis ( i . e . , T-O being "tonic", T-5 being "subdominant", and T-7 being "domin-ant"). The hierarchy of T-levels in " I I I " , based on frequency of occurrence and t o t a l time-span, i s ! T-O, T-5, T-8, T-2, T-7, T - l l , T-4, T-9, T-1, T-6, T-3, and T-10. Hence, the more s i g -n i f i c a n t T-levels of t h i s hierarchy would be included in the middleground/background harmonic structure. 164 19. As suggested by Ex. 3-22, i t could be, on the other hand, the dominant o-f Ftt/Gb. I <b5" CHAPTER FOUR OTHER SYSTEMS OF PITCH-CLASS ORGANIZATION IN TROIS COMPOSITIONS Our attention i s now turned to systems of PC organization that are to some degree apparent in the three pieces, namely octatonicism, and s e r i a l i s m . Octatonicism, which w i l l be considered f i r s t , can be c l a s s i f i e d as a form of t o n a l i t y in the general sense of the term because of i t s h i e r a r c h i z a t i o n of PCs. Because Russian contem poraries of Roslavets (e.g., Nikolai Rimsky-Korsakov, S t r a v i n -sky, and Scriabin) used the octatonic c o l l e c t i o n as a basis fo some of t h e i r music, 1 we need to investigate the extent of i t s a p p l i c a b i l i t y in Trot's Compositions. Example 4-1 i l l u s t r a t e s the resemblance of the ICCs of the three pieces to octatonic col 1ecti ons. 166 Example 4-1. ICCs o-f Trois Compositions compared with octatonic c o l l e c t i o n s . ICC OF "I" AT T-O ICC OF - i r AT T-O m OCTATONIC (1 - 2! D) OCTATONIC (1 - 2; CI) J o "bo h OCTATONIC 12 - 1! 0) 0 _ OCTATONIC 12-11 CI) 3*= cr o — OCTATONIC (2 - If Ob) V 0 OCTATONIC (2 - i i CI h *> IT ICC OF 'III' AT T-O ltd OCTATONIC (1 - 25 6) OCTATONIC 12 • 1} 61 OCTATONIC (2 - l i 6bI HE The ICC o-f "I" c l o s e l y resembles octatonic c o l l e c t i o n 1 ( i . e . , semitone-tone) while that o-f "II" resembles both octa tonic c o l l e c t i o n s 1-2 and 2-1, with each ICC having six o-f eight PCs common to those o-f the respective octatonic collec 167 t i o n . With the ICC of " I I I " , there are f i v e PCs matching the octatonic c o l l e c t i o n 1-2. Deliberate use of the octatonic c o l l e c t i o n might be i n d i -cated by some consistency in the temporal-textural location and/or function of ICC elements not belonging to the clos e s t octatonic c o l l e c t i o n . Although non-octatonic elements usually occur in f u n c t i o n a l l y less s i g n i f i c a n t s i t u a t i o n s , 2 such pat-terns of occurrence are s t i l l not consistent enough to be strongly i n d i c a t i v e of deliberate octatonicism. The fac t that these non-octatonic elements are components, a l b e i t inner-voice components, of the various harmonies would seem to rule out the idea that Roslavets used the system at a l l . A l l e l e -ments appear in nearly a l l v e r t i c a l p o s i t i o n s of harmonies. Invariant and "quasi-invariant" PCs in T-level f a m i l i e s of " I " and " I I I " <see Chapter Two section e n t i t l e d "PC Inv a r i -ance in IC-3-Related T-Levels," and fn. 40 in Chapter Two) form octatonic 1-2 c o l l e c t i o n s while those of "I I " form an oc-tatonic 2-1 c o l l e c t i o n . While some s i m i l a r i t i e s could be ob-served in Roslavets's music and that of Scriabin, based on Taruskin's descriptions of octatonicism in the l a t t e r ' s music (see Chapter Two, fn. 40), there i s no re a d i l y apparent pat-tern of location or function of non-octatonic PCs of a T-level family. Hence, the octatonic system does not appear s i g n i f i -c antly applicable to PC events assessed as to function and pos i t i on. 3 168 S e r i a l PC Organization In the pertinent l i t e r a t u r e , there seems to be some con-f l i c t regarding the extent to which Roslavets's music r e f l e c t s dodecaphonic thinking. Some writings refer to the composer as a "Russian Schoenberg."** In f a c t Gojowy's e a r l i e r writings indicate that he may have regarded aspects of Roslavets's works to be dodecaphonic. These are, for example: a reference in Gojowy's Neue sowjet ische Musik to Roslavets's use in " I I " of " a l l twelve l e v e l s of one complex . . . in a perceivable methodical ordering;""* an e a r l i e r reference in t h i s same text to "the prompt reappearance of a t r a n s p o s i t i o n -l e v e l " being "usually avoided—a p r i n c i p l e that likewise underlies the twelve-tone row;"** and an e a r l i e r a r t i c l e by Gojowy e n t i t l e d "Nikolaj Andreevic Roslavec, ein fruher Zwo 1 f tonkompon i e r t . '"* Perle q u a l i f i e s his use of the terms "set" and "s e r i e s " with regard to the music of S c r i a b i n and Roslavets. I n i t i a l l y he defines the term "set" as comprising " a l l 12 notes of the semitonal scale, arranged in a s p e c i f i c linear order" and that "Cno3 note appears more than once within the set."° Later, he states: In a s t r i c t sense the term " s e r i e s " denotes an or-dered succession of elements, such as the Schoenbergian 12-tone set. Hauer*s "tropes" are only p a r t i a l l y ordered, while in the works of Scriabin and some other composers the set i s a c o l l e c t i o n of pitches the s p e c i f i c ordering of which i s purely compositional. The term " s e r i a l composition" i s used in the present study as a general designation f o r music based on any of these types of sets.** 169 In addition, Perle states: "[The] term unordered set w i l l designate such a c o l l e c t i o n . . . employed . . . only in a s i n g l e aspect [ i . e . , not applicable in inverted and retrograde forms], as in the works of Scri a b i n ; for . . . a s p e c i f i e d succession of the notes [ i s not] assumed to be a defining c h a r a c t e r i s t i c of the s e t . " l o Recently, Gojowy has suggested that Roslavets's music was not i n t e n t i o n a l l y dodecaphonic. Through systematic a p p l i c a t i o n of such transposi-tions [ i . e . , through the use of a l l twelve T - l e v e l s ] , Roslavets's compositions revealed elements s i m i l a r to dodecaphonic s e r i a l thinking as ea r l y as 1914-15 in the works mentioned above. For t h i s reason, George Perle LSerial Composition and A t o n a l i t y , pp. 40-44] has c l a s s i f i e d Roslavets's system, together with that of S c r i a b i n , as "nondodecaphonic s e r i a l composition." I cannot e n t i r e l y agree with t h i s designation, since i t seems to imply that the Russian system amounted merely to a kind of p r e - f i g u r i n g of the f u l l y dev-eloped twelve-tone system. In r e a l i t y , the Russian system, which had already been i d e n t i f i e d as such in S c r i a b i n ' s work by the P o l i s h musicologist Z o f i a L i s s a in the 1930's, stands as an independent method with i t s own p r i n c i p l e s . A s e r i e s or row, whether dodecaphonic or not, i s defined by the invariable order of i t s members. But in the tone complex, as used by Scriabin and Roslavets, the order of i t s elements remains free; the complex i s defined only by i t s i n t e r v a l l i c structure. Composition based on the manipulation of tone complexes may at times approach the technique of twelve-tone writing, as happens occasionally in Roslavets as a consequence of his p a r t i c u l a r choices of scale degree for transposition of a tone complex. This, however, occurs f o r t u i t o u s l y , not out of necessity. The method may also generate other structures unrelated to twelve-tone proce-dures . 1 *• While there i s no apparent use of invariant PC ordering c h a r a c t e r i s t i c of s e r i a l music as previously established in 170 studies of element ordering, there are aspects o-f Roslavets's music that approach s e r i a l dodecaphonic organization. Such organization i s not c o n s i s t e n t l y applied, thus r e f l e c t i n g no conscious use o-f s e r i a l techniques. Yet, i t s existence i s nonetheless important, symptomatic perhaps of the highly chro-matic and sometimes atonal musical s t y l e s prevalent in the post-Romantic era at the time of Trois Compositions. An examination of T-level successions and c e r t a i n melodic segments of the three pieces w i l l i l l u s t r a t e such s e r i a l and/or dodecaphonic sequences. 1 2 S e r i a l Ordering of T-Levels and of PCs in T-Levels The succession of T - l e v e l s in the three pieces i s "quasi-s e r i a l " in the sense that a l l or most T-levels are used in the three pieces i n d i v i d u a l l y while c e r t a i n T-levels are r e i t e r a -ted. Moreover, there appears to be some coincidence between the completion of the s e r i e s of twelve T - l e v e l s and formally important time-points. This i s shown in F i g . 4-1, with the f i r s t occurrence of each T-level given separately below the sequence of T - l e v e l s . Figure 4-1. S e r i a l ordering of T - l e v e l s in Trois Compositions. • I " M E A S U R E : 1 2 3 4 3 6 7 8 10,11 12 13 T - L E V E L : 0-3-10 1-4 7-10-4 11-9-2 5 11-0 11-2 7 3-6 9-4-9 0 T - L E V E L * S F I R S T (T -8 O C C U R R E N C E : 0-3-t0--l-4--7 tl-9-2-3- 6 lissing) 171 Figure 4-1 continued. • I I " M E A S U R E : 1 2 3 4 5 6 7 8 9 10,11 12-13 T - L E V E L : 0-5 8-1 10-3 10-3 6-9 2-5 10-3 8-11-4 7 0-5 0 T - L E V E L * S F I R S T O C C U R R E N C E : 0-5--8-1-10-3 6-9-2 11-4--7 •nr M E A S U R E : 1 2 3 4 3,6 7 8 9 10,11 12 1 3 1 4 T - L E V E L : 0-5 8-3-7-10 1-4 7-0-5 8 11 2-6 9 2 5-0 5-0-4-7 0 T - L E V E L ' S F I R S T O C C U R R E N C E : 0-5--8-3-7-10--1 -4 11 -2-6-9 In " I " , the s e r i e s - f i n a l 1 3 T-level (T-6, m. 10) occurs in the f i r s t measure of the r e c a p i t u l a t i o n . In " I I " , the s e r i e s -f i n a l T-level (T-7, m. 9) precedes the r e c a p i t u l a t i o n in m. 10. In " I I I " , the s e r i e s - f i n a l T-9 (m. 9) forms with T-2 (mm. l O - l l ) the cadence which precedes the r e c a p i t u l a t i o n in m. 12. Despite the six to eight d i f f e r e n t PCs per harmony, there is no true PC complementarity involving PCs of adjacent harmon-ies. At least one and usually more PCs are not part of two ad-jacent harmonies, with completion of a PC s e r i e s involving three or more adjacent harmonies. Moreover, there i s no consistency in occurrences and completions of such PC s e r i e s , in terms of r e g i s t r a l or temporal location. 172 S e r i a l Ordering o-f Melodic Pitches Certain primary melody and bass-line segments of the three pieces exhibit limited -forms o-f s e r i a l ordering. Again, what is o-f interest i s the coincidence o-f s e r i e s - f i n a l PCs with -formally important time-points. Additionally, many PCs o-f individual se-r i e s are stated in i n i t i a l measures o-f the respective pieces, a sign o-f the chromatic nature o-f these melodies. Example 4-2 presents the primary melodies and bass lines o-f the pieces, and indicates the PC series involved with each. Melodic pitches are designated both by st a f f notation and by PC numbers. T-levels are also indicated for the purposes of comparison. Example 4-2. Ser i a l ordering of primary melody and bass-line PCs. •r N.: (11 (21 (31 141 (51 T-: 0 3 10 1 4 7 10 4 II 9 2 5 r — t o » ' "°:— i " 1 i 5 10 0 2 1 3 4 f !~n—^ 6 11 9 1 1 * • 1 1 l» ' - 1 1 1 • i ..... „ bo I » t r * rT> 8 9 6 0 3 1 2 7 5 4 1 0 (11 NISSIN6) « . : [6] (71 [81 (101 T-: 11 0 11 2 7 3 6 (T-8 NISSIN6) (8) 8 173 Example 4-2 continued. •II* M. (11 [21 131 (41 151 161 171 [81 T- 0 3 8 1 10 3 10 3 6 9 2 3 10 3 8 11 (T-4,7 IN M. 8-9) H — r 0 2 3 6 7 8 10 1 11 (4 NISSIN6). BSE *> 'ft Ibo 1 10 9 6 3 3 4 0 8 1 (11 NISSIN6) •nr N. (11 T- 0 (21 (31 3 8 3 7 10 1 to • ^ V far (41 1 4 7 0 5 1 ° I I !E az i_ 3 * x 10 4 5 6 8 9 3 2 11 7 1 •*c— j f a ± 8 4 11 10 TT ZZ = 2 9 N. 13-61 (7) T- 8 11 (81 (91 (10-11) (12) 2 6 9 N — 0 6 7 3 1 174 The primary melodies o-f " I " and " I I I " and the bass l i n e o-f " I I I " have twelve PCs each. The primary melody and bass l i n e o-f "I I " and the bass l i n e o-f " I " have eleven PCs each. In addition, there i s a c e r t a i n amount o-f coincidence be-tween the s e r i e s - f i n a l PCs and formally s i g n i f i c a n t time-points, at least in " I " and " I I " . The s e r i e s - f i n a l bass-line PC in " I " <Bb, m. 5) occurs in the cadence of the second phrase. The s e r i e s - f i n a l primary melody PC (G*», m. 10) and the s e r i e s - f i n a l T-level (T-6) coincide with the r e c a p i t u l a t i o n . (There i s how-ever, an e a r l i e r s i g n i f i c a n t occurrence of G# CG#6, m. 73, the pit c h climax in the piece.) In " I I " , both the s e r i e s - f i n a l p r i -mary melody PC (A) and the s e r i e s - f i n a l bass-line PC (Db) occur in m. 8, adjacent to m. 9 and the s e r i e s - f i n a l T-level (T-7), which precedes the r e c a p i t u l a t i o n . In " I " and " I I " , there i s a r e l a t i v e coincidence of s e r i e s - f i n a l PCs and T- l e v e l s with each other, and with formally important time-points. Such c o i n c i -dence i s not as evident in " I I I " , however, with d i s j u n c t i o n of the s e r i e s - f i n a l primary melody PC (C#, mm. 5-6), the s e r i e s -f i n a l bass-line PC (Ctt, m. 12, co i n c i d i n g with the r e c a p i t u l a -t i o n ) , and the s e r i e s - f i n a l T-level (T-9, m. 9). The l a t t e r does, however, form a cadence with the T-2 harmony (mm. 10-11) preceding the r e c a p i t u l a t i o n . In a l l three pieces, there are no apparent r e p e t i t i o n s of numerical sequences representing the se-r i e s of PCs or T-levels, or of IC patterns underlying such PC and T-level s e r i e s (although there are limited s i m i l a r i t i e s un-der inversion in the IC pattern underlying the T-level s e r i e s ) . 175 It i s d i f f i c u l t td determine whether completions of such p a r t i a l l y or f u l l y dodecaphonic s e r i e s are coincidental or are deli b e r a t e . The recurrences of T - l e v e l s , T-level successions, and melodic-harmonic f i g u r a t i o n s in " I " (mm. 10-13) and " I I " (mm. 10-13), and the r e i t e r a t i o n of such material within these r e c a p i t u l a t i v e measures, indicate a complete use of a l l o r i g i n a l p i t c h and rhythmic material by m. 9 of both pieces. In one sense then, there should be some manner of coincidence between t h i s formally important time-point, the r e c a p i t u l a t i o n , and com-p l e t i o n of PC or T-level s e r i e s . Whether these s e r i e s represent delib e r a t e dodecaphonic s e r i a l ism i s questionable since some of the s e r i e s ( p a r t i c u l a r l y those involving T-levels) are based on non-dodecaphonic, non-serial techniques (e.g., the i n t e r v a l 5 cycle of T-levels which includes a l l twelve T - l e v e l s ) . However, such s e r i e s , whether deliberate or not, are manifestations of the highly chromatic nature of Roslavets's music. Notes 1. Some writings that examine octatonicism in early 20th-century Russian music are: Arthur Berger, "Problems of Pitch Organization in Stravinsky," Perspectives on Schoenberg ana" Stravinsky, ed. Benjamin Boretz and Edward T. Cone (New York: W. W. Norton, 1972), 123-154; Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven: Yale University Press, 1983); and more recently, Richard Taruskin, "Chernomor to Kashchei: Harmonic Sorcery; or, Stravinsky's 'Angle'," Journal of the American MusicologicaI Society, 38/1 (Spring 1985): 72-142. 2. In general, non-octatonic elements occur in less s i g n i f -icant s i t u a t i o n s more than 50% of the time. In " I " the non-oc-tatonic element i s "8"; in " I I " , "1" (the variant element) and "4"; and in " I I I " , "8" and "11" (one of the three variant e l e -ments). In the case of element "8" in " I " , 17 of 25 occurrences of the element can be described as f u n c t i o n a l l y less s i g n i f i -cant, that i s , in a r e l a t i v e l y concealed inner voice, or on a 176 r e l a t i v e l y weaker metric time-point, sometimes with a corre-spondingly short duration. (6 of these 17 occurrences are in the primary melody, on weaker metric time-points and with short durations.) O-f the 24 in d i v i d u a l harmonies or T - l e v e l s in " I I " , the non-octatonic element "1" occurs only three times (in the bass line) while element "4" occurs -fourteen times in more ex-posed outer voices although only eleven o-f these can be de-scribed as -functionally s i g n i f i c a n t s i t u a t i o n s according to the c r i t e r i a stated above. On the other hand, i-f one were to con-sider the octatonic 1-2 scale as the r e f e r e n t i a l c o l l e c t i o n , then elements "8" and "11" would be non-octatonic. Element "8" occurs 75% of the time ( i . e . , in 75% of element "8"'s occur-rences) as an inner-voice p i t c h although i t occurs in half of the T-l e v e l s as the second highest p i t c h in the harmonies (and seven times in the outer voices). Element "11" occurs 60% of the time as an inner voice p i t c h although i t occurs 40% of the time as the second highest p i t c h in the harmonies (and ten times in the outer v o i c e s ) . In " I I I " , element "8" occurs 66% of the time as a less s i g n i f i c a n t outer-voice p i t c h or an inner-voice p i t c h , while element "11" occurs only twice in the piece, each of these as a less s i g n i f i c a n t melodic p i t c h . 3. To r e i t e r a t e , c e r t a i n observations made by Taruskin con-cerning octatonicism in Scriabin's l a t e r music (Taruskin, "Stravinsky's 'Angle'," 99, fn. 47) have implications for Roslavets's music: the three octatonic sets (or IC-3-related T-level f a milies) act as r e f e r e n t i a l c o l l e c t i o n s , f u n c t i o n a l l y akin to keys in the t r a d i t i o n a l sense; a sense of tonal motion achieved by modulations from one octatonic grouping to another, or, in the case of the three pieces, transference from one T-level family to another; and the return to the same octatonic key (T-level) with which the piece began. There may be some basis for the a p p l i c a t i o n of octatonic theory and structures to the music of Roslavets, i f not to the three pieces in p a r t i c u -l a r . However, one point of d i f f e r e n c e between the music of the two composers i s the f a c t that, in Scriabin's l a t e r music, the octatonic c o l l e c t i o n "does not i n t e r a c t with diatonic harmony or emphasize t r i a d i c cognates" (Taruskin, "Stravinsky's 'Angle,'" 99, fn. 47), while diatonic harmonies and t r i a d i c cognates are observed to e x i s t , a l b e i t in a limited way, in the three pieces. 4. One such reference occurs in Schwarz, Music and Musical Life in Soviet Russia, 86. 5. Gojowy, Neue sowjetiscAe Musik, 171-2, in a section e n t i t l e d "Fruhe Ansatze von Zwd1ftontechnik bei Roslavec und Lourie: Zwolftontechnik und Zwo1ftonkomp1exe." 6. Ibid., 140. 7. Gojowy, "Nikolaj Andreevic Roslavec, ein friiher ZwoIftonkomponist," Die Musikforschungt 22/1 (January-March 1969): 22-38. 177 8. Perle, Serial Composition, 2. 9. Ibid., p. 40, fn. 1, in a chapter e n t i t l e d "Nondodeca-phonic S e r i a l Composition." 10. Ibid., 46. 11. Gojowy, "Hal* Time," 212. 12. Some o-f Gojowy's analyses o-f Roslavets's works likewise deal s p e c i f i c a l l y with i d e n t i f i c a t i o n of dodecaphonic and non-dodecaphonic s e r i e s . 13. " S e r i e s - f i n a l " means the f i n a l PC or T-level of a ser i es. 1 7 6 CHAPTER FIVE CONCLUSION The ICC System What can we conclude about Roslavets's compositional tech-niques in Trois Compositions'? Each piece has a complex PC orga-n i z a t i o n , involving a basic ICC r e a l i z e d as a PCC at various T-le v e l s , whose content can be varied within c e r t a i n l i m i t a t i o n s . Transposition and element variance o-f a r e f e r e n t i a l PCC thus de-termine the content o-f most PC c o l l e c t i o n s in a given piece, ex-pressed v e r t i c a l l y , divided into sparser harmonies made up of ICC subsets, and, in a few instances, l i n e a r i z e d . The ICCs of the three pieces d i f f e r in PC and element content. One T-level (T-O) acts as a r e f e r e n t i a l sonority -for the given piece, in the sense that the sonority begins and concludes the piece, and i s most s i g n i f i c a n t as to frequency of occur-rence, greater t o t a l time-span, and coincidence with formally important time-points. A l l T - l e v e l s can in fac t be hie r a r -chized, as to these c r i t e r i a , in assessment of the s i g n i f i c a n c e of each in a given piece. T-5, T-3, and T-8, aside from T-O, are s i g n i f i c a n t T - l e v e l s in the three pieces. Successions o-f T-levels are generally based on ascending i n t e r v a l 3 and 5 cyc l e s . P a r t i c u l a r l y in " I " and " I I I " , three or four T-levels of an int e r v a l 3 c y c l e are employed in an as-cending succession, before y i e l d i n g to another i n t e r v a l 3 cycle 179 or component (s) thereof. PC invariance in al'l four (or even three or two) T-lev e l s o-f a -family o-f IC-3-related T-levels, and transferences from one family (or component) to another, are somewhat analogous to the PC c o l l e c t i o n s of tonal keys and modu-la t i o n s between such keys. In f a c t , many of the transferences from one in t e r v a l 3 T-level family (or component) to another i n -volve IC-5-related T - l e v e l s . Since the three d i f f e r e n t i n t e r v a l 3 T-level cycles can be mapped onto the int e r v a l 5 cycle, as shown in Chapter Two, i t i s possible to view the i n t e r v a l 3 T-level f a m i l i e s as components of the int e r v a l 5 c y c l e . There are no r e a d i l y apparent consistencies of PC and e l e -ment occurrence and ordering, within i n d i v i d u a l PC c o l l e c t i o n s or through adjacent c o l l e c t i o n s , i n d i c a t i v e of delibe r a t e con-t r o l . Because most T-level successions involve IC-3- or 5-related T - l e v e l s , there are on average three or four invariant PCs in a given succession, one of these involving p i t c h continu-i t y . Likewise, there are no apparent, c o n s i s t e n t l y applied p r i n c i p l e s of voice leading or p i t c h succession, despite Roslavets's i n d i c a t i o n to the contrary, although these may have evolved with l a t e r works. There are, however, c e r t a i n limited tendencies in element occurrence ( i . e . , in the primary melodies and bass l i n e s of the three pieces, and in ranges of v e r t i c a l positions) and ordering ( i . e . , s i m i l a r i t i e s in v e r t i c a l element orderings of harmonies, as well as frequent occurrences of c e r t a i n element adjacencies), tendencies suggesting that elements, and not just PCs, are de-terminants of chord structures. 180 Tonality, Octatonicism, and S e r i a l ism The ICC system and various p r i n c i p l e s discussed above con-s t i t u t e an "expanded" tonal system, which can be manipulated to produce d i f f e r e n t types of structures, including tonal s t r u c -tures. In a sense, two systems are employed at once: a theor-e t i c a l ICC system, and a more perceptible tonal system. The ICCs resemble tonal scales, and have consequent p o t e n t i a l for tonal e x p l o i t a t i o n . In " I " , three t o n a l i t i e s - - D minor, Eb (major/minor), and G minor — are evident, while one t o n a l i t y , F, i s evident in " I I " . Tonality in " I I I " i s best described as fluctuant, involving references to various t o n a l i t i e s , since i t i s d i f f i c u l t to i d e n t i f y any pervasive c e n t r i c i t y . Studies of midd1eground-background structures in f a c t reveal large-scale tonal structures and procedures in " I " and " I I " , which are not r e a d i l y apparent in " I I I " . Moreover, while tonal e x p l o i t a t i o n of harmonic resources of a given piece i s dependent upon, and may be limited by, p r i o r decisions concerning the ICC system and T-level successions, there are instances where ICC system-based structures and successions are altered to allow for tonal impli-cations (one example being the r e p e t i t i o n of T-10,T-3 C " 11", mm. 3-43, f o r emphasis on Eb t r i a d components of T-10). Both octatonicism, which can be a basis of t o n a l i t y in the broad sense of the term, and s e r i a l ism (both dodecaphonic and non-dodecaphonic) are applicable to a limited extent in Trois Compositions. Such inconsistent use of octatonic and s e r i a l methods, quite uniike the deliberate use of tonal structures and 181 procedures in the pieces, i s t y p i c a l o-f the music o-f the com-poser's era. Implications o-f " I I I " Concerning Matters o-f St y l e and Large-Scale Form As l i t t l e i s known about d e t a i l s o-f Roslavets's li-f e , his compositional a c t i v i t i e s and pr a c t i c e s , influences upon t h i s music, and his personal and professional contacts, there i s much upon which one can speculate. One matter, a r i s i n g in the pre-sent study, upon which one can make some i n t e r e s t i n g and impor-tant speculations, i s the circumstance of pronounced differences between " I " and " I I " on the one hand, and " I I I " on the other. P l a u s i b l e reasons for such d i f f e r e n c e s could be: a time lapse between the composition of the f i r s t two pieces and the t h i r d , intervening influences from various sources, and/or deliberate r e d i r e c t i o n s in Roslavets's compositional techniques. Whatever the actual reasons for these d i f f e r e n c e s , " I I I " would seem to represent the more experimental and, perhaps, mature of the three pieces, one involving fewer references to tonal proce-dures, more linear structures, and a more contrapuntal texture. On the other hand, there are c e r t a i n s i m i l a r i t i e s between "I " and " I I I " that perhaps suggest t h e i r formal association, even suggesting a large-scale ternary form in Trois Compositions as a whole. This study has established some basic p r i n c i p l e s of Roslavets's compositional technique, based on Trois Composi-tions, which belong to an early phase of the composer's career. 182 It i s hoped that i t w i l l contribute to a deepened understanding and appreciation o-f Roslavets's music, which i s l a r g e l y unknown, and w i l l encourage -further study and performance o-f t h i s music. With such study, the composer and his music w i l l be accorded a p o s i t i o n of deserved importance in twentieth-century Russian musical development. IS2> SELECTED BIBLIOGRAPHY Abraham, Gerald. "The Reaction Against Romanticism: 1890-1914." In New Oxford History of Music, edited by Martin Cooper, v o l . IO, 80-144. Toronto: Ox-ford University Press 1970. Asa+iev, Boris. Russian Music from the Beginning of the Nine-teenth Century. Translated by Al-fred J. Swan. Ann Arbor, Michigan: J. W. Edwards, 1953. Berry, Wallace. Structural Functions in Music. Englewood C l i f f s , New Jersey: P r e n t i c e - H a l l , 1976. Chrisman, Richard. "A Theory o-f Axis-Tonality for Twentieth-Century Music." Ph.D. d i s s . , Yale University, 1969. Das Srosse LexiMon der Musik. 1982 German ed. of Diet ionnai re de la Musique. S.v. "Ross 1awetz," by E. S t o c k l . Die Musik in Geschichte und Segenwart. S.v. "Roslawetz, Nikolai Andrejewitsch," by Guido Waldmann. Forte, A l l e n . The Structure of Atonal Music. New Haven, Con-necticut: Yale University Press, 1973. Gojowy, Detle-f. "Nikolaj Andreevic Rosl avec, ein -fruher Zw61f-tonkomponist." Die Musikforschung. 22/1 (January-March 1969): 22-38. Gojowy, Detle-f. Neue sowjetische Musik der 20er Jahre. Laabe Laaber-Verlag, 1980. Gojowy, Detlef. "Das transmentale Sprache der Neuen Musik." Musik-Konzepte 32/33. Aleksandr Skrjabin und die Skrjabin isten, edited by Heinz-Klaus Metzger and Rainer Riehn, 127 144. Munich: E d i t i o n Text + K r i t i k , 1983. Gojowy, Detle-f. "Hal-f Time -for Nikolai Roslavets (1881-1944): A Non-Love Story with a Post-Romantic Composer." In Russian and Soviet Musi a Essays for Boris Schwarz. E d i -ted by Malcolm Hamrick Brown, 211-220. Ann Arbor, Michi-gan: University Microfilm International Research Press, 1984. Goldstein, Michael. "Skrjabin und die Skr j a b i n i s t e n . Das Schaffen Skrjabins und seiner Nach-folger — Induktion und Deduktion." Translated from Russian by P. Ruhl. In Musik Konzepte 32/33. Aleksandr Skrjabin und die Skrjabinisten, edited by Heinz-Klaus Metzger and Rainer Riehn, 178-190. Munich: E d i t i o n Text + K r i t i k , 1983. 184 Montagu-Nathan, Montagu. Contemporary Russian Composers. London: C e c i l Palmer and Hayward, 1917; Westport, Connec-t i c u t : Greenwood, 1970. Perle, George. Serial Compos i t i on and Atonality. 4th rev. ed. Berkeley, Los Angeles: University of C a l i f o r n i a Press, 1977. Perle, George. "Scriabin's Self-Analyses." Music Analysis. 3/2 (July 1984): 101-124. Riemann Musiklexikon: £rg'anzungsband, 1975 ed. S.v. "Rosslawets, Nikolaj Andrejewitsch." Roslavets, "Nik. A. Roslavets o sebe i svoem tvorchestve." Sovremennaia muzyka 5 (1924): 132-138. Translated in Gojowy, Neue sowjetische Musik der 20er J afire (Laaber: Laabei—Verlag, 1980), 395-400. Sabaneyeff CSabaneevJ, Leonid. Modern Russian Composers. Translated by Judah J o f f e . New York: International Publishers, 1927; Da Capo, 1975. Salzman, E r i c . Twentieth-Century Music: An Introduction. 2d ed. Englewood C l i f f s , New Jersey: P r e n t i c e - H a l l , 1974. Saminsky, Lazare. Music of Our Day: Essentials and Prophe-c i e s . New York: International Publishers, 1927; Da Capo, 1975. Samson, Jim. Music in Transition: A Study of Tonal Expansion and Atonality, 1900-1920. London: J. M. Dent and Son, 1977. S c h i b l i , S i g f r i e d . Alexander Skrjabin und seine Musik. Grenz-uberschre itungen eines prometheischen Geistes. Munich, Zurich: R. Piper and Co. Verlag, 1983. Scholes, Percy A^  ed. The Oxford Companion to Music. 9th ed. New York, Toronto: Oxford University Press, 1955. Schwarz, Boris. Music and Musical Life in Soviet Russia: Enlarged Edition 1917-1981. 2d. en 1. ed. Bloomington, Indiana: Indiana U n i v e r s i t y Press, 1983. Slonimsky, Nicholas, ed. Baker's Biographical Dictionary of Musicians, 7th ed. S.v. "Roslavetz, N i c o l a i . " Taruskin, Richard. "Chernomor to Kashchei: Harmonic Sorcery; or, Stravinsky's 'Angle'." Journal of the American Musico-logical Society 38/1 (Spring 1985): 72-142. The New Grove Dictionary of Music and Musicians, 6th ed. S.v. "Roslavets, Nikolay Andreyevich," by Detlef Gojowy. 185" APPENDIX A Chronological L i s t o-f Works by Roslavets This chronological l i s t i n g of works by Roslavets, -followed by a c l a s s i f i c a t i o n by genre, represents an amalgamation o-f the -following l i s t i n g s : Gojowy, Neue sowjetische Musik, 327-329; Gojowy, "Half Time," 217-219} Gojowy, "Roslavec," Die Musik-forschung, 22/1: 36-38; Grove Dictionary, 6th ed., s.v. "Roslavets" (by Gojowy); and Die Musik in Geschichte und Gegen-watrt CMGG3, s.v. "Roslawetz" (by Guido Waldmann). This present l i s t i n g i s the most complete of any published, to date. Dates with square brackets indicate approximate dates of composition; in some cases, only the decade has been estimated. If the date of composition i s not known or cannot be approximated, the date of p u b l i c a t i o n (e.g., pub. 1925) i s indicated. With songs, the name of the poet i s given in parentheses, and a piano accompani-ment i s assumed. For most unpublished works, an i n d i c a t i o n of extant manuscripts i s given, with the Soviet l i b r a r y in which these are located ( i . e . , Central State Archive f o r L i t e r a t u r e and Art CCSALA3; Glinka Museum of Musical Culture CGMMC3; Moscow Conservatory Library CMCL3; Lenin Library, Moscow CLLM3). 186 1907 nenuet -for S t r i n g Quartet. CSALA. Reverie -for V i o l i n and Orchestra. Score. CSALA. 1908 Romance, Reverie, Morgenstimmung, Sonata (beginning), Gavotte, Elegie, Serenade, etc. Pieces for v i o l i n and piano. CSALA. 1909 Serenada -for Two V i o l i n s . CSALA. 1909- 3 Poemes and Romance-arabesque -for V i o l i n and Piano. 1910 CSALA. C 1910s] 1/ chasy novoluniia CIn the Hours o-f the New Moon]. Sym-phonic poem -for large orchestra. Score with parts. CSALA. Liricheskaia poemaJPoeme lyrique -for V i o l i n and Piano. CSALA. 1910 S t r i n g Quartet. GMMC. Symphony in C Minor. Score. CSALA. 1912 Tantsy belykh dev/Danses des vierges blanches -for V i o l i n and Piano. CSALA. Heaven and Earth. Cantata, a f t e r Byron. Unpublished, apparently lost (included in MGG and Gojowy l i s t i n g s ) . 1913 Premier Ouatuor a cordes; also Quartet/Quatuor No. 1, •first v i o l i n part, at CSALA.) Tri sochineniia CThree Compositions]. Songs: 1."Sumrak t i k h i i " (V. Briusov); 2."Ty ne ushla" (A. Blok); 3.-Vetere n a l e t i t e " (A. Blok). Grustnye peizazhy CPaysages t r i s t e s ] (Verlaine). Songs: 1. "Osenniaia pesnia" (Russian trans. N. M i n s k i i ) ; 2. "Zakat" (Russian trans. V. Briusov); 3."B1agos1ovennyi chas." Noktiurn/Nocturne. Harp, oboe, two v i o l a s , v i o l o n -ce1lo. 1913- Sonate pour violon et piano. 1914 Chetyre sochineniia [Four Compositions]. Songs: 1."Margaritki" (I. Severianin) 1914; 2."Vy nosite liubov" (K. Bol'shakov) 1913; 3."Volkovo kladbishche" (D. Burliuk) 1913; 4."Kuk" (V. Gnedov) 1914. 1914 Trois compositions pour piano. 187 1914 Tri Et iuda/Tro is Etudes pour piano. 1915 D\/a sochineni ia/Deux compositions pour piano. "Quasi prelude," "Quasi poeme." Prelude pour piano. Poema. V i o l i n and piano. Pub. 1915. Pesenka Arlekina [Harlequin's L i t t l e Song] (E. Guro). Song. 1916 Quartet, second and t h i r d movements. Score; piano score. CSALA. 1917 Sonata No. 2 -for V i o l i n and Piano. CSALA. Quartet No. 2. Incomplete score. CSALA. 1919- Five Preludes. Piano. 1922 [1920s] 7 Pieces f a r V i o l i n and Piano: Etude mortelIe, Etude in Eb Major, Canon, Pugar Adagio, Pre Iiud i i a, Pomant i cheskai a poema [Romantic poema]. CSALA. [1920s Orchestral work, without t i t l e . Lento. Unfinished -1930s] score. CSALA. Orchestral work, without t i t l e . Unfinished score. CSALA. 1920 Dve Poemy/Deux Poemes. Piano. Third Quartet. T r i o No. 2. CSALA. 1921 Sonata. V i o l o n c e l l o and piano; also, Sonata for V i o l o n c e l l o and Piano at GMMC. Trois Danses. V i o l i n and piano. Paxdum'e/ Meditation. V i o l o n c e l l o and piano. Third T r i o . V i o l i n , v i o l o n c e l l o , piano. Man and Sea. Symphonic poem, after Baudelaire. Unpublished, apparently lost (included in MGG l i s t i n g ) . 1922 Symphony in four movements. Without beginning and ending. Score. CSALA. (Grove Dictionary, 6th ed., s.v. "Roslavets," indicates unpublished symphony, 1922.) 188 1922 Sonata No. 2 -for V i o l o n c e l l o and Piano. CSALA. 1923 World's End. Symphonic poem, af t e r Laforgue. Unpub-lished, apparently lost (included in MGG l i s t i n g ) . Symphony No. 2 -for Orchestra and Chorus. Unfinished score and sketches. CSALA. Sonata No. 5. Piano. 1924 Fourth Sonata. V i o l i n and piano. (Pub. 1924.) Piano Quintet for Two V i o l i n s , V i o l a , V i o l o n c e l l o , and Piano. Score. CSALA. 1925 V i o l i n Concerto. Arranged for v i o l i n and piano. Poslednee chudo (A. Andreev). Agit-prop, song (baritone voice). (Pub. 1925.) LLM. Contributions to agitation-propaganda song cycles (pub. 1925-26) Song c y c l e Pesni rex/oliutsii [Revolutionary Songs! : l."Na pervoe maia" (P. Oreshin). (Baritone voice.) (Pub. 1925); 2. "Na poliach" (P...Oresh i n) . Choir a cappella. (Pub. 1925); 3."Oktiabr'" (S. Rodov). Choir a cappella. (Composed 1924.) LLM. Song cycle Poeziia rabochikh professii [Poetry of the workers' c a l l i n g ] : l."Tkach" (Litkovsky). (Middle voice.) (Pub. 1925); 2."Shveia" (G. Korenev). (Pub. 1926.) LLM. 3."Tokaria" (A. Tverdyi). Choir a cappella. (Pub. 1926.) Song cyc l e Pesni o 1905 gode [Songs of the year 19053: 1. "Smolkli zalpy . . . " (E. Tarasov). (Pub. 1925); 2. "Mat' i Syn" (G. G a l i n a i a ) . (Pub. 1926.) LLM. Song c y c l e Dekabristy [The Decembrists]: 1."Poslanie v S i b i r ' dekabristam" (A. Pushkin). (Pub. 1925.) MCL; 2."Otvet' na poslanie v S i b i r ' " (F. Odoevskii). (High voice.) (Pub. 1925.) LLM. 1926 Chamber Symphony. Unfinished piano score with notes for orchestration. CSALA. Sonata for V i o l a and Piano. CSALA. 189 1926 Gimn sovetskoi raboche-krest' ianskai militsii [Hymn of the Soviet workers' and peasants' m i l i t i a ] ( V i a t i c h -Berezhnich). Wind band and chorus, orchestra ad. l i b . 1927 T r i o . V i o l i n and v i o l a parts. CSALA. Concerto -for V i o l i n and Orchestra, in -four movements. Without beginning. Piano score. CSALA. 1928 Concerto No. 1 -for V i o l i n and Orchestra. Sketches -for vi o l i n - p i a n o score. CSALA. KomsomoI'skaia. Symphonic Poem -for Orchestra, Chorus, and Piano Solo. Sketches -for score. CSALA. Sonata No. 1 -for V i o l a and Piano. Incomplete. CSALA. 1929 Bab'ia dolia (P. Druzhinin). Agit-prop. song. LLM. Kon'ki <A. S h i r i a e v e t s ) . Agit-prop. song. LLM. 1929- Quartet. Fragments o-f score. CSALA. 1931 C 1930s! Sonata No. 2 -for V i o l a and Piano. CSALA. Uzbekistan. Symphonic Poem. Piano score with notes •for orchestration. CSALA. Orchestral work. Unfinished score. CSALA. Pakhta [Cotton peasant]. B a l l e t . (Listed in Gojowy, "Half Time," 215) . 1930 Stuchite! KOMSOMOL [Communist Youth Group] March (I. Utkin). 1932- Geroi'a [Song of the Hero]. Song arranged for 1933 orchestra. CSALA. 1934- Quartet for Four Domras, on themes of Chechen f o l k 1935 songs. Score. CSALA. 1935 Invention and Nocturne f o r V i o l i n and Piano. CSALA. Dance for V i o l i n and Piano. GMMC. Kolybel'naia [Lullaby] for V i o l i n and Piano. GMMC. Scherzo for V i o l i n and Piano. GMMC. Valse for V i o l i n and Piano. GMMC. 190 1936 Concerto for V i o l i n and Orchestra, in three movements. Score. CSALA. 1939 Quartet No. 4. Unfinished score. CSALA. Potpou.fr-f-Fantasie, on themes of Soviet popular songs, for Xylophone and Piano. CSALA. 1940 Legends for V i o l i n and Piano. CSALA; also Legenda for V i o l i n and Piano in D minor, n.d., at GMMC. 1941 Quartet No. 5 in Eb Major. GMMC. 1941- 24 Preludes for V i o l i n and Piano. GMMC. 1942 \ 1942 Tabachok (A. P r i s h e l e t s ) . Agit-prop song. LLM. n.d. Rondo and Polonaise for V i o l i n and Piano. GMMC. 191 L i s t i n g o-f Works by Genre A.Orchestral Works Reverie -for V i o l i n and Orchestra. 1907. Symphony in C Minor. 1910. 1/ c/tasy novoLun i ia. Symphonic poem -for large orchestra, t1910s.3 nan and Sea. Symphonic poem, af t e r Baudelaire. 1921. Unpublished, apparently l o s t . Symphony in -four movements. 1922. Without beginning, ending. World's End. Symphonic poem, af t e r Jules Laforgue. 1922. Unpublished, apparently l o s t . Symphony No. 2 for Orchestra and Chorus. 1923. Unfinished. V i o l i n Concerto. Arranged for v i o l i n and piano. 192S. Chamber Symphony. 1926. Unfinished. Concerto for V i o l i n and Orchestra, in four movements. 1927. Without beginning. Concerto No. 1 for V i o l i n and Orchestra. 1928. Sketches for v i o l i n - p i a n o score. KomsomoI'skaia. Symphonic Poem for Orchestra, Chorus, and Piano Solo. 1928. Sketches for the score. Orchestral work, without t i t l e . Lento. C1920s-1930s.3 Unfinished. Orchestral work, without t i t l e . C1920s-1930s.3 Unfinished. Pakhta. B a l l e t . C1930s.3 Uzbekistan. Symphonic Poem. C1930s.3 Orchestral work. C1930s.3 Unfinished. Geroia. Arranged for orchestra. 1932-33. Concerto for V i o l i n and Orchestra, in three movements. 1936. 192 B.Solo and Chamber Works 1.Works -for Solo Piano. Trots Compositions pour piano. 1914. Tri Etiuda/Trois Etudes pour piano. 1914. Dva sochineniia IDeux Compositions pour piano. 1915. Prelude pour piano. 1915. Five Preludes. 1919-1922. fli/e Poemy/Deux Poemes. 1920. Sonata No. 5. 1923. (No i n d i c a t i o n s o-f other piano sonatas.) 2.Sonatas for V i o l i n and Piano. (Grove Dictionary, 6th ed., s.v. "Roslavets," indicates that -five v i o l i n sonatas were written.) Sonate pour violon et piano. c. 1913-1914. Sonata No. 2 -for V i o l i n and Piano. 1917. Fourth Sonata. Pub. 1924. 3.Other Works -for V i o l i n and Piano. Pomancet Reverter Morgenstimmungf Sonata (beginning), Gavotte, E leg ie, Serenade, etc. Pieces -for v i o l i n and piano. 1908. 3 Poemes and Romance-arabesque for V i o l i n and Piano. 19O9-1910. Liricheskaia poema/Poeme lyrique for V i o l i n and Piano. C1910s.3 Tantsy belykh dev/Danses des vierges blanches for V i o l i n and Piano. 1912. Poema. Pub. 1915. 7 Pieces -for V i o l i n and Piano: Etude mortelle, Etude in Eb Major, Canon, Fugat Adagio, Pre Iiudiia, Romanticheskaia poema. C1920s.3 193 7rot's Dansss. 1921. Invention and Nocturne for V i o l i n and Piano. 1935. Dance -for V i o l i n and Piano. 1935. Ko lyt>e I'nsi's -for V i o l i n and Piano. 1935. Scherzo -for V i o l i n and Piano. 1935. i/alse -for V i o l i n and Piano. 1935. Legends -for V i o l i n and Piano. 1940. (Also Legends for V i o l i n and Piano in D minor. n.d.; l i k e l y the same work) 24 Preludes for V i o l i n and Piano. 1941-42. Rondo and Polonsise for V i o l i n and Piano. n.d. 4.Sonatas for V i o l a and Piano. Sonata for V i o l a and Piano. 1926. Sonata No. 1 for V i o l a and Piano. 1928. Incomplete. Sonata No. 2 for V i o l a and Piano. C1930s.3 5.Sonatas and Other Works for V i o l o n c e l l o and Piano. Sonata. 1921. Sonata for V i o l o n c e l l o and Piano. 1921. Pszdum'et Ned i tst i on. 1921. Sonata No. 2 for V i o l o n c e l l o and Piano. 1922. 6.Piano t r i o s . T r i o No. 2. 1920. Third T r i o . For v i o l i n , v i o l o n c e l l o , and piano. 1921. T r i o . V i o l i n and v i o l a parts. 1927. 194 7.String Quartets. Nenuet for S t r i n g Quartet. 1907. S t r i n g Quartet. 1910. Quartet/Quatuor No. 1. F i r s t v i o l i n part. 1913. Premier Quatuor a cordes. 1913. Quartet, second and t h i r d movements. 1916. Quartet No. 2. 1919. Incomplete. Third Quartet. 1920. Quartet. 1929-1931. Fragments of score. Quartet No. 4. 1939. Unfinished. Quartet No. 5 in Eb Major. 1941. 8.Other Miscellaneous Chamber Works Serenada for Two V i o l i n s . 1909. NoktiurnJNocturne. Harp, oboe, two v i o l a s , v i o l o n c e l l o . 1913. Piano Quintet for Two V i o l i n s , V i o l a , V i o l o n c e l l o , and Piano. 1924. Quartet for Four Domras, on themes of Chechen f o l k songs. 1934-1935. P o t p o u r r i - f a n t a s i ' e , on themes of Soviet popular songs, for Xylophone and Piano. 1939. C.Vocal Works 1.Choral Works. Heaven and Earth. Cantata, aft e r Byron. 1912. Unpublished, apparently l o s t . From song cycle Pesni Revo I iutsi i'. "Na poliakh" (P. Oreshin). Choir a cappella. (Pub. 1925)5 "Oktiabr*" (S. Rodov). Choir a cappella. 1924. 195 From song cycle Poeziia rabochikh professii'. "Tokaria" (A. Tverdyi). Choir a cappella. 1926. Simn sox/etskoi raboche-krest' ianskoi militsii ( V i a t i c h -Berezhnich). Wind band and chorus, opt. orchestra parts. 1926. 2.Songs for Voice and Piano. T r i s o c h i n e n i i a . 1913. l."Sumrak t i k h i i " (V. Briusov); 2. ne ushla" (A. Blok); 3."Vetere n a l e t i t e " (A. Blok). Srustnye peizhazy (Verlaine). 1913. l."Osenniaia pesnia"; 2."Zakat". 3."B1agos1ovennyi chas." Chetyre soch inert iia. 1913-1914. 1. "Margar i tk i " (I. Severianin). 1914J 2."Vy nosite liubov" (K. Bol'shakov). 19135 3."Volkovo kladbishche" (0. B u r l i u k ) . 1913; 4."Kuk" (V. Gnedov). 1914. Pesenka ArZekina (E. Guro). 1915. 3.Agitation-propaganda songs. Poslednee chudo (A. Andreev). Baritone voice. (Pub. 1925. From song cycle Pesni Pewo I i utsi i'. "Na pervoe maia" (P. Oreshin). Baritone voice. (Pub. 1925.) From song cycle Poeziia rabochikh professii'. "Tkach" (Litkovsky). Middle voice. (Pub. 1925); "Shveya" (G. Korenev). (Pub. 1926.) From song cycle Pesni o 1905 gode: "Smolkli zalpy. . ." <E. Tarasov). (Pub. 1925); "Mat' i Syn" (G. G a l i n a i a ) . (Pub 1926.) From song cycle Dekabristy. "Poslanie v S i b i r ' dekabristam" (A. Pushkin). (Pub. 1925); "Otvef na poslanie v S i b i r ' " Odoevskii). High voice. (Pub. 1925.) Bab' ia dolia (P. Druzhinin). 1929. Kon'ki (A. S h i r i a e v e t s ) . 1929. Stuchite.' (KOMSOMOL-March) (I. Utkin). 1930. Tabachok (A. P r i s h e l e t s ) . 1942. i ^t. APPENDIX B This appendix provides a b r i e f examination o-f issues of PC content tangential to the discussions in Chapter Two. T-level I d e n t i t i e s o-f Individual Harmonies in " I " , Measures 6-8 \ . • A further, conceivable explanation of T-level identity in mm. 6-8 of " I " involves designating each harmony with a T-level of most sim i l a r PC content, with individual harmonies conforming to the T -O,T-2,T-7 transpositional relationship assumed for mm. 6, 7, and 8, respectively (Ex. 6-1). Example 6-1. Collections in mm. 6-8 and the most similar T-1 eveIs. (6) 4TH J'-TIHE-SPAHJ 5TH .P-TIHE-SPAHi 6TH J'-TINE-SPAN T-O 15) T - l (5) T-O (5) T-9 (5) T-4 (5) T-7 (6) 197 Example 6-1 continued. 171 4TH 7-TIHF.-SPMII 5TH J'-TIflE-SPAHl 6TH /-TIME-SPAR is ZLT. f T-2 1S1 T-3 (31 / T - l l 131 T-2 (3) / T-6 (3) 7 T-9 (61 (81 1ST j'-TINE-SPAR| 210 J'-TIK-SPAMJ 3RD ^-TIRE-SPAN ) 1 J - L o rz—i a ° °\ bo T-7 (3) T-8 (5) T-7 (51 tt»** T-4 (31 T - l l (31 T-2 (61 Note:. PCs in T-levels that match the collection's PCs are l i s -ted as whole notes, with the number o-f common PCs being given i brackets. Moreover, the -first and t h i r d c o l l e c t i o n s of m. 6, second half (and likewise of m. 7, second half, and of m. 8) have four PCs out of six in common, as do the second and thi r d . Because of these common PCs and because the middle c o l l e c t i o n of each group of three tends to function as an auxiliary, decorative c o l l e c t i o n (a function that i s e a s i l y perceived since many PCs of these middle c o l l e c t i o n s are approached and/or l e f t by step) 198 the outer c o l l e c t i o n s o-f each group o-f three are designated as the same T - l e v e l . The T-level succession thus adduced -for mm. 6-8 i s : T-ll,T-0,T-l/T-9,T-0 (m. 6), T-11,T-2,T-3/T-11,T-2 (m. 7), T-7, T-8/T-4, T-7 (m. 8). Such a succession o-f T-levels r e f l e c t s ! the a p p l i c a t i o n o-f i n d i v i d u a l c o l l e c t i o n s rather than subsets o-f an enlarged ICC; the T-0,T-2,T-7 tr a n s p o s i t i o n a l r e l a t i o n s h i p o-f mm. 6, 7, and 8; a consistency o-f T-level sequence in the three measures; and the s i m i l a r i t y o-f the -first and t h i r d c o l l e c t i o n s o-f each time-span, as noted above. Gojowy's Analysis o-f T-Levels in " I I I " Gojowy's -four ICCs o-f " I I I " include the -four most -frequent-ly occurring PC c o l l e c t i o n s or transpositions thereof. His sequence of ICCs and th e i r T-levels i s i l l u s t r a t e d in F i g . 6-1. 199 Figure 6-1. T-level successions in " I I I " , as given in Gojowy'5 analysis. (a)ICCs of " I I I " : 7 •b-(b)T-level successions in " I I I " : MEASURE 111 [21 13) ICC, T-LEVEL i,0—a,3 c ,0—c,7—c, l l—e ,2 IRRE6ULAR—b, 1—b,4 (a,l/b,l) H. (41 15-61 171 181 (91 (10-111 ICC, T- b ,7—b,0™b,3 4,0-—c,3-—c,6—*,( )—4,1 c,6 (a,5) <d,10) N. (121 113) (14-131 ICC, T- a,3—IRRE6ULAR—-c,9—c,4—c,8—c,ll c,4 (•,0 TIMERS'*) There i s , however, a compromise of Goj owy's system of four ICCs that i s more p r a c t i c a l . The s i m i l a r i t i e s between ICCs "a" and "b", and between ICCs "c" and "d" (in ei t h e r case with only one PC that d i f f e r s ) , are such that two of the ICCs could be ci t e d instead of four; "a" and "d" are more i n c l u s i v e . Figure 6-2a presents the two ICCs; the altered sequence of T-levels i s given in Fig . 6-2b. 200 Figure 6-2. ICCs "a" and "d" in " I I I " . (a)Modi-fied ICCs: "aO" : Db-D*t-E-F-G-Gtt— Bb — B "cO": Eb-E-Gb-G-Bbb-B "bO" : Db-Dtt-E-F-G-Gtt B "dO": Eb-E-Gb-G-Bbb-B — Db "new "new aO": Db-Dtt-E-F-G-G**- (Bb) -B dO": Eb-E-Gb-G-Bbb-B-(Db) ICAs: 2—1-1-2-1 3 2 1-2—1-2 2 4 (2 +1) (2 + 2) (b)T-levels o-f ICCs "a" and "d": n. [1] (21 (31 (41 (5,6] ICC, T- a,0 a,5 d,0 4,7 df11 4,2 a,l a,l a,4 a,7 a,0 a,5 4,0 M. (71 (81 [9] [10,111 (121 [131 (14,13] ICC, T- 4,3 4,6 4,10 4,1 4,6 a,5 4,0 4,9 4,4 4,8 4,11 4,4 (c)T-level occurrences and t o t a l time-spans: ICC, T- aO al a4 a5 a7 a( I OCCURRENCES 2 2 1 3 1 9 TOTAL TINE-SPAN (8TH VALUES): 4 5 1 8 2 20 ICC, T- 40 41 42 43 d4 46 47 48 49 410 dll d( I OCCURRENCES 3 1 1 1 2 2 1 1 1 1 2 16 TOTAL TINE-SPAN 14 6 1 9 9 10 1 2 2 3 3 60 This system o-f two ICCs represents a compromise between Gojowy's -four ( i . e . , the most -frequently occurring PC c o l l e c -tions and transpositions thereof, with no variant elements), and Perle's use o-f a s i n g l e ICC with three variant elements not occurring with every c o l l e c t i o n . An examination o-f locations and -functions o-f variant e l e -ments ( i . e . , represented by the bracketed PCs in ICCs "a" and "d", F i g . 6-2a) establishes no consistent r e l a t i o n s h i p between 201 these elements and t h e i r location and function in the music. Figure 6-2c shows the occurrences and t o t a l time-spans of ICC T-leve l s in order to e s t a b l i s h which of the c o l l e c t i o n s can be considered more s i g n i f i c a n t . In t h i s l i g h t , T - l e v e l s "dO" and "d6" (and to a lesser extent "d3" and "d4") can be i d e n t i f i e d as of greater s i g n i f i c a n c e . An A n a l y t i c a l A l t e r n a t i v e : A Single ICC for " I " , " I I " , and " I I I " S i m i l a r i t y of content makes i t possible to analyze the har-monic successions of the three pieces in terms of a s i n g l e ICC including elements "0", "3", "4", "6", and "8". If the i n i t i a l T-level of t h i s common ICC, occurring as the f i r s t harmony of " I " , were to be designated as T-O, then the f i r s t T-level of "II " would be T - l l , and the f i r s t T-level of " I I I " would be T-5. There are obvious a n a l y t i c a l advantages in using a s i n g l e common ICC; however, there are some problems with t h i s method. The use of a s i n g l e common ICC implies that i n i t i a t i n g harmonies in two of the three pieces are somehow subordinate to that of the piece whose i n i t i a l T-level i s designated as T-O. And since there are differences in variant elements associated with each piece (e.g., element "IO" in " I " , "1" in " I I " , and "9", "IO", and "11" in " I I I " ) , and in the extent of t h e i r use, and also differences in the notational orthography of ICC T-levels in the music, par-t i c u l a r l y that of " I I I " , three i n d i v i d u a l ICCs are taken as a basis for analyses in t h i s t h e s i s . 202 Prolongation o-f T-Levels Reiterated T - levels, with only a -few harmonies separating occurrences, imply a prolongation of the T-levels and t h e i r con-sequent, special s i g n i f i c a n c e . PC invariance and p i t c h - c l a s s continuity can play a ro l e in the perception o-f prolongation, t h i s perception being f a c i l i t a t e d when: there are no more than three or four i n t e r p o l a t i n g T -levels; the v e r t i c a l p o s i t i o n or r e g i s t e r of r e i t e r a t e d pitches remains the same in both appear-ances of the T - l e v e l ; pitches in the recurring T-level appear also in the interpolated T-levels, preferably in the same r e g i -ster; the r e i t e r a t e d T - l e v e l s appear on stranger metric time-points, and/or have s i m i l a r rhythmic patterns; and both appear-ances of the r e i t e r a t e d T-level are given s i m i l a r forms of emphasis, exposure, accentuation, or a r t i c u l a t i o n . Example 6-2 presents prolonged T-levels, with the musical notation of these i l l u s t r a t i n g invariant PCs and pit c h c o n t i nuity. 203 Example 6-2. Prolonged T-levels in Trois Compositions. 204 Example 6-2 continued. (101 ( i l l [121 T-3 T-6 T-3 T-9 T-4 T-9 5(2) 5(2) 4(2) 412) —en— r-jr-e-1 1_ 1 1 OS*? 1 0—\  0— | 1 i ! 11 »>• 1 i " I V l l n 1 — — -• . I 1 MEASURE 3 4 7 1 10 11 12 13 T-LEVELS 10-3 10-3. . . . 10-3 0 - 5 . . . . 0 - 5 0-3 0 0 PROLONGED [10 10 101 10 0 0 0—0J LEVELS: [3- 3 31 (5.. . . . . .5 31 20S Example 6-2 continued. •Ill* MEASURE 2 3 4 8 9 10 12 13 14-15 T-LEVELS 8—3—7—10 1-4 7 - 0 - 3 2-6 9 2 5-0 5 - 0 - 4 - 7 0 PROLONGED [7 71 1 2 — — 2 1 (0 0 01 LEVELS 15.... 5 51 206 Nate: Lines in the - f i r s t a-f two staves with each example o-f prolongation connect invariant PCs in adjacent harmonies. The unbracketed and bracketed numbers above each harmonic succession indicate the number o-f invariant PCs and the number o-f p i t c h c o n t i n u i t i e s , r e s p e c t i v e l y . On the second o-f two staves, horizontal l i n e s i l l u s t r a t e invariance o-f PCs o-f the prolonged T - l e v e l s through interpolated T - l e v e l s . Given the above-stated conditions, T - l e v e l s T - l l (mm. 6-7), T-3 and T-6 (mm. 10-11), and T-9 (m. 12) in " I " , T-10 and T-3 (mm. 3-4), and T-0 and T-5 (mm. 10-11), and T-2 (mm. 8-11) in " I I I " are p a r t i c u l a r l y convincing, while other r e i t e r a t e d T-l e v e l s less e a s i l y i n t e r r e l a t e d as prolongations. 

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