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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 IN NIKOLAI  ROSLAVETS'S  PITCH-CLASS  TROIS  ORGANIZATION  COMPOS IT IONS  POOR  PIANO  By DAVID WILLIAM  A THESIS SUBMITTED  MCISAAC  IN PARTIAL FULFILLMENT OF  THE REQUIREMENTS FOR  THE DEGREE OF  MASTER OF ARTS MUSIC THEORY i n THE FACULTY OF GRADUATE STUDIES (Department  We  accept t h i s to  o-f M u s i c )  thes'i/S as con-forming  the. - r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA July  ©  David W i l l i a m  1986  McIsaac,  1986  (1914)  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree a t the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may  be granted by the head o f  department o r by h i s o r her r e p r e s e n t a t i v e s .  my  It is  understood t h a t copying o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be  allowed without my  permission.  Department o f  Music  .  The U n i v e r s i t y o f B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date  DE-6  rvR-n  J u l y , 1986  written  i i  ABSTRACT  Nikolai in  Russian  His  system  Andreevich  avant-garde of  tonal  Roslavets musical  (1881-1944)  developments  is a  o-f  unique  this  figure  century.  organization,  . 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 chordal c o m p l e x . . . 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 or more t o n e s , used . . . as s u b s t i t u t e s f o r the f u n c t i o n a l r e l a t i o n s h i p s of 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 r a t h e r 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 invariable 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 n o t o n l y to the seven p i t c h e s of the c l a s s i c a l d i a t o n i c s c a l e , but a l s o to a l l t w e l v e d e g r e e s of the c h r o m a t i c scale. Through systematic a p p l i c a t i o n of such transpositions, Roslavets's compositions revealed elements 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 Roslavets," i n Russian and Soviet Musics Essays for Boris Sctowarz , 2 1 2 . ) Trois  Compositions  teristics. George  G o j o w y *s  Perle's  references  mentary  about  studies  music  this  the  ines  certain  (designated system)  in  harmonies  thereof,  of  the  Trois  of  the  thesis  as  the  are  with  related  20er  well  are  (PC)  the  based  to  include general  on  However,  thesis  chord"  in  PC  exam-  system  complex  or  contents  ICC of  transposition-1evels  pieces—and the  com-  Proceeding  present  (1)  and  t  organization  lacking.  "synthetic  the  as  charac-  Jahre  techniques.  including:  associated  such  both  i n t e r v a l - c 1 ass  pieces--contents  which  as  Perle,  Roslavets's  Compositions,  ICCs  some o f  and  der  Atonality  pitch-class  composer  Gojowy of  and  compositional and  exhibit  Musi A  Compositions  little-known  in  (1914)  sov/jetische  Trois  pitch  aspects  in  (T-levels)  to  of  analyses  piano  Composition  Roslavets's  detailed  •from  Neue  Serial  limited  by  pour  forms  of  variances the  pieces;  iii  (2)  harmonic  successions  aspects  of  these  a  o-f  hierarchy  basis  successions nuity by  T-levels  to  tion  These  of are  and  as  to  their  discussed  consideration  involves  while  Chapter  an Four  h i s music of  are  invariance  patterns  Two,  involves  a  which  and  which  of are  and  following  an  contirelated verti-  T-levintroduc-  One. a  post-Romantic  tendencies  in the  thesis.  in  the  three  octatonicism to  T-level  T-levels  and  tonality  study  indicate  pitch  linear  p o s i t i o n as  investigated of  of  in Chapter  techniques  examination  rhythmic  i n c l u s i o n in p a r t i c u l a r  Roslavets's  some c h a r a c t e r i s t i c s o f  Compositions.  (5)  (3)  c h a r a c t e r i s t i c s of  particularly  in Chapter  compositional  Compositions  Three  and  PC  T-levels,  T-levelss  successions,  (4)  and  3s  In  Trois  their  (IC)  Roslavets  other  and  content,  to  composer,  ism,  PCs  associated  T-levelss  involving adjacent  ordering  els.  of  PC  i n t e r v a l - c 1ass  cal  in  as  and  be  found  and in  evident Chapter pieces, serialTrois  iv TABLE OF CONTENTS  Abstract List  •  o-f Examples and  •••  i i  Figures  vii  Acknowledgements  xi  Chapter One: Introduction Biographical Information. A s p e c t s o-f R o s l a v e t s ' s C o m p o s i t i o n a l and Techn i que Notes Chapter Trots  Two: Compos  The  4 10 15  Terminology..  The  Compos f t ions.  in  ••  I n t e r v a l - C 1 ass Complex i n  i t ions.  I n t r o d u c t i o n and ICC  Style  ......1 ......1  Trois  .15 22  ICC of " I " 22 ICC O f " I I " 30 ICC of " I I I " 34 Harmonic S u c c e s s i o n s and S u c c e s s i o n s o-f Transposition-Levels 44 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 Adjacent T-Levels 44 T r a n s p o s i t i o n a l C y c l e s o+ T-Levels...............46 "I " 47 "II" . . 51 "III" 52 T-Level Occurrences and T h e i r Rhythmic Characteristics: Towards a H i e r a r c h y 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 H i e r a r c h y o-f T - L e v e l s .62 T-Level Occurrences and T h e i r R e l a t i o n s h i p s to Form: "I" 64 "II" 65 "III" 66 Recurrent Harmonic S u c c e s s i o n s 67 C h a r a c t e r i s t i c s o-f T-Level Occurrences as t o PC Content 71 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 71 PC I n v a r i a n c e i n IC-3-Related T - L e v e l s . . 85  V  Element O c c u r r e n c e and O r d e r i n g i n Trois  Compos i t i ons  L i n e a r Element Occurrence and O r d e r i n g : Element o c c u r r e n c e i n bass l i n e s V e r t i c a l Element Occurrence and O r d e r i n g in I n d i v i d u a l Harmonies: "I" "II" "III" " I " , " I I " , and " I I I " as a whole V e r t i c a l Element A d j a c e n c i e s Conclusion Notes Chapter Three: T o n a l i t y i n Trois Compositions Introduction Tonality in " I " S u r f a c e Tonal F e a t u r e s Midd1eground/Background L i n e a r S t r u c t u r e s o-f " I " Initiating single-pitch exposure. Linear structures in " I " M e l o d i c fragments Bass-line linear structures Middleground/BacWground Harmonic S t r u c t u r e s of " I " Tonality in " I I " S u r f a c e Tonal F e a t u r e s Midd1eground/Background L i n e a r S t r u c t u r e s of " I I " Diminished-seventh l i n e a r s t r u c t u r e s i n mm. 6-9. Mi dd1eground/Background Harmonic S t r u c t u r e s of " I I " Tonality in " I I I " S u r f a c e Tonal F e a t u r e s Midd1eground/Background L i n e a r S t r u c t u r e s of " I I I " . . . Midd1eground/Background Harmonic S t r u c t u r e s of " I I I " Conclusion Notes  ........91  "I" 91 "II" .93 "111 "... 93 95 95 99 lOl 104 105 113 117 .125 125 127 127 131 131 134 136 137 139 140 .140 146 146 150 151 151 154 157 159 161  vi Chapter  Four:  Organization  Other Systems o-f P i t c h - C l a s s i n Trois  Compositions  165  S e r i a l PC O r g a n i z a t i o n S e r i a l O r d e r i n g of T - L e v e l s and o-f PCs i n T - L e v e l s S e r i a l O r d e r i n g o-f Melodic P i t c h e s Notes  .168 170 172 175  Chapter F i v e : C o n c l u s i o n The ICC System T o n a l i t y , O c t a t o n i c i s m , and S e r i a l ism. I m p l i c a t i o n s o-f " I I I " Concerning M a t t e r s o-f S t y l e and L a r g e - S c a l e Form..  181  Selected Bibliography...  183  Appendix A: C h r o n o l o g i c a l L i s t by R o s l a v e t s L i s t o-f Works by Genre  178 178 180  o-f Works  Appendix B: T-Level I d e n t i t i e s o-f I n d i v i d u a l Harmonies i n " I " , Measures 6-8 GDjowy's A n a l y s i s o-f T - L e v e l s i n " I I I " An A n a l y t i c a l A l t e r n a t i v e : A S i n g l e ICC •for " I " , " I I " , and " I I I " P r o l o n g a t i o n o-f T - L e v e l s . .  185 191  196 198 201 202  vii LIST OF EXAMPLES AND  FIGURES  Example 2-1. P i t c h c o l l e c t i o n s i n " I " , m. and c o r r e s p o n d i n g PCC T - l e v e l s  1, 17  Example 2-2. T r a n s p o s a b l e PCCs o-f " I " , " I I " , and " I I I " , as i l l u s t r a t e d by P e r l e , with numbering o-f PCs added  19  Example 2-3.  ICC o-f " I " , with T - l e v e l  23  Example 2-4.  PC c o l l e c t i o n o-f m.  Example 2-5.  Expanded ICC and T - l e v e l s  successions  13 i n " I" i n mm.  26 6-8  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 o t h e r PC c o l l e c t i o n s i n " I " and "II" Example 2-7.  ICC o-f " I I " , with PCs p a r t i t i o n e d  28  29  into  harmonies  .31  Example 2-8.  The ICCs o-f " I I I "  35  Example 2-9.  M u s i c a l 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" i n mm.  42  3-4  Example 2-12. T-O c o l l e c t i o n , m. 12, as an i n v e r s i o n o-f ICC a t T-0 F i g u r e 2-1. 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 between s u c c e s s i v e T - l e v e l s i n " I " , " I I " , and " I I I " F i g u r e 2-2. T-level the IC c y c l e s  the  T-level  45  s u c c e s s i o n s o-f " I " and 48  F i g u r e 2-3. T - l e v e l s u c c e s s i o n s o-f " I I " and the i n t e r v a l 5 c y c l e F i g u r e 2-4.  .43  51  s u c c e s s i o n s o-f " I I I " and  IC c y c l e s  Example 2-13.  Harmonic rhythm and -form o-f " I "  Example 2-14.  Harmonic rhythm and -form o-f " I I "  Example 2-15.  Harmonic rhythm and -form o-f " I I I "  52 55 ...58 60  vi i i F i g u r e 2-5. H i e r a r c h y o-f T - l e v e l s based on o-f o c c u r r e n c e and t o t a l time-spans.... F i g u r e 2-6. Trois  Recurring Compos  -frequency  T-level successions in  i t i ons.  68  Example 2-16. I n v a r i a n t PCs o-f I C - i - t o IC-6related T-levels Example 2-17. in  62  72  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  T-level  s u c c e s s i o n s of Trois  Compositions  .76  Example 2-18. PC i n v a r i a n c e i n I C - 3 - r e l a t e d T-level families.....  87  F i g u r e 2-7.  88  Successions  of T - l e v e l f a m i l i e s  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 p i t c h e s r e p r e s e n t e d by element numbers.  96  F i g u r e 2-8. Element o c c u r r e n c e s i n 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 r e p r e s e n t e d by element numbers. Example 2-24. Harmonies of " I I I " with r e p r e s e n t e d by element numbers  pitches lOO pitches  F i g u r e 2-9. V e r t i c a l element o c c u r r e n c e i n ranges of p o s i t i o n s i n Trois Compositions.  102 105  Example 2-25. S i m i l a r i t i e s o-f harmonies i n " I " (with p i t c h e s r e p r e s e n t e d by element numbers)....... 106 Example 2-26. S i m i l a r i t i e s of harmonies i n " I I " (with p i t c h e s r e p r e s e n t e d by element numbers)  108  Example 2-27. S i m i l a r i t i e s of harmonies i n " I I I " (with p i t c h e s r e p r e s e n t e d 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 o r d e r i n g s of harmonies i n " I and " I I I "  113  Example 3-1.  127  ICC T - l e v e l s T-0, T - l i , and T-4 i n " I "  ix Example 3-2. S u r f a c e s t r u c t u r e s and p r o g r e s s i o n s o-f Eb, D, and G t o n a l i t i e s i n " I" Example 3-3. their  T r i t o n e sequences o-f mm.  tonal  6-8 and  implications....  130  Example 3-4.  I n i t i a t i n g single pitches  Example 3-5.  Linear  Example 3-6.  M e l o d i c -fragments o-f mm.  and  structures  in " I " .  132  in " I "  .134 1-5  10-13 o-f " I "  136  Example 3-7.  The PC p r o g r e s s i o n  Example 3-8.  Bass-line  Example 3-9.  Midd1eground/background harmonic  G-G*t/Ab i n mm.  6-8. . . . . . 137  s t r u c t u r e s o-f " I "  138  s t r u c t u r e o-f " I "  140  Example 3-10.  ICC o-f " I I " and i t s resemblance t o F  Example 3-11.  T-O  Example 3-12.  S u r f a c e t o n a l -features  Example 3-13.  Harmonies o-f mm.  harmonies i n mm.  Eb i n mm.  in " I I "  6-9 and t h e i r  143 tonal 145  3-5  145  Example 3-15. A r p e g g i a t e d d i m i n i s h e d - s e v e n t h harmonies in the primary melody o-f mm. 6-9 Example 3-16. Midd1eground/background l i n e a r s t r u c t u r e s o-f " I I " Example 3-17. Midd1eground/background harmonic s t r u c t u r e s o-f " I I " Example 3-18.  141  13, 1, and 10-12. .... 142  imp 1 i cat i o n s . . . . Example 3-14.  128  147 149 150  The ICC o-f " I I I "  151  Example 3-19. Surface tonal s t r u c t u r e s in " I I I " Example 3-20. I C - 5 - r e l a t e d PC s u c c e s s i o n s i n mm. 3-7 of " I I I " Example 3-21. Midd1eground/background l i n e a r s t r u c t u r e s of " I I I "  152 153 154  Example 3-22.  F#/Gb and the l i n e a r  Example 3-23.  Bass-line  structure  s t r u c t u r e s of "III"..155 in " I I I "  156  X  Example 3-24. Midd1eground/background harmonic s t r u c t u r e s o-f " I I I "  158  Example 4-1. ICCs o-f Trois Compositions with o c t a t o n i c c o l l e c t i o n s  166  F i g u r e 4-1. Serial ordering T r o i s Compositions Example 4-2. Serial ordering and b a s s - l i n e PCs  compared  o-f T - l e v e l s i n .170 o-f primary melody  Example 6-1. C o l l e c t i o n s i n mm. most simi l a r T - l e v e l s  172 6-8 and the 196  F i g u r e 6-1. T-level successions in " I I I " , as g i v e n i n Gojowy's a n a l y s i s . . . . . . .  199  Figure  200  6-2.  Example 6-2.  ICCs "a" and "d" i n " I I I " Prolonged T - l e v e l s i n T r o i s Compositions...  203  ACKNOWLEDGEMENTS  I wish t o extend my a p p r e c i a t i o n t o the -following people: P r o f . Wallace B e r r y , able c r i t i c i s m s , whom I f i r s t uing  my t h e s i s a d v i s o r ,  and encouragement; P r o f . W i l l i a m Benjamin,  began t h e t h e s i s r e s e a r c h ,  interest;  f o r h i s help  P r o f . John Roeder, f o r r e a d i n g  giving valuable c r i t i c i s m s ; formation  -for h i s guidance, v a l u -  on c u r r e n t  the t h e s i s and  into Roslavets;  pianist  Rothenberg of New York, who g r a c i o u s l y p r o v i d e d a t New York's The Kitchen  premiere performances of works by R o s l a v e t s , Compositions  pour  piano,  Guillermo  Figueroa,  with  me with  a tape  which  featured Trois  violinist  J e r r y Grossman; P r o f .  G o e t z - S t a n k i e w i c z , f o r her a s s i s t a n c e with  Sarah  including  Ms. Rothenberg,  and c e l l i s t  P r o f . Barbara H e l d t ,  and c o n t i n -  Dr. D e t l e f Gojowy, f o r p r o v i d i n g i n -  research  r e c o r d i n g of a c o n c e r t  with  Marketa  German t r a n s l a t i o n s ;  f o r her a s s i s t a n c e 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 t h e Music L i b r a r y and I n t e r l i b r a r y Loan S e r v i c e ; and f a m i l y and f r i e n d s i n Vancouver and Ontario,  for their  especially  help and encouragement.  l i k e t o thank my w i f e F r a n c i n e ,  l o v i n g support Excerpts  have helped  Finally,  I would  whose a s s i s t a n c e and  me t o complete the t h e s i s .  from t h e s c o r e a r e used with  the p e r m i s s i o n of  Music A s s o c i a t e s of America, r e p r e s e n t a t i v e s f o r Boe1ke-Bomart, Inc.,  copyright  owners of Trois  Compositions.  1 CHAPTER ONE  INTRODUCTION  At the b e g i n n i n g of t h i s c e n t u r y , Russian a r t was i n the vanguard of European development and i t c o n t i n u e d t o be so w e l l i n t o the S o v i e t p e r i o d . The S t a l i n i z a t i o n of S o v i e t music and the subsequent i n s i s t e n c e on a n a t i o n a l and popular symphonic s t y l e have served t o obscure the work and the v e r y e x i s t ence of an important and o r i g i n a l group of Russian composers a c t i v e i n the f i r s t q u a r t e r of the c e n t u r y , i n c l u d i n g the remarkable N i k o l a y R o s s l a v e t z [ N i k o l a i R o s l a v e t s ] (1881-1944), who a n t i c i p a t e d a s p e c t s of twelve-tone music. . . . 1  Although, described of  from an h i s t o r i c a l  p e r s p e c t i v e , R o s l a v e t s may be  as a "minor e x p e r i m e n t a t o r , "  he i s , n o n e t h e l e s s , one  the more s i g n i f i c a n t but l i t t l e - k n o w n f i g u r e s of avant-garde  music  i n R u s s i a d u r i n g the f i r s t  Biographical  r e g i o n of the Ukraine,  R o s l a v e t s came from a r u r a l  background.  "should be a peasant  pur  sang,  January  5,  Saminsky f i n d s i  "curious" that Roslavets, a s o p h i s t i c a t e d musician  and  century.  Information"  Born i n the Chernigov 1881,  t h r e e decades of t h i s  and t h i n k e r ,  h i s p a r e n t s being former  serfs  he h i m s e l f a shepherd boy up t o the age of twelve.""*  R o s l a v e t s was i n i t i a l l y cates that h i s musical  s e l f - t a u g h t i n music.  He h i m s e l f  indi-  t a l e n t appeared around the age of seven  or e i g h t , and was m a n i f e s t e d  under the i n f l u e n c e of h i s u n c l e ,  with whom he s t u d i e d the v i o l i n .  L a t e r , R o s l a v e t s had l e s s o n s  in Konotop, and e v e n t u a l l y was admitted  t o the music c l a s s e s of  2 A. M.  Abaza,  t h e o r y , and  i n Kursk, harmony.  From 1902  where he s t u d i e d the v i o l i n ,  0  to 1912  tory, studying v i o l i n  he was  a student at the Moscow  with Jan Hrimaly  1915)3, c o u n t e r p o i n t , fugue, Il'inskii  (1859-1920); and  and  He graduated and  A.  i n 1912 based  Earth,  There a r e i n d i c a t i o n s o-f h i s r a d i c a l  a student at the Conservatory."*  little  (1844-  c o m p o s i t i o n and o r c h e s t r a t i o n  s i l v e r medal f o r h i s c a n t a t a Heaven  was  Conserva-  CIvan G r z h i m a l i  -form with Alexander  S e r g e i N. V a s i l e n k o (1872-1956).  by Byron.  elementary  with  with a  on the t e x t  views w h i l e  he  However, t h e r e seems to be  i n f o r m a t i o n a v a i l a b l e c o n c e r n i n g the composer's p o s t -  Conservatory  l i f e and m u s i c a l a c t i v i t i e s up t o the e a r l y  What i s known about graphical  article,  t h i s p e r i o d , l a r g e l y through i s h i s development of a new  1920s.  h i s autobio-  system  of  tonal  organization. ' 5  In  1922,  servatory.* S t a t e Music  he was  the temporary  d i r e c t o r of the Khar'kov Con-  He then worked on the e d i t o r i a l  staff  P u b l i s h i n g House, n o t a b l y as the e d i t o r of and  tributor  to the M a r x i s t and p r o g r e s s i v e p e r i o d i c a l  Aul'tura  (1924).  lished.) critic  R o s l a v e t s was  mity of v i r t u a l l y everybody One  Muzykal'nara  g e n e r a l l y q u i t e a c t i v e i n the 1920s as a venting "his radical  ous e s s a y s i n the mid-twenties,  T  con-  (Only t h r e e i s s u e s of the j o u r n a l were pub-  and w r i t e r on music,  ernists, "  of the Moscow  . . .  except  ideas in v a r i -  [which] earned  him  the en-  a s m a l l group of extreme mod-  group with which he came i n t o c o n f l i c t  more c o n v e n t i o n a l l y o r i e n t e d A s s o c i a t i o n of P r o l e t a r i a n  was  the  Musi-  c i a n s C l a t e r , Russian A s s o c i a t i o n of P r o l e t a r i a n M u s i c i a n s , or  3 RAPM3, which Until  "reproached him -for h i s bourgeois  ideology."*-  0  1929, he was a board member of the modernist  •for Contemporary Music, with ICSM.  Association  the S o v i e t a s s o c i a t i o n c l o s e l y  linked  In 1928-29, ACM was r e o r g a n i z e d as the A l l - R u s s i a n  S o c i e t y -for Contemporary Music, but i t ceased t o e x i s t by 1931. to  1  1  In t h e l a t t e r h a l f o-f t h e 1920s, the l i m i t e d  response  h i s works, and p r e s s u r e -from RAPM and S o v i e t a u t h o r i t i e s l e d  him t o abandon h i s avant-garde s t y l e of c o m p o s i t i o n -for a more acceptable tonal ous e r r o r s  (i.e.,  emotional") Muzykant,  style.  Roslavets p u b l i c l y  " h i s modernist s t y l e and h i s avoidance of the  i n 1930 i n the Proletarian  journal  confessed h i s p r e v i -  of RAPM 3 .  Musician  LProletarsk  ii  1 2  R o s l a v e t s "then accepted an i n v i t a t i o n  t o Tashkent  t i n Uz-  b e k i s t a n , a r e g i o n of the S o v i e t Union] where he s w i t c h e d t o f o l k music opera.  i n Uzbek s t y l e and composed the f i r s t  A l l music  national  Uzbek  d i c t i o n a r i e s p u b l i s h e d i n the West s p e c u l a t e  t h a t R o s l a v e t z was banished from Moscow and that he d i s a p p e a r e d without t r a c e Perhaps  i n the wake of the p o l i t i c a l  he moved t o Tashkent  purges of the 1930s.  t o escape p o l i t i c a l  reprisals." " 1  More r e c e n t l y however, Gojowy has p r o v i d e d l i t t l e - k n o w n  informa-  t i o n about R o s l a v e t s and h i s a c t i v i t i e s a f t e r the 1920s, d i s m i s s i n g rumours about R o s l a v e t s ' s e x i l e t o and death t h a t arose as a consequence  of h i s "non-person"  cultural  and Z h d a n o v .  p o l i c i e s of S t a l i n  in Siberia  s t a t u s under the  14  R o s l a v e t s went t o U z b e k i s t a n i n 1931, where he became one of the f i r s t Russian m u s i c i a n s t o c o n t r i b u t e t o the development of musical c u l t u r e i n Middle A s i a . He was d i r e c t o r of the Radio Center of the Uzbek Sov i e t R e p u b l i c and conductor of the Uzbek Music Theater. He composed music based on [Uzbek] n a t i o n a l  4 melodies and rhythms. H i s b a l l e t Pakhta ["Cotton p e a s a n t " ] , d e d i c a t e d to the s t r u g g l e f o r independence o-f the c o t t o n i n d u s t r y i n the USSR, and h i s symphony, " S o v i e t U z b e k i s t a n , " composed -for the 15th a n n i v e r s a ry o-f the October R e v o l u t i o n , were performed with g r e a t s u c c e s s under h i s baton. He was awarded an honorary diploma by the government of the Uzbek Republie. In November 1933, he r e t u r n e d to Moscow as a producer f o r the A l l - U n i o n Radio Committee (1933-35) and as d i r e c t o r of the A l l - R u s s i a n Concert A s s o c i a t i o n ( u n t i l 1939); from 1936, he served as head of the s e c t i o n of s c i e n t i f i c c o l l a b o r a t o r s i n the t r a d e union RABIS. He taught c o m p o s i t i o n i n the M u s i c a l P o 1 y t e c h n i c a l S c h o o l , l e c t u r e d to m i l i t a r y band d i r e c t o r s , and c o n t i n u e d to compose. During these y e a r s he wrote important t h e o r e t i c a l works, such as " C o u n t e r p o i n t " and "Fugue," which remain u n p u b l i s h e d . Although he was s e r i o u s l y i l l d u r i n g the Second World War, he became i n t e n s e l y i n v o l v e d i n the g e n e r a l s t r u g g l e and composed p a t r i o t i c songs d e d i c a t e d to the defenders of h i s c o u n t r y . . . . » ie  R o s l a v e t s d i e d i n Moscow, August 23, A s p e c t s of R o s l a v e t s ' s C o m p o s i t i o n a l R o s l a v e t s ' s student were i n f l u e n c e d by French completion  S t y l e and  compositions  and  Technique  e a r l i e r chamber works  impressionism. "*  But  1  of h i s s t u d i e s , h i s s t y l e changed.  R o s l a v e t s developed nality,  1944.  soon a f t e r In the  the  1910s,  a s e r i e s of harmonic p r i n c i p l e s of a new  a p p l i c a b l e to h i s music.  He  to-  i n d i c a t e s having a vague  n o t i o n of these p r i n c i p l e s , even f i n d i n g them to be e v i d e n t i n h i s student c o m p o s i t i o n s posed the f i r s t manifested the next  of 1913,  In e a r l y  s o n a t a and  1919,  he continued  Gojowy c i t e s the songs Volkovo  1 7  Vy  nosits  liubov'  1913,  techniques,  and f o r  to develop  these  kladbishche  (Bo1'shakov), both  as p i e c e s i n which R o s l a v e t s  he com-  some songs, which  i n d i v i d u a l ,compositional  s i x years, u n t i l  by B u r l i u k ) and end  1909-1911.  works, a v i o l i n  h i s own  techniques.  of  "achieved  from a new  (text the har-  5 manic o r d e r i n g which w'as nat d i a t o n i c and which he r e f e r r e d t o as the synthetic  chord  technique."  1 0  These chords,  the b a s i s of  the harmonic o r g a n i z a t i o n i n h i s music, c o n s i s t of s i x t o e i g h t and  more p i t c h e s , a r e t r a n s p o s a b l e  els,  t o a l l twelve chromatic  and can i n c l u d e t e r t i a n chords o-f c o n v e n t i o n a l  tonality.  Such " s y n t h e t i c " chords a r e used not o n l y -for c o l o u r i s t i c poses but, more i m p o r t a n t l y , al  structures.  graphical  article  pur-  to s u b s t i t u t e f o r conventional  Although the p r i n c i p l e o-f c l a s s i c a l  absent -from R o s l a v e t s ' s  lev-  ton-  tonality is  works up t o the time of h i s a u t o b i o -  (1924), " t o n a l i t y  as a concept of harmonic  u n i t y e x i s t s unchanged and appears i n the form o-f the aforement i o n e d synthetic vertically leading.  chords.  . . . " » 1  These chords can be  expressed  or h o r i z o n t a l l y , and i n v o l v e some r u l e s of v o i c e -  2 0  In a d d i t i o n , p r i n c i p l e s of "a new polyphony," and  "new rhythmic forms" were developed, so t h a t , by the end of 1919,  he came t o a f u l l e r  awareness of a l l these  elements of a "new system of sound o r g a n i z a t i o n . "  p r i n c i p l e s as T h i s system,  i n h i s o p i n i o n , was " d e s t i n e d t o u l t i m a t e l y r e p l a c e t h a t of the obsolete c l a s s i c a l der  the i n t u i t i v e  system . . . and t o l a y a f i r m f o u n d a t i o n (in f a c t , only a n a r c h i s t i c )  un-  compositional  methods with which the m a j o r i t y of contemporary composers operateCdl.  . .  In g e n e r a l , R o s l a v e t s ' s music of d i f f e r e n t gist,  i n f l u e n c e s and t r e n d s .  i s c h a r a c t e r i z e d by a number The noted Russian  musicolo-  B o r i s A s a f i e v , d i s c u s s e s one of these: Somewhat a p a r t , i n view of i t s sharp antagonism to contemporary c u r r e n t s , stood the output of R o s l a v e t z . . . . 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, R o s l a v e t z a l r e a d y then set up, i n a f a r - s i g h t ed and d a r i n g manner, the problem o-f c o n s t r u c t i v i s m t h a t we are at present so much concerned with. It was n e c e s s a r y to speak o-f h i s works at that time using a t e r m i n o l o g y that has now become elementary, as: the o r g a n i z a t i o n a l p r i n c i p l e , a s t r i c t l y c o n s t r u c t i v e system, and a b u s i n e s s - l i k e a c c u r a c y i n m a s t e r i n g the material. R o s l a v e t z was, and has remained q u i t e a l o o f from modernism. Though he used a d i f f e r e n t type of m a t e r i a l , R o s l a v e t z f u n d a m e n t a l l y sought the same as Schoenberg --the p r e c i s e laws of a s e v e r e l o g i c of sounds. R o s l a v e t z r e a l i z e d that t r u e c l a s s i c i s m does not l i e in s a f e g u a r d i n g the methods of the " o l d 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 u s i n g a r c h a i c m a t e r i a l , but that the q u e s t i o n i s of e l a b o r a t i n g a s t r i c t system of s o u n d - o r g a n i z a t i 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 p e r f e c t c o m p o s i t i o n s , through a f o r m a t i o n of new material. 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 t h a t was f i r s t i n f l u e n c e d by Cubism and F u t u r i s m and i s genera l l y c o n s i d e r e d to have been i n i t i a t e d in 1913 with the " p a i n t i n g r e l i e f s " — a b s t r a c t geometric c o n s t r u c t i o n s — of V l a d i m i r Tat 1in. A n t o i n e Pevsner and Naum Gabo j o i n e d T a t l i n and h i s f o l l o w e r s in Moscow, and upon p u b l i c a t i o n of t h e i r j o i n t l y w r i t t e n Realist Manifesto i n 1920 they became the spokesmen of the movement. I t i s from the m a n i f e s t o that the name C o n s t r u c t i v i s m was d e r i v e d ; one of the d i r e c t i v e s was "to c o n s t r u c t " a r t . Because of t h e i r a d m i r a t i o n f o r machines and t e c h n o l o g y , F u n c t i o n a l i s m , and modern i n d u s t r i a l m a t e r i a l s such as p l a s t i c , s t e e l , and g l a s s , they were a l s o c a l l e d a r t i s t - e n g i n e e r s . S o v i e t o p p o s i t i o n to the C o n s t r u e t i v i s t s ' a e s t h e t i c r a d i c a l i s m r e s u l t e d i n the group's d i s p e r s i o n . 2 3  Roslavets's  development of a new  class organization, that c h a r a c t e r i z e d musical  and  the  system of p i t c h and  "anti-emotionalism  manifestation  of  constructivism. references  d e n i e s t h a t h i s system  2  in part  a  2 0  i n a number of  t o the composer as a "Russian Schoenberg" and Roslavets  formalism" "*  h i s work, would seem to r e p r e s e n t  J u s t as s i g n i f i c a n t are  ist. "  and  pitch-  sources  as a " S c r i a b i n -  i s influenced  by  7 S c r i a b i n , or by Schoenberg, although musical-formal  r e s p e c t , but  of c o u r s e -far nearer t o me fess,  he admits  i n no wise i d e o l o g i c a l l y  i n d i c a t i o n s of  (in a  . . .) i s  than Schoenberg, whose work, I con-  I have got t o know o n l y c o m p a r a t i v e l y  are i n f a c t  "Skryabin  limited  recently." * 2  There  c o n t a c t between S c r i a b i n  and  Roslavets: N. A. R o s l a v e t s i s regarded as a s t r o n g f o l l o w e r of S c r i a b i n . . . . Indeed, he [ R o s l a v e t s ] c o n s i d e r e d S c r i a b i n as h i s most important t e a c h e r . Apart from the f a c t t h a t R o s l a v e t s f r e q u e n t l y submitted h i s works to S c r i a b i n , t h e r e was no d i r e c t c o n t a c t between the two. I t i s known t h a t S c r i a b i n c o n s i d e r e d R o s l a v e t s ' s a t o n a l works f a v o u r a b l y , 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 p e r i o d , R o s l a v e t s f o r m u l a t e d h i s ideas i n 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 O r g a n i z a t i o n ] , R o s l a v e t s here based h i s t h e o r y on the works of S c r i a b i n ; l i k e w i s e t h i s t h e s i s a l s o c o n t a i n s c o n s i d e r a t i o n of the works of A. Schoenberg. R o s l a v e t s observed with S c r i a b i n c e r t a i n sound complexes and d e s c r i b e d them as "synt h e t i c chords." T h i s t h e o r y 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 i n a s e r i e s of symphonic and chamber music works by R o s l a v e t s of the p e r i o d from 1919 t o 1 9 2 4 . ^ However, a c c o r d i n g to Schwarz, R o s l a v e t s ' s V i o l i n (1913) was  the f i r s t  S t r i n g Quartet No. In f a c t , tional  Sonata  a t o n a l work by a Russian composer, and  3 of 1920  employed a "tone row"  his  technique.  2 8  t h e r e are a number of s i m i l a r i t i e s between the composi-  t e c h n i q u e of R o s l a v e t s with t h a t of Schoenberg:  [ R o s l a v e t s ] developed the [ " s y n t h e t i c chord"] technique i n piano m i n i a t u r e s , so t h a t by 1915 i t had become a 12-note system, embracing concepts of 12note s e r i a l ism and m i r r o r symmetry. In the V i o l i n Concerto (1925) he added the p r i n c i p l e of complement a r y p i t c h - c l a s s groups which t o g e t h e r form 12-note sets. H i s s e n s i t i v e , c o n s i s t e n t 12-note w r i t i n g has many s i m i l a r i t i e s with t h a t of Schoenberg, whose work, however, R o s l a v e t s d i d not encounter u n t i l 1923. R o s l a v e t s ' s works "found  only l i m i t e d  response.  Even-  3 tually,  he seemed to r e l e n t  in h i s d o c t r i n a i r e a p p r o a c h . "  R o s l a v e t s ' s s t y l e changed to a more a c c e s s i b l e t o n a l  3 0  style.  R o s l a v y e t s ' s C R o s l a v e t s ' s ] Marxism and h i s assoc i a t i o n with communistic t h e o r i e s and p r a c t i c e c o u l d not f a i l to a f f e c t h i s c o m p o s i t i o n s . He c o n s i d e r e d i t h i s duty to come out as composer of r e v o l u t i o n a r y music. B e g i n n i n g with 1913, r e v o l u t i o n a r y music i n R u s s i a was c r e a t e d i n bulk and p o o r l y , and i n a c c o r dance with s p e c i f i c a t i o n s and r e q u e s t s from the r e s p e c t i v e o r g a n i s a t i o n s . R o s l a v y e t s was the f i r s t "convinced" composer of music f o r the p r o l e t a r i a t . He s e t h i m s e l f 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 a b l y poor s t y l e and t a s t e , u s u a l l y d e r i v e d from the r e p e r t o r y of the o p e r e t t a and " l i g h t " music. Even f o r the p r o l e t a r i a t R o s l a v y e t s endeavoured to w r i t e m a s t e r l y and complex music. But i n s p i t e of h i s t h e o r e t i c premises t h a t the most complex music i s w i t h i n the grasp of the workingman, i f i t but "organ i s e s t o n a l m a t t e r " w e l l , R o s l a v y e t s f i n a l l y had to make a number of c o n c e s s i o n s , and h i s r e v o l u t i o n a r y c o m p o s i t i o n s , w r i t t e n f o r workmen's c l u b s , d i f f e r s t r o n g l y i n s t y l e from h i s " s e r i o u s " c o m p o s i t i o n s . E v e r y t h i n g i s s i m p l e r , more p r i m i t i v e and h i s usual complex musical language (the m o d e r n i s t i c one) g i v e s way to a p l a i n e r one. As an i n t e r m e d i a t e essay, R o s l a v y e t s wrote s e v e r a l songs to r e v o l u t i o n a r y t e x t s by present-day Russian poets and some of bygone years, preserving h i s s t y l e i n t a c t . Such are Songs of the Labouring Pevolutionr two  structural  Professions,  Roslavets's s t y l e  i n the c a n t a t a October  Songs  of  the  their  (1924) was  described  " r e m i n i s c e n t of S t r a u s s  as  and  3 S B  Schwarz mentions t h a t , i n the lighter  The  1  "somewhat too s e n t i m e n t a l " and Wagner. "  and  volumes which cannot be denied musical m e r i t s . "  1930s, R o s l a v e t s  t h e a t r e music, as w e l l as c o m p o s i t i o n s  e s p e c i a l l y Uzbek, m u s i c .  3 3  tion-propaganda music, and, l i s t i n g s of p i e c e s by tonal compositions  wrote  based on -folk,  In a d d i t i o n , R o s l a v e t s wrote a g i t a as suggested  the composer  i n the 1930s and  by Gojowy*s r e c e n t  (see Appendix A),  classical  1940s. "*  C o n s i d e r i n g these o b s e r v a t i o n s , one  3  might  tentatively  9 i d e n t i f y four periods in Roslavets's compositional  career,  namely:  (2)  1919,  (1) an e a r l y , student  a post-Conservatory  compositional period  technique  p e r i o d , up to 1912;  or development p e r i o d i n which h i s  was  developing;  t h a t i n c l u d e s both p o l y p h o n i c  e x p r e s s i o n s of tone complexes) and, more Romantic s t y l e s  (3) 1919-1925, a mature  styles  er's  Compositions  songs and pour  phase of h i s c a r e e r .  t h e t i c chord  technique  strict  technique  two  chord" or p i t c h - c l a s s complex s t r u c t u r e s of a p i e c e . composed towards 1915,  R o s l a v e t s developed  h i s syn-  as Trois  Compo-  p i e c e s of the s e t i n v o l v e a  (PCC)  whereby one " s y n t h e t i c determines  the harmonic  Moreover, such p i e c e s , e s p e c i a l l y e x h i b i t c e r t a i n f e a t u r e s of  sowjetiscfte  Musi A  numerous a r t i c l e s on Russian musical those d e a l i n g s p e c i f i c a l l y  those  twelve-tone  der  20er  and  Ja/>re,  developments,  the former  with R o s l a v e t s , " present 3  i n c l u d e s an a n a l y s i s of Trois  George P e r l e ' s b r i e f Composition  English-language  analytical and  Atonality  his  including  d e t a i l e d p u b l i s h e d s t u d i e s of the composer's l i f e and  in Serial  post-  3 d  Gojowy's Neue  date;  (4)  songs.  i n the second,  i n piano m i n i a t u r e s , such  the f i r s t  and  (1914) r e p r e s e n t s the compos-  a p p l i c a t i o n of the technique  ser i a l i s m .  1925,  i n c l u d i n g the w r i t i n g  music based on f o l k  piano  Conservatory  in f a c t ,  towards 3  development of c o m p o s i t i o n a l  sitionsi  linear  (e.g., use of T r i s t a n h a r m o n i e s ) ; *  agitation-propaganda Trois  (involving  especially  1925-1944, a p e r i o d of t o n a l c o m p o s i t i o n s , of  1912-  the most works to  Compositions.  d i s c u s s i o n of the t h r e e p i e c e s r e p r e s e n t s one  a n a l y s e s of R o s l a v e t s ' s  music.  3 0  of the  first  IO  Although Gojowy and Trois  as PCCs a s s o c i a t e d  Compositions  sition  P e r l e together  with the p i e c e s ,  transpo-  l e v e l s o-f these PCCs (which -form the bases o-f harmonic  units),  and  general  d e t a i l s concerning the p i e c e s present  c h a r a c t e r i s t i c s of R o s l a v e t s ' s p i t c h - c l a s s (PC)  are p r o v i d e d .  Two  e x c l u s i v e l y with the  deal  presenting  the o b s e r v a t i o n s  c o n t e n t , and  the o r d e r i n g  chords" w i l l  a l s o be  " s y n t h e t i c chord"  examined  within  and  i n some d e t a i l .  p i t c h e s , and  a s p e c t s of o c t a t o n i c and  serial  Chapter technique,  their  PC  individual "synthetic Chapter Three  deal with t o n a l i t y as t h a t concept a p p l i e s to of PCs  pitch  P e r l e as a b a s i s f o r  Harmonic s u c c e s s i o n s ,  of PCs  in the  and  been t r e a t e d elsewhere.  of Gojowy and  further analytical studies.  organization  few  pitch organization  t h e s i s i s a comprehensive i n v e s t i g a t i o n of PC beyond what has  will  and  style,  Hence, the primary o b j e c t i v e of  organization,  will  identi-fy such a s p e c t s o-f  Roslavets's  Chapter Four w i l l  organization  that apply  treat 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 J e r s e y : 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 i n d i c a t e s the s i g n i f i c a n c e of Roslavets: "The importance of R u s s i a as a c e n t r e f o r p r o g r e s s i v e t h i n k i n g i n the a r t s at the t u r n of the century has only r e c e n t l y been f u l l y a p p r e c i a t e d . . . . The a t o n a l V i o l i n Sonata and  proto-serial  Three  Piano  Pieces  of  Rosslavetz  [Roslavets],  both d a t i n g from 1913-14, and the m e c h a n i s t i c c o m p o s i t i o n s of Mossolov CMosolov] and Desschevov CDeshevovl i n the t w e n t i e s help to p l a c e i n some s o r t of p e r s p e c t i v e the second decade achievements of S t r a v i n s k y and P r o k o f i e v . (Jim Samson, Music in Transition:  [London:  A  J . M.  Study  of  Dent and  Tonal  Son,  Expansion  and  Atonality,  1900-1920  19773, 73-74.)  2. The d e s c r i p t i o n of "minor e x p e r i m e n t a t o r " i s found i n B o r i s Schwarz, Music and Musical Life in Soviet Pussia: Enlarged  11  1917-1981, 2nd, enlarged ed. (Bloomington, Indiana: Indiana U n i v e r s i t y Press, 1983), 9 ( h e r e a f t e r c i t e d as Mus.  Edition Soviet  Puss i a) .  3. Information i n t h i s chapter on R o s l a v e t s i s taken from the f o l l o w i n g authors (see b i b l i o g r a p h y -for a d d i t i o n a l information): N i k o l a i R o s l a v e t s , D e t l e f Gojowy, Lazare Saminsky, and Leonid L. Sabaneyeff CSabaneev]. Encyclopaedic sources include: New  Grove  Dictionary  "Roslavets"  of  Music  and  Musicians,  6th  ed.,  s.v.  ( h e r e a f t e r c i t e d as Grove, 6th ed.)J Die Musik in und Gegenwart, s.v. "Ros1awetz" ( h e r e a f t e r c i t e d as  Geschichte MGG); Das Grosse Lexikon der Musik, Baker's Biographical Dictionary of  s.v. "Ross1awetz"i Musicians, 7th ed.,  and s.v.  "Roslavetz". 4. Lazare Saminsky, Music of Our Day: Essentials and (New York: I n t e r n a t i o n a l P u b l i s h e r s , 19275 New York: Da Capo, 1975), 264. Concerning the date of b i r t h , some sources i n d i c a t e the J u l i a n calendar date ( i . e . , December 24, 1880). C u r i o u s l y , Das Grosse lexikon der Musik i n d i c a t e s January 4, 1881 (December 23, 1880, J u l i a n 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 i n the v i l l a g e of Dushatino, and laterl i v e d and worked in Konotop, both communities i n the former government d i s t r i c t of Chernigov i n the Ukraine. ( R o s l a v e t s , "Nik. A. R o s l a v e t s o sebe i svoern t v o r c h e s t v e , " CNik. A. R o s l a v e t s on Himself and His Work], Sovremennaia muzyka CContemporary Music], Prophecies  5  C1924]: 132-133 Ctrans.  i n Gojowy, Neue  sowjetische  Musik  der  (Laaber: Laaber-Ver1ag, 1980), 395; h e r e a f t e r c i t e d as "Ros1avets"-NsM.]) Apparently, Dushatino was renamed Surazh, now p a r t of the Briansk Oblast [ r e g i o n ! , based on i n f o r m a t i o n in  20er  Jahre  Piemann  Musiklexikon:  "Ross 1awets", and "Rosslawets".  £rganzungsband,  in Das  Grosse  1975  Lex ik on  5. R o s l a v e t s , "Ros1avets"-NsM,  der  ed., Musik,  s.v.  s.v.  395.  6. Saminsky echoes R o s l a v e t s in i n d i c a t i n g t h a t , "while at the c o n s e r v a t o r y he [ R o s l a v e t s ] was d i s l i k e d f o r r a d i c a l i s m ." and that once he -finished h i s s t u d i e s , he " r i d himself of the conservatory p r e s c r i p t i o n s very q u i c k l y . " (Saminsky, Music of Our Day, 264; see a l s o R o s l a v e t s , "RosIavets"-NsM, 396.) 7. R o s l a v e t s , "Ros1avets"-NsM, 396-393. 8. Gojowy's i n d i c a t i o n that a c e l l o sonata was composed in Khar'kov, in March of 1921, suggests that R o s l a v e t s was l i v i n g in or near the town b e f o r e h i s d i r e c t o r s h i p . (Gojowy, " N i k o l a j Andreevic Roslavec, e i n f rCiher 2w6 1 f tonkompon i s t , " Die Musikforschung, 22/1 [January-March 19691: 37.) I n t e r e s t i n g l y , one source provides i n f o r m a t i o n on the founding in 1922 of a school of composers at the Khar'kov Musical I n s t i t u t e ( l a t e r the cons e r v a t o r y ) by S. Bogatiryov, although there i s no mention of R o s l a v e t s . (Grove, 6th ed., s.v. "Khar'kov".)  12  9. Schwarz, Mus. Soviet Russia, 86. Among h i s accomplishments was the f i r s t Russian i n t r o d u c t i o n t o Schoenberg's Pierrot Luna ire. ("Lunnly P'yero Arnol'da Shyonberga," K novim beregam 3 [19233: 28; r e f e r e n c e i n S w e , 6th ed. , s.v. "Roslavets".) 10. Grove,  ibid.  11. "[The3 ACM's j o u r n a l Sovremennaia Muzyka ceased p u b l i c a t i o n i n March 1929, f o l l o w e d i n 1930 by the demise of the exc e 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 c o n s e r v a t o r y circles. Only the brash v o i c e of Pro letarsk i i fiuzyk ant [ j o u r n a l of RAPM3 was l e f t , p r e t e n d i n g t o speak f o r a l l the musicians. In the meantime, many important members had abandoned the ACM, among them Miaskovsky, and the o r g a n i z a t i o n simply ceased to f u n c t i o n even p r i o r t o i t s d i s s o l u t i o n i n 1931." (Schwarz, Mus. Soviet  Russia,  58-59.)  12. Percy A. Scholes, ed., The Oxford Companion to Music, 9th ed. (New York, Toronto: Oxford U n i v e r s i t y Press, 1955), 895. R o s l a v e t s , i n h i s a u t o b i o g r a p h i c a l a r t i c l e ("Roslavets"NsM, 398), argued h i s a e s t h e t i c a l p o s i t i o n u s i n g "a M a r x i s t defence of an a e s t h e t i c of musical positivism, which opposed the i d e a of an o b j e c t i v e l y d e f i n a b l e emotional q u a l i t y and which saw the c r e a t i v e act as a moment of the human intellect's highest exertion,  l o o k i n g forward  the form of the conscious system of tone organization."  t o the subconscious  and t o music based  "Roslavets".)  (Gojowy,  Grove,  being  realized  on a new  6th ed.,  in  fixed s.v.  13. Schwarz, Mus. Soviet Russia, 86. There a r e no i n d i c a t i o n s i n the l i t e r a t u r e to date that R o s l a v e t s i n f a c t wrote an opera, much l e s s the f i r s t n a t i o n a l Uzbek opera. Curiously, his former composition and o r c h e s t r a t i o n teacher, Sergei V a s i l e n k o , in c o l l a b o r a t i o n with Uzbek composer M. A s h r a f i , i s c r e d i t e d with t h i s accomplishment: "In 1938 he [ v a s i l e n k o ] worked i n Tashkent on the f i r s t Uzbek opera, Burian [The Snowstorm3." (Grove, 6th ed., s.v. "Vasilenko.") 14. One such "unconfirmed r e p o r t " about the death of R o s l a v e t s i n S i b e r i a i s given i n MGG, s.v. "Rosiawetz". 15. Gojowy, "Half Time f o r N i k o l a i R o s l a v e t s (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; q u o t a t i o n from In the World of Music [V mire muzyki3, (Moscow, 1981): 5. Gojowy a l s o r e f e r s to another source concerning the a c t i v i t i e s of R o s l a v e t s i n the 1930s. iMuzyka I'naia entsiklopediia, [Moscow, 19783, s.v. "Roslavets" [ v o l . 4, c o l s . 711-7123.) 16. Grove,  6th ed., s.v. "Roslavets".  Interestingly,  13 Montagu Montagu-Nathan s t a t e s t h a t R o s l a v e t s had been " i n f l u enced a l i t t l e by Rebikof. . . . " (Montagu Montagu-Nathan, Contemporary Russian Composers [London: C e c i l Palmer and Hayward, 1917; Westport, C o n n e c t i c u t : 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 s c a l e 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".) T h i s "earned him a r e p u t a t i o n as the -finest Russian i m p r e s s i o n i s t , and he a l s o became known as the -father o-f Russian modernism." (Grove, 6th ed., s.v. "Rebikov".) 17. R o s l a v e t s , "Ros1avets"-NsM, 396-398. 18.  Grove,  6th  ed.,  s.v.  "Roslavets".  19. R o s l a v e t s , "Roslavet5"-/Vs/>i 396-397. The r e f e r e n c e to " p i t c h " i s c l a r i f i e d i n Chapter Two with d i s c u s s i o n of the term " p i t c h - c l a s s " (PC). 20. I b i d . , 397. Saminsky s t a t e s : "From h i s harmonic found a t i o n he evolved s e v e r a l years ago a p e c u l i a r system of v o i c e l e a d i n g and a new polyphony which led to h i s tonal organization."  (Saminsky, Music  of  Our  Day,  265.)  21. R o s l a v e t s , "Ros 1 avets "-/V^/9, 397. 22. B o r i s A s a f i e v , Russian Music from the Beg inn ing of the Century, t r a n s . A l f r e d J . Swan (Ann Arbor, Michigan:. J . W. Edwards, 1953): 262.  Nineteenth  23.  The  New  Encyclopaedia  Britannica,  15th  ed.,  s.v.  "Constructivism". I n t e r e s t i n g l y , M. Montagu-Nathan i n d i c a t e s R o s l a v e t s ' s i n t e r e s t i n a r t i s t i c a s p e c t s a s s o c i a t e d with the movement: "Roslavets i s a v e r s a t i l e composer and e v i d e n t l y a man of c u l t i v a t e d t a s t e s and wide sympathies. . . . As t o e x t e r nal symptoms i t i s worthy of mention t h a t R o s l a v e t s a f f e c t s c o l oured ink, a circumstance which w i l l have some s i g n i f i c a n c e f o r students.of l a t t e r - d a y tendencies; more s t r i k i n g than t h i s are the C u b i s t designs which adorn the covers of some of h i s p i e c e s . " (Montagu Montagu-Nathan, Contemporary Russian Composers,  315.)  24. Leonid Sabaneyeff [Sabaneevl, Modern Russian Composers, t r a n s . Judah J a f f e (New York: I n t e r n a t i o n a l P u b l i s h e r s , 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 popul a r i n the l a t e r 1920s, but none was as h i g h l y acclaimed as Mosolov's Iron Foundry, c a l l e d a mighty hymn to machine work by one S o v i e t 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, v o l . 1, p.  14 169.) Gerald Abraham l i k e w i s e r e f e r s to R o s l a v e t s as an a n t i romantic c o n s t r u c t i v i s t . (Abraham, "The Reaction A g a i n s t Romanticism: 1890-1914," New Ox ford History of Music, ed. Martin Cooper [Toronto: Oxford U n i v e r s i t y Press, 19743, v o l . 10, p. 137. ) 26. Abraham,  ibid.  27. Michael G o l d s t e i n , " S k r j a b i n und d i e S k r j a b i n i s t e n . Das Schaffen S k r j a b i n s und s e i n e r N a c h f o 1 g e r — I n d u k t i o n 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), v o l . 32-33 (September 1983): 181 (my translation). G o l d s t e i n a l s o i n c l u d e s a s h o r t a n a l y s i s of R o s l a v e t s ' s Uetre nalet i te (1913; text by A. Blok) on p. 188. Other sources i n d i c a t e R o s l a v e t s ' s a s s o c i a t i o n with S c r i a b i n ; f o r example, S i g f r i e d S c h i b l i i n c l u d e s R o s l a v e t s i n "a c l o s e c i r c l e of S c r i a b i n i s t s . " ( S i g f r i e d S c h i b l i , Alexander Skrjabin und seine Geistes.  my  Musik.  Grenxuberschreitungen  [Munich, translation.)  Zurich:  28. Schwarz, Mus. 29.  Grove,  6th  Soviet  ed.,  30. Schwarz, Mus.  s.v.  Soviet  31. Sabaneev, Modern  eines  prometheischen  R. P i p e r and Co. V e r l a g , 19833, 348; Russia,  86.  "Roslavets". Russia,  Russian  86.  Composers,  206-207.  32. Schwarz, Mus. Soviet Russia, 86; quotation from E. Braudo, fl/'e Musik, 20/7 ( A p r i l 1928): S3. Although Schwarz ind i c a t e s 1927 as the date f o r October, i t was a c t u a l l y composed in 1924. 33. Schwarz, /?us. Soviet  Russia,  86.  34. Gojowy, "Half Time," 217-219. 35. Gojowy s t a t e s : "Around 1920 (Third Quartet, Meditahe again changes from the polyphony and c o n t r a p u n t a l forms to a m i l d e r Tristan harmony with the V i o l i n Concerto (1925)." (Gojowy, Neue sowjetische Musik, 985 my t r a n s l a t i o n . ) tion),  36. sowjetische  Grove,  6th  Musik,  ed.,  s.v.  " R o s l a v e t s " ; Gojowy,  Neue  138.  37. Gojowy, "Roslavec," Die Musikforschung, 22-38, and "Half Time," 211-220.  22/1  (1969):  38. George P e r l e , Serial Composition and Atonality, 4th rev. ed. (Berkeley, Los Angeles: U n i v e r s i t y of C a l i f o r n i a Press, 1977), 43-44.  I  5"  CHAPTER  THE  INTERVAL-CLASS  COMPLEX  Introduction  As  the  pioneering to  them  which  analyses studies  o-f  by  the  -for p r e l i m i n a r y  they  both  Detlef work  and  TWO  IN  COMPOSITIONS  Terminology  Gojowy a-f  insights  TROIS  and  George  Roslavets, into  Trois  we  Perle turn  are initially  Compositions,  with  deal.  The c o m p o s i t i o n a l s y s t e m o-f m o s t e a r l y w o r k s b y R o s l a v e t s i s b a s e d o n 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 ent i r e tone c o l l e c t i o n in a given time-span. A g i v e n t o n e complex d e t e r m i n e s which t o n e need or need not sound, a l t h o u g h not in which order, octave, or motive. Within the chromatic s c a l e , there 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 possible complex. T h i s s y s t e m was not i n v e n t e d and u t i l i z e d exclus i v e l y b y N. A. R o s l a v e t s , b u t i n d e e d , i-f o n e bel i e v e s h i s own t e s t i m o n y , was developed independently 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  recently,  Gojowy  states:  [Roslavets's s y s t e m ] was b a s e d o n c h o r d s o-f s i x to e i g h t o r m o r e 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 to expand. These " 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 a n d invariable interv 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 ] the 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 a n d R o s l a v e t s , the 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 de-fined o n l y by its intervallic structure. 2  More  specifically,  able  tone  Gojowy's  complexes"  transposition  levels  analysis  associated  with  (T-levels)  of  i d e n t i f i e s the the  each  "transpos-  three  pieces,  complex  from  and  which  the pitch  16 collections  i n the r e s p e c t i v e p i e c e s a r e d e r i v e d .  P e r l e ' s study a listing  i n Serial  i n musical  Composition  and  Atonali  ty  includes  n o t a t i o n of the " s e t s " or t r a n s p o s a b l e  tone  complexes a s s o c i a t e d with each p i e c e , an a n a l y s i s o-f the PC cont e n t o-f a s h o r t e x c e r p t o-f " I I I " and i d e n t i f i c a t i o n plex T - l e v e l s ,  and a b r i e f  Ros1avets's c o m p o s i t i o n a l  of tone com-  d e s c r i p t i o n of the s a l i e n t p o i n t s of technique,  p a r t of which i s quoted  below: In h i s Trois Compositions f o r piano, R o s l a v e t z employs an independent s e t f o r each movement. . . . As i n S c r i a b i n ' s works, the s e t f u n c t i o n s s i m u l t a n e o u s l y as s c a l e and chord. Transpositions are used much more f r e e l y , p i v o t a l c o n n e c t i o n s b e i n g employed, i n g e n e r a l , merely as a means of immediate assoc i at i o n . 3  To begin, some c l a r i f i c a t i o n required  to f a c i l i t a t e f u r t h e r a n a l y s i s .  complex," an important ganization  pitch-classes  tone  (PC)  or-  (Gojowy),  i t i n v o l v e s a c o l l e c t i o n of  (PCs) and hence i s more a c c u r a t e l y termed a  posed and employed  (PCC).°  To understand  how PCCs a r e t r a n s -  i n the music, Ex. 2 - l a i l l u s t r a t e s m. 1 of  with the p i t c h e s segmented  into c o l l e c t i o n s .  t i o n s can be t e n t a t i v e l y d e s i g n a t e d multaneous o c c u r r e n c e s cal  s  by t h e d i f f e r e n t  ( R o s l a v e t s ) , "Tonkomplex"  Specifically,  " p i t c h - c l a s s complex"  "I",  The " t r a n s p o s a b l e  i n R o s l a v e t s ' s music, i s d e s i g n a t e d  " s e t " . (Per le) .  terminology i  aspect of p i t c h and p i t c h - c l a s s  a u t h o r s as " s y n t h e t i c chord" and  and a d d i t i o n a l  as harmonies, g i v e n the s i -  of p i t c h e s i n v o l v e d and g e n e r a l l y v e r t i -  o r i e n t a t i o n of p i t c h e s i n most c o l l e c t i o n s . ' *  the p i t c h - c l a s s e s (PCs) r e p r e s e n t e d 2 - l a a r e ordered  These c o l l e c -  In Ex.  2-lb,  i n the c o l l e c t i o n s of Ex.  t o 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 through t r a n s p o s i t i o n . the  PC i n t e r v a l  Example 2-1. (a)Pitch  v  Each ordered PC i s numbered a c c o r d i n g to  i t -forms with the - f i r s t PC o-f the c o l l e c t i o n .  Pitch collections PCC T - l e v e l s .  i n " I " , m. 1, and c o r r e s p o n d i n g  c o l l e c t i o n s i n " I " , m. 1:  (b) T-O  T-3  0 1 3 4 6 8  910  0 1 3 4 6 8 9  0 1 3 4 6 8 9  13 3 3 4 4 21  13 3 3 4 4 2)  INTERVAL VECTOR: 14 S 6 S 3 31  Segmentation o-f p i t c h e s tify  the PCC T - l e v e l s ,  T-10  into c o l l e c t i o n s  as shown  ted  i n Gojowy's a n a l y s i s  the  s u c c e s s i o n s o-f PCC T - l e v e l s  Moreover, both P e r l e associated  o-f Trois  collections i s a relatively erally  i n Ex. 2-1, i s p a r t i a l l y Compositions  includes  the t r a n s p o s a b l e PCCs  But, segmentation o-f p i t c h e s  into  simple matter anyhow, g i v e n the gen-  homophonic t e x t u r e o+ the p i e c e s ,  l e c t i o n s a p p e a r i n g as s i m u l t a n e i t i e s tions thereof.  which  indica-  (and measure i n d i c a t i o n s ) .  and Gojowy i n d i c a t e  with each piece.''  i n o r d e r t o iden-  with many o-f t h e c o l -  or recognizable  arpeggia-  More i m p o r t a n t l y however, the time-spans and  temporal placements of the p i t c h c o l l e c t i o n s g e n e r a l l y  coincide  18 with the notated meter,  i n the sense  p o i n t s of many harmonies correspond  t h a t the i n i t i a l  attack-  t o the b a r l i n e or to conven-  tional  t i m e - p o i n t s o-f m e t r i c s u b d i v i s i o n w i t h i n the bar  in 4/4  meter, time-spans i n i t i a t e d  on the second,  (e.g.,  third,  or  fourth "beats")." In as T-O  Ex.  2 - l b , the - f i r s t harmony i n m.  1 o-f " I " i s d e s i g n a t e d  because i t i s the - f i r s t o-f the p i e c e , the - f i r s t  o-f the PCC. the sense  More i m p o r t a n t l y , i t i s a r e f e r e n t i a l  t h a t , as l a t e r a n a l y s e s w i l l  b e g i n s and "II"  and  "III",  respectively),  and,  "I",  i t o c c u r s most f r e q u e n t l y and  harmony i n  show, t h i s PC  ends the p i e c e (as do the i n i t i a l of any  T-level  collection  PC c o l l e c t i o n s of  T-level  of the PCC  has the g r e a t e s t t o t a l  of  time-  span . A l s o i n Ex. lection  i n m.  2 - l b , the  1, with PCs  they -form with the f i r s t second to  and  third  the f i r s t ,  (i.e., tion, ted,  numbered a c c o r d i n g to the PC PC of each s c a l e ,  harmonies of m.  the i n t e r v a l  based  interval  i l l u s t r a t e s how  i n T-3  and  T-10).  v e c t o r s " of the t h r e e harmonies are  (IC)  1 0  have the same IC The  col-  the  1 are t r a n s p o s i t i o n a l 1 y r e l a t e d  not b e i n g transposed  to i l l u s t r a t e t h a t T-O  T-10  of each  i n terms of PC c o n t e n t , with one minor e x c e p t i o n  C i n T-0  interval-class  is similar  content t o T-3  In a d d i indica-  to a l i m i t e d extent in  and  to T-10,  w h i l e T-3  and  content.  p a r t i c u l a r o r d e r i n g of T-O  PCs,  s t a r t i n g with D,  is  i n p a r t on P e r l e ' s p r e s e n t a t i o n of PCCs f o r each p i e c e  (each at T-O), Ex.  l i s t i n g of ordered PCs  2-lb.  shown i n Ex.  2-2  with ordered PCs  numbered as i n  19 Example 2-2.  T r a n s p o s a b l e PCCs of " I " , " I I " , and " I I I " , as i l l u s t r a t e d by P e r l e , with numbering o-f PCs added.  PCC OF T , T-0:  0  1  3  4  8  9 (101  0  (1)  3  4  8  9  11  1  3  4  8  (9) (10)  tin  P C C O F •ii*, T - O : V  P C C O F -in-, T - O :  0  The b r a c k e t e d PCs i n each ordered c o l l e c t i o n r e p r e s e n t those PCs or t r a n s p o s i t i o n s t h e r e o f not a p p e a r i n g with every Tlevel,  an i s s u e which w i l l  be -further i n v e s t i g a t e d  lowing s e c t i o n o-f t h i s c h a p t e r . "III"  Given  i n the -fol-  t h a t t h e PCCs of " I " and  a r e i n the prime -form, when one e x c l u d e s -from c o n s i d e r a -  t i o n t h e v a r i a n t PCs, and g i v e n the s i m i l a r i t i e s o-f the t h r e e t r a n s p o s a b l e PCCs, D i s the - f i r s t PC o-f the ordered PCC at T-0 for  " I " , and l i k e w i s e C#/Db i s the f i r s t  and  G f o r the PCC of " I I I " .  illustrated  Based on the PC numbering scheme  i n Exx. 2-1 and 2 - 2 ,  11  any PC i n a g i v e n T - l e v e l i s  d e s i g n a t e d with a number, an "element" its  not  number,  i n o r d e r t o show  r e l a t i o n s h i p s t o t h e o t h e r PCs of t h a t T - l e v e l .  n e a r l y every T - l e v e l will  f o r the PCC of " I I " ,  occurrence  (i.e.,  be d e s i g n a t e d with element number  collection  One PC i n  i n t h e music)  "O", although t h i s does  imply any g r e a t e r s i g n i f i c a n c e t o t h i s PC.*-  2  Given  that  20  c e r t a i n elements do not appear Ex.  2 - 2 , these w i l l  likely  l e c t i o n s of the p i e c e s . ment i n one  T-level  i n the PCCs (at T-O)  not be r e p r e s e n t e d  O-f course,  as shown i n  i n the p i t c h  a PC which i s a g i v e n  cannot be the same element  colele-  i n another  T-  1eve1. Because the PCC invariable  interval lie  to a l l twelve be r e f e r r e d Such an uent  as R o s l a v e t s uses i t has a " s p e c i f i c s t r u c t u r e " which can  degrees of the chromatic  to i n the t h e s i s as an  (as shown i n Ex.  ascending  scale.  The  interval  component PCs  such  identities  A g i v e n ICC constitute  a PCC  the  i s transposable  by v a r i o u s PCCs.  "T-x", "x"  are a s s i g n e d  In o t h e r words, an  ( I t i s understood  ends a g i v e n p i e c e  s i m p l e way  of  registral  (T-O).  registral  Compositions.  d e r i n g of elements can  and  be  t h a t the o p e r a t i o n T-levels  location.  The  PCC  Hence, the T - l e v e l  i n d i c a t i n g a harmony's PC content  i n Trois  that  ICC may  of the r e f e r e n t i a l  most i f not a l l of a g i v e n T - l e v e l * s PCs harmony  nec-  r e p r e s e n t i n g the number of semitones  b e g i n s and  and  an  of a PCC  i n the sense t h a t the PCs  of t r a n s p o s i t i o n above the T - l e v e l  temporal  For  are a b s t r a c t e d as  of t r a n s p o s i t i o n does not a p p l y to i n t e r v a l s or ICs.)  specific  constit-  i n the music.  i t are t r a n s p o s a b l e .  are d e s i g n a t e d  will (ICC).  vector).  IC r e l a t i o n s h i p s between PCs  remain the same when those PCs  temporal  realized  4 3  . . .  i n t e r v a l - c 1 ass complex  2-1 with the  purposes of c l a s s i f i c a t i o n ,  and  scale,"  transposed  ICC c o n s i s t s of an ensemble of ICs spanning  PCs  essarily  "be  and  that is a  independent of  With some e x c e p t i o n s , appear i n any  temporal  and  given  registral  u s u a l l y does vary with every  or-  harmony  21 or T - l e v e l .  The d e s i g n a t i o n  i n t h i s t h e s i s o-f a T - l e v e l  g i v e n measure i s used t o r e f e r level with  or harmony.  t o the PC c o l l e c t i o n o-f t h a t T-  I t i s o f t e n not necessary  the temporal and r e g i s t r a l T h i s chapter  system,  will  t o be concerned  c o n f i g u r a t i o n s of PCs.  p r o v i d e more i n s i g h t  i n c o r p o r a t i n g the a n a l y t i c a l  i n t o R o s l a v e t s ' s ICC  o b s e r v a t i o n s of Gojowy and  P e r l e as a b a s i s f o r f u r t h e r d e t a i l e d examination tional  technique  in a  i n the p i e c e s .  The f i r s t  of composi-  p a r t of t h i s  chapter  examines the ICCs of the t h r e e p i e c e s and how the harmonic u n i t s are d e r i v e d from these  ICCs.  monic s u c c e s s i o n s and T - l e v e l t i o n s deal with  The second p a r t occurrences,  T - l e v e l s as t o PC c o n t e n t ,  ear element o r d e r i n g w i t h i n i n d i v i d u a l successions  i n v o l v i n g adjacent  i n v e s t i g a t e s har-  w h i l e the f i n a l and v e r t i c a l  and  seclin-  harmonies and i n element  harmonies.  22 The  ICC  in  Gojowy i n d i c a t e s that based on  The  observations  Compositions  o-f these three PCC  t h a t we  piece  We  can  are  each  to be  a  Perle generally  clarify  i n a l l t h r e e p i e c e s by  the  con-  organiza-  segmenting each  i n t o PC c o l l e c t i o n s .  o-f " I " P e r l e and  Gojowy c i t e the same PC  collection  -for the harmonies o-f " I " , except that P e r l e eted  v a r i a n t element  2-2). not  pieces  consider  o-f Gojowy and  with some minor e x c e p t i o n s .  t i o n o-f the PC m a t e r i a l  ICC  two  a s i n g l e transposable  s i n g l e ICC. cur,  Trot's  The  "10"  (i.e.,  b r a c k e t e d PCs  C i n T-O,  in Perle's  i n c l u d e s the  These are d e r i v e d elements, as tematic tion. "  not  brackin  Ex.  ICCs are those elements He  i n d i c a t e s that  l e s s c o n s i s t e n t l y employed.  through the chromatic  i n S c r i a b i n ' s Seventh  basis  as r e p r e s e n t e d  a p p e a r i n g with e v e r y T - l e v e l o c c u r r e n c e .  " C v l a r i a n t s o-f the s e t are more or  as the  Sonata,  i n f l e c t i o n of but  through the  o m i s s i o n of c e r t a i n components of the b a s i c  setsys-  forma-  1 0  The  ICC  of  t i o n of p i t c h e s indicated)  " I " i s presented i n t o ICC  i n Ex.  2-3b. «* 1  T-levels  in Ex.  2-3a,  and  the  ( i n s c a l e form, with  segmentaT-levels  23 Example 2-3.  ICC of* " I " , with  T-level  successions.  (a)T-O PCCs o-f the ICC o-f " I " : n [no ELEMENT:  0  (b)Pltches  1  3  4  6  8  o-f " I " segmented  910  i n t o PCCs a t v a r i o u s 121  MEASURE: ( 1 ) PITCHES: A  2 SCALAR REPRESENTATION OF P C C : T-LEVEL: O 3  0  10  T-levels:  24 Example 2-3b c o n t i n u e d . (41  (31  (61  25 Example 2-3b  continued.  (10,111  (12)  [131  ¥*f-—STV•  6  • 1  ,  r -—  Vr'*"  r~7zb*  ffr*-—  Some harmonies c o n t a i n as p a r t o-f the PCC T-ii);  B5  (m.  7,  Gojowy d e s c r i b e s :  T-ll);  and  Eb4  (m.  C5 7,  (m.  "IO"  but  l a s t o-f these anomalous p i t c h e s , Eb4  which i s not "10"  PCs  i n h i s v e r s i o n o-f the T-O  -found with any  in question  although element the other  "2"  hand, the  other  (an exact  understood  T-O);  (Eb)  B4  Perle's  PCC  being  T - l e v e l in " I " .  element The  function,  i s a significant bass-line pitch.  l o c a t i o n s of c o l l e c t i o n s c o n t a i n i n g significance:  t r a n s p o s i t i o n of the T-O  T-O  harmony, m.  second p h r a s e s of the p i e c e ,  (m. 4)  c1imax of the p i e c e  cal  to T-O,  i t as T-O;  r e s p e c t i v e l y ; and  T-  pitches  time-span with the p i t c h -  (G#6).  Another p r o b l e m a t i c identifies  T-  initiate  d i f f e r e n t t e m p o r a l - r e g i s t r a l c o n f i g u r a t i o n of T - l l ) precedes the  On  variant  1) and  11  to the p r e v i o u s  "2"  element  and  7,  4,  variant  the f i r s t (m.  (m.  a c c o u n t s -for a l l  have a s u b s i d i a r y or e l a b o r a t i v e  elements have a c e r t a i n formal 11  1,  T-ll).  element the  (C)  p i t c h e s which cannot be  PC  collection  in f a c t ,  the PC  i s t h a t of m. content  13.  i s nearly  except t h a t G appears i n s t e a d of Gb.  Perle  Gojowy identispeaks  26 of the p i t c h m a t e r i a l the s e t  statement o-f the s e t . " *  -from " t r a n s p o s i t i o n s o-f  o-f seven PCs  It i s p o s s i b l e to  1 5  f y the c o l l e c t i o n  lection  derived  [complex] t h a t are c l o s e l y r e l a t e d i n p i t c h content  the o r i g i n a l  nation  as being  as the  belonging  involves i n m.  ICC  at T-9  as w e l l  to e i t h e r T - l e v e l .  i t s connective  as at T-0, One  f u n c t i o n with  13  is identical  to the PCC  PC  c o l l e c t i o n of m.  of  identi-  since six  plausible  "II":  to  expla-  the PC  " I I " at T-10  col(Ex.  2-4) .  Example 2-4. ICC  of  " I " at  T-O:  ICC  of  " I " at  T-9:  13  in " I " .  oM4 PC  ICC  Content of m.  of  " I I " at  T-level fewer PCs be  per  13:  T-10:  identification c o l l e c t i o n and  adduced t o e x p l a i n  in mm.  6-8  i s problematic  because more than one  the PC content of each  Gojowy*s a n a l y s i s of T - l e v e l s u c c e s s i o n  because of  T-level  collection.  (Ex. 2-3b)  explains  can  27 these i n d i v i d u a l excerpts," not  c o l l e c t i o n s as " d i f f e r e n t ,  e x c e r p t s of the ICC at some T - l e v e l .  1 0  d i s c u s s these measures s p e c i f i c a l l y .  trates  that  ICC r e a l i z e d  (i.e., are  i n mm.  1, 4, and 7.  (b) shows these PCs combined  T-levels  compared  staff (c).  2-5  illus-  ICC, which d i f f e r s from the above-mentioned Example  i l l u s t r a t e s the PC content of the i n d i v i d u a l  while s t a f f  P e r l e does  6 and 7, and of m. 8, a r e d e r i v e d from an expanded  v e r s i o n of the b a s i c  (a),  Example  scale-  each of the complete PC c o l l e c t i o n s of the second  h a l v e s of mm.  expanded  irregular  of the expanded  with s i m i l a r  into  2-5,  harmonies,  larger  ICC), both i n s c a l e  T-levels  of the b a s i c  staff  collections form.  These  ICC of " I " on  28 Example 2-5.  Expanded  ICC and T - l e v e l s  161 (SECOND HALF) UIPC CONTENT  i n mm. 6-8.  (7) (SECOND HALF)  (b)EXPANDED ICC AI T-0  ...AT T-2  (c)BASIC ICC AT T-0  ...T-2  ...AT T-2  .AT T-9  (81 (a)PC CONTENT  ^  1  il  Jl *'\  1  f  (b)EXPANDED ICC AT T-7 •j ) , * J » > IcIBASIC ICC AT T-7  '  W  ...AT T-2  2^  The expanded PCCs a r e t r a n s p o s i t i o n a l l y r e l a t e d , w i t h 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 t e m p o r a l - r e g i s t r a l  configuration  of p i t c h e s i n  these t h r e e time-spans r e f l e c t s t h i s T-O,T-2,T-7 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 of t h e expanded PCC (Ex. 2-3, mm. panded T-0 (m. 6) c l o s e l y resembles t h e b a s i c T-O and T-7, the expanded T-2 (m. 7) the b a s i c 9, and the expanded T-7 (m. 8) t h e b a s i c  6-8). The exICC of " I " both at ICC a t T-2 and T-  ICC at T-7 and T-2,  with o n l y a -few PCs d i f f e r i n g  i n each case.  Moreover, t h e r e a r e s i m i l a r i t i e s between  the expanded  i n PC and element content  ICC, the b a s i c ICC, the PC c o l l e c t i o n  i n m.  13, and the ICC of " I I " (Ex. 2-6).  Example  2-6.  ICC OF T  Expanded ICC at T-0 and i t s r e l a t i o n s h i p t o o t h e r PC c o l l e c t i o n s i n " I " and " I I " .  AT T - 0 :  7  EXPANDED ICC AT T - 0 :  \}0\o  9  • I " , T - 0 ( H . 131 / M P ,  T-10  I C C O F *ir AT T - I :  U n i l U e the harmonies of mm. a given T-level  are v e r t i c a l i z e d  s i n g l e harmonic u n i t , subdivided harmonies. each with  1-5 and 10-13, where a l l PCs of or v e r t i c a l l y o r i e n t e d i n a  the expanded  PCCs of mm.  6-8  are p a r t i a l l y  i n t o subset c o l l e c t i o n s o r , more s p e c i f i c a l l y ,  The s u b d i v i d e d PCs form more than one harmonic u n i t , i t s PCs v e r t i c a l l y  oriented.  Individual  subset harmo-  n i e s have PCs t h a t d i f f e r with those of other subset and o t h e r PCs t h a t a r e i n v a r i a n t ; tially  subset  subdivided."  harmonies  hence, the d e s i g n a t i o n "par-  T h i s r e p r e s e n t s 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 p r e s e n t a t i o n of a T - l e v e l ' s PCs,  i n the  30 sense t h a t a T - l e v e l ' s PCs  can  be s u b d i v i d e d  subset c o l l e c t i o n s to the p o i n t individual  PCs.  Roslavets,  although the  in  l i n e a r i z e d , as  " I " are  by  s u b d i v i s i o n , as w e l l  " I I " (T-2,  T-5).  i s T - l l (m.  6-8  and  and  ICC  7  (T-ll)  (The t e r t i a n  in these  lin-  Such T - l e v e l  Similarly,  there  i s a greater  i n t o subset c o l l e c t i o n s i n mm. and  m.  4 of  " I I I " (T-7,  In c o n t r a s t  T-O,  with  6-8 and de-  " I " and  tendency towards these harmonic s u b s e t s  l i n e a r i z a t i o n s i n " I I I " , with the more c o n t r a p u n t a l .  are examined  tex-  there  Thus a l l such T - l e v e l s u b d i v i s i o n o c c u r s i n middle,  phonic and "III"  actually  in chord s t r u c t u r e and  velopmental s e c t i o n s of the p i e c e s . "II",  7) o-f " I I I " .  as a formal u n i t .  T-8),  6 and  o-f p i t c h e s  more  l a t e r works by  i n Chapter Three.)  as d i f f e r e n c e s  of T - l e v e l s  T-10,  T - l e v e l s o-f mm.  the s u c c e s s i o n s  t u r e , d i s t i n g u i s h mm.  of  initial  T - l e v e l s , are examined  are s u b d i v i s i o n s  where the s u b s e t s are  Such l i n e a r i z a t i o n c h a r a c t e r i z e s  harmonies, i m p l i e d earized  i n t o more and  later  texture  being  l e s s homo-  These d i s t i n c t i v e f e a t u r e s  of  in t h i s chapter.  of " I I " As  i n " I " , one  structures  in " I I " . " * 1  which r e a l i z e s the analysis,  ICC  2 0  ICC  i s the b a s i s of a l l harmonic and  melodic  Example 2-7a  shows the r e f e r e n t i a l PCC  of  Ex.  " I I " , and  shows the p i e c e ' s  PCs  2-7b,  segmented  based on  Gojowy's  into T-levels.  31 Example 2-7. (a)ICC  The ICC of " I I " , and PCs p a r t i t i o n e d harmonies.  into  of " I I " :  ELEMENT:  0  1  3  <b)"II" segmented  4  o  o  6  8  9  11 0  i n t o PCCs at v a r i o u s  MEASURE: I D PITCHES  T-levels:  121  2  (31  hi  5t  *p-  v—i i  3  .  W  J  4  u.  2=2:  -r  SCALAR PRESENTATION OF PCCS T-LEVEL: O 3  8  1  I 10 I  _L  ZZZE  133  141  \±  h i  5£ i^j  -9—r  3  10  a—TT^* i__J,Jy«__.. r<  7T  s  1*.  X»  1  w  *  —  w  3  rtT L  hf^  r  yjarr*^  A'?-  32  33 Gojowy shows no v a r i a n t element Perle  includes  ferential in mm.  a v a r i a n t element  PCC), b r a c k e t e d  6-8  "1" ( i . e . ,  i n Ex. 2-7a.  i n the b a s s - l i n e  (m. 6 ) , T-10  i n h i s -form o-f the ICC, but  (m. 7 ) , and T-8  in p a r t i a l  not p a r t  Element  o-f the r e -  "1" only  occurs  arpegg i at i ons o-f the T-2  (m. 8) harmonies, r e s p e c t i v e l y .  The o c c u r r e n c e o-f T - l e v e l s with element "1" i n mm.  6-8 o-f  2 1  "II",  in the middle development s e c t i o n o-f a r e c a p i t u l a t i v e t e r n a r y •form, i s s i m i l a r t o the use o-f expanded and c o n t r i b u t e s  ICCs i n mm.  6-8 o-f " I " ,  t o the -formal r o l e o-f these measures.  Unlike  v a r i a n t element "10" i n " I " , however, v a r i a n t element "1" i n "II"  i s not a s s o c i a t e d  with  less s i g n i f i c a n t functions  melodic-harmonic s t r u c t u r e s . conventional  tonal  It plays  an important r o l e i n a  i n t e r p r e t a t i o n of the harmonic s t r u c t u r e s , a  t o p i c t o be t r e a t e d more f u l l y  i n Chapter T h r e e .  The ICCs of " I " and " I I " a r e q u i t e s i m i l a r . that  i n the  2 2  Gojowy notes  the PCs of the ICCs of " I " and " I I " are i n v e r s i o n a l 1 y r e -  lated.  2 3  In f a c t , the T - l e v e l s of " I I " could  be r e d e s i g n a t e d  T - l e v e l s of the PCC of " I " i t s e l f , with the i n i t i a l  PCC of  as T - l l of the PCC of " I " . However, the above-mentioned elements i n the PCCs of " I " and " I I " make i t d i f f i c u l t p l a i n PC o r g a n i z a t i o n  as  "II"  variant  t o ex-  i n " I " and " I I " i n terms of a s i n g l e ICC.  34 ICC of " I I I " U n l i k e " I " and a t i o n s o-f t h e i r  " I I " , which have a l i m i t e d  r e s p e c t i v e ICCs,  v a r i a t i o n s o-f i t s ICC suggested  " I I I " a p p a r e n t l y has  -follow the segmentation  seven  of p i t c h e s 2  p r e s e n t s these v a r i a t i o n s at T-0,  with a lower case  letter.  each  labelled  To the r i g h t of these PC  collections  of T - l e v e l s of these v a r i a t i o n s , with the  indications  of measures i n which they appear. "a" t o "d" correspond  Those v a r i a t i o n s with  "10",  and  "11".  Example 2-8b  t a t i o n of p i t c h e s i n t o PC c o l l e c t i o n s , of Exx.  2-3b  and  letters  t o Gojowy's f o u r ICCs f o r the p i e c e .  c l u d e d with these i s P e r l e ' s " s e t " with b r a c k e t e d v a r i a n t ments "9",  vari-  by Gojowy's p r e s e n t a t i o n of T - l e v e l s u c c e s s i o n s . " *  Example 2-8a  is a l i s t  i-f we  number of  2-7b.  Inele-  i l l u s t r a t e s the segmen-  similar  to the a n a l y s e s  35 Example 2-8.  The ICCs o-f " I I I " .  (a)Seven v a r i a n t ICCs, with T - l e v e l s and l o c a t i o n s ; Gojowy's -four ICCs (a, b, c, d) and P e r l e ' s s i n g l e ICC with v a r i a n t elements: ELEMENTS:  0  1  2  3  4  6  8 9  60J0VY a  10  11 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, 10l D 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)  f. T-5  «N. 4)  mJOLm  L,, 9: T-0 (N. 12) L. L. PERLE  f  f  =  Iv  l i  36 Example 2-8  continued.  (b)"111" segmented i n t o PC  collections: (21  MEASURE: [ 1 1 PITCHES  3 I  3E  5? S C A L A R P R E S E N T A T I O N O F PCCs T-LEVEL: 0 S  1  I 8  JUL.  (31  (2)  [41  HP J  33 I I I  10  J  1  s  i  4" -  i  ' 7  37  38 The d i f f e r e n c e s between the ICCs c i t e d reflect  the i nc 1 us i veness o-f t h e i r  Gojowy uses -four ICCs  by Gojowy and  r e s p e c t i v e ICCs.  (with no v a r i a n t PCs)  While  t o account -for the  most -frequently o c c u r r i n g c o l l e c t i o n s or t h e i r P e r l e has o n l y one ICC with t h r e e v a r i a n t  Perle  transpositions,  PCs.  Although Gojowy's ICCs and T - l e v e l s account -for the PC cont e n t o-f most harmonies ICCs employed  in "III",  the concept o-f -four d i f f e r e n t  in " I I I " i s problematic.  Why  should the f i n a l  p i e c e of t h i s s e t be deemed so r a d i c a l l y d i f f e r e n t "II"  i n terms of c o m p o s i t i o n a l  four  ICCs, e s p e c i a l l y  t e c h n i q u e that  i t s h o u l d embrace  i n l i g h t of i t s s m a l l e r dimensions?  over, the p e r c e p t i o n of f o u r d i s t i n c t four d i f f e r e n t  from " I " and  ICCs would  Perhaps the s t r o n g e s t  be  More-  harmonies based on these  unlikely.  i n d i c a t o r f o r the use of one  ICC i s  the r a t h e r unique m u s i c a l orthography of the ICC of " I I I " ( i . e . , the m i x t u r e of s h a r p s and f l a t s as a c c i d e n t a l s p r e s e n t a t i o n of the ICC PCs, and PC  i n the s c a l a r  i n t e r v a l s formed), and the  c o n s i s t e n c y with which p i t c h e s of i n d i v i d u a l c o l l e c t i o n s music conform to i n t e r v a l l i e PCs  (Fig. 2-1).  2 0  i n the  r e l a t i o n s h i p s suggested by the ICC  39 Example 2-9. (a)ICC at  Musical orthography o f the ICC o-f " I I I "  T-0:  T-0 LEVEL PCs:  6 - 6 1 - Bb - B - Db - DI - <E - F - Gb) - 6  ELEMENT: PC INTERVALS  0  1 1  3 2  4 1  6 2  8 2  9 1  1  1 0 11 0 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 " I I I " :  MEASURE: 111 T-LEVEL: O  [2]  C2)  131 1  10  7  (3)  141  (3) 4  7  (3)  (3)  (3)  40 Example 2-9  continued.  (41 5  (5-6) 8  [71 11  [8) 2  ii)  n  $ ~ — ^ — L T y-n+v  ' v > ^ "  0  (81 6  [?] 9  [10-111 2  [121 0  [121 5  As'*'*** *v*—  rial  t  — — -  [131 5  ,  0  ,  L j l j i i  4  0)  (131 7  (14-151 0  Note: Boxed p i t c h e s are those elements (e.g., "9", "10", "11") not o c c u r r i n g with every T - l e v e l , and bracketed in P e r l e ' s "set". Elements m i s s i n g from a T - l e v e l are i n d i c a t e d by a gap in the s c a l e and a bracketed element number above the s t a f f . P i t c h e s that are added to the T - l e v e l are included i n the s c a l e with b r a c k e t s . F i n a l l y , p i t c h e s that are enharmonical1y named in the music, as to the ICC at T-O, are included in the s c a l e with the name (based oh the ICC) above or below as a bracketed s o l i d notehead. Thus the musical s i n g l e ICC  orthography s t r o n g l y suggests that  i s the source f o r the PC  (Hence, Gojowy's o b s e r v a t i o n s Appendix B.) quately  to the c o n t r a r y  Some v a r i a t i o n s shown in Ex.  explained  as forms of any  example, the  initial  "11"  "3"  (G) and  c o l l e c t i o n s of  3  (B)j Gojowy d e s i g n a t e s  "III".  are d i s c u s s e d  2-8a  cannot be  of the suggested  c o l l e c t i o n of m.  a  ICCs.  in  adeFor  (T-l) i n c l u d e s elements t h i s PCC  as  "irregular."  41 These a d d i t i o n a l second  can be thought  o-f as b e l o n g i n g to the  T-1 harmony i n m. 3 (Ex. 2-10).  Example 2-10.  PC c o l l e c t i o n s ,  T-1  T-1  T h i s second 3),  elements  m. 3. T-4  T-1 c o l l e c t i o n o-f m. 3 i s tranposed a t T-4  and T-7 and T-O  (m. 4 ) .  P e r l e i n -fact c i t e s these PC c o l -  lections  as evidence t h a t R o s l a v e t s c o n s i s t e n t l y omits  elements  ( i n t h i s case, elements  ant T - l e v e l s . * * second  T-1 harmony, m. 3, and i t s o c c u r r e n c e  (F, m. 4 ) , and T-O (Ex. 2-11)  specific  "3" and "11") t o produce  S i m i l a r t o the o m i t t e d B (element  (T-1) harmony, element  (m.  "3") of the  i n the p r e c e d i n g  "3" PCs, o m i t t e d from T-4  (Bb, m. 4 ) , a r e found  vari-  (D, m. 3 ) , T-7  i n p r e c e d i n g harmonies  42 Example 2-11.  As niscent and  Element  indicated o-f mm.  T-7),  "3"  earlier,  6-8  in mm.  the  texture  i n " I " where the  embodying a m u l t i p l e  monic -figure, are  3-4.  o-f m.  three T - l e v e l s  transposition  each s u b d i v i d e d  4 is strongly (T-O,  remiT-2,  o-f a m e l o d i c - h a r -  into three separate  "subset"  harmonies.  tion  Finally,  Ex.  o-f ro. 12  (T-O)  2-12  demonstrates t h a t  i s a modified  the  second PC  i n v e r s i o n of t h a t of  collecT-0.  43 Example  PCs:  2-12.  T-0 c o l l e c t i o n , m. T-O.  12,  as an  i n v e r s i o n of ICC at  Db - Eb - 6b - 6 - Bbb - Bb - B - Db  INTERVAL*. 2  3  1  2  1  1  2 ICC AT T-0  PCs:  Ob - 0 1 - E - F - 6 - 6 1 - Bb - B - Db  INTERVAL:  2  Ultimately, useful  the ICC  as the unbracketed  T - l e v e l s o-f " I I I " ,  and  although element  as i t o c c u r s o n l y Two-thirds "III"  short  (i.e.,  elements  occur  1  2  i n at l e a s t 80% of the  the b r a c k e t e d elements is logically  "11" might as w e l l  less often.  not i n c l u d e d  occurring  i n the  have been excluded  as i n n e r - v o i c e p i t c h e s , and/or  between element o c c u r r e n c e and  With the ICCs e s t a b l i s h e d ,  of the v a r i a n t  having not  the f u n c element.  the groundwork has been l a i d f o r  d i s c u s s i o n of harmonic s u c c e s s i o n s and 2 3  too  in  Hence, t h e r e i s a r e l a t i o n s h i p , although  t i o n or r e l a t i v e s t r u c t u r a l importance  ciated T-levels. *  Ele-  or o t h e r w i s e s t r u c t u r a l l y l e s s s i g n i f i c a n t  consistent,  the subsequent  2  of o c c u r r e n c e s of these v a r i a n t elements  durations).  altogether  2 1  t w i c e i n the e n t i r e p i e c e .  are d e c o r a t i v e  pitches  1  i n d i c a t e d by P e r l e proves to be most  ment "2" o c c u r s o n l y once and PCC,  1  the asso-  44  and The volves,  study  Harmonic S u c c e s s i o n s S u c c e s s i o n s of T r a n s p o s i t i o n - L e v e l s  of harmonic s u c c e s s i o n s  to a large extent,  As has been e x p l a i n e d ,  the study  the PC content  g i v e n p i e c e i s , with some e x c e p t i o n s , content  o-f one T - l e v e l  T h i s study  will  cencies  in  ceeding  i t will  Trois  initially  Compos  it  o-f a s i n g l e harmony  be concerned with  in a  that piece.  transpositional re-  T - l e v e l s i n a harmonic s u c c e s s i o n , and  Compositions.  tentatively  adja-  T h i s s e c t i o n and the one suce s t a b l i s h which T - l e v e l s a r e harmon-  i n the p i e c e s .  R e l a t i o n s h i p s o-f Adjacent  T-Levels in  Trois  i n v o l v e s 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 a d j a -  cent T - l e v e l s and the -frequencies o-f tionships  in-  u l t i m a t e l y based on the PC  One o-f the c h a r a c t e r i s t i c s o-f harmonic s u c c e s s i o n s Compositions  i ons  o-f s u c c e s s i o n s o-f T - l e v e l s .  c y c l e s which -form the b a s i s o-f many such  ically significant  Transpositional  Trois  o-f the ICC a s s o c i a t e d with  l a t i o n s h i p s o-f a d j a c e n t transpositional  in  (Fig. 2-1).  occurrence  o-f such  rela-  45 Figure  2-1  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 between T - l e v e l s i n " I " , " I I " , and " I I I " .  ( a ) T - l e v e l s and  IC  relationships:  •r MEASURE: I 5 6 8 10 T-LEVEL: 0 - 3 - 1 0 1 - 4 7 - 1 0 - 4 11 - 9 - 2 5 11 - 0 11 - 2 7 3 - 6 PC INTERVALS: 3 7 3 3 3 3 6 7 1 0 5 3 6 1 11 3 5 8 3 IC: 3 5 3 3 3 3 6 5 2 5 3 6 1 1 3 5 4 3  10 1 1 1 2 13 6 - 3 - 6 - 9 - 4 - 9 0 9 3  3 3  7 5  5 5  3 3  •IV MEASURE: 1 2 3 4 T-LEVEL: 0 - 5 8 - 1 1 0 - 3 10 PC INTERVALS: 5 3 5 9 5 7 5 IC: 5 3 5 3 5 5 5  9 7  10 0- 5 5 5  5 5  11 0- 5 7 5  5 5  5 6 7 8 9 - 3 6 - 9 2 - 5 10 - 3 8 -11 - 4 7 3 3  3 3  5 5  3 3  5 5  5 5  5 5  3 3  5 5  3 3  1 2 13-14 0 0 7 5  0 0  •ur MEASURE: 1 2 T-LEVEL: 0 - 5 8 - 3 - 7 PC INTERVALS: 5 3 7 4 3 IC: 5 3 5 4 3  10,11 12 2 - 5 - 0 3 3  7 5  3 4 10 1 - 1 - 47 - 0 - 5 3 3  0 0  3 3  3 3  13 14,15 5 - 0 - 4 - 7 0 5 7 5 3  4 4  3 3  5 5  5 5  5 5  5,67 8 9 10,11 8 11 2 - 6 9 2 3 3  3 3  3 4 3 5 3 4 3 5  successive  46 F i g u r e 2-1  continued.  ( b ) F r e q u e n c i e s of o c c u r r e n c e 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 a d j a c e n t T - l e v e l s i n " I " , " I I " , and " I I I " : PC INTERVAL: •I":  3  l l l l O 1  1  1  •ir: •IIP: TOTAL:  l  I  l  9  11 6 11  1 1  28  2  4  8 1  3 3  1  5  7  6  6  3 2 3  2  li 20  8  2  3  IC:  l  2  3  4  5  6  •P: •IP: •HP:  2  l  12 7 11  1  2  3  6 13 9  TOTAL:  2  30  4  28  2  The  l  IC r e l a t i o n s h i p s o-f a d j a c e n t  -frequently are ICs 3 and teristic  T - l e v e l s o c c u r r i n g most  5, which Gojowy i d e n t i f i e s as  charac-  o-f many harmonic s u c c e s s i o n s i n R o s l a v e t s ' s works.  In the s u c c e s s i o n 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 p r o g r e s s i o n i s d e f i n i t e l y avoided, but, on the other hand, p r o g r e s s i o n s by minor t h i r d s are f r e q u e n t , as are those by f o u r t h s and f i f t h s . 2 0  Transpositional Not 5, but  C y c l e s of  o n l y are a d j a c e n t  T-Levels T-levels usually related  T - l e v e l s are r e l a t e d e x c l u s i v e l y by one  ICs, f r e q u e n t l y ascending. 2-la),  sively  the T - l e v e l  For example,  i n " I " , mm.  of  1-3  these (see  s u c c e s s i o n T-IO,T-1,T-4,T-7,T-10 e x c l u -  i n v o l v e s an ascending  IC 3.  T-x+3, T-x+6, T-x+9, T-x+O, and T-7,  IC 3 or  t h e r e o f t e n appears a s u c c e s s i o n of s e v e r a l T - l e v e l s i n  which a d j a c e n t  Fig.  by  Where T-x  so on  T-10), such a s u c c e s s i o n w i l l  i s followed  (e.g., T-10,  T-1,  be termed a T - l e v e l  by  T-4, cycle,  47 specifically are  a PC-interval  i n f a c t three  3 cycle  (or i n t e r v a l 3 c y c l e ) .  interval 3 cycles:  There  T-O, T-3, T-6, and T-9  ( c y c l e 3-0)5 T - l , T-4, T-7, and T-10 ( c y c l e 3-1)5 and T-2, T-5, T-8,  and T - l l ( c y c l e 3-2).  The i n t e r v a l 5 c y c l e  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 c y c l e s of T - l e v e l s a r e the b a s i s of harmonic s u c c e s -  sions  i n the p i e c e s . " 2  O f t e n t i m e s , however, only  o-f a c y c l e a r e used be-fore a t r a n s f e r e n c e components t h e r e o f . cycle  t o another c y c l e or  a s i n g l e T - l e v e l of one  i s i n t e r p o l a t e d with T - l e v e l s of another c y c l e .  a T - l e v e l of a c y c l e out  In some i n s t a n c e s ,  a few T - l e v e l s  ( e s p e c i a l l y an i n t e r v a l 3 c y c l e ) may occur  of o r d e r with r e s p e c t  "I".  Figure  illustrating  Moreover,  t o other members of the c y c l e .  2-2a p r e s e n t s the T - l e v e l successions- of " I " ,  the T - l e v e l components b e l o n g i n g t o each i n t e r v a l 3  c y c l e , w h i l e 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 c y c l e s t o the i n t e r v a l 5 c y c l e .  48 F i g u r e 2-2.  T-level successions  of  " I " and  IC c y c l e s .  ( a ) I n t e r v a l 3 c y c l e s and T - l e v e l s b e l o n g i n g to each, u n d e r l y i n g balanced p a t t e r n o-f s u c c e s s i o n : MEASURE 1 T-LEVEL CYCLES 3-0: 0--3 3-1: 3-2:  3-o: 3-1: 3-2:  2  3  5  4  6  7  8 10,11  9 10--1-4-7--10--4  12  with  13  7  3--6--3-6--9...9--0 4  *  HHimillH...fW t  1 1 . . . 2 — 5 — — 2  «« IHIIHIIIIHIHII 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 " I " d e r i v e d -from t h i s c y c l e and the i n t e r v a l ( i n d i c a t e d i n b r a c k e t s on the l e - f t ) : INTERVAL 5 CYCLE*. 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 MEASURE: 1 T-LEVEL: 0 (3-0) MEASURE: T-LEVEL: (3-1)  I..! 2 IO 1  4-  MEASURE: T-LEVEL: (3-D  -10  3 4 : •  MEASURE: T-LEVEL: (3-2)  4 . . : 5 11-- - 2 — - 5 -  MEASURE: T-LEVEL: (INTERVAL 5 )  7 8 -11— -2-7  MEASURE: tn 10-11 T-LEVEL:(0-31...3 6 (3-0) NEASURE: T-LEVEL:  6 -11-  12 9 : 12.: 4-  13 -0  T-levels 3 cycles  49 Note: The T - l e v e l s u c c e s s i o n o-f " I " i s i n d i c a t e d by f o l l o w i n g the h o r i z o n t a l dash l i n e from l e f t to r i g h t and c o n t i n u i n g on the f o l l o w i n g l i n e . In F i g . 2-2a, of  the  i n t e r v a l 3 c y c l e s on  from one  ( r a t h e r than a p u r e l y  appearance.  The  to 3-2  progression  (mm.  4-7)  f u l l y balanced u n l e s s as r e f e r e n c e s components. (mm.  10-13).  organization  of  ponents i n mm. level sion  (m.  finally  one  i n t e r p r e t s T-7  (mm.  back to 3-0 (m.  of  4-7)  in part.  of the p i e c e ,  T-9  of  10-13) i s not  and  T-4  (m.  12)  T-levels  are  3-0  cycle  The  3-0  cycle  harmonic (with com-  The  with the  i n mm. two  10-13  other  initial (the  T-  T-0,T-3 s u c c e s -  recapitulation)  i n t e r v a l 3 c y c l e s , 3-1  development.  The  are  and  i n some degree  c e n t r a l 3-2  cycle  with the approximate midpoint of " I " .  i n t e r v a l 3 c y c l e s are components of the i n t e r v a l  5 c y c l e whereby each and  (mm.  10-13) a c t s as the framework f o r the  with the p i e c e ' s  three  (mm. 8)  cycle  to 3-1  balanced s t r u c t u r e upon which the  1 and  coincides  1)  of  a  interval 3 T-level cycles is  i n v o l v e most of the o t h e r T - l e v e l s , and  The  T-6,  (m.  c y c l e , of which these two  1) b e i n g completed  associated  based on  c y c l e o c c u r s b e f o r e the f i n a l  with T-3,T-6,T-9,T-O. 3-2,  from c y c l e 3-0  " I " i s based  successions  transference  symmetrical) p a t t e r n  Such a p r o g r e s s i o n  then the u n d e r l y i n g  The  i s apparently  and  to the 3-1 T h i s 3-1  are shown with components  separate l i n e s .  i n t e r v a l 3 c y c l e to another  "balanced"  1-3)  T-level successions  interval 3 cycle T-level  the 3-0  the  interval 5 cycle;  the  top of F i g . 2-2b).  cycle)  (e.g.,  appears at a r e g u l a r  i n other words, every t h i r d One  c y c l e s , whose components are  can  thus r e l a t e the  i s o l a t e d on  T-O,  T-3,  i n t e r v a l in  component  (see  interval 3  s e p a r a t e l i n e s in F i g .  50 2-2b,  to the  all-inclusive  interval 5 cycle.  c y c l e apparently c o n t r o l s cifically, er.  The  cycles,  the  from one  interval 5 cycle,  (e.g., T-9, The  m.  4,  initial  (mm.  1-3)  cycle  (T-3  to T-10,  F i g . 2-2b  in conjunction  T-4,  m.  12,  among  T-0,T-3 ( c y c l e 3-0,  cycle  by moving one m.  1).  c o n n e c t i n g the  2-2b  vertical  connect the  T - l e v e l on  component of the  to the the  in m.  i n the  3-0  cycle  dotted  12  cycle  (i.e.,  ease of  r e l a t i o n s h i p s between the  T-levels  (mm.  (mm.  t i o n of the T-2,T-7,T-O p o r t i o n  of  viewing, of  Fig. interpo-  the  The  by the  3-1  derived  4  In  the  (i.e.,  c y c l e of  involve  in question.  i s based  also  the  i n m.  i n the 3-2  by  (m.  in d i r e c t i o n in  T - l e v e l , T-9  explained  6-8),  to  Similarly,  10-13) i s  interpolations  not  line  4-7),  a s i m i l a r procedure.  and  n i f i c a n t T-level succession  top  component of  c y c l e of mm.  by  l i n e in  aforementioned  interpolated  i s likewise explained  T-0,T-2,T-7 sequence  interval 5  horizontal  For  3-1  i s completed with T-4  3-2  Another i n t e r p o l a t e d 3-0  the  interval 5 cycle.  words, such t r a n s f e r e n c e s  the  t r a n s f e r s to the  i n t e r v a l 5 c y c l e through a r e v e r s a l  c y c l e ' s order.  4-7),  level  interpolated  from the  line.  cycle  interval 3  interpolations  l i n e s b e g i n n i n g at the  Once the 3-1  i n t e r p o l a t i n g T-4 cycle  1)  T - l e v e l ending one  there i s a transference  moving back one  m.  (Note the v e r t i c a l  dotted  anoth-  others).  i n t e r v a l 5 c y c l e to the  lated T-levels.) 3),  with the  T - l e v e l back on  t h a t b e g i n n i n g another h o r i z o n t a l additional  i n t e r v a l 3 c y c l e to  b a s i s f o r some i n c o m p a t i b l e  and  interval 5  the sequence o-f T - l e v e l s or, more spe-  transference  i s a l s o the  The  mm.  other  interval 7 other  sig-  interval 3  cycles,  in part  a rota-  on  interval 5 cycle.  51 In c o n c l u s i o n , the i n t e r v a l the  interval  successions  5 c y c l e - - i n conjunction  with  3 e y e l e s - - w o u l d appear t o be the b a s i s of most i n " I " , e s p e c i a l l y the a s p e c t s o-f t r a n s f e r e n c e and  i n t e r p o l a t i on.  "II". terval ever,  The T - l e v e l  5 cycle.  s u c c e s s i o n s o-f " I I " are based on the i n -  F i g u r e 2-3 shows the c y c l e i s m o d i f i e d ,  because c e r t a i n T - l e v e l s a r e omitted,  where i n the p i e c e . labelled  These t r a n s f e r r e d T - l e v e l  MEASURE: 1 T - L E V E L : 0--5  T-level eyele.  T-level  Ba  ••••aaaa  Da  a a a  0.... -6--11--4--9-2  Aa  a a a  -7-0  s u c c e s s i o n C (T-10,T-3) and D ( T - l i , T - 4 ) i n v o l v e  5 c y c l e components  (T-5,T-10,T-3,T-8,  mm.  p i t u l a t i o n s of e a r l i e r  6-8)  out of s e q u e n c e . and A  i n the development, b e g i n n i n g  with  B  10-12) are r e c a -  s u c c e s s i o n s ; A r e c a p i t u l a t e s the  initial  of the i n t e r v a l  B would a l s o seem t o have some formal  the melodic climax  Successions  3 0  (T-O,T-5, mm.  s u c c e s s i o n of " I I " f o l l o w i n g the completion  with  5  6 7 8 9 10-13 -9.-2-5-10-3--8-11--4-7--0-5-0  • a •  INTERVAL A . . . C . . . 5 0--5--10--3--8--1 CYCLE: B  occurs  s u c c e s s i o n s are  s u c c e s s i o n s of " I I " and the i n t e r v a l  2 3-4 5 8-1--10--3--6 Ca  cycle.  inserted else-  as A, B, C, and D i n F i g . 2-3.  F i g u r e 2-3.  interval  and  how-  5  s i g n i f i c a n c e as i t  the harmony a s s o c i a t e d  p o i n t of the p i e c e .  52 F i g u r e 2-4 p r e s e n t s the T - l e v e l  "III".  "III"  and the T - l e v e l  F i g u r e 2-4.  s u c c e s s i o n s of  c y c l e s t h a t a r e components t h e r e o f .  T - l e v e l s u c c e s s i o n s o-f " I I I " and the T - l e v e l eye 1es.  (a)Surface successions: MEASURE: T-LEVEL: CYCLES:  1 3 4 5-6 7 8 9 1 0 - 1 1 1 2 1 3 0--5--8—3--7--10—I~4—7—o~5—8—11—2-16-9)-2 5- io) -5 1  3-1  MEASURE: T-LEVEL: MEASURE: T-LEVEL:  1 1  I  (  * * INTERVAL 5  ( ).  )  T  3-2  8 9 10-11 2—6—9—2 1 1 1 1 1 1 1 1  12 13 : : : 14-15 5--0--5-0-4--7-0  (b) Under 1 y i ng symmetrical  T-level  s t r u c t u r e o-f " I I I " :  MEASURE: 1 2 3 4 5,6 7 8 9 10 12 1 3 14 T-LEVEL: 0 - 5 8 - 3 - 7 - 1 0 1 - 4 7 - 0 - 5 8 11 2 - 6 92 5 - 0 5 - 0 - 4 - 7 0 0(5)  7 3-1  The the  T-level  7 - 0 - 5 INTERVAL 5 3-2  s u c c e s s i o n s o-f mm.  5  (7)0  2, S-iO, and 13-15 (shown on  l e f t s i d e of F i g . 2-4a) a r e r e l a t e d  sition  as the d o t t e d v e r t i c a l  figurations  i n mm.  lines  suggest.  1-2 a r e transposed  12-13, w h i l e the f i n a l  two phrases  i n p a r t through  Harmonic-melodic  with m o d i f i c a t i o n s i n mm.  (mm. 8-11 and 12-15) cadence  on t r a n s p o s i t i o n s of the same a r p e g g i a t e d f i g u r a t i o n . T-level  s u c c e s s i o n s i n v o l v e c y c l e s 3-1  13), connected T-5).  i n m. 4 by an i n t e r v a l  In a sense,  The other  (mm. 2-4) and 3-2 (mm. 45 c y c l e segment  The complete 3-0 c y c l e does not occur  l e v e l s as do the o t h e r  transpo-  (T-7,T-O,  i n a d j a c e n t T-  IC-3 c y c l e s .  c y c l e s i n i t i a t e d by T-7 i n mm.  2-4 and T-5 i n  53 mm.  4-13  involve prolongations  text, prolongation r e i t e r a t e d , with initial  o-f these  T-levels.  In t h i s con-  r e f e r s to a s i t u a t i o n whereby a T - l e v e l i s  a limited  occurrence  and  number of other  the r e i t e r a t i o n .  through the  T - l e v e l s between  Invariance  erated  T - l e v e l ' s PCs  cially  i n 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  t i o n of T - l e v e l p r o l o n g a t i o n .  ICs 3 or 5,  Such PC ly,  there  T - l e v e l and  i n c i d e n c e of PC  interval  3 cycle, will  intervening  to each  other  invariance.  i n Appendix B.  symmetrical  s t r u c t u r e i n v o l v i n g T-O,  T-level  successions  related  t o T-O  Hence, t h e r e  ( F i g . 2-4b).  (i.e.,  interval  Because of t h i s symmetrical p o i n t of the p i e c e . i n the melody and  sure's s i g n i f i c a n c e .  be examined  T-5  is a and  T-7  and  T-7  are  5 above and  textural,  and  "I",  l i k e those  of  c y c l e s with  c y c l e segment  4 i s an  apparent octave  inner v o i c e s c o n t r i b u t e to t h i s mea6-8  in " I " appear t o be  reasons.  The  harmonic,  the e x c e p t i o n  of mm.  a  rhyth-  harmonic s u c c e s s i o n s  " I I I " , are g e n e r a l l y based on  (i.e.,  the  symmetrically  f e a t u r e s such as the  S i m i l a r l y , mm.  formal  underlying  below).  s t r u c t u r e , m.  Surface  is  simpler  T-5,  f o c a l p o i n t of t h a t p i e c e , a s i d e from melodic, mic,  in a  a d i s c u s s i o n of p r o l o n g a t i o n  to be found  level  percep-  i n v a r i a n c e i n I C - 3 - r e l a t e d T - l e v e l s or, more s p e c i f i c a l -  l a t e r s e c t i o n of t h i s c h a p t e r ;  ascent  the  P a r t i c u l a r l y when the  i s a greater  i n T - l e v e l s of an  focal  reit-  i n t e r v e n i n g T-1eve 1 ( s ) - - e s p e -  T - l e v e l s are r e l a t e d t o the r e i t e r a t e d by  of the  the  6-8,  T-O,T-2,T-7) o c c u r s .  interval  where the The  f o l l o w s , r a t h e r than precedes, T-2,T-7 i n the  fact  3  of T-  interval  that  T-O  interval 5 cycle  does not d i m i n i s h the s i g n i f i c a n c e of the c y c l e ' s appearance.  5  54 Moreover, both mm.  6-8 i n " I " and m. 4 i n " I I I " i n v o l v e the sub-  d i v i s i o n o-f T - l e v e l PCs o-f t h r e e s u c c e s s i v e three d i s t i n c t ,  subset  t i o n o-f the i n i t i a l  harmonies, with  T - l e v e l s each i n t o  the m u l t i p l e t r a n s p o s i -  three-harmony - f i g u r a t i o n i n each case.  s i m i l a r i t y a l s o rein-forces the o v e r a l l  This  s i m i l a r i t i e s of these  measures and t h e i r -function i n the r e s p e c t i v e p i e c e s . Based on t h i s p r e l i m i n a r y successions,  one can say t h a t  study o-f harmonic and T - l e v e l " I I " and e s p e c i a l l y " I I I " i n v o l v e  a t i g h t e r c o n t r o l o-f harmonic o r g a n i z a t i o n t h i s greater successions.  r e l i a n c e on i n t e r v a l This  than " I " because o-f  3 and 5 c y c l e s as bases -for  l i m i t a t i o n o-f harmonic s u c c e s s i o n s  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 R o s l a v e t s ' s tional  technique.  T-Level  The  3 1  O c c u r r e n c e s and T h e i r Rhythmic C h a r a c t e r i s t i c s : Towards a H i e r a r c h y o-f T - l e v e l s  analytical  examples i n d i c a t e t h a t c e r t a i n T - l e v e l s oc-  cur more f r e q u e n t l y than o t h e r s . l e v e l s a r e more s i g n i f i c a n t p i e c e s , so that t h e r e  T h i s suggests t h a t c e r t a i n T-  i n the harmonic s t r u c t u r e of the  i s in fact  a hierarchy  a h i e r a r c h y might be based not o n l y currence  but a l s o on the t o t a l  T - l e v e l s throughout each p i e c e ,  of T - l e v e l s .  Such  on T - l e v e l frequency of oc-  time-spans a l l o t e d  to individual  and on the l o c a t i o n of T - l e v e l s  in r e l a t i o n s h i p t o f o r m a l l y s i g n i f i c a n t archy i t s e l f  composi-  time-points.  This h i e r -  s u g g e s t s a form of t o n a l i t y s i n c e t o n a l i t y  involves  in p a r t  "the h i e r a r c h i c o r d e r i n g of PC f a c t o r s " whereby " p i t c h  content  i s perceived  as f u n c t i o n a l l y r e l a t e d t o 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 . " ferent  a s p e c t s of T - l e v e l  T-level to  which e s s e n t i a l l y concern  rhythmic c h a r a c t e r i s t i c s , a r e examined  i n f e r such a h i e r a r c h y  rhythm of T - l e v e l s  Harmonic  ic  occurrence,  of T - l e v e l s .  i n the three pieces  rhythm  of "Z".  rhythms of T - l e v e l s  Example 2-13a p r e s e n t s  i n d i c a t i n g the form of " I " i s a l s o  by d u r a t i o n a l  the purpose of a n a l y z i n g  notation  T-level  independent of p i t c h . included  location  Harmonic  rhythm and form of  "I".  (a)Harmonic rhythm of " I " : 1 0 3 10  2 1 4  3 7  DURATION OF T - L E V E L :  V\-  4 11  10 4  9 2  5 5  6 11 0  li •>) J  iU  J  RHYTHM OF SUBSET HARMONY: MEASURE:  T-LEVEL:  8  9  10  7 (J3  J<  11  12  13  3 6 3 6 9 4 9 0 c) J  P  J  0  J  J  J.  7 11 2  A  (Ex. 2-13b),  in r e l a t i o n to  important t i m e - p o i n t s .  MEASURE: T-LEVEL:  the harmon-  i n " I " with t h e time-spans of each T-  chart  Example 2-13.  section  i s i n d i v i d u a l l y analyzed.  indicated  formally  in this  To begin, t h e harmonic  level  for  These d i f -  3 2  56 (b)Form of C A3: mm.  " I " (modified r e c a p i t u l a t i v e ternary expos i t i on  1-3  1st phrase m. 1 tc3 m. 2 Cc3  mm. 1 and 2 (Cc3-extension) have 4 m o d i f i c a t i o n s of i n i t i a l motive, m. 1 3 Cd3..... cadence (with e l i s i o n , i n t o m. 4)  m. mm.  4-5  CB3:  6-9  CA'3: mm.  10-13  above the and  tially  T-7  and  8-9  s t a f f that  (Ex.  the  3-4  including  the  and  r e s t s which f o l l o w . i n the  sense of d e c e l e r a t i o n ,  8-9  rhythms  time-spans of harmonies  i r r e g u l a r i t y produced  such r e s t s and  harmonies (mm.  2-13a), t h e r e are b r a c k e t e d  i n d i c a t e the  respectively)  because of  rhythm by  recapitulation  4th phrase m. 10 Cc"3 m. 11 Cc"3...mm. 10-11 m o d i f i e d (arpeggiated) t r a n s p o s i t i o n 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 l i m i t e d s i m i l a r i t i e s with mm. 1-3  3-4  T-7,  material  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 m o d i f i c a t i o n s i n m. 7 m. 8 Cg"3....modified t r a n s p o s i t i o n of Cg3, m. 6 in mm. 7 and 8; abrupt cadence, m. 9 with r e s t  modified  In mm.  T-4  2nd phrase m. 4 [ c * 1 . . . . i n i t i a l f i g u r a t i o n t r a n s p o s i t i o n of i n i t i a l f i g u r a t i o n , m. 1, f o l l o w e d by r e p e t i t i o n of another m o d i f i c a t i o n ( a r p e g g i a t i o n s ) of i n i t i a l mot i ve m. 5 Ce3 ..... cadence (with e l i s i o n , i n t o m. 6); 3-2 T - l e v e l c y c l e components i n mm. 4-7 might suggest mm. 4-5 as b e g i n n i n g of development  development/new  mm.  form) :  respectively)  (i.e., Par-  harmonic the  delineate  T-4  and  phrases.  57 The harmonic rhythms o-f T - l e v e l important r o l e the  s u c c e s s i o n s i n " I " p l a y an  i n d e l i n e a t i n g form.  F o r one t h i n g , v a r i a n c e s i n  time-spans o-f harmonies concur with apparent -formal  sions.  In mm.  1-5 (the i n i t i a l  divi-  "A" s e c t i o n of the t e r n a r y  form), the most common and s h o r t e s t  time-span of the i n d i v i d u a l  harmonies i s the q u a r t e r v a l u e , with  longer h a l f - and d o t t e d -  h a l f v a l u e s found a t phrase b e g i n n i n g s and i n m. 5, the f i n a l measure of t h i s s e c t i o n .  Measures  10-13 a r e s i m i l a r , with quar-  t e r - v a l u e harmonic rhythm and the d o t t e d - h a l f - v a l u e In  c o n t r a s t , the harmonic rhythm of mm.  6-9 i s more complex.  one d e f i n e s the harmony i n terms of t h e T - l e v e l s expanded), t h e most common and s h o r t e s t 6-9 i s the d o t t e d - e i g h t h v a l u e . in the harmonic rhythm between quent a c c e l e r a t i o n if  T-level  If  (both b a s i c and time-span of mm.  This indicates a deceleration mm.  (mm. 6-9 t o mm.  1-5 and mm. 10-13).  6-9, and a conse-  On the o t h e r  the rhythm of t h e subset harmonies i s taken i n t o  tion,  i n m. 13.  then the most common and s h o r t e s t T - l e v e l  hand,  considera-  time-span of mm.  6-9 i s the e i g h t h - v a l u e , which i n d i c a t e s an a c c e l e r a t i o n and consequent d e c e l e r a t i o n pectively. the  i n v o l v i n g mm.  1-5, 6-9, and 10-13, r e s -  However one p e r c e i v e s harmonic rhythm  acceleration  i n mm. 6-9,  and/or d e c e l e r a t i o n c o n c u r s with changes i n  o t h e r m u s i c a l parameters (e.g., the compound rhythm, and meter) in t h e s e measures.  Har-monic  r-hythm  in "II".  i c rhythm and form of " I I " .  Example  2-14 p r e s e n t s the harmon-  58 Example 2-14.  Harmonic rhythm  <a)Harmonic rhythm MEASURE: T-LEVEL:  1 O  5  2 8  and -form o-f " I I  o-f " I I " : 3,4 10 3  I  5 6  6 2  9  5  7 10  3  8 8  11  4  DURATION OF T - L E V E L :  X4.  MEASURE: T-LEVEL:  9 10 7 0  3  J <  * )  5  11 0  J  J  5  J  12 0  13 0  14  J J  (b)Form o-f " I I " ( r e c a p i t u l a t i v e CAD:  t e r n a r y -form):  exposition  mm.  1-5  1st phrase mm. 1-2 Cc3 mm. 3-5 Cc'3..two-pitch motive with a r p e g g i a t e d harmony repeated i n mm. 1-45 2nd sub-phrase u n i t Cc'3 has repeated T - l e v e l s u c c e s s i o n (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 i n m. 5; c o n t i n u a t i o n i n t o CB3 without cadence (unl e s s i n m. 6, T-2,T-5)  CB3  development/new m a t e r i a l  mm.  6-9  2nd phrase m. 6 Cd3 m. 7 Cd'3 mm. 8-9 C d " 3 .. cadence- 1 i ke - f i g u r a t i o n with s i m u l t a n e i t i e s repeated i n t r a n s p o s i t i o n in mm. 6-85 e x t e n s i o n with cadence in mm. 8-9  59 Example 2-14b c o n t i n u e d . 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 p r o g r e s s i o n repeated m. 13 Cd"' 3 ... t r a n s p o s e d s i m u l t a n e i t y -from CB3 •for -final cadence chord  What d i f f e r e n t i a t e s things,  among o t h e r  i s the r e g u l a r i t y of harmonic change through much of the  p i e c e , namely nies.  " I I " from " I " and " I I I " ,  the common q u a r t e r - v a l u e time-span of most harmo-  The o n l y  i r r e g u l a r i t i e s occur  i n mm.  9 and 11-14 (Ex. 2-  14) because of r e s t s f o l l o w i n g the harmonies, again  interpreted  as s i l e n c e s through which harmonic p e r c e p t i o n s c o n t i n u e . these measures, results.  rhythmic d e c e l e r a t i o n ,  U n l i k e the d i f f e r e n c e  6-9 i n " I " ( i . e . ,  a factor  In  i n cadence,  i n the harmonic rhythm of mm.  another i n d i c a t o r of the t e r n a r y form), the  harmonic rhythm of " I I " i s g e n e r a l l y r e g u l a r and thus not a factor  i n the p e r c e p t i o n of the formal d i s t i n c t i o n of mm.  Harmonic  rhythm  of "III".  Example  harmonic rhythm and form of " I I I " .  2-15  p r e s e n t s the  6-9.  60 Example 2-15.  Harmonic  rhythm and form of  (a)Harmonic rhythm, with MEASURE.' T-LEVEL:  1 O  "III".  time-spans of harmonies g i v e n  2 3 S 8 3 7 1 0 1  4 4 7 0 3  5 8  -  j  6  below:  7 11  DURATION OF T - L E V E L S ! «  j-  ~  j  -  J  -  TIM-SMNS:U> 5 6 4 2 4 2 MEASURE: T-LEVEL:  8 2  6  6  J. J. 6  <b)Form of  6  9 9  10 2  10  -  - ^  2 4 3 5  12 5  0  1  19  ;  ^  19  17 IS  13 14 5 0 4 7  5J.  J* c/ 12  11  ;  -  JNJ- W 5  6  4 2 4 2  7 7  13  "III":  CA3: e x p o s i t i o n mm.  1-2  mm. 3-6 (continuat i o n of exposition with new material)  1st phrase m. 1 C c 3 m. 2 Cd3 2nd phrase m. 3 Ce3  c o n t i n u a t i o n i n t o m. no cadence  3,  with  i n i t i a l f i g u r a t i o n has l i m i t e d s i m i l a r i t i e s with i n i t i a l f i g u r a t i o n , m. 1 m. 4 Cf3 climaxing action, consisting of two-fold m o d i f i e d t r a n s p o s i t i o n of three-harmony f i g u r a t i on mm. 5-6 Cg3 . . . . . . h i g h p o i n t or cadence of c l i maxing a c t i o n of m. 4 m. 7 Ch3 b r i d g e to "B"  61 Example 2-15 c o n t i n u e d . CB3: development/new m a t e r i a l mm.  8-11  3rd phrase m. 8 C i 3 m. 9 C i ' 3 . mm.  CA'3: m o d i f i e d mm.  12-15  m o d i f i e d r e p e t i t i o n of 2nd f i g u r a t i o n , m. 8 10-11 Cj3 .... cadence  recapitulation  4th phrase m. 12 Cc'3 m o d i f i e d t r a n s p o s i t i o n of m. 1 m. 13 Cd'3 m o d i f i e d t r a n s p o s i t i o n 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 c o n s i s t e n t harmonic rhythm of " I " and " I I " . the  initial  the notated  t i m e - p o i n t s of some harmonies do not c o i n c i d e with barline,  examples of such b e i n g T-O <m. 1), T-5 (m.  4 ) , T - l l (m. 7 ) , T-5 (m. 12), and T-O Up t o m. 5 t h e r e a r e r e l a t i v e l y except  an apparent phrase b e g i n n i n g .  there riod  (m. 14). s h o r t harmonic  f o r T - l <m. 3 ) , which i s s i g n i f i c a n t  tively  Moreover,  durations,  as i t c o i n c i d e s with  Measures 5-7 r e p r e s e n t  a rela-  sudden d e c e l e r a t i o n i n the harmonic rhythm, a f t e r  which  i s some degree of a c c e l e r a t i o n with m. 8, and another peof d e c e l e r a t i o n with mm.  9 - l i . The r e c a p i t u l a t i o n  13) r e p r e s e n t s an a c c e l e r a t i o n , with f o l l o w e d by a f i n a l  (mm. 12-  s h o r t e r harmonic d u r a t i o n s ,  d e c e l e r a t i o n at the cadence  (mm.  14-15).  There a r e 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 "III".  with, or occur portant  Some s i n g l e T - l e v e l s of longer d u r a t i o n c o i n c i d e in c l o s e proximity  t o , cadences or f o r m a l l y im-  t i m e - p o i n t s : T-8 (mm. 5-6)5 T - l l (m. 7 ) , a melodic  " b r i d g e " t o the resumption of harmonic a c t i v i t y  i n m. 85 T-2  62 (mm. mm.  10-11), p r e c e d i n g the m o d i f i e d r e c a p i t u l a t i o n of mm. 12-13; and T-O  (mm.  t r a n s p o s i t i o n of T-2 and  14-15),  harmony  the f i n a l  (mm.  the e f f e c t mentioned  of cadence. time-spans  measures and exact  10-11).  the sense of d e c e l e r a t i o n produced Interestingly,  1-2 i n  The  longer d u r a t i o n s ,  thereby, c o n t r i b u t e to each of the f o u r  afore-  i s approximately nine eighth values in  durat i on.  H i e r a r c h y of T - l e v e l s F i g u r e 2-5 ual p i e c e s and quency level  p r e s e n t s a h i e r a r c h y of T - l e v e l s i n the i n Trois  as a whole, based on  Compositions  of o c c u r r e n c e and t o t a l  individ-  time-spans.  h i e r a r c h i e s f o r the i n d i v i d u a l  pieces  In F i g . 2-5c, ( F i g . 2-5a  and  are combined  by a v e r a g i n g .  F i g u r e 2-5.  H i e r a r c h y of T - l e v e l s based on f r e q u e n c y of o c c u r r e n c e and t o t a l time-spans. occurrence'.  DESCENDING HIERARCHIC ORDER, LEFT TO RIGHT "I":  0  2/3/4/7/9/11  •II":  0  5  3/10  •Iir:  0  3  7  0  5  3/7  T-'Iir:  8  2 /4 /8  6/10  (1 / Si  NO 8)  (1/2/4/6/7/9/11) (1 / 3 / 6 / 9 / 10 / 11)  2 / 4 / 10  the T2-5b)  3 3  ( a ) H i e r a r c h y of T - l e v e l s from most s i g n i f i c a n t f r e q u e n c y of  fre-  9 / 11  6/8  1  to l e a s t based  on  63 F i g u r e 2-5  continued.  (b) H i e r a r c h y o-f T - l e v e l s based on t o t a l •I':  0  11  4/7  •II":  0  5  3 / 10  8  7  1 / 2 / 4 / 6 / 9 / 11  •III':  0  8  2 /5  11  9  1/7  8  7  •r-'III":  0 5  11  3/5/9  2  2  9  6/ 10  time-spans:  1  4 /6  3  4  3 / 10 10  1/6  (c) H i e r a r c h y o-f T - l e v e l s based on combination above: 0  11  4/7  •11".  0  5  3 / 10  •Iir:  0  5  8  2  7  0  3  7  2  3  •I":  •I'-'Iir:  3/9 8  2 7  3  6/10  o-f (a) and  (b),  1  1 / 2 / 4 / 6 / 9 / 11  4  11  / 11  9  1  6  4 8 / 9  3  10  / 10 1 6  Note: In ( a ) , T - l e v e l s i n d i c a t e d i n b r a c k e t s are those t h a t occur o n l y once. The s o l i d u s s e p a r a t e s two or more T - l e 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 o c c u r r e n c e and t o t a l time-span. T-O  i s most important  rence and T-level it  total  o-f the  time-span, and individual  In " I I " and  "III",  second most important important  T-level  cur with T-O formally  T-level,  a f t e r T-O.  in T-level  significant  pecially  t o n i c and  overall while  -final that  i n each  i n the p i e c e s , T-5  i s the  i n " I " , T - l l i s the most  While T-5  and  T - l l f r e q u e n t l y oc-  s u c c e s s i o n s i n the r e s p e c t i v e p i e c e s at  time-points,  g i e s with c o n v e n t i o n a l  T h i s s t r o n g l y suggests  s o n o r i t y , or " t o n i c , "  and  occur-  because i t i s the - f i r s t and  pieces.  f u n c t i o n s as a r e f e r e n t i a l  piece.  and  i n a l l t h r e e p i e c e s , based on  it is difficult  to make a n a l o -  t o n a l i t y and  i t s h i e r a r c h y of chords,  es-  dominant chords.  Perhaps the f u n c t i o n of  T-5  i s best d e s c r i b e d as a u x i l i a r y ,  es-  T - l l with r e s p e c t to T-O  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  i m p l i c a t i o n s of these T - l e v e l  c h i e s a r e , however, e x p l o r e d  hierar-  i n Chapter Three.  T - l e v e l s t h a t a r e s i g n i f i c a n t due t o t h e i r r o l e s i n s p e c i f ic  IC c y c l e s a r e a l s o s i g n i f i c a n t i n the h i e r a r c h i e s  in F i g . 2-5.  For example,  illustrated  i n " I " , T - l l (m. 4) i s the i n i t i a l  3-2 c y c l 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 c y c l e . and  In " I I " , T-10 and T-3, which occur  7, a r e the f i r s t  "III", rical  3, 4,  T - l e v e l s out of the i n t e r v a l 5 c y c l e .  T-0, T-5, and T-7 a r e important  i n the u n d e r l y i n g  In  symmet-  s t r u c t u r e which i s c e n t e r e d a t m. 4. T-level  s i g n i f i c a n c e , b e s i d e s b e i n g determined by frequency  of o c c u r r e n c e and t o t a l  time-span,  rence i n r e l a t i o n t o f o r m a l l y  i s a l s o suggested by o c c u r -  important  time-points.  s i o n , 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 - l e v e l w i l l another f o r m a l l y at f o r m a l l y dividual  T-level  important  time-point.  with  occurrences  important t i m e - p o i n t s a r e examined below i n the i n -  Occurrences and T h e i r R e l a t i o n s h i p s  t o Form  In a d d i t i o n t o reasons c i t e d above, T-0 i s more s i g -  s e c t i o n s , which help  form of " I " .  sitional  coincide  Such T - l e v e l  n i f i c a n t because of i t s o c c u r r e n c e s i n the f i r s t  to form:  On o c c a -  pieces.  "I".  mal  i n mm.  to delineate  and f i n a l  the r e c a p i t u l a t i v e t e r n a r y  P e r l e notes the r e l a t i o n s h i p of T - l e v e l  "The l a r g e r formal  recurrence  i m p l i c a t i o n s of c o n t r o l l e d  r e l a t i o n s are r e a l i z e d to a l i m i t e d extent  d e r i v a t i o n of the c o n c l u d i n g  for-  b a r s of the f i r s t  piece  transpo-  in • from  the trans-  65 p o s i t i o n s o-f the s e t that the  are c l o s e l y r e l a t e d  o r i g i n a l statement o-f the s e t . " ' * 3  i n PC content to  In a d d i t i o n ,  T-O  occurs  in m. 6, at the approximate midpoint o-f " I " . T-ll pitch  i n i t i a t e s the second phrase  transposition  middle s e c t i o n ingly,  o-f the T-0 harmony  (m. 6 ) , and r e c u r s  section, are  and s t r o n g l y  discussed  4-5) with an exact  (m. 1), and i n i t i a t e s the  within  the T-11,T-0,T-11 s u c c e s s i o n  most s i g n i f i c a n t T - l e v e l s  (mm.  (mm.  i t (m. 7). * 3  Interest-  31  6-7), employing the two  i n " I " , o c c u r s i n the middle -formal  implies  i n more d e t a i l  two c o n v e n t i o n a l  tonalities,  i n Chapter Three.  T-4, T-5, and T-7 a r e used t o t e r m i n a t e the - f i r s t , and  t h i r d phrases, r e s p e c t i v e l y .  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 r e c u r s  Other T - l e v e l s which recur and  7 ) , as p a r t  second,  T-3, which succeeds T-0 (m. i n i t , i n m. 11.  i n s i m i l a r s i t u a t i o n s a r e T-2  o-f c a d e n t i a l  which  harmonic s u c c e s s i o n s ,  (mm.  and T-4  (mm.  2 and 12), d e c o r a t i n g  or c o n n e c t i n g more important T - l e v e l s i n  c y c l i c progressions.  Hence, T-O, T - l l , and, t o a l e s s e r  T-3,  T-4, T-5, and T-7 can be c o n s i d e r e d t o be the most  cant T - l e v e l s T-level  "II".  form. place  signifi-  ( F i g . 2-5) and because of t h e i r l o c a t i o n s i n  t o the p i e c e ' s  form.  There a r e a few p o i n t s  r e l a t i o n s h i p of T - l e v e l s t o form. (mm.  extent,  i n " I " both because of t h e i r p o s i t i o n s w i t h i n the  hierarchies  relation  4  of i n t e r e s t c o n c e r n i n g the First,  the T-0,T-5  succession  1 and 10-12) i s one i n d i c a t o r of the r e c a p i t u l a t i v e Interestingly,  the only  ternary  o t h e r o c c u r r e n c e of T-5 takes  i n m. 6 (T-2,T-5), the f i r s t  measure of the middle s e c -  66 t i o n , with the T-2 s o n o r i t y c o n t a i n i n g the h i g h e s t melodic o-f the p i e c e .  Another s u c c e s s i o n o-f i n t e r e s t  3, 4, and 7 ) , o c c u r r i n g i n both t i o n s , although  the - f i r s t  i s T-10,T-3  and middle  n e i t h e r T - l e v e l o c c u r s elsewhere  pitch (mm.  -formal s e c -  in " I I " .  Sur-  f a c e -features o-f the t h r e e o c c u r r e n c e s b e t r a y no s i m i l a r i t y (other than the PC c o n t e n t o-f the harmonies),  so t h a t t h e r e i s  no r e a d i l y p e r c e i v a b l e c o n n e c t i o n between the two formal t i o n s due t o t h i s recurrence. T-7 (m. 9) c o n c l u d e s "I"  Finally,  the middle  (T-7, m. 8 ) , and precedes  section  sec-  the o n l y o c c u r r e n c e of (mm. 6-9), l i k e t h a t of  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 s u c c e s s i o n s . * 3  "Ill".  T-O and T-5, which appear t o g e t h e r  i n a number of  harmonic s u c c e s s i o n s i n " I I I " , occur at f o r m a l l y important points: first  m. 1, the f i r s t  p a r t of " I I I " ,  and mm.  s u c c e s s i o n ; m. 4, a f o c a l  i n c i d e n c e of these T - l e v e l s with such lar in  p o i n t i n the  p r e c e d i n g the harmonic "repose"  12-13, the m o d i f i e d r e c a p i t u l a t i o n of mm.  time-  of mm.  1-2.  5-7;  The c o -  time-points i s quite simi-  t o t h a t i n " I I " , where T-O,T-5 begins the p i e c e and i s used the r e c a p i t u l a t i o n .  (Of course, t h e r e a r e the formal  c a t i o n s of T-O's appearance as the f i r s t  and f i n a l  impli-  T - l e v e l of  " I I I " , which P e r l e has n o t e d . ) " 35  Associated  with r e c u r r e n c e s of the T-O,T-5 T - l e v e l  sion are three other T - l e v e l s : occurs first  i n both mm.  T-4, T-7, and T-8.  succes-  T-O,T-5,T-8  1-2 and 4-6, the b e g i n n i n g and end of the  formal s e c t i o n .  T-4,T-7,T-O o c c u r s  i n mm.  3-4, i n connec-  t i o n with the approach t o the harmonic repose of mm.  5-7, and  67 also occurs  i n mm.  13-15, the f i n a l  cadence.  T-4, T-7, and T-8  f u n c t i o n as T - l e v e l s e i t h e r f o l l o w i n g or p r e c e d i n g T-O and/or T-5,  g e n e r a l l y with a d j a c e n t T - l e v e l s r e l a t e d by ICs 3 or 5.  One other T - l e v e l concludes  of s i g n i f i c a n c e  the f i r s t  phrase  i s T-2, which i n i t i a t e s and  of s e c t i o n  "B" (mm. 8-11) of the t e r -  nary form of " I I I " . In g e n e r a l , T - l e v e l s t h a t a r e more s i g n i f i c a n t , the h i e r a r c h i e s p r e s e n t e d ly  important  Recurrent  based on  i n F i g . 2-5, u s u a l l y appear at f o r m a l -  time-points.  Harmonic  Successions  Components of the t h r e e i n t e r v a l 5 c y c l e of T - l e v e l  3 c y c l e s and the i n t e r v a l  s u c c e s s i o n s r e c u r , some with more frequency  than o t h e r s , and some i n two or t h r e e p i e c e s ( F i g . 2-6).  68 F i g u r e 2-6.  Recurring T-level Compos  successions  (a)Frequent 1y occurring T-level s u c c e s s i o n s , with the number of occurrences:  (b)Multiple  T-level  T-1 eve 1 successions  4 4  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  3 3 3 3 3 3 3  T-l,T-4 T-3,T-10 T-7,T-10 T-8,T-ll T-10,T-1 T-ll,T-2  2 2 2 2 2 2  (c)Recurring T-level M  J  1  2  "II" "III  1-2 1-2 4-5  T-O,T-5,T-O T-5,T-O,T-5  5-5-5-5 5-5-5  "II" "III"  10-12 12- 13  T-4,T-7,T-O  3-5  "II" "III"  8-10 3-4 13- 15  T-4,T-7,T-O,T-5  3-5-5  T-9, T-2, T-5  5-3  T-6, T-9, T-2,T-5 T-IO,T-l,T-4,T-7  II " III "  8-10 3-4  J "II" "III"  4-5 5-6 9-12  3-5-3  "II" "III"  5-6 8-12  3-3-3  J "III  1- 3 2- 4  3-3  J "II"  10-12 4-5  II  II  II  4  3 6  7  8 10,11 12  MEASURE:  1  T-LEVEL:  0 - 5 8-1 10-3 6 - 9 2 - 5 10-3 8--11-4 7 0 - 5  RECURRENT * SUCCESSIONS:  1  II  II  II  s u c c e s s i o n s o+ two and more T - l e v e l i  3  3,4  Measure  5-3  T-LEVEL: 0—3—10 1-4 7 - 1 0 - 4 1 1 - 9 - 2 5 11-0 11-2 7 3 - 6 RECURRENT * * • * i SUCCESSIONS: *—*  2  Pi ece  T-O,T-5,T-8  II  MEASURE:  Trots  successions:  IC s u c c e s s i ons  T-O,T-5 T-4,T-7 T-5,T-O  in  ttions.  3  t t—• *  6  7  8  9 10,11 12 13  *  * * *—I  I  * * *  13  9-4-9 0 ( )—•  0 0 *  69 F i g u r e 2-6c "Ill  continued.  ll  MEASURE: T-LE«EL: RECURRENT SUCCESSIONS:  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-  i  i  t  f  f—f  *  f-  f  {  )  —  f  Note: R e c u r r i n g T - l e v e l s u c c e s s i o n s are i n d i c a t e d above u s i n g "* with "*" d e n o t i n g f i r s t and l a s t s o n o r i t i e s of the r e curring successions. "#- ( ) i n d i c a t e s an i n t e r p o l a t e d Tl e v e l , not p a r t of the r e c u r r i n g s u c c e s s i o n . In t h i s f i g u r e , r e c u r r i n g t w o - T - l e v e l s u c c e s s i o n s are only i n d i c a t e d when they are not p a r t of m u l t i p l e T - l e v e l s u c c e s s i o n s . Based on F i g . 2-6a, successions utilized  only 44 of the  144  possible T-level  i n v o l v i n g d i f f e r e n t combinations of two  i n the t h r e e p i e c e s  non-recurrent).  (16 r e c u r r e n t s u c c e s s i o n s and  Some of these f r e q u e n t l y o c c u r r i n g  s u c c e s s i o n s are components of m u l t i p l e T - l e v e l 2-6b), a l l of which have adjacent 5.  F i g u r e 2-6c  important  forms of  " I " , " I I " , and  g i n s " I I " and  " I I I " and  j u n c t i o n of the  have c e r t a i n  "III".  The  occurs  in mm.  i n t e r v a l 5 and  c e s s i o n T-7,T-O,T-5 o c c u r s both 4),  although  the o c c u r r e n c e s  another  cyclic  12)  " I I " (mm.  and  successions (Fig.  i l l u s t r a t e s the r e c u r r e n t T - l e v e l  time-points,  formal  function.  4-6  of  " I I I " at the con-  c y c l e s (mm.  i n " I I " (mm.  occurs  i n the f i r s t  earlier,  phrases of  formal-  r e l a t i o n s h i p s to the  1-3)  and  " I I I " (m.  in " I " (mm.  10-  a different  succession  and  Suc-  Similarily,  having  the c y c l i c  " I " (mm.  4-7).  9-10)  in function.  with each o c c u r r e n c e  As noted  successions.  r e c u r r e n c e s at  s u c c e s s i o n , T-3,T-6,T-9, o c c u r s 4-5),  ICs 3 or  s u c c e s s i o n T-0,T-5,T-8 be-  the 3-2  differ  28  two-T-level  T - l e v e l s r e l a t e d by  Some s u c c e s s i o n s , by v i r t u e of t h e i r ly  T - l e v e l s are  " I I I " (mm.  3-1 2-  70  4).  The  T-6,T-9,T-2,T-5 inciding the 5,  and  12.  5-6,  i n the  els  are  "B"  s e c t i o n ; and  there  "III",  discounted),  "B"  i s the  4-5)  "III",  mm.  i n mm.  mm. both  3-4  and  in " I " , at the  in "III",  s e c t i o n with alternation  12-13  (mm.  the  "A"  o-f w h i c h  are  T-4,T-7 w i t h  o-f " I I I " and  cadence  coof  s e c t i o n , mm. the  1-  -first  recapitulation  o-f two  in  T-levels in-  occurs  in " I I " ,  i-f i n t e r p o l a t e d  concluding T-O  recur,  linking the  12-15,  i t s variant  8-12)  T-O,T-5,T-0,T-5 w h i c h  interpolated levels,  occurred  and  mm.  section! in " I I " , linking  succession  10-14, and  ("I",  junctures:  c a d e n c e o-f t h e  mm.  ly  mm.  important  Finally,  volved  Those  ("II",  the middle  phrase m.  with  -form's "A" to  T-9,Y-2,T-5  succession  lev-  successions.  -following, p r e v i o u s -  i n " I I " , mm.  8-10  (i.e.,  T-4,T-7,T-O,T-5). To  complete  successions tions  underlying  o-f t h i s  content,  and  this  chapter element  study  o-f t h e  the  harmonic  will  ICC  system  and  the  T-level  progressions,  the  next  examine T - l e v e l  occurrence  and  successions  as  secto  ordering, respectively.  PC  71 C h a r a c t e r i s t i c s o-f T-Level S u c c e s s i o n s as to PC  PC  I n v a r i a n c e and  Pitch  Continuity  With s i x or more PCs v a r i a n t PCs  in the  indicated  t e r v a l vector  IC  by  the  1,  ICC  t h e r e are  the  invariance  in a PCC  i n c l u d i n g element  T-levels.  a f f e c t one's p e r c e p t i o n  two  a  IC content o-f the  t h r e e i n v a r i a n t s between  must be m u l t i p l i e d by  and  PCC,  Q u i t e simply, with the  i n t e r v a l vector  of s i m i l a r i t i e s and  be-  T-levels, IC-6-  (in t h i s  in order to determine and  be-  T-levels  T - l e v e l s , -five  number -for IC 6  in-  "10")  In the case o-f  Such i n v a r i a n c e  3  continuity  differences  the can  i n har-  progression. PC  16 and  invariance 2-17.  and  In Ex.  pitch continuity  2-16,  PCs  to  the  i l l u s t r a t e differences  i n the  are b r a c k e t e d , with the  numbers of Variant  implication  i n those  successions.  2-  pieces,  IC r e l a t i o n -  invariant  PCs.  elements i n each  that  in c e r t a i n harmonic s u c c e s s i o n s i n the music w i l l fewer i n v a r i a n t PCs  in Exx.  three  the b a s i s of T - l e v e l  Boxes h i g h l i g h t these i n v a r i a n t PCs. T-level  are examined  of T - l e v e l s of  in s c a l e form, are compared on ships  i s , PC  T - l e v e l s , -four between I C - 4 - r e l a t e d  number o-f i n v a r i a n t P C s . "  monic  total  a number o-f i n -  a number o-f these  that  t h r e e between I C - 2 - r e l a t e d  T-levels,  case, two)  the  o-f " I " < not  -four between I C - 5 - r e l a t e d  related  and  number o-f i n v a r i a n t s  interval vector.  o-f the  tween I C - 3 - r e l a t e d and  The  o-f i t depends on  ing C3 3 5 4 4 23, r e l a t e d by  T - l e v e l , t h e r e are  involve pitch continuity,  same r e g i s t e r .  transposition as  per  i n most T - l e v e l s u c c e s s i o n s ,  i n v a r i a n t PCs  Content  t h e i r absence mean p o s s i b l y  •" 72 Example 2-16.  I n v a r i a n t PCs o-f IC-1-  to IC-6-re 1 ated  •r I T-0  T-0  /*  *  hn  n a n  1«  *  yo  II  I  1-1  * t«i nj  1  l_m  _  — J t f —ILK-  L-I/L,,\ i  1  ELEMENT 9 NUMBERS: 0  1  10  0  1  8  10  9  4  6  4 T-4  T-l  ELENENT NUMBERS:  0  3  8  9  8  T-0  T-0  J2ZE  0  3  6  8  10  0  1 3  6  8  9  1  3 4  T-5  T-2  bo  10  0  1  4  ft?  "  6  8  10  0  T-0  T-0  jzzz 0  1  3  4  6  9  0  3  4  6  9  10  3  4  T-6  T-3  rr-\o ^0 9  10  0  1  3  6  6  9  10  0  A  T-level<  73  Example  2-16  continued.  •II' T-O  T-O  0  4  1  0  1  3  4  9  11  0  T-4  T-l  11  0  3  8  T-O  T-O  H  d h 0  1  3  6  8  11  <>0 4  0 1  6  P  8 9 1 1  T-3  T-2  11  0  1  4  6  11  9  0  1  3  4  6  T-O  T-O  -n  H P 0  3  4  m  & 6  9  11  0  3  6  9  T-6  T-3  3sc  ID  |HH|° ) T (n  9  0  1  3  6  8  6  9  0  3  7 4  Example 2-16 continued. •nr T-0  T-0  0 1  9 10 11  4  0 1  3 4  8  10  11 0  4  6  8 9  11  T-4  T-1  11 0  8  3  9 10  8 9  T-0  T-0  0 1  3  6  8  10 11  0 1  3 4  6  T-5  T-2  IT  10 11 0 1  4  6  8  8  9  10 11 0 1  3 4  6  T-0  T-0  •55  as 0 1  3 4  6  9  11  0  3  4  6  9 10  9 10  0  3 4  T-6  T-3  9 10  0 1  3  6  8  6  75 There may be as few as two and as many as seven PCs common to a d j a c e n t harmonies. (which occur very PCs,  IC-l-related T-levels  infrequently)  usually  w h i l e IC-3- and I C - 5 - r e l a t e d  frequently  i n " I " and " I I "  have only  T-levels  four  common  (which occur most  i n a l l t h r e e p i e c e s ) have f i v e t o seven  invariant  PCs. Example 2-17 i l l u s t r a t e s PC i n v a r i a n c e in  t h e harmonic s u c c e s s i o n s of the p i e c e s .  cessions  a r e shown on t h e f i r s t  continuity  highlighted  These harmonic suc-  of t h r e e systems, with p i t c h  i s o l a t e d i n the t h i r d , with  the i n v a r i a n t PCs.  total  (invol-  l i n e s con-  A p a i r of numbers (the f i r s t un-  b r a c k e t e d , the second bracketed) f o r every s u c c e s s i o n the  continuity  i n the second, and PC i n v a r i a n c e  ving d i f f e r e n t registers) necting  and p i t c h  indicates  number of i n v a r i a n t PCs and p i t c h c o n t i n u i t i e s , r e s -  pect i v e l y . Following continuity sented  the systems i l l u s t r a t i n g PC i n v a r i a n c e  in a given piece,  i n the s y s t e m s — v i s u a l l y  ing PC content line An  a graph—based  on i n f o r m a t i o n  i n each s u c c e s s i o n ,  i n the l i n e  fewer i n v a r i a n t PCs.  with the h e i g h t of the s o l i d  indicates  succession.  l e s s s i m i l a r i t y because of  In order t o account f o r p i t c h  an  additional  on  one u n i t v a l u e per i n v a r i a n t PC as i n d i c a t e d  of  the graphs.  nu i t y .  pre-  i l l u s t r a t e s the degree of chang-  i n d i c a t i n g the number of i n v a r i a n t PCs i n each  elevation  and p i t c h  continuity,  h a l f - u n i t v a l u e i s a s s i g n e d t o such p i t c h e s , on t h e l e f t  based side  Dash l i n e s i n t h e graphs i l l u s t r a t e p i t c h c o n t i -  76 Example 2-17.  PC i n v a r i a n c e successions  and p i t c h c o n t i n u i t y  p+  Trois  Compositions.  •r MEASURE:  111  T-LEVEL:  O  121 3  io  4  l  F  131 7  io  PITCH COLLECTIONS:  - t o — ^ —  "rw—  THW—  JN %S—b  HO  JO  PITCH CONTINUITY:  Jit—-  b,-*  V PC INVARIANCE (WITHOUT P I T C H C O N T I N U I T Y ) :  3(4)  4(1)  5(1)  5(11  5(2)  5(2)  in T - l e v e l  2(1)  3(1)  4(2)  4(3)  4(2)  3(1)  4(2)  4(1)  78 Example 2-17 c o n t i n u e d . [81  [10,111  «7  (121  3  6  (131  9  1 ^  4  9  0  tf/ M  ^  K»  =i—  ^  | o  ^8  Sf ^.remso=a»=l —  j?  i s ai  —  •  •  \ °  /  —  ¥ 4(1)  3(1)  "  3(2)  —  !rt  \<r  'o 4(2)  PC c o n t e n t  !  1  te' 3(1)  j  i>8  1  5(2)  Graph o-f changing  t|0—  ' ^ " " o 4(2)  "  6(3)  in " I " :  NUMBER OF INVARIANT PCs 0 1 2 3 4  5  , 11  6 7  j  1 'I  1 I  ^ r J U " I  i •  T-:  0 3  N.:  1  10  1 4 7 10 4 2  3  11  9 2 3  4  3  11 0 6  11 2 7 3 6 9 4 9 0 7  8  10,11 12  13  79  80 Example (41  '  2-17  continued.  [SI  3(01  (6)  5(4)  5(1)  S(l)  4(2)  5(3)  5(2)  5(2)  5(2)  4(2)  4(0)  4(0)  3(2)  8(1)  81 Example 2-17 c o n t i n u e d . Graph of changing  PC content  in " I I " :  NUMBER OF INVARIANT PCs  Li T-: N.:  0 3 8 1 1 2  10 3 10 3 6 9 2 5 3 4 5 6  10 3 8 7 8  11 4 7 0 5 0 0 9 10,11 12 13  "III"  5(0)  4(1)  3(2)  3(0)  3(0)  3(0)  7(1)  82  E x a m p l e 2-17 [31 1 W fci  ftojft  continued. [41 7  4  0  [81 2  (71 11  13,61 8  5  J  in hi}  -43—-  fr*  i * —  —*a_hP  5HF-  k g — ^ tg. fry i ^  e — w°t to '* 1  ^  ,  Jt.fl fro  t.n  1  BO  y  ^  -Jol  ...  <»—  2  A °  1  i^H  I  =*e—  413)  410)  313)  191  9  3(3)  [10,111 2  3(0)  3(0)  1121  3(2)  [131  3  0  3  J2S-  ^7* »? JFfr Iff y t te  3(2)  3(1)  4(3)  i  i i —  0„_^O  3(3)  4(1)  312)  3(2)  ha  :—1  83 Example 2-17  3(0)  continued.  3(1)  3(2)  Graph of changing PC content  in "III"  NUMBER OF INVARIANT PCs 012345-  6-  I-: N.:  -»  0 5 8 3 7 1 2  10 1 4 7 0 5 8 11 2 6 9 2 5 0 5 0 4 7 0 3 4. 5 7 8 9 10 12 13 14  In " I " and " I I " , I C - 3 - r e l a t e d i n v a r i a n t PCs, w h i l e  IC-5-related  T - l e v e l s g e n e r a l l y have f i v e T - l e v e l s have -four} i n " I I I " ,  t h e r e a r e on average f o u r , and t h r e e ly-  •  IC-1-, 2-, 4-, and 6 - r e l a t e d  i n v a r i a n t PCs, r e s p e c t i v e -  T - l e v e l s which occur  infre-  84 quently (i.e.,  i n a l l t h r e e p i e c e s g e n e r a l l y have fewer i n v a r i a n t PCs u s u a l l y between t h r e e and -four PCs) .  the t o t a l  number o-f s u c c e s s i o n s  When one compares  i n each p i e c e and the t o t a l  num-  ber o-f i n v a r i a n t PCs, t h e r e a r e -fewer i n v a r i a n t PCs i n " I I I " -for the number of harmonic s u c c e s s i o n s , compared with (There a r e i n t o t a l in  " I I " than  hibit  " I " and " I I " .  s l i g h t l y more i n v a r i a n t PCs i n s u c c e s s i o n s  i n "I".)  In other words, s u c c e s s i o n s of " I I I " ex-  a g r e a t e r degree of harmonic change, based on PC i n v a r i -  ance.  T h i s i s due i n p a r t t o the f r e q u e n t  occurrence  of PCCs  with few or no v a r i a n t elements. Moreover, PC i n v a r i a n c e has c e r t a i n , c a t i o n s f o r the forms of the p i e c e s .  albeit  limited,  In the f i r s t  phrases of " I " (mm. 1-3 and 10-13, r e s p e c t i v e l y ) , 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 than  progressions T-5,T-ll  tinuity  than  and f i n a l there  i n mm. 6-8  i s more  (including  tmm. 5-6] and T-7,T-3 [mm. 8-10]).  1-4 and 9-13 of " I I " , t h e r e  impli-  In mm.  i s l e s s PC i n v a r i a n c e and p i t c h  the middle s e c t i o n .  In " I I I " , mm.  con-  1, 2 (from T-  l O ) , 3, and 8-12 (the t h i r d phrase) have more 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 than mm. 2, 4-8 (development), and 12-15 ( r e c a p i tu1 at i on) . An e q u a l l y important  factor  i n the p e r c e p t i o n of s i m i l a r i t y  i n two harmonies i s t h e e x t e n t of p i t c h c o n t i n u i t y . i n v a r i a n t PCs i n a s u c c e s s i o n , larity as  i tisdifficult  i n the two harmonies with  little  In going from " I " t o " I I I " ,  dency f o r harmonic s u c c e s s i o n s with  with  to perceive simi-  or no p i t c h c o n t i n u i t y ,  i s the case with most harmonic s u c c e s s i o n s  tions.  Even  i n Trois  Composi-  t h e r e i s an i n c r e a s i n g t e n no p i t c h c o n t i n u i t y  (i.e.,  85 -from 11% t o 33% of s u c c e s s i o n s ) . L i k e PC i n v a r i a n c e , p i t c h c o n t i n u i t y has some i m p l i c a t i o n s f o r form. and  In " I " , s u c c e s s i o n s T-O,T-3 (m. 1), T-10,T-4  T-9,T-O  each, occur T-ll and  (mm.  (mm.  12-13), with at l e a s t  at the b e g i n n i n g  or at cadences.  3-4) and T - 5 , T - l l  (mm.  fewer i n v a r i a n t PCs than  cent formal  sections.  T-4,T-7 (mm. immediately  s e c t i o n , mm.  continuities  4-8.  each,  successions  the c l i m a x i n g a c t i o n of the f i r s t 9-12, t h i r d phrase c a -  Structurally  significant  three PC  8-9), and Attl  ("III", mm.  pitch  invari-  pitch  conti12-  7-8), a l l of  at c a d e n c e s . " 3  PC I n v a r i a n c e The  In " I I I " ,  C4 and Ftt/Gb4 ("I", m. 3 ) , D4 ("I", mm.  13), E2,3 ("II", mm. which occur  3-4, with  sections.  i n each component s u c c e s s i o n , although  include:  T-4,  span a d j a -  three p i t c h c o n t i n u i t i e s  t o the r e c a p i t u l a t i o n ) have a t l e a s t  ance i s l e s s i n mm. nuities  successions,  1-7) and T-9,T-2,T-5 (mm.  dence and l i n k  Successions  In " I I " , s u c c e s s i o n s T-6,T-9 (m. 4) and  precede new formal (mm.  continuities  5-6), with no p i t c h c o n t i n u i t y  preceding  8-9), with at l e a s t  T-4,T-7,T-O,T-5  three p i t c h  (m. 3 ) ,  i n IC-3-Related  T-Levels  g r e a t e r number of i n v a r i a n t PCs i n T - l e v e l s r e l a t e d by  IC 3, the b a s i s of i n t e r v a l successions  3 c y c l e s which govern many T - l e v e l  i n the t h r e e p i e c e s , s u p p o r t s  f a m i l i e s based on T - l e v e l s c o m p r i s i n g  the concept  the i n t e r v a l  of T - l e v e l  3 cycles  (e.g., T-O, T-3, T-6, and T-9 of the 3-0 c y c l e c o m p r i s i n g the 3-0 T - l e v e l  family).-*  n o t i o n of "modulation"  0  In f a c t ,  t h e r e may be some b a s i s f o r the  from one T - l e v e l  family  (or component T-  86 level and  thereof)  " I I " at  to another.  least),  a conventional  there  In a given i s an  i n v a r i a n t PC  d i m i n i s h e d - s e v e n t h chord  posed IC 3 i n t e r v a l s , elements "0", T-level),  t h i s c o l l e c t i o n being  of the f a m i l y .  In " I I I " , element "9"  d i m i n i s h e d - s e v e n t h PC  invariance  illustrated T-0,  T-3,  " I I I " , four  2-18.  and  T-9  In Ex.  indicated  presentation occurring  noteheads. T-level, The  the  The  and  PCs,"  T-4,  three  pieces  i n g l y , the PC 1 ec t i ons. "*  x  PCs  T-levels  consistently  of the  3-0)  T-10)  are a l s o  of  oc-  invariant any  pieces  is  " I " , " I I " , and  by  with s o l i d  (i.e.,  the  vertical  open noteheads i n a s c a l a r  i n v a r i a n t PCs.  Those f o u r  PCs  of the f o u r T - l e v e l s , r e f e r r e d to i n Ex.  2-18b  with  i f v a r i a n t elements are  and  3-2  PCs  illustrated  c o l l e c t i o n s shown i n Ex.  T-5,  i n Ex. 2-18b  T-8,  one  employed.  of T - l e v e l f a m i l i e s  (T-2,  as  solid  i n a f a m i l y occur with only  quasi-invariant  and  of each  2-18a, which p r e s e n t s T - l e v e l s  are h i g h l i g h t e d  p o s s i b l y two,  T-7,  three  highlighted  2-18b  o t h e r f o u r PCs  i n v a r i a n t and  (T-1,  i n Ex.  l e a s t two  "quasi-invariant  "9"  i n each T - l e v e l of a f a m i l y  of T - l e v e l f a m i l y  i n at  does not  (T-level family  i n v a r i a n t PCs  and  superim-  family.  d i m i n i s h e d - s e v e n t h chord) are lines,  and  in T - l e v e l f a m i l i e s in a l l three  i n Ex.  T-6,  "6",  three  c o l l e c t i o n of a f a m i l y occur with  T - l e v e l of the PC  (i.e.,  "3",  (in " I "  c o l l e c t i o n forming  i n v a r i a n t to the f o u r  cur with every T - l e v e l ; hence only  given  T-level family  and  2-18b.  3-1  T - l l ) in Interest-  are o c t a t o n i c c o l -  87 Example 2-18.  PC i n v a r i a n c e  in IC-3-related  (a)T-O, T-3, T-6, and T-9 in " I " , " I I " , and 'II'  T-level  -families.  "III":  •III'  T-O  bo Wi^ 4 "1*  ,-3  I  bo  £21  T-6  3iS  loi te  315  T-9  (b) Co 1 1 ect i ons o-f i n v a r i a n t and q u a s i - i n v a r i a n t -families 3-0, 3-1, and 3-2: T-LEVEL FAMILY 3-0:  T-LEVEL FAMILY 3-1: T-l T-4 T  - E&,fr« 2Z 7  T-10 T-LEVEL FAMILY 3-2: T-2 T-5 T-8 T-U  in  zz  PCs o-f T - l e v e l  S3 F i g u r e 2-7 p r e s e n t s the s u c c e s s i o n s o-f T - l e v e l the  three pieces,  •family  o c c u r r e n c e s and t o t a l  F i g u r e 2-7. M  based on the T - l e v e l s ,  and t a b l e s  time-spans.  S u c c e s s i o n s o-f T - l e v e l  -families.  jM MEASURE:  1  2  T-LEVEL:  0-3-10  1-4  T-LEVEL FAMILY: 3-0/1/2: 0 MEASURE: T-LEVEL: 3-0/1/2:  3 7-10-4  1  10,11 1 2 13 3 - 6 9- 4- 9 0 0  1—0—  4  5 6  11-9-2  5 11 - 0 1 1 - 2 7  2—0—2  0—2  T-LEVEL FAMILY: OCCURRENCES: TOTAL TINE-SPANS I8TH V A L U E S ) :  I I I  1  3-0 7 28  8  7  3-1 5  1 3-2 5  1 83 0  "II MEASURE: T-LEVEL:  1 2 3,4 5 0 - 5 8 - 1 10 - 3 6 - 9  3-0/1/2:  0—2-  T-LEVEL FANILY: OCCURRENCES: TOTAL T I N E - S P A N S :  1- - - 1 - - - 0  3-0 7 29  3-1 4 13  6 7 8 2 - 5 10 - 3 8 - 1 1 - 4  — - 2 —  3-2 5 18  1—0- - 2 —  9 10,11 12 70 - 5 0 1 0 — 2 -- 0  -families i n o-f T - l e v e l  39 Figure  2-7  continued.  "Ill" MEASURE: T-LEVEl:  1 2 0-5 8-3-7-10  3 1-4  3-0/1/2:  0—2——0—1  MEASURE: T-LEVEL:  13 14 5-0-4-70  I 1 I  3-0/1/2:  2—0—1  I  4 7-0-5  5 7 8 9 10 12 8 11 2 6 9 2 5 0  0—2  0  0  T-LEVEL FAMILY: OCCURRENCES: TOTAL TINE-SPANS  2  0  3-0  3-1 3-2 6 2 4 26.5 15 42.5  There a r e no c l e a r c o n s i s t e n c i e s  i n the l o c a t i o n s and f u n c -  t i o n s of the i n v a r i a n t d i m i n i s h e d - s e v e n t h PCs of each T - l e v e l family,  although with  be exposed  " I " there  i n some sense  (i.e.,  exposure through temporal be  explained  l o c a t i o n i n the outer  isolation).  v o i c e s , or  Such i n c o n s i s t e n c y  cannot  by t o n a l procedures, such as r e s o l u t i o n s of the two  t r i t o n e s comprising (i.e.,  i s a tendency f o r these PCs t o  the i n v a r i a n t d i m i n i s h e d - s e v e n t h  outward or inward semitonal  apparent c o n s i s t e n c i e s  resolution).  structures  Nor a r e t h e r e  i n the l o c a t i o n s and f u n c t i o n s of the  q u a s i - i n v a r i a n t PCs. In g e n e r a l ,  F i g . 2-7 i l l u s t r a t e s the f a c t  t h a t 3-0 and 3-2  f a m i l y T - l e v e l s each tend t o occur more f r e q u e n t l y tal  time-spans g r e a t e r Perle  in  Trois  than 3-1 f a m i l y T - l e v e l s .  i n d i c a t e s t h a t p i v o t a l c o n n e c t i o n s between harmonies  Compositions  a r e g e n e r a l l y used "merely as a means of  immediate a s s o c i a t i o n . " " * is  defined  and have t o -  2  This  i s generally  as a p i t c h c o n t i n u i t y i n adjacent  t r u e when " p i v o t " harmonies,  such p i v o t p i t c h e s g e n e r a l l y e x i s t between only harmonies i n Trois  Compositions.  two  On average, t h e r e  since  adjacent i s one p i t c h  90 c o n t i n u i t y per s u c c e s s i o n , although tion  there i s constant  fluctua-  i n the number o-f such p i v o t p i t c h e s with each s u c c e s s i o n .  When " p i v o t " i s understood adjacent shown.  harmonies, then  more b r o a d l y as any i n v a r i a n t PC i n  t h e r e a r e more p i v o t s as Ex. 2-17 has  The above-mentioned d i m i n i s h e d - s e v e n t h  to I C - 3 - r e l a t e d T - l e v e l  -formations common  f a m i l i e s r e p r e s e n t a more s p e c i f i c  of p i v o t r e m i n i s c e n t of S c r i a b i n ' s Seventh  Sonata.,  type  as analyzed  by P e r l e . Another p i v o t a l f o r m a t i o n i s t h e " d i m i n i s h e d seventh" chord, c o m p r i s i n g the o n l y notes common t o a l l f o u r members of the t r a n s p o s i t i o n a l complex [ i . e . , the s e t a t T-0, T-3, T-6, and T-93. . . . Of importance i n i t s c o n n e c t i o n with l a r g e r formal e l e ments i s the group of notes c o m p r i s i n g the t r i t o n e r e l a t i o n s h i p s w i t h i n t h e s e t , the i n v a r i a n c e of which at the t r a n s p o s i t i o n of a t r i t o n e r e s u l t s i n a s i x note segment common t o any two s e t s a t r i t o n e apart."*»= While t h e r e i s , on average, c e s s i o n , approximately positions  76% of such  p i v o t p i t c h e s of Trois  Com-  (79% i n " I " , 77% i n " I I " , and 73% i n " I I I " ) a r e i n v a r -  iant diminished-seventh <•  one p i t c h c o n t i n u i t y per suc-  ther T - l e v e l  PCs of t h e T - l e v e l  of the g i v e n s u c c e s s i o n  f a m i l y t o which e i -  belongs.  91 Element O c c u r r e n c e and  Besides there and cent  Ordering  the study o-f T - l e v e l  i s the matter o-f v e r t i c a l  o-f h a r m o n i c a l l y  Although  l i n e a r element  currence  and  Gojowy observes  of  o r d e r i n g which w i l l  Example 2-19  Primary  MEASURE! 1 T-LEVEU 0  10  I I  8  10  9  8  3  now  be  (and  not  content order-  system,'**  13 I 7  2 1  8  3  I 4 I 3  9  oc-  examined.  the p i t c h e s of the primary  element  numbers.  melody of '" I'  I 4 I 3  between adja-  t h a t o n l y PC  collections  |4 10  4|  I 3I 9  11  o ELEMENT* NUMBERS! 3  occurrence  Ordering  presents  " I " , with c o r r e s p o n d i n g  Example 2-19.  contents,  though l i m i t e d , p a t t e r n s of element  L i n e a r Element Occurrence and "I".  harmonies and  l o c a t i o n ) i s determined by the ICC  t h e r e are i d e n t i f i a b l e ,  ody  and  or l i n e a r l y d i s p o s e d  ing or r e g i s t r a l  Compositions  s u c c e s s i o n s as to PC  o r d e r i n g , both w i t h i n i n d i v i d u a l harmonies.'*'*  i n Trois  0  I 6 I 3  8  10  3  2 | 5 |  Q  II 0 I 0 I  mel-  9 2  Example 2 - 1 9 c o n t i n u e d . I 7 I 11  M. | 6 T- 111  fee. •#  -4n 5*^  NO.| 8  4  6 0  g  ^bni^ L ~ — VW<>.  9  9  3  I 7  9  8  1  10  9  8  3|3  larly  Q—&  1 OJL  r, o  7  , \ u,\ n  —"—  1  I 8 4 6 0 9 10 3 1 10 9 8 5 |  | 13  I 8  3  - t —  4 | 3  Elements " 3 " , " 8 " , and rence)  "  6 | 9 4 9 | 0  \b0  Q\uW)  3  ,i  r i*n"  -TJ  | 12  13  E> NO.| 3  10  I 10,11  N. | 8 T-  1  1  8  3  I 3 |  " O " ( i n descending  order o-f o c c u r -  are used more -frequently i n the primary melody, i n mm.  1 - 5  and  1 0 - 1 3 .  Where t h e r e are two  melody p i t c h e s per harmony, one extent,  " 1 " , " 8 " , and  or more primary  -finds t h a t " 3 " and,  to a  " 9 " occur -frequently as i n i t i a l  elements. - In most c a s e s , these elements r e p r e s e n t the ly  isolated  initial  p i t c h e s o-f harmonies.  Hence  r  element  with t h i s i n i t i a t i n g q u e n t l y succeed  " 3 " would seem to be  -function.  c u r s i n c e r t a i n cadences m.  3 )  .  (i.e.,  melody.  T - 5 , m.  melodic textural-  " O " -frequently  l i m i t e d l y associated  Elements " O " , " 4 " , and  " 3 " i n the primary  lesser  Where t h e r e i s only  one melody p i t c h per harmony, elements " 3 " and occur.  particu-  Element  5 ; T - O , m.  " 8 " -fre-  " O " a l s o oc1 3 ; and T - 1 0 ,  93 "II". of  Example 2-20  p r e s e n t s p i t c h e s o-f the primary  melody  " I I " , with c o r r e s p o n d i n g element numbers.  Example 2-20. K.|  1  12  T-|  0  3 18  Primary 4  I 5  I 6  1 | 10 3 I 10  3 | 6  9 | 2  9|3  3 I 3  "3",  and  | 3  NO.I 11 8 | 8  4|8  I  melody o-f " I I "  4 I 11  5  0  I 7  18  |10  3 18  11 1 3  0  11 | 3 0  | 11  4 |  11  31  H. I 9 I 10-11 I 12 I 13 I T-| 7 L 0 5 I 0| 0 1  8 1 11 I 11 I  N0.| 9 | 11  Elements "11",  "8" occur most -frequently i n the  primary melody, with element "11" as i t i s the i n i t i a l tion,  and  (T-O,  m.  element o-f the p i e c e and  a l s o the -final element. 13)  i s transposed  i t s p i t c h c l imax), "11"  the most s i g n i f i c a n t  m.  i n m.  o-f the  o-f these recapitula-  Moreover, the -final 6  7 (T-3), and  (T-5, which succeeds m.  r e t a i n e d i n the primary melody i n each case.  There are no apparent  the primary  "III".  of  f-2  and  8 - . ( T - l l ) , with e l ement However,  t h e r e i s no a s s o c i a t i o n with -function, as with element "I".  T-level  "3" i n  p a t t e r n s o-f element o r d e r i n g w i t h i n  melody.  Example 2-21  p r e s e n t s p i t c h e s pf the primary  "III",, with c o r r e s p o n d i n g element numbers.  melody  94 Example 2-21.  Primary melody o-f " I I I " . 12  5  MM  3 9  10 6 8 9 | 0 4 4  T- | 0  I 1  31 3  I 5-6 I 8  N. | 4  I 4 4 | 7  |3  | 8 3 7 10  1  11 9  10 9  10 10  I 7 I 11  *\&9*<>"''  N0.| 10 0 1 10 0 (8)  H. I T- |  I 6  (3) 10  I 8 3 0 1 4 6  I 9 | 10-11 I 12 6|9|2 13  8 2  3p  I 10 0 1  :  13) 8 0  I 13 15  1 41  | 14-15 0  4 7 10  I I  fee  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 -  q u e n t l y and have t h e g r e a t e s t t o t a l parent c o n s i s t e n c y  time-spans, t h e r e i s no ap-  i n element r e c u r r e n c e or o r d e r i n g .  a number of element sequences t h a t do r e c u r , such as: "10"  i n mm.  "0"-"l"  1 and 125 "O"-"4"-"4"-"3"  i n m. 4.  i n mm.  A l l t h r e e i n v o l v e the t r a n s p o s i t i o n of harmon<m. 1) and "3"-  (m. 3) i n v o l v e no such r e p e t i t i o n .  ment r e c u r r e n c e s suggest a l i m i t e d element  form of element  Certain  element, and i n mm.  ele-  control:  "10" i n m. 1, i n m. 3 as a l o c a l melodic g o a l ,  as an i n i t i a l  »3»_»9»_  2 and 13; and "10"-  i c - m e l o d i c f i g u r e s , w h i l e sequences «3»-»9"-"10" "ll"-"9"-"10"  t h e r e are  i n m. 4  5-6 as a melodic g o a l ; and the  95 a l t e r n a t i o n o-f "8" In the •frequently  and  "O"  three pieces,  occurrence  and  i n " I " , "4"  "III"  "6"  in  bass  harmonies r e v e a l  Vertical  and  "6"  and  in " I I " , and  In g e n e r a l ,  "1"  three  "8"  occur most  Ordering  o-f v e r t i c a l  to some e x t e n t ,  "1" and  "6"  and  occur most  "6"  involving  no c o n s i s t e n t p r i n c i p l e s o-f  patterns  in  adjacent  ordering.  4 1 9  i n I n d i v i d u a l Harmonies  element o c c u r r e n c e and  significant  "1",  pieces.  element s u c c e s s i o n s  Element Occurrence and  Limited are,  "0",  In the bass l i n e s ,  lines.  i n the bass l i n e s o-f the  A n a l y s e s o-f l i n e a r  ing  elements "3",  occur most -frequently.  •frequently  7-11.  in the primary melody.  Element  "O",  in mm.  despite  any  order-  inconsisten-  c i es.  "I". with Ex.  Example 2-22a i l l u s t r a t e s the PCs 2-22b p r e s e n t i n g  sta-f-f n o t a t i o n  and,  the v e r t i c a l i z e d  ted both  linearly  ICC  In the case o-f two  harmony, the r e p r e s e n t a t i v e (i.e.,  on one  r a t i n g element numbers) and  at  T-O,  harmonies o-f " I " i n  below t h i s , with p i t c h e s r e p r e s e n t e d  p r o p r i a t e element numbers. melody p i t c h e s per  o-f the  by  ap-  or more primary elements are  sta-  l i n e u s u a l l y with dashes sepa-  vertically.  B r a c k e t s and  highlight  these v e r t i c a l i z e d  melody p i t c h e s .  the s c o r e  have stems that are connected to beams.  asterisks  Melody p i t c h e s  in  96 Example  (a)PCs  Harmonies of " I " with e l e m e n t numbers.  2-22.  o-f I C C A T  ho  ^ 10  o  (b)Verticalized  T-levels,  with  r e p r e s e n t a t i v e element  "it ^  kg AN —^  VERTICAL P O S I T I O N 8 I §(10) §8 7 1 i(8) 6 1 *3-8-10 3 0 5I 0 9 V) 4 1 i 31 4 1 1 21 6 4 11  1  I I  1  0 8  1  4  1  «(4)  1  *3 0 9 *8 1 6  13-4 1  9 1 6  1  T-LEVEL: MEASURE:  1 1 1  0 8  1  *(4)  1  3  10  1 1  1  #3-4 1  1 9 6  1  0 1  1  9 6 0 8 4 9 *3 M •6 0 8 1 3 4 4 1 9 3 6 1 8  1 1 1 1  1 2  4  1 1 1 1  gg-frg f  *(10> «3 i(8) H-8-10 9 1 0 9 0  1  4  4  1  1 6  8 6  1  •  1  to  1  6 9 3 8  1  4  1  1  1  7 3  1 1  10  4  1  11  1  4  9  2  I H081 1 1 *97 10 1 *91 1 10 | *011 6|6 *04 11 4 10 I ••' 1 M l *83 4 | *810 3 10 4 1 31 4 Hi(3) U10) *(8) | *6- •13) *(10) »I8) | 4 1 1 * 1 *10-9 *8-5 | 4 | *10-9 *8-3 | *4*3-i 3|8 *3-l «4" (3) | (3) (3) (3) I (3) (4) (1) (3) 11) 21 3 1 1 1,3 1,3 1 1,3 1,3 1 1,3-2,4 0,1 0,1 1 1 9 (9-3-8) I 1,3  T- 1 3 N. | 3  1 1  1  1  11 6  0  1 1  11 7  2  1 1  1  1 1  \fnO P  1  1  1  Jfre-  1  by  T-O:  L„ ELEMENTS:  pitches represented  1 1  numbers:  97 Example 2-22  7  continued,  1  4 1 SI  1 11  4  S  10  1 •(3) 1 •3-1 2 1 (0) 1 1 11,0 1 T- 1 7 N. 1 8 4 3  |  10  9 *3 0 •14)  4 | 9  •(10) •10-9 (1)  •3-4  | 18  •(8)  1  •8-3 |  6  8  |  1  6  1 1 1 1  4  0  3  6  (3)  0,1  1,3  10,11  1 8 1 •3 1 0 1 9 1 6 1 1 1 4 1 1 9 1 12  8 1 •0 3 •3 1 6 0 0 1 3 9 9 1 1  •8  6  6  4 1  1 4  4  9  1 9 1 8 1 3 1 1 0 1 13  1 1 1 1 1 1 1 1 1 1  Note: A s t e r i s k s (*) i n d i c a t e p r i m a r y melody elements, w h i l e "+" (m. 4, T-9 and T-2) i n d i c a t e s a s i m p l i f i c a t i o n i n the r e p r e s e n t a t i o n of these s o n o r i t i e s whereby melody elements "3" and "0", r e s p e c t i v e l y , doubled one octave below, are d e l e t e d i n o r d e r to show the seven-element s o n o r i t y . "++" (m. 5, T-5) shows an a l t e r n a t e way o-f r e g a r d i n g the lower p i t c h e s o-f T-5 harmony, as melodic approach p i t c h e s t o Eb4. In Ex. 2-22 tion  i n a chord  one,"  the next  and t h o s e t o -follow, the lowest v e r t i c a l (i.e.,  lowest p o s i t i o n  Hence, the f i r s t p o s i t i o n one, and so on. pecially  the lowest p i t c h )  " p o s i t i o n two,"  harmony of " I " (Ex. 2-22)  "1"  i s designated  i n p o s i t i o n two,  "4"  posi-  "position  and so on.  has element  "6" i n  i n t h r e e , "9" i n f o u r ,  Because seven-PC harmonies c o n s i s t e n t l y appear,  i n mm.  1-5  and  10-13, c e r t a i n p a t t e r n s of element  c u r r e n c e i n the i n d i v i d u a l as i l l u s t r a t e d  in Figure  vertical 2-8.  p o s i t i o n s can be  esoc-  observed,  98 F i g u r e 2-8.  Element o c c u r r e n c e s i n v e r t i c a l harmonies o-f " I " .  (a) Most -frequent element occurrences in p o s i t i o n s in " I " :  (b)Most f r e q u e n t element occurrences in p o s i t i o n ranges i n " I " : P o s i t i o n | Elements ranges I  E1ements  0,*8 3 *0 *9 *4 *1 1  7: 6: 5: 4: 3: 2: 1:  p o s i t i o n s of the  9 4 4 3,8 6 *3 *6  4- 8: 1-3: 1 8,9 0,4  5- 8: i-3:  I I I I I I I I  0, 3 8, 9 4, IO 1 4  6  3  O  3  4  8  1  3  4,6,9  9 8  Note: In p r o c e e d i n g -from l e f t t o r i g h t i n F i g . 2-8a and 2-8b, t h e r e i s a d e s c e n d i n g order o-f element f r e q u e n c y i n 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) i n d i c a t e s that elements "O" and "4" occur the same number of times i n a c e r t a i n p o s i t i o n . "#" i n d i c a t e s the most f r e q u e n t o c c u r r e n c e s of an element i n any p o s i t i o n . P a t t e r n s of v e r t i c a l cal  positions  extent,  ( F i g . 2-Sb)  "3", "4", and  element o c c u r r e n c e i n ranges of v e r t i have elements "1", and, t o a  "6" as o c c u r r i n g f r e q u e n t l y  lesser  i n the lower  p o s i t i o n s of harmonies, w h i l e elements "0", and, t o a l e s s e r tent,  "3", "4",  "8", and  "9" occur more f r e q u e n t l y  ex-  i n the upper  posi t ions. However, as shown i n F i g u r e 2-Sa,  a different  element i s  g e n e r a l l y the most f r e q u e n t l y o c c u r r i n g  i n each v e r t i c a l  posi-  t i o n , except f o r p o s i t i o n s one and two,  i n both of which  element  "1"  i s most f r e q u e n t .  element,  I f we s u b s t i t u t e the next most f r e q u e n t  "6", f o r "1" i n p o s i t i o n one, we o b t a i n a  harmony -for " I " , i n the sense t h a t istral  "referential"  i t r e f l e c t s the average r e g -  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 i n " I " , e s p e c i a l l y variations  o-f t h i s  est  ,  ,  ,,  ,,  in r e g i s t e r .  this  ticality  o-f " I " .  ,  ,,  ,,  which i s m a i n t a i n e d ,  a distribution  due  6-8  elements,  In o t h e r words, the - f i r s t v e r t i c a l i t y o-f " I "  the PCC,  in mm.  I t c o n s i s t s o-f e l e -  harmony i s Ab-Eb-Gb-Cb-D-F-Bb, the - f i r s t v e r -  registral  "I".  10-13, are  PCs -for these  e s t a b l i s h e s a normative  throughout  and  , ordered -from lowest t o h i g h -  When we s u b s t i t u t e T-O  "referential"  1-5  " re-f e r e n t i a l " s t r u c t u r e .  ments »6• -' l '-"4 -"9 -• 0"-"3"- 8 ,  i n mm.  This s t a t i s t i c a l  distribution  o-f elements o-f statistically,  u n i f o r m i t y i s not maintained  t o the use o-f the expanded  ICC, and  the  textural  d i fferences.  "II". lustrated  The p a t t e r n s o-f v e r t i c a l element i n Ex.  2-23.  o c c u r r e n c e are i l -  lOO  Example 2-23.  Harmonies o-f " I I " with p i t c h e s r e p r e s e n t e d by element numbers.  (a)PCs o-f the ICC at T-O:  9  bo ELEMENTS:  o  1  11  (b)Verticalized  VERTICAL POSITION  81 7 1 11 6 1 8 31 0 41 31 2 1 11 1  T-LEVEL MEASURE  T - l e v e l s , with r e p r e s e n t a t i v e element  1 8 1  1 3 1 8 1 2  1  4  1 9 1 6 1 4 1 0 1  9  3 1  1 0 1 1  3 1 1 1 1 1 1 1 9 1 «3 t3 | 11 U 1 8 « 11 11 I 1 1 9 1 3 4 | 9 6 | 11 8 8 8 | 6 6 1 9 3 19 1 1 I 6 1 1 | 8 3 0 0 1 4 0 I 6 1 1 18 9 3 I 1 1 8 1 0 11 6 1 0 8 | 0 6 10 6 14 0| 4 6 31 8 16 3 9 13 8 10 9| 9 4 9 1 9 3 1 4 0 14 0 18 4 | 6 t l t4 1 t4 I 4 1  11  0 6  i  8  1  1  fe—I  41  8  3 0 11  11 8  0 6  3 1 8 1 61 41  1  1  T- 1 10 N. 1 7  3 1 8 1 8  1 41  9 |  10  1 3 1  |  6  1  r  IS  —  9 1 11 3 1 8  8 1 U 1 11 1 U 1 81 81 0 1 3 91 91 0 1 6 1 0 61 0 1 61 3 1 91 3 1 41 9 4 0 1 4 1 91 11 1  3 0 1 3 1 4 9 9 9 91 9 1 2 1 6 t l t4 t4 | 6 t l t4 t4 t i l | t8 | 1 1 -  6  ho.  ~0~  11 1 3 0 8 8 1 11 0 1 8 3 6 1 0 11 3 1 4  •  1 5  E  JZL 0  I  1 10 3 1 14  3  ^  7 *  7 1 3 6 1 11 5 1 8  I  it  5E  3  I 103  I  1 7 1  6  41 1  6 1 t4 | 1  1  0 51 0 1 01 I 12 I 13 I 1 9 1 10-11  numbers:  lOl  Note: A s t e r i s k s (#) i n d i c a t e d e l e t e d d o u b l i n g s o-f primary melody and bass elements, s i m p l i f i c a t i o n s of harmonies i n order to show the seven-element s o n o r i t y . "+" (m. 6) i n d i c a t e s a m o d i f i c a t i o n of the T-2 harmony, with a l l elements i n c l u d i n g "1" in the v e r t i c a l r e p r e s e n t a t i o n . Unlike  the harmonies of  primary melody element regard  i n the uppermost v e r t i c a l  the upper f o u r , as suggested by  p o l y r h y t h m i c f i g u r e s of mm. lesser extent,  "9",  "6",  ly)** * occur f r e q u e n t l y and  "3"  (A, C,  1-5 and  i n the  5  "11",  " I I " always have  and  and "O"  With  (lower  three  the d u p l e - t r i p l e  10-13), elements "4" (F, Bb,  the  position.  to element o c c u r r e n c e i n ranges of p o s i t i o n s  p o s i t i o n s and  a  " I " , those of  G and  and,  to  Ctt, r e s p e c t i v e -  lower t h r e e p o s i t i o n s w h i l e  "8",  E, r e s p e c t i v e l y ) occur f r e q u e n t l y  in  the upper f o u r p o s i t i o n s . As with  "I", a "referential"  harmony of  from the f r e q u e n t l y o c c u r r i n g elements »  4  . .  of 6  _ M » _ . , . . _ » . . _ . . 9  3  6  o  n  _ n  8  » _ n  X 1  n) _  " I I " can  (from lowest to  L i k e the  (T-5), 7  (T-3), and  8  harmony, and  Exx.  2-22 be  and  2-24  (T-O),  "III",  in  the  inner  consistent.  attempts to i n t e r p r e t the music s i m i l a r to  2-23.  Elements w i t h i n one  i n t e r p r e t e d as melodic  semitone or tone from adjacent 24 with the adjacent also v e r t i c a l i z e d  13  i n the c o n t r a p u n t a l  v o i c e fragments, the harmonic s t r u c t u r e s are not However, Ex.  harmony  (T-ll).  Because of the v a r i a b l e t e x t u r e of  number of elements per  derived  highest,  "referential"  " I " , t h i s s t r u c t u r e a c t u a l l y o c c u r s i n " I I " , i n mm.  "III''.  can  be  T - l e v e l or harmony that  ( e s p e c i a l l y those separated elements) are  element(s) i n one  so t h a t only one  included  p o s i t i o n , but  by  i n Ex. these  element o c c u r s i n one  a 2-  are  posi-  102 t i on,  Example 2-24,  Harmonies o+ " I I I element numbers.  with p i t c h e s r e p r e s e n t e d by  (a)PCs o-f the ICC a t T-0:  bo \\o ELERENTS:  (b)Verticalized  VERTICAL 10 POSITION 9 |  T-LEVEL MEASURE  bo  X o  n  o  10  11  T - l e v e l s , with r e p r e s e n t a t i v e element  numbers  103 Example 2-24 c o n t i n u e d .  l i p  3g  i2  -*e-  10 1  HO-0 |  1  1  91 8 1  81 0—1 I  1  1  71 I10--0--1—10—0—1- 9 8--6 8-6 4 61 0 1 - 0 10 0--1--0 SI 4 1 9 31 4 2 1 1 1  8-9 9 - 4  8  0  i I I I «8 | 0 | 3 | 6 | 10 -3 | 41-0-11  I T-1 6 | 9 • . 1 8 1 9  3  I I I  I 1 I  I 1 I  1 3 8  §3-  1 *8-  I 1  1  §0-1-  1  0  1 1 *8--0- -8 1 3 8 0  1 *6— 8*0-l-  |  0 4 6  |  6 3 4  1 4 6 3 1-  1  Ml  1 1 1 8 1 11 1 3-6 1 7  I I  3 #4- 4  I 4 1 1 tt 1 0 3 1 •10 1 10 1 •6-10 |  10  1 T- 1 7 M. 1 4  91 8 1 71 M 6| 8 S| 3 4 1 4 31 6 2 | 10 1 II  — 8  10 8  io i  9  1 |  iZ2I  »  1 1 2 1 8  I  M-6 | I *3-9~10 11 I 4 I *10 8 4 | tO 3 I *9 I M 1 6| 8 0 8 I 4 8 6 »3 I 13--1I *3~l-0 | 0 6 I tO M *4 0 | t l *1 I 8 11 I 4 13 8 14 4 I 6 2 I 1 6 0 1| 6 I 1  I I 2 I 10-11  I I S I 12  I I  I 5 0 4 7| 0 13 I 14-13  104 A study of element o c c u r r e n c e i n lower and upper ranges o-f p o s i t i o n s r e v e a l s a tendency -for elements "1", "4", and "6" (G#, B, and Db) t o appear more -frequently  i n lower v e r t i c a l  posi-  t i o n s , and "0", "3", and "8" <G, Bb, and Dt*) i n the upper tions.  T h i s p a t t e r n o-f o c c u r r e n c e i s s i m i l a r  posi-  t o t h a t o-f " I" . *»  s  Elements "2", "5", "9", "10", and "11" do not appear as consistently  as elements "0", "1", "3", "4", "6", and "8", the  i n v a r i a n t or unbracketed elements o-f the ICC. ment o c c u r r e n c e i n i n d i v i d u a l  p o s i t i o n s a r e such t h a t o f t e n  and more elements a r e s t r o n g l y r e p r e s e n t e d hence, t h e r e i s no c l e a r  "I",  "II",  consistencies  and  "referential"  "III''  in v e r t i c a l  t h r e e p i e c e s as a whole.  as  P a t t e r n s of e l e -  i n one p o s i t i o n ;  harmony.  There a r e no apparent  a whole.  element  two  l o c a t i o n and o c c u r r e n c e i n the  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  h i g h e s t r e g i s t e r s ) and " I I " ("4"-"9"-"3"-"6"-"0"-"8"-"11"), v e r tical  element d i s t r i b u t i o n s  to be q u i t e d i f f e r e n t .  i n harmonies of the two p i e c e s tend  With " I I I " ,  t h e r e i s no  "referential"  harmony, a l t h o u g h a few harmonies bear some resemblance t o those of  " I " . F i g u r e 2-9 i l l u s t r a t e s  vertical  limited  t e n d e n c i e s i n ranges of  element p o s i t i o n s i n the t h r e e p i e c e s as a whole.  105 F i g u r e 2-9.  Vertical  element o c c u r r e n c e  in  Compos  Groups o-f vert i cal pos i t ions:  Trois  i n ranges  o+ p o s i t i o n s  i t i ons.  F r e q u e n t l y o c c u r r i n g elements (descending order o-f f r e q u e n c y ; elements with fewer o c c u r r e n c e s i n brackets):  4- 7 1-3  O, 3, 8, 9 (4, 9, 11) 4, 1, 6 (8, 0, 9)  5- 7 1-4  8, 3, O (4, 9, 11) 6, 4, 1, 0 (8, 9, 3) Elements "1", "4", and "6" (Eb, Gb, and Ab) tend t o occur  in t h e lower "8",  t h r e e or f o u r v e r t i c a l  p o s i t i o n s while  and "9" <D, F, Bb, and Cb) tend t o occur  "0", "3",  i n upper  vertical  posi t ions.  Vertical  Element  Adjacencies  Element a d j a c e n c i e s , which a r e independent sition,  l i k e w i s e have no c o n s i s t e n c i e s i n d i c a t i v e of d e l i b e r a t e  PC c o n t r o l .  There a r e however a few i d e n t i f i a b l e a d j a c e n c i e s  (e.g., e l e m e n t s - p a i r s , and e1ement-trichords) enough frequency  t o be of i n t e r e s t .  worthy i s the f a c t  t h a t the v e r t i c a l  note-  element o r d e r i n g s of many (especially  " I I " ) appear t o be d e r i v e d from a l i m i t e d  i n " I " and  number of v e r t i c a l  element s t r u c t u r e s i n the r e s p e c t i v e p i e c e s . m a r i l y through  o c c u r r i n g with  What i s p a r t i c u l a r l y  of the harmonies i n each of the p i e c e s  and  of v e r t i c a l po-  Derivation i s p r i -  rearrangements of e l e m e n t - p a i r s and - t r i c h o r d s ,  i n v e r s i o n s of elements w i t h i n these p a i r s and t r i c h o r d s .  T h i s would suggest  t h a t elements,  p o r t a n t determinant  in vertical  and not j u s t PCs, a r e an im-  element o r d e r i n g .  Example 2-25  i l l u s t r a t e s such a p r o c e s s of d e r 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 i n " I " (with r e p r e s e n t e d by element numbers).  I 10 I 8 I I I I I I I  I  » 4 1 6  T-LEVEL | 0,11 MEASURE | 1,4  7  3, 9  4  3  1,12  12  a?  £3£  l  0 6 0  I 3 I 9 I (3) 9 I 1 3 I 0 I 4 8 I 8 4  0 6 0  0 1 6 |9 |3  9 3  4 1 8 110  3  8  I  1 8 6 0  I T-LEVEL | MEASURE |  4 1 3  I I I I I I I I I  3  I  0  0 | 0 9 I 9 8 I  |1  9 4 1  1 6  6 0  io 1  6 4  9 4  1 2  I I I I I I I I I I 0 I I  | 8 3  I I I  4 1 6  I 0 2 | 1  8 3 0 9 4 1 6 0 1  2  2  3 1(0)  6  4  4  5 1(1)  10,11  I |  I I  4 11 3 | 10 I 3 10 3 | (1) 9  0 8  I 1 1 I 0 I  9  I 9 4  0 8  8  te  9 14 4 3 | 1 1 1 8 16  16  3 10,11  0 8  1  11 6,7  10 3  10 4  3 1  1  4 10 3 1 0  10  11  0  |  0, 2  7  I  6, 7  8  11 5 9 1  10 4  pitches  107 Note: In t h i s and f o l l o w i n g Examples d e a l i n g with v e r t i c a l e l e ment a d j a c e n c i e s , gaps i n the v e r t i c a l p r e s e n t a t i o n s of elements are f o r 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 a d j a c e n t elements used i n o t h e r harmonies. T-O (m. 1) i s r e s t a t e d f o r purposes of compar i son. Many of the harmonies  are c l e a r l y  d e r i v e d from T-0, m.  which e x p l a i n s the resemblance between the " r e f e r e n t i a l " and the T-O harmonies (m.  harmony of m.  1.  1) except f o r an exchange  T - l (m. 2) i s the same as of "4" and  t o T-O  rotated  t o the bottom of the harmony, w h i l e T-4  mony.  T-9  1) i f the uppermost  "8".  similar  wise s i m i l a r  i f "3" and  <m.  T-O  3) i s "4" are  (m. 3) i s l i k e -  to the top of the har-  i n a harmony s i m i l a r  i n t e r p o l a t e d elements are removed.  T-10  elements "6" and  "8" are r o t a t e d  (m. 4) r e s u l t s  harmony  However, the d e r i v a t i o n of some  require explanation.  (m.  1,  t o T-O  <m.  1) i f  In o t h e r words, "8" and  "0"  (upper p o s i t i o n elements) a r e i n t e r p o l a t e d with »6"-"4"-"l" to produce  "6"-"8"-"4"-"0"-"1", with «9»-»3»  tions.  L i k e w i s e , T-6  of elements.  (mm.  Although T-2  i n the upper  10-11) i n v o l v e s a s i m i l a r (m. 4) and T-5  with the v e r t i c a l  an e 1 e m e n t - t r i c h o r d .  rearrangement  measures comprise a d i s t i n c t  and  6-8  do not appear to  i n the p i e c e , but these  ICC.  which has l i m i t e d s i m i l a r i t i e s to the f i n a l (m.  i s derived  formal s e c t i o n with d i f f e r e n t  monic s t r u c t u r e s based on an expanded  7, and 8 i s T-O  readily  of e l e m e n t - p a i r s and  The harmonies of mm.  have been d e r i v e d from o t h e r harmonies  T-2  har-  However, one harmony harmonies of mm.  13), which s h a r e s elements "1", "3",  "8" with t h i s f i n a l  posi-  alternation  (m. 5) do not  resemble element f o r m a t i o n s of o t h e r harmonies, from T-5,  two  "4",  harmony.  S i m i l a r methods of element r e o r d e r i n g are used t o  illu-  6,  108 strate  the d e r i v a t i o n  Example 2-26.  I I I 11 11 I 8 8 I 3 3 I 0 0  of some harmonies i n " I I " (Ex. 2-26).  S i m i l a r i t i e s o-f harmonies i n " I I " (with p i t c h * r e p r e s e n t e d by element numbers).  11  I 11 8 I 8 11  3 11 8  3  8 11  9 9  0 11  6  4  3  9  0  6--1--4  9  3  4 3  8 11 9 6 0 3 4  I T-LEVEL |  0  2,10,8  3,3,11,0 |  0  3  MEASURE |  1 10-12 6, 7,8  0  6,7,8,13 I  1  1 10,11  10 3  109 Example 2-26 c o n t i n u e d .  I 11 8 I 8 11  8 4 11 11 6 0 8  11 11 8  4 9  3 3 1 0 11  I 8 I 1  11 3  61 0 I 6 I  3 11  0 8 3  8 11 0  I 3 1  1 9  9  3  9|  3  6  9  41  4  4  6—1—4  3 | 10 7 1 3  10 4  I T-LEVEL |  0  8  1  0  3  MEASURE |  1  2  2  1  3  10 7  110 Example 2-26  I  3  continued.  £ 3 i*i f c  11  1 1  4  3  1  11  9  1  6  6 | U  1  0  6 11  1  8  4  1  3| 1  3  3  1  11  6  1  8  11  1  9  8  6  0  11 4  6  81  3  0  1  I 8  |  0 |  9 9  0 8  9 | 4|  1  3  8  4  1  1  6  9 |  6  11  1  2  3  3 |  3  8  0  1  0 6  1  4  9  1  4  1  3  3  8  1 1  3  1  1 1  11  9  8  1  0  1  0  6  6 4  4 0  6  1  3  1  11  9  1  4  1  1  1  9  8  9 11  9 1 0 3 | 10  7  4  11  1  9  8  8  1  1  1  1  The a s c e n d i n g o r d e r o-f elements elements  i n T - l <m.  2;  particularly  " 9 " - "8 " - "0" - " 6" - " 11 " ) would seem t o be d e r i v e d -from the  e x t r a c t i o n -from T-5  <m.  1) o* every second  element  i n an  ascend-  includes rotation  through  ing o r d e r .  T h i s p r o c e s s o-f e x t r a c t i o n  the element  o r d e r , i n the sense t h a t once the uppermost  or next to uppermost element has been used, one proceeds ment, r e s p e c t i v e l y ,  Similarly,  lower elements  <i.e.,  every second ments.  T-7  element  o-f the harmony's ascending order to the next-lowest or lowest  o-f the harmony to e x t r a c t the next  i n the o r d e r .  o-f T-4's  <m.  ele-  element  the descending order o-f T - l l ' s  "O"-"6"-"3"-"9"-"4") are used  (m. 9) then  element  <m.  8)  to d e r i v e  8) a s c e n d i n g order o-f e l e -  i n v o l v e s a p a r t i a l l y symmetrical  reor-  Ill  der ing  o-f T-4's  (m. 8) elements.  U n l i k e those o-f " I " and "III"  a r e not c l e a r l y  harmonies.  i l l u s t r a t e s those harmonies w i t h  in vertical  Example 2-27.  I 1 0 1 4 1 1 1 6 1 1 3 1 8 1 1 8 1 2  d e r i v e d -from element r e o r d e r i n g s o-f other  Example 2-27  similarities  4  6  3 0  8  3  8 0 3 2  element a d j a c e n c y .  S i m i l a r i t i e s i n the harmonies o-f " I I I " (with p i t c h e s r e p r e s e n t e d by element numbers).  4 1  " I I " , many o-f the harmonies o-f  1 81 6 3 1 3 11 8 1 4 |  1  6 7 2  61 01 1 10 I 21  0 4 1  3  8 0 4 1  6  1  I 4 18 6 13  6  3|0  8  4 3 0  1 0 16 8 14 111  1 5  0  4  13  13  13  7|2  13 |  8  0  8  3 4  6  8  0  0  8  3  3  6  10 1  10 4 1  6 8  9 9  1 4  6 2,0 10,14  112 Example 2-27  1 3 1 8 1 4 1 0 1 10 1 6 1 1 1 | 8  T-LEVEL MEASURE |  3-6  continued.  0  8 3 4 6 10 1 6  8  8|  0  0|  4  1 4 1 1 3 1 1 8 1 6 6 1 1 10 I 6 0 1 3 4 I 3 4 1 8 8 1 1 0 H 1 1 91 8 3 1 3 9 1 2 13 I 2  In g e n e r a l , "III"  6 3  1 4 81 3 0 1 0 1 4 1 8 I 1 1 6 1 6 1 0 1 7 13 I 2 3  81 1 1 3 6 1 8 1 1 4 1 4 3 1 6 0 1 0 1 4 1 10 13 I 2  4 6 3 0  8 1 7 13  1 1 8 1 3 1 1 1 4 1 6 1 1  0  0 14  i  1  the v e r t i c a l element o r d e r i n g s o-f harmonies in  a r e such t h a t -fewer c h o r d s a r e d e r i v e d -from p r e c e d i n g  chords.  T h i s c o n s t r a s t s t o some degree with  " I " , many.o-f which a r e d e r i v e d preceding  the harmonies o-f  i n some r e c o g n i z a b l e e x t e n t -from  harmonies, p a r t i c u l a r l y  T-O, m.  c e r t a i n s i m i l a r i t i e s between the chord  1.  In -fact, t h e r e are  s t r u c t u r e s o-f " I " and  " I I I " , because o-f the common element content  (i.e.,  "4"-"6"-"8") o-f t h e i r  r e s p e c t i v e ICCs, as shown  many o-f the harmonies  i n " I " a r e d e r i v e d -from T-O  will  be the o n l y harmony o-f " I " c i t e d  s t r u c t u r e s o-f " I I I " .  »0"-"l"-"3"-  i n Ex. 2-28. (m. 1) , t h i s  i n the comparison  with  As  113 Example 2-2S.  T-LEVEL MEASURE  1 1 1 10 1 8 1 3 1 0 1 9 1 4 1 1 1 6 1 1 0 1 1 1 1  S i m i l a r i t i e s i n v e r t i c a l element o r d e r i n g s of harmonies i n " I " and " I I I " . 8 (0) (8) (6) 0  3  (4)  8  8  3  3 1 4  0 4  0 6  1  4  6  6  1  2,0  0  2  10,14  13  8  3  3  3  Such v e r t i c a l  1 1 1 1 1 1 1 1 1 1 1 1 1 1  10 3  9  8  8  1 4  4 6  6  0  0  1  10  1  2  3  3  3  1 1 1 01 81 3 1 6 1 4 1 10 I  3 9  11  4  10  3  9  1 8 6  8 1  1 0 1 6 1 6 8 1 10,11 3 1 1 1  0 6  1 3 3  a d j a c e n c i e s and d e r i v a t i o n s o-f harmonies by  element r e o r d e r i n g s o-f p r e c e d i n g  harmonies may w e l l be t y p i c a l  o-f Ros 1 a v e t s ' s music.  Cone 1us i on Having examined the ICC system i n Trois  and  Compositions  c h a r a c t e r i s t i c s t h a t p e r t a i n t o i t s a p p l i c a t i o n i n the music, we should  summarize some of the important  points raised  in this  chapter. Each p i e c e ' s harmonic o r g a n i z a t i o n i s based ICC  a s s o c i a t e d with  transposed  the g i v e n p i e c e , the ICC whose PC content i s  t o produce the PC c o l l e c t i o n s c o m p r i s i n g  u s u a l l y expressed there  i n p a r t on the  harmonically  but at times  a piece,  linearly.  Although  i s a b a s i c ICC -for each p i e c e , and each PC c o l l e c t i o n  rep-  r e s e n t s a t r a n s p o s i t i o n o-f t h a t b a s i c ICC, t h e r e a r e v a r i a t i o n s in element c o n t e n t .  I n t e r e s t i n g l y , though the PC content  t h r e e b a s i c ICCs d i f f e r s , element c o n t e n t s  <i.e.,  t h e r e a r e important  elements "O",  o-f the  s i m i l a r i t i e s in  "3", "4", "6", and "8",  114 with  "1" and  "9"  i n two  In each p i e c e , one o r i t y -for the g i v e n  of the t h r e e T-level  piece,  c o n c l u d e s the p i e c e and  and  as t o f r e q u e n t  T - l e v e l s can  a c t s as a r e f e r e n t i a l  i s most s i g n i f i c a n t  occurrence,  coincidence  i n f a c t be  (T-O)  i n the sense that the s o n o r i t y  and  the p i e c e , and  ICCs).  greater  with  total  formally  in that  time-span  important  h i e r a r c h i z e d , based on  T-3,  and  a different T-8  begins  respect through  time-points.  these  criteria,  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 i n a g i v e n p i e c e . p i e c e has  son-  Each  h i e r a r c h y of T - l e v e l s , although T-0,  T-5,  are s i g n i f i c a n t T - l e v e l s in the t h r e e p i e c e s as a  who 1e. Harmonic s u c c e s s i o n s ted T - l e v e l s , and ent  generally  i n v o l v e IC-3-  f r e q u e n t l y employ two,  T - l e v e l s of an a s c e n d i n g i n t e r v a l  tions thereof.  three,  and  and  IC-5-rela-  f o u r compon-  3 or 5 c y c l e , or combina-  E s p e c i a l l y i n " I " and  "III",  l e v e l s of an  interval  with  c y c l e , T-O,T-3,T-6,T-9) are employed b e f o r e  the 3-0  ceeding  to another  3 T-level family  t h r e e or f o u r  interval  in c y c l i c  order  3 c y c l e or component(s)  (e.g., pro-  thereof.  However, a number of the t r a n s f e r e n c e s  from one  level  involve IC-5-related  family  levels.  l o r component) to another  In f a c t ,  i n " I I " , as opposed to " I " and  harmonic s u c c e s s i o n PC  invariance  i s based on a reordered in a l l four  of a f a m i l y of I C - 3 - r e l a t e d  interval  "III",  interval  3  TT-  the  5 cycle.  (or even three or two)  T - l e v e l s and  T-  transferences  T-levels 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 t o n a l key  modulations between such  keys.  and  115 S t u d i e s of PC and element o c c u r r e n c e , o r d e r i n g , and ation, within individual collections,  PC c o l l e c t i o n s and  show no r e a d i l y apparent  0-f d e l i b e r a t e c o n t r o l  i n v o l v i n g adjacent  consistencies indicative  o-f PC o r g a n i z a t i o n .  Because most harmonic  s u c c e s s i o n s i n v o l v e IC-3- or I C - 5 - r e l a t e d T - l e v e l s , u s u a l l y t h r e e or -four i n v a r i a n t PCs o n l y one o-f these i n v a r i a n t PCs 1- , -2-,  -4-,  and  -6-related  proceed  by  IC-1  l e s s by  IC-5,  and  and  i n v a r i a n t PCs.  IC-  infrequently  P i t c h e s tend t o  IC-3 and  -4,  t o those p i t c h e s of s u c c e e d i n g  in the same v o i c e or v e r t i c a l sistently  involves pitch continuity.  -2, somewhat l e s s by  -6,  t h e r e are  in a given succession, while  T - l e v e l s , which occur  in a l l t h r e e p i e c e s , have fewer  associ-  and much harmonies  p o s i t i o n , with no apparent,  a p p l i e d p r i n c i p l e s of v o i c e - 1 e a d i n g or p i t c h  con-  succes-  s i on. Elements "3",  "0",  the primary melodies  and  "8" tend to occur most f r e q u e n t l y i n  of the t h r e e p i e c e s , with  i t s o c c u r r e n c e as i n i t i a l  found  Elements "1" and  apparent  i n the melodies  "11" i n  "6" occur most  i n the b a s s - l i n e s of the t h r e e p i e c e s .  however, few  i n " I " (as to  element of most T - l e v e l s ) and  " I I " having added s i g n i f i c a n c e . frequently  "3"  In g e n e r a l  4 -  c o n s i s t e n c i e s i n element o r d e r i n g are and  b a s s - l i n e s of " I I " and  even moreso i n  "III". Some s i g n i f i c a n t p a t t e r n s of v e r t i c a l  element  occurrence,  o r d e r i n g , and a s s o c i a t i o n are t o be found, e s p e c i a l l y "II".  In the t h r e e p i e c e s as a whole, elements  "6" tend to occur in the upper.  i n the lower  register,  "0",  "1",  "3",  " R e f e r e n t i a l " harmonies of " I " and  i n " I " and "4",  "8",  and  and  "9"  "II" consist  116 of the most f r e q u e n t l y o c c u r r i n g element placements.  in particular  Many harmonies i n " I " and " I I " r e p r e s e n t  t i o n s of the r e s p e c t i v e " r e f e r e n t i a l "  modifica-  The study of  vertical  element a d j a c e n c i e s  chords),  and the d e r i v a t i o n s of element o r d e r i n g s of many harmo-  n i e s from those  (i.e.,  harmonies.  vertical  element-pairs  -tri-  of a few, bear t h i s out t o some e x t e n t .  d e r i v a t i o n s a r e through the f o l l o w i n g means: element-pairs  and  Such  rearrangements of  and - t r i c h o r d s ; i n v e r s i o n s of elements w i t h i n  these p a i r s and t r i c h o r d s ; r o t a t i o n s upward and/or downward; the d e r i v a t i o n of a l t e r n a t e elements of one chord  ( i n one d i r e c t i o n  or another) t o produce the element o r d e r i n g of another; and symmetrical and  r e o r d e r i n g s of elements.  T h i s suggests t h a t elements,  not j u s t PCs, a r e a determinant  of the harmonies i n f a c t  in vertical  i n v o l v e some r e c o g n i z a b l e ,  m o d i f i c a t i o n of the element o r d e r i n g of o t h e r s . "II",  there  ordering.  Many  minimal  With " I " and  i s a c e r t a i n homogeneity of element o r d e r  i n the  harmonies, much l e s s t r u e of " I I I " . In g e n e r a l ,  there are c e r t a i n s t y l i s t i c  that d i f f e r e n t i a t e these b e i n g : use  " I " and " I I " from  (1) the PC c o n t e n t s  "III",  characteristics the more s a l i e n t of  and ICAs of the ICCs, and the  of more v a r i a n t T - l e v e l s i n " I I I " ,  i n d i c a t i v e of f r e e r ap-  p l i c a t i o n s of the ICC system i n the l a s t p i e c e ; flexibility  i n harmonic rhythm i n " I I I " ,  consistency  i n T - l e v e l time-spans, compared with  (2) the g r e a t e r  specifically  the i n -  the harmonic  rhythms of " I " and " I I " ; (3) the more p e r v a s i v e use of complete, uninterrupted  ascending  as compared with  interval  3 c y c l e s of T - l e v e l s i n " I I I "  " I " ; (4) fewer i d e n t i f i a b l e p a t t e r n s of PC and  117 element o c c u r r e n c e , o r d e r i n g , and a s s o c i a t i o n  i n " I I I " , due i n  p a r t t o the v a r i a n c e s i n t e x t u r e , and the t e n d e n c i e s toward ear, c o n t r a p u n t a l a c t i v i t y ;  and <5) fewer, o v e r t l y  t u r e s and p r o c e d u r e s i n " I I I " , which  tonal  i s made e v i d e n t  lin-  struc-  i n Chapter  Three. However, t h e r e a r e c e r t a i n s i m i l a r i t i e s between " I " and "III"  t h a t perhaps suggest a r e c a p i t u l a t i v e t e r n a r y  relating  the t h r e e p i e c e s as a s e t .  structure  Such a s t r u c t u r e  i n -fact  i m i t a t e s the r e c a p i t u l a t i v e t e r n a r y -form o-f each p i e c e . s i m i l a r i t i e s a r e : (1) the use o-f complete T-levels  i n " I " and " I I I " ,  as opposed  interval  These  3 c y c l e s o-f  t o the use o-f the i n t e r v a l  5 c y c l e which c h a r a c t e r i z e s " I I " ; (2) both " I " and " I I I " have p o r t i o n s o-f t h e i r development  sections  (mm. 6-8, and m. 4, r e s -  p e c t i v e l y ) , employing s u c c e s s i o n s -from t h e i n t e r v a l (3) the g e n e r a l  i r r e g u l a r i t y o-f the harmonic  rhythm,  5 cycle; as opposed  to t h a t o-f " I I " ; (4) the tendency t o have elements "1", "4", "6" i n the lower range o-f v e r t i c a l  p o s i t i o n s , with "0",  and  "3",  "8", and "9" i n t h e upper range; and (5) the procedure o-f subd i v i d i n g PC c o n t e n t s o-f a T - l e v e l i c c o n t e n t i n mm.  t o produce c o n t r a s t i n g harmon-  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. P e r l e , Serial 4.  Gojowy, Neue  Composition, sowjetische  43. Musik,  138.  118  5. Wallace B e r r y de-fines a p i t c h - c l a s s (PC) as " p i t c h independent o-f s p e c i f i c r e g i s t r a l o c c u r r e n c e " and p i t c h - c l a s s - c o m plex (PCC) as "a complex o-f such p i t c h e s g e n e r i c a l l y unders t o o d . " (Wallace B e r r y , Structural Functions in Music CEnglewood Cli-f-fs, New J e r s e y : P r e n t i c e - H a l l , 19763, 27n. ) 6. Although the PCs o-f a T - l e v e l can be expressed l i n e a r l y in the music, as they are t o some degree i n " I " ( T - l l , mm. 6 and 7) and " I I I " ( T - l l , m. 7 ) , a T - l e v e l i n Trois Compositions usua l l y o c c u r s i n the music as a s i n g l e harmonic u n i t with c e r t a i n melodic components ( i . e . , p i t c h e s o-f the primary melody, bass l i n e , or inner m e l o d i e s ) . "Primary melody" r e f e r s t o a l i n e a r p i t c h c o n t i n u i t y u s u a l l y -found i n the upper v o i c e of a p i e c e , a l t h o u g h i t may appear f o r a time elsewhere i n the t e x t u r e . Such a placement i n the uppermost p a r t of the t e x t u r e , i n cont r a s t to o t h e r l i n e a r p i t c h c o n t i n u i t i e s found i n i n n e r v o i c e s or those forming a bass l i n e , f o c u s e s one's a t t e n t i o n on i t ; hence the primacy of t h i s melody. The "bass l i n e " i s the sequence of p i t c h e s formed by the lowest p i t c h e s of harmonies, u s u a l l y one f o r each harmony. 7. P e r l e , Serial Composition, 43; Gojowy, Neue sowjetische 138-141. However, Gojowy does not a p p a r e n t l y e x p l a i n the method of segmentation i n t o p i t c h c o l l e c t i o n s used t o a r r i v e at these T - l e v e l s u c c e s s i o n s . In Gojowy's n o t a t i o n a l system, which i s used f o r h i s c h a r t s t h a t i d e n t i f y the ICCs and t h e i r PC cont e n t s i n m u s i c a l e x c e r p t s , the twelve-PC system ( i . e . , PCs of a chromatic s c a l e b e g i n n i n g with C) i s used. PCs of the ICC, i n a s c e n d i n g s c a l e form, are r e p r e s e n t e d by X's, w h i l e those PCs not of the ICC are r e p r e s e n t e d by O's. Hence, the ICC of " I " i s r e p r e s e n t e d by the f o l l o w i n g : 0-0-X-X-O-X-X-O-X-O-X-X. Gojowy a l s o r e p r e s e n t s t h i s ICC with a short-hand d e s i g n a t i o n XII=1,2, 5,8,IO, where an ICC based on a 12-PC system (XII) l a c k s e l e ments 1(C), 2(C#/Db>, 5 ( E ) , 8(G), and 10(A). In n o t a t i n g the ICC T - l e v e l s , Gojowy uses a d e s i g n a t i o n very s i m i l a r to t h a t used by P e r l e ; namely, "TI" t o r e p r e s e n t the i n i t i a l appearance of the PCC i n the p i e c e , "T2" as t h i s PCC transposed up a semitone, and so on. In my study, as i n P e r l e ' s , the i n i t i a l PCC w i l l be r e f e r r e d t o as the "T-O" level. Musik,  3. More s p e c i f i c g u i d e l i n e s of segmentation should be established. 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 del i n e a t e p i t c h c o l l e c t i o n s u s i n g t i m e - p o i n t s where t h e r e are i n t e r r u p t i o n s i n p i t c h a c t i v i t y i n a l l v o i c e s or p a r t s . In other words, one groups t o g e t h e r i n t o s i n g l e c o l l e c t i o n s those p i t c h e s whose time-spans o v e r l a p . While not p r o h i b i t i n g the i n c l u s i o n of s i n g l e p i t c h e s i n t o two a d j a c e n t T - l e v e l s , t h i s i n i t i a l p r i n c i p l e makes t h a t l e s s l i k e l y w h i l e a l l o w i n g most p i t c h e s that are t e m p o r a l l y a s s o c i a t e d t o be i n c l u d e d i n 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 t h e r e i s c o n s i s t e n c y i n 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 f o r PC and IC s i m i l a r i t i e s . Combining s m a l l e r c o l l e c t i o n s i n t o 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 i n t o s u b s e t s i n order t o main-  119 t a i n c o n s i s t e n c y 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 i n det e r m i n i n g the d e r i v a t i o n of harmonies from ICCs i n R o s l a v e t s ' s music. There are a few e x c e p t i o n s to the above-mentioned g u i d e l i n e s of PC segmentation. In m. 3, the t h r e e harmonies (T-7, TlO, and T-4) would o t h e r w i s e be c o n s i d e r e d as one, because of the s u s t a i n e d C4 and the g u i d e l i n e s i n d i c a t i n g t h a t o v e r l a p p i n g p i t c h e s are i n c l u d e d i n a s i n g l e ICC T - l e v e l . The c o n s i s t e n t occurrence of s i x to e i g h t PCs per harmony, o f t e n as s i m u l t a n e i t i e s , i s the c r i t e r i o n f o r d e s i g n a t i n g t h r e e harmonies i n m. 3. Although the second h a l v e s of mm. 6 and 7, and m. 8, would appear to r e p r e s e n t 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, d e s p i t e the t r i l l s , are segmented i n t o t h r e e harmonies), a d i f f e r e n t approach i s employed i n a s s e s s i n g the segmenting of these time-spans, as d i s c u s s e d l a t e r i n t h i s s e c t i o n of Chapter Two. 9. A l l e n F o r t e , The Structure of Atonal Music C o n n e c t i c u t : Y a l e U n i v e r s i t y P r e s s , 1973), 13f.  (New  Haven,  10. B e r r y d e f i n e s an i n t e r v a l c l a s s (IC) as i n c l u d i n g "any g i v e n i n t e r v a l w i t h i n the octave t o g e t h e r with i t s i n v e r s i o n (complement) and a l l compound e x t e n s i o n s (expansions by one or more octaves) of the g i v e n i n t e r v a l or i t s i n v e r s i o n . If enharm o n i c a l l y e q u i v a l e n t forms are c o n s i d e r e d of the same c l a s s , t h e r e are s i x i n t e r v a l c l a s s e s (the unison e x c l u d e d ) . ..." (Berry, Structural Functions, 193n.) 11. To r e i t e r a t e , each ordered PC i s numbered a c c o r d i n g 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 i n s p e c i f i c p o s i t i o n s w i t h i n the ICC s c a l e form) have numbers i n q u o t a t i o n marks (e.g., "0") in the t e x t of the t h e s i s to d i s t i n g u i s h these from other a r a b i c numbers. Again, element "O" i n an ICC or i t s T - l e v e l would repr e s e n t 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 t o n a l s c a l e . 13. Gojowy, "Half Time," 212. Elsewhere, Gojowy r e f e r s to " s c a l e - d e f i n e d 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 t i o n s h i p s between the component PCs. (Gojowy, Neue sowjetische Musik,  138.)  14.  P e r l e , Serial  15.  Ibid.,  Composition,  43.  44.  16. See f n . 8 f o r p r i n c i p l e s u n d e r l y i n g segmentation p i t c h e s i n t o PC c o l l e c t i o n s . 17. P e r l e , Serial  Composition,  of  43.  18. In t h i n k i n g ahead to the d i s c u s s i o n of " I I I " and to Gojowy's a n a l y s i s of ICC s t r u c t u r e (he i d e n t i f i e s f o u r s i m i l a r but i n d i v i d u a l ICCs), one wonders why he i n d i c a t e s t h a t f o u r  120 ICCs are o p e r a t i v e i n " I I I " w h i l e o n l y one i s o p e r a t i v e i n " I " , t h i s d e s p i t e the f a c t that the o r i g i n a l ICC of " I " does not easi l y e x p l a i n the PC c o l l e c t i o n s of mm. 6-8. Another approach to T - l e v e l i d e n t i t y i n mm. 6-8 i s t o base each of the t h r e e harmon i e s i n the t h r e e aforementioned time-spans on an ICC T - l e v e l most c l o s e l y resembling the PC content of the harmony i n question. T h i s i s examined i n more d e t a i l i n Appendix B. 19.  Gojowy, Neue  20.  Ibid.,  sowjetisc/?e  Musik,  138-139.  139.  21. I n t e r e s t i n g l y , i n Gojowy*s l i s t i n g of T - l e v e l s u c c e s s i o n s , t h e r e i s an "X" i n m. 7 which i s l i k e l y meant to d e s i g nate the T - l e v e l with element "1" although t h i s p a r t i c u l a r v a r i a t i o n a l s o o c c u r s i n mm. 6 and 8 (which have no "x" i n Gojowy's 1i s t i ng) . 22. That i s , element "1" p i t c h e s occur a p e r f e c t f o u r t h (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 minorminor-seventh chord t h a t c o n s t i t u t e s the lower component of these harmonies. In a sense, element "1" has s t r o n g t o n a l imp1icat ion. 23.  Gojowy, Neue  24.  Ibid.,  sowjetische  Musik,  139.  141.  25. P e r l e , Serial Compos i t i on, 43-44. A r e c e n t a r t i c l e by P e r l e prompted an examination of " I I I " i n terms of i t s musical orthography. ( P e r l e , " S c r i a b i n ' s S e 1 f - A n a l y s e s , " 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 cons t a n c y i n the i n t e r v a l s formed between ordered ( s c a l e form) PCs of T - l e v e l s i n " I I I " undoubtedly l e d P e r l e to suggest the use by R o s l a v e t s of a s i n g l e ICC. Q u i t e l i k e l y although u n s u b s t a n t i ated i s the f a c t t h a t R o s l a v e t s may have been i n f l u e n c e d by S c r i a b i n i n t h i s r e g a r d . Although the ICC of " I I I " i s noted because of i t s d i f f e r e n t PC i n t e r v a l p a t t e r n , those of " I " and " I I " are s i m i l a r i n the sense t h a t the r e s p e c t i v e T - l e v e l s cons 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 p a t t e r n of the p a r t i c u l a r p i e c e ' s ICC. 26. P e r l e i n d i c a t e s the p r a c t i c e of element o m i s s i o n but the i l l u s t r a t i o n of the ICC or " s e t " of " I I I " f a i l s to b r a c k e t PC Bb ( i . e . , element "3" i n ICC at T-O) as such a v a r i a n t e l e ment. ( P e r l e , Serial Composition, 43-44.) 27. Another approach t o T - l e v e l i d e n t i t y i n the t h r e e p i e c e s , g i v e n the s i m i l a r i t i e s of the t h r e e ICCs, i s to have one s i n g l e ICC f o r a l l t h r e e p i e c e s . T h i s i s b r i e f l y examined i n Appendix B. 28. Gojowy, Neue  sowjetische  Musik,  140  (my  translation).  121 29. L a t e r s t u d i e s of PC i n v a r i a n c e i n I C - 3 - r e l a t e d T-levels w i l l group such T - l e v e l s i n t o T - l e v e l -families ( i . e . , with Tl e v e l -family 3-0 i n c l u d i n g T-0, T-3, T-6, and T-9, and 3-1 and 3-2 -families i n c l u d i n g T - l e v e l s c o r r e s p o n d i n g to those i n the 3-1 and 3-2 c y c l e s , r e s p e c t i v e l y ) . 30. The reasons -for these d i s p l a c e m e n t s would seem to be r e l a t e d to the t o n a l a s p e c t s o-f the p i e c e , which w i l l be d e a l t with in Chapter Three. The T-10,T-3 s u c c e s s i o n , r e i t e r a t e d i n mm. 3-4 (which in i t s e l - 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 g e n e r a l l y i n v a r i a n t through these measures. The T - l l , T - 4 s u c c e s s i o n (m. 8) s i m i l a r l y has an E-major PC component which i s i n v a r i a n t i n mm. 8-9. Both o-f these t r i ads have important s t r u c t u r a l i m p l i c a t i o n s -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 - l e v e l d e s i g n a t i o n s were a l t e r e d so as to r e f l e c t the use of one ICC f o r a l l t h r e e p i e c e s , t h e r e would be no conn e c t i o n s between the c y c l i c T - l e v e l s u c c e s s i o n s of the t h r e e p i e c e s , i n terms of some s t r u c t u r e i n v o l v i n g a l l t h r e e . Such Tl e v e l s u c c e s s i o n s appear to be independent of one another. 32.  B e r r y , Structural  27.  functions,  33. T h i s i s done i n o r d e r to p r o v i d e a more r e a l i s t i c e v a l u a t i o n of T - l e v e l s i g n i f i c a n c e i n the event t h a t a T - l e v e l occ u r s f r e q u e n t l y but has r e l a t i v e l y s h o r t time-spans, or with the opposite s i t u a t i o n . 34. (m.  Perle,  Serial  Composition,  43.  35. I n t e r e s t i n g l y , T - l l i n " I " (mm. 6 and 7) 7) both i n v o l v e l i n e a r i z a t i o n s of the T - l e v e l  and i n " I I I " PCs.  36. Both T-5 and T-7, I C - 5 - r e l a t e d to T-O, have a somewhat symmetrical or "opposing" r e l a t i o n s h i p . The t o n a l a n a l o g i e s ass o c i a t e d with T-O ( t o n i c ? ) , T-5 (subdominant?) and T-7 (dominant?) w i l l be examined i n Chapter Three. 37.  Perle,  Serial  38. A l l e n F o r t e , e s p e c i a l l y 31-32.  Composition, The  Structure  43. of  Atonal  29f.,  Music,  39. 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 as p e r t a i n i n g prolonged T - l e v e l s i s d i s c u s s e d i n Appendix B. 40. T - l e v e l s T-1, T-4, T-7, and T-10 are p a r t f a m i l y 3 - l j T - l e v e l s T-2, T-5, T-8, and T - l l , p a r t family 3-2.  of of  to  T-level T-level  41. With T - l e v e l f a m i l i e s of " I " and " I I I " , these i n v a r i a n t and " q u a s i - i n v a r i a n t " PCs form o c t a t o n i c 1-2 ( i . e . , semitonetone) c o l l e c t i o n s w h i l e such a PC c o l l e c t i o n d e r i v e d from T-  122 l e v e l -families o-f " I I " -forms an o c t a t o n i c 2-1 ( i . e . , tone-semitone) c o l l e c t i o n . In a recent a r t i c l e on the development of oct a t o n i c i s m in Russian and non-Russian music, Richard Taruskin has some i n t e r e s t i n g o b s e r v a t i o n s c o n c e r n i n g the o c t a t o n i c c o l l e c t i o n i n the music o-f S c r i a b i n that have some i m p l i c a t i o n s -for the music o-f R o s l a v e t s . He s t a t e s that in "the music of h i s C S c r i a b i n ' s l l a s t p e r i o d , . . . the o c t a t o n i c c o l l e c t i o n does not i n t e r a c t with d i a t o n i c harmony or emphasize t r i a d i c cogn a t e s . . . . Rather, i n a work l i k e the S i x t h Sonata, Op. 62 (1911-12) . . . the t h r e e o c t a t o n i c s e t s 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 a k i n to keys i n the t r a d i t i o n a l sense. . . . A sense o-f t o n a l motion i s achieved by m o d u l a t i o n s from one o c t a t o n i c g r o u p i n g to another. That t h i s was a cons c i o u s t e c h n i q u e based on t r a d i t i o n a l t o n a l p r o c e d u r e s i s made c l e a r by the f a c t t h a t a S c r i a b i n essay i n o c t a t o n i c i s m , whatever the v a g a r i e s along the way, w i l l always end i n the same oct a t o n i c key as i t began. That S c r i a b i n c o n c e p t u a l i z e d the o c t a t o n i c c o l l e c t i o n as a p a i r of i n t e r c a l a t e d d i m i n i s h e d - s e v e n t h collections . . . i s r e v e a l e d by h i s note s p e l l i n g . ..." (Richard T a r u s k i n , "Chernomor to K a s h c h e i : Harmonic Sorcery; or, S t r a v i n s k y ' s 'Angle'," Journal of the American Musicological Society, 38/1 CSpring 19853: p. 99, f n . 47). In the case of the t h r e e i n d i v i d u a l p i e c e s by R o s l a v e t s , the t h r e e o c t a t o n i c c o l l e c t i o n s are d e r i v e d from the i n v a r i a n t and " q u a s i - i n v a r i a n t " PCs of 3-0, 3-1, and 3-2 T - l e v e l f a m i l i e s , r e s p e c t i v e l y . Moreover, t r a n s f e r e n c e from one o c t a t o n i c c o l l e c t i o n to another, o r , in other words, from one T - l e v e l f a m i l y to another, whether a Tl e v e l f a m i l y i s r e p r e s e n t e d by one or by more T - l e v e l s (as i s the case with the t h r e e p i e c e s , where s e r i e s of T - l e v e l s ascending by IC 3 are common). With regard to the f i n a l cadence, R o s l a v e t s not o n l y c o n c l u d e s with the same T - l e v e l f a m i l y with which the p i e c e b e g i n s , 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 i n the usage of o c t a t o n i c t e c h n i q u e s by S c r i a b i n and R o s l a v e t s may be l i m i t e d because of such t h i n g s as the PCs i n a T - l e v e l f a m i l y which occur with only one T - l e v e l . (There i s no r e a d i l y apparent p a t t e r n to the l o c a t i o n or f u n c t i o n of these " n o n - o c t a t o n i c " PCs i n Trois Compositions. Hence, the o c t a t o n i c system as a p p l i e d to the p i e c e s i s p r i m a r i l y theor e t i c a l i n nature, and i s not i n d i c a t e d i n PC events.) There are s i t u a t i o n s i n the t h r e e p i e c e s (as w i l l be demonstrated i n the d i s c u s s i o n of t o n a l i t y i n Chapter Three) where t e r t i a n t o n a l s t r u c t u r e s and t o n a l p r o c e d u r e s are employed, which d i f f e r from S c r i a b i n ' s p r a c t i c e of n o n - i n t e r a c t i o n between the o c t a t o n i c c o l l e c t i o n and t o n a l s t r u c t u r e s . Yet, d e s p i t e such d i f f e r e n c e s i n the form of o c t a t o n i c i s m in the music of R o s l a v e t s , t h e r e may be some b a s i s f o r the a p p l i c a t i o n of o c t a t o n i c theory and s t r u c t u r e s to the music of R o s l a v e t s , i f not to the t h r e e p i e c e s . In Chapter Three, t h e r e i s some a d d i t i o n a l d i s c u s s i o n of o c t a t o n i cism i n the t h r e e p i e c e s .  enth  42.  P e r l e , Serial  43.  P e r l e , Serial Composition, 41-42. E x c e r p t s of the Sev(pp. 42-43) i l l u s t r a t e such PC i n v a r i a n c e i n " s e t s "  Sonata  Composition,  43.  123 (T-levels) a t r i t o n e apart. Jim Samson c h a l l e n g e s some o-f these o b s e r v a t i o n s when he s t a t e s : "In Serial Composition and Atonality, George P e r l e has drawn a t t e n t i o n t o p i v o t a l segments D t h e r than the 7/3 u n i t which c r e a t e l i n k s between t r a n s p o s i t i o n s , not a b l y the d i m i n i s h e d seventh and the segment superimposing two minor t h i r d s a p e r f e c t -fourth a p a r t . Undoubtedly S k r y a b i n 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 (occ a s i o n a l l y ) combining t r a n s p o s i t i o n s , but I have found no e v i dence to support P e r l e ' s c l a i m [excluded in the above q u o t a t i o n ] that t h e r e i s a " c l o s e d system of t r a n s p o s i t i o n s " based on these segments. The c h o i c e of t r a n s p o s i t i o n s in the seventh sonata has been governed by the t r i t o n e l i n k and by the work's q u a s i t o n a l s t r u c t u r e , not mentioned by P e r l e . " (Samson, Music in Transition, 209). In f a c t , i n Trois Compositions, the f r e q u e n t use of I C - 3 - r e l a t e d T - l e v e l s as the b a s i s f o r harmonic s u c c e s s i o n s ( o f t e n p r o c e e d i n g through t h r e e or more T - l e v e l s of a Tl e v e l c y c l e [e.g., " I " , mm. 1-3, T-10,T-i,T-4,T-7,T-103), i n combination with the i n t e r v a l 5 c y c l e , i n d i c a t e s a l i m i t e d s y s tem of t r a n s p o s i t i o n . With regard to the term " p i v o t " , another i n t e r p r e t a t i o n might i n c l u d e 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 g i v e n harmony. T h i s o c c u r s f r e q u e n t l y with the harmonies of " I " and " I I I " . Such a p i t c h would be p i v o t a l i f i t (or r a t h e r the PC) were common to the harmony preceding i t as w e l l as i t s own harmony. Of those a d j a c e n t harmonies with s i n g l e , i n i t i a t i n g p i t c h e s i n " 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 i n c l u d e s a l l a d j a c e n c i e s of harmonies), w h i l e 60% of a d j a c e n t harmonies with s i n g l e , i n i t i a t i n g p i t c h e s i n " I I I " have an i n i t i a t i n g p i t c h (56% i n c l u d i n g a l l a d j a c e n t harmonies. Hence, t h e r e i s no s t r o n g tendency f o r such i n i t i a t i n g p i t c h e s to a c t 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" r e p r e s e n t s the pos i t i o n of a PC w i t h i n an ordered c o l l e c t i o n of P C s — i n t h i s thes i s , a s c a l e — w i t h the element numbered a c c o r d i n g 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 . The f i r s t PC of each PCC of the t h r e e p i e c e s i s determined by u s i n g the prime forms of the PCCs of " I " and " I I I " , as they are most s i m i l a r when one e x c l u d e s from c o n s i d e r a t i o n the v a r i a n t PCs as shown i n P e r l e ' s a n a l y s i s . ( P e r l e , Serial Composition, 43.) The prime form of the PCC of " I " has elements "0", "1", "3", "4", "6", "8", and "9" ( F o r t e s e t 7-32), w h i l e t h a t of " I I I " has e l e ments "0", "1", "3", "4", "6", and "8" ( F o r t e s e t 6-Z24). (The numbering should not be confused with F o r t e ' s i n t e g e r n o t a t i o n , 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 " , t h e r e 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 t h r e e p i e c e s (as i l l u s t r a t e d i n Ex. 2-2). Hence, D, the f i r s t PC of the o r dered PCC at T-0 f o r " 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" i n the PCC of " I I I " at T-0. Again, the d e s i g n a t i o n element "0" does not nece s s a r i l y imply primacy of the PC r e p r e s e n t e d by "0" i n 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 r a t h e r d i f f i c u l t f o r the l i s t e n e r to r e l a t e each PC to the "0" PC. However, as w i l l be noted i n the d i s c u s s i o n of " I " , element "3" has  124 a l i m i t e d form o-f primacy, given i t s -frequent i n i t i a l element o-f many T - l e v e l s . 45.  Gojowy, Neue  sovtjetische  Musik,  o c c u r r e n c e as  the  133.  46. Element s u c c e s s i o n s in harmonic s u c c e s s i o n s with the same T - l e v e l sequences were examined, whether the PC c o n t e n t 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 b e i n g used -for a l l t h r e e p i e c e s ) or not ( i . e . , i n d i v i d u a l ICCs used •for the p i e c e s ) . Harmonic sequences whose T - l e v e l s were r e l a t e d by the same IC v a l u e (e.g., I C - 3 - r e l a t e d T - l e v e l s , such as T-O, T-3, T - l , T - 4 , and so on) and those t h a t were not, thus a l l Tl e v e l s u c c e s s i o n s , were i n v e s t i g a t e d -for c o n s i s t e n c i e s i n e l e ment s u c c e s s i o n s . Even element s u c c e s s i o n s i n v o l v i n g the same v e r t i c a l p o s i t i o n s ( i . e . , s u c c e s s i o n s o-f elements i n p o s i t i o n one, two, t h r e e , and so on) o-f a d j a c e n t harmonies were e v a l u ated. I t appears t h a t t h e r e are no c o n s i s t e n c i e s 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 o r d e r i n g . Temporal o r d e r i n g o-f elements not n e c e s s a r i l y i n the same melody or l i n e , p a r t i c u l a r l y e l e ments t h a t are i s o l a t e d or exposed (e.g., through s i n g l e p i t c h a t t a c k s , or b e i n g o u t e r elements o-f s i m u l t a n e i t i e s ) were examined -for any p a t t e r n s o-f o r d e r i n g , r e v e a l i n g no c o n s i s t e n t p r i n c i p1es. 47. S i m i l a r r e f e r e n c e s to PCs i n 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 p i e c e b e i n g examined, or o-f " I " i-f no reference to a p i e c e i s made). 48. In a d i s c u s s i o n o+ chord s t r u c t u r e s i n R o s l a v e t s ' 5 music, Gojowy i n d i c a t e s t h a t the t r i t o n e i s -frequently -found, w h i l e the p e r f e c t -fourth i s i n f r e q u e n t l y used, and the minor second g e n e r a l l y a v o i d e d . IC 1 u s u a l l y appears as a major seventh or minor n i n t h . Gojowy p r o v i d e s one example from " I " (m. 6) where IC l s ( i n the form of minor n i n t h s ) are r e s o l v e d to more consonant i n t e r v a l s . (Gojowy, Neue savjjetische Musik, 196197. ) 49. Although not d i s c u s s e d i n Chapter Three, the t o n a l imp l i c a t i o n s of v e r t i c a l element o c c u r r e n c e s are noteworthy. Elements "O", "3", and "8" form the dominant chord of the minor t o n a l i t y suggested by the PCs of any of the t h r e e 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 f r e q u e n t l y occur as uppermost p i t c h e s , are the mediant and dominant PCs of the major t o n a l i t y t h a t the ICC of " I I " s u g g e s t s . Elements "1" and "6" o c c u r r i n g f r e q u e n t l y i n the b a s s - l i n e s are the t o n i c 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 absent  i n h i s works up t o 1924,  o-f harmonic chords."  unity" exists  tonality  i s completely  although " t o n a l i t y  i n the form of the  as a concept  "synthetic  1  [ R o s l a v e t s ' s system] was based on [ s y n t h e t i c ] chords . . . used . . . as s u b 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 d i d not r e j e c t but r a t h e r t r i e d t o expand. . . . Composition based on the m a n i p u l a t i o n o-f tone complexes [ i . e . , the s y n t h e t i c c h o r d s ] may at times approach the t e c h nique o-f twelve-tone w r i t i n g . . . . T h i s , however, o c c u r s - f o r t u i t o u s l y , not out o-f n e c e s s i t y . The method may a l s o generate o t h e r s t r u c t u r e s u n r e l a t e d t o twelve-tone p r o c e d u r e s [ i . e . , t o n a l s t r u c t u r e s 3 . 2 5  The s i g n i f i c a n c e o-f 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 i s noted by Goj owy: T h i s system o-f t r a n s p o s i n g tone-complexes i s to be observed p r i n c i p a l l y i n the composers of the Moscow r e g i o n . However, one need not regard t h i s necess a r i l y as as a r e v o l u t i o n a r y r e v i v a l of c o m p o s i t i o n : R o s l a v e t s r e g a r d s h i s system not so much as the means of emancipation from t r a d i t i o n as an instrument f o r imposing o r d e r i n o p p o s i t i o n t o the present impression istic-ex music to a  pressionistic dead-end.  tonal  anarchy,  which  Chapters Three and Four e x p l o r e s t r u c t u r e s and of o t h e r systems of PC o r g a n i z a t i o n particular ial  i n Trois  procedures  Compositions.  i n t e r e s t a r e t o n a l , a c t a t o n i c , and dodecaphonic  ordering procedures.  tonali ty.  guides  9  Initially,  we w i l l  be concerned  Of serwith  126 Although ventional o-f the  t h i s p r e s e n t study c e n t e r s p r i m a r i l y on more con-  t o n a l s t r u c t u r e s and  procedures  (i.e.,  characteristic  "common p r a c t i c e p e r i o d " ) , R o s l a v e t s * s ICC system  r e p r e s e n t an expanded t o n a l system, i n the sense o-f  may  Wallace  B e r r y ' s d e f i n i t i o n o-f t o n a l i t y , * * whereby these c o n v e n t i o n a l al ICC  s t r u c t u r e s and system.  with T-O  The  procedures  are but one  system has an apparent  as a r e f e r e n t i a l  (i.e.,  -facet o-f R o s l a v e t s ' s h i e r a r c h y o-f T - l e v e l s ,  harmony or " p i t c h - c l a s s - c o m p l e x  r e s o l u t i o n , " " as w e l l as procedures  the use of c y c l e s of T - l e v e l s i n ICs 3 and  T-level  s u c c e s s i o n s and  of  f o r harmonic s u c c e s s i o n 5).  archy D f T - l e v e l s as w e l l as c e r t a i n symmetrical of  ton-  The  hier-  characteristics  of I C - 3 - r e l a t e d T - l e v e l  f a m i l i e s sug-  gest c e r t a i n mi dd 1 eground/background s t r u c t u r e s ' not u n l i k e such 9  l a r g e - s c a l e s t r u c t u r e s in tonal It  compositions.  i s from the r e s o u r c e s of t h i s expanded t o n a l system t h a t  R o s l a v e t s d e r i v e s t o n a l s t r u c t u r e s and tional  orthography  the f a c t  the f a c t  IC-5-related T-level  system i s c o n t i n g e n t T h i s study w i l l  The  nota-  " I I " in p a r t i c u l a r , the minor  t h a t c e r t a i n harmonic s u c c e s s i o n s are based successions  dominant or tonic-dominant  for  " I " and  t h a t a l l t h r e e p i e c e s have ICCs resembling  s c a l e , and on  f o r ICC PCs of  procedures.  (which  progressions)  i n d i c a t e t h a t the  i n p a r t on t r a d i t i o n a l  i n v o l v e an examination  resemble t o n i c - s u b -  tonal  ICC  procedures.  of the i n d i v i d u a l  pieces  s u r f a c e and midd1eground/background t o n a l i m p l i c a t i o n s and  t o n a l l y suggestive  procedures.  127 Tonality  in " I "  S u r f a c e Tonal F e a t u r e s Perhaps  the t o n a l i t i e s most c l e a r l y suggested  Eb, D, and G ( g e n e r a l l y minor mode). the most -frequently  occurring  This  T-levels  i s not s u r p r i s i n g as  i n " I • (T-O,  T-4)  c o n s i s t o-f PCs -forming these minor s c a l e s ,  (Ex.  3-1).  Example 3-1.  ICC T - l e v e l s T-0,  i n " I " are  T - l l , and  T-4  T-11,  and  respectively  in " I " .  T-0 (Eb MINOR)  T-ll  (D MINOR)  ^ 0  °  T  Note t h a t two o-f the l e s s s i g n i f i c a n t t o n a l i t i e s i n " I " , F major and Bb major  (mm.  nor, r e s p e c t i v e l y .  7-8),  are r e l a t e d  Of course, not a l l harmonies s u g g e s t i n g the  Eb, D, and G t o n a l i t i e s are n e c e s s a r i l y spective music  to D minor and G mi-  derived  from these r e -  T - l e v e l s , nor do these T - l e v e l s as they appear  necessarily  suggest  the r e s p e c t i v e  tonalities.  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 tures,  and a number of d i f f e r e n t t o n a l i t i e s .  t e r e s t i n g to note that mined by e v a l u a t i n g  in the  struc-  However, i t i s in-  the most s i g n i f i c a n t PCs of " I " (deter-  both frequency of o c c u r r e n c e and  total  time-  128 spans of a l l o c c u r r e n c e s o-f each PC) i n c l u d e t o n i c t r i a d these three  tonalities.  Example 3-2 p r o v i d e s a comprehensive a n a l y s i s s u r f a c e harmonic and melodic three  PCs o-f  illustrating  s t r u c t u r e s a s s o c i a t e d with  these  tonalities.  Example 3-2.  S u r f a c e s t r u c t u r e s and p r o g r e s s i o n s of Eb, D, and G t o n a l i t i e s in " I " .  [11  T-O HARMONIES  (HARMONIC SUCCESSION)  [21  (31  T-4  (41 T-4 T-ll  129  E x a m p l e 3-2 c o n t i n u e d . Ml  [51  (6)  <T-9>  17]  T-ll  T-O  I—vii—I  ii Eb: v i i - - -  1  [81  T-ll  I--A6,bII  vii--——I  vii—I  Bb:  F: v i i  [10-111 (T-3)  [121 (T-6)  I  1——-  [131  (T-9)  T-4  (T-9)  T-O  1  1  a  l  o •  •  I  '  i  I  x  To  - T W T  vii7  c: I  9: IV V7  those  Eb: I  \°  by p l a c i n g  »lft  II  I V V  IV V/IV I  I I  v  the temporal-textural con-figuration  a tonal  simultaneities  structures  ) "  V V/IV I I  some d e g r e e ,  monies p e r m i t s  0  ["fTT  T P - ^  OR a: ii7  J \  •  *  r -  A:  >-  }o  i n t e r p r e t a t i o n , a s i n mm.  with  10-13.  s i x and more PCs i m i t a t e  apparent  chord  "roots,"  tonal  thirds,  of harEven tertian  fifths,  130 and  sevenths i n the lower r e g i s t e r o-f the harmonies as w e l l as  in exposed upper v o i c e s . tonally, not al  There-fore,  as Ex. 3-2 shows i n mm.  chord e x t e n s i o n s  vertical  (i.e.,  ninths,  Many o-f the PCs that are  configurations.  elevenths,  succession  In g e n e r a l ,  with some  cession  i n Bb.  n i e s of mm. their  i n F.  analy-  exceptions.  i n v o l v e s the e n t i r e  i n the f i r s t  to a D minor-to-Eb major harmonic s u c c e s s i o n succession  t h i r t e e n t h s , or  the t o n a l harmonic  from D minor t o Eb that  of m. 6 i s r e i t e r a t e d but reduced  vii-I  as ton  a l t h o u g h t h i s a l s o depends upon  i n Ex. 3-2 i s s e l f - e x p l a n a t o r y , The  ty  1-8.  p a r t o-f t h e s e t o n a l t e r t i a n s u b s e t s can be p e r c e i v e d  chromatic a l t e r a t i o n s thereof)  sis  they can be i n t e r p r e t e d  h a l f of m. 7  t h a t p r e c e d e s the  Measure 8 i n v o l v e s a m o d i f i e d  What i s i n t e r e s t i n g about the f i n a l  v i i - I sue  t h r e e harmo  6 and 7 and of m. 8 a r e the t r i t o n e sequences and  i m p l i c a t i o n s 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 p i t c h e s  i n d i c a t e these t o n a l i t i e s ,  suggested by the r e f e r e n c e s  t o Eb i n m. 6 and Bb i n m. 8.)  Example 3-3. (61  Eb:  T r i t o n e sequences of mm. implications. (71  I  F:  6-8 and t h e i r  (81  I—  Bb:  I  as i s  tonal  131 The  -final harmony o-f " I " , T-O  combination ciated  13), r e p r e s e n t s i n p a r t a  of G minor and Eb t o n a l i t i e s .  Although  T-O i s asso-  with Eb minor, T-O i n m. 13 has been m o d i f i e d by the r e -  placement o-f Gb with G. ICC  <m.  (The PC c o l l e c t i o n  i s a l s o T-10 o-f the  i n " I I " , s e r v i n g a c o n n e c t i v e -function between the two  pieces.) (i.e.,  An examination  o-f middleground/background  primary melody- and b a s s - 1 i n e - d e r i v e d )  s t r u c t u r e s , and  midd1eground/background harmonic s t r u c t u r e s , w i l l minate t o n a l  implications  linear  -further  illu-  i n the p i e c e , and i n p a r t i c u l a r the  i n t e r a c t i o n s o-f these t h r e e 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 L i n e a r S t r u c t u r e s o-f Pitches comprising  "I"  the o u t e r v o i c e s of a t e x t u r e a r e c r i t i -  cal  f o r p e r c e p t i o n , e s p e c i a l l y s i n c e the harmonies,  six  and more d i f f e r e n t PCs ( o f t e n with no octave d o u b l i n g s ) ,  produce a r e l a t i v e l y s t e p motion. in  While  t h i c k t e x t u r e , and g e n e r a l l y p r o g r e s s by certain  l i n e a r s t r u c t u r e s or a s p e c t s t h e r e o f  the t h r e e p i e c e s have t o n a l  that do not.  comprising  implications,  there are others  These a r e , n o n e t h e l e s s , d i s c u s s e d i n t h i s  because of t h e i r apparent  significance.  One important  l i n e a r s t r u c t u r e s i n " I " i s t h a t of i n i t i a t i n g  Chapter aspect of  single-pitch  exposure.  Initiating  single-pitch  t e x t u r a 1 l y - i s o 1ated ted  exposure.  The sequence of  s i n g l e primary melody p i t c h e s  i n Ex. 3-4 with open noteheads on the f i r s t  7  initial,  is illustra-  of two s t a v e s .  132 The  second s t a f f  i n v o l v e s a r e d u c t i v e a n a l y s i s o-f t h i s sequence  o-f i n i t i a t i n g p i t c h e s viewed as a background s t r u c t u r e . the -frequency o-f IC 3 r e l a t i o n s h i p s between a d j a c e n t pitches,  i t i s p o s s i b l e to p e r c e i v e such adjacent  dyads, with  t h r e e or more s u c c e s s i v e  chords.  IC r e l a t i o n s h i p between two  An  than IC 3 r e p r e s e n t s these two  Example 3-4.  (21  T-0  \  .'  T-3  T-1  :  - ii  • i  [61 T-ll  T-10  [31 T-4  I  (71 T-0  T-il  T-2  X i  T-7  I  T-4  T-ll  j  T-9  T-2  ;  (81  (10,111  [121  [131  T-7  T-3  T-9  T-0  T-6  as  IC 3 as other  the second of  [51  ;  iI  pitches  in " I " .  [41 T-10  pitches  a pitch following i t .  Initiating single pitches  [11  1  a "break," so to speak, with  p i t c h e s forming a dyad with  initiating  p i t c h e s r e l a t e d by adjacent  Given  T-5  >*:...  133 In most cases the d u r a t i o n represents  with  m e t r i c a l l y stronger  accent  as a r e s u l t of  time-points.  Duration  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  cedence.  Therefore,  notes Fb3  and  initiating  Bb3,  the  Eb4  (m.  the t r i l l  i s thus as  p i t c h e s as  initiating  chromatic ascent The  p i t c h , given  i s pre-  grace  the  6 and  8 as w e l l as those  a continuation initial  p i t c h D4  initial  (and  p i t c h e s of mm.  E4)  p i t c h e s could  be  initial  thought of as a other  3  In the r e d u c t i v e summary of Ex. IC 3 dyads, formed by  3-4,  the sequence of  p a i r s of these i n i t i a t i n g  prim-  single  i s seen to form a s t r u c t u r e i n d i c a t i v e of a l a r g e - s c a l e  p l a n of PC  control.  cends from D-F harmonies  7  i n these measures.  " p i t c h a x i s " , a s e r i e s of prominent p i t c h e s around which pitches gravitate.*  and  6 and  i s the primary  harmonies suggested  initiating  the  of that sequence through a  trill not  fol-  7 are deemed p a r t of  p i t c h e s because of t h e i r d u r a t i o n s ,  from the  trill  T h i s sequence of  pitches,  im-  a p a r t of t h i s sequence of  p i t c h e s of m.  p i t c h e s of mm.  because they r e p r e s e n t  arily  agogic  coincidence  5), although preceded by  i s thus c o n s i d e r e d  initial  sequence of  (D4-E4).  or  pitches.  Similarly, lowing  p i t c h equals  Hence, these p i t c h e s have a s u r f a c e  i n a d d i t i o n to m e t r i c  portant  initiating  a s i g n i f i c a n t p o r t i o n o-f the time-span o-f the harmony  to which i t belongs. value  o-f an  T h i s s e r i e s of IC 3 dyads c h r o m a t i c a l l y  to F-Ab,  ( i . e . , mm.  1-3  with and  arpeggiations 7-13).  can  be p e r c e i v e d  diminished-seventh  However, t h e r e appears to  be a b i f u r c a t i o n in t h i s s t r u c t u r e in mm. s i o n from E-(G)  of  as-  4-5  when the  progres-  to descend as w e l l , through  Eb  134 to  D.  T h i s a l t e r n a t e path  d a s h - l i n e beam i n mm.  Linear  plete  Ex.  "I".  Example 3-5 p r e s e n t s a more com-  o-f l i n e a r s t r u c t u r e s i n " I " .  line,  pitches.  "X"s) t h a t occur h i g h e r than c u r r e n t melody  Primary melody p i t c h e s having d u r a t i o n s longer than an with open noteheads w h i l e  p i t c h e s a r e d e s i g n a t e d with s o l i d  Example 3-5.  (21  u — , b* \-> t  Arfa  fa,  -**f>  noteheads.  Linear structures in " I " .  (11  "  melody, the  and those uppermost harmonic p i t c h e s ( i n d i c a t e d i n  e i g h t h v a l u e a r e denoted  n  The sequence of  i n c l u d e s those e x t r a c t e d -from the primary  3-5 with  ued  i n Ex. 3-4 with a  4-7.  in  illustration  pitches bass  structures  i s represented  i—m— j  -J-—V-n—£e—|—  v- — — f r o -  1  i  „ u  (31  «— —W & \>T  O—  (41 (31 (BIFURCATION IN LINEAR STRUCTURE)  e—o_  11 4 v  -01  *'^>  v— &  A\  9—  1  shorter-val-  135 Example 3-5 c o n t i n u e d . [6]  171  •V-  •jlo <  ' Vin? h a  '  T/0  ± -/-  "—P  fcs*-  181  ^5—  [10-111  «#3toT  — fen  O  I>  ^  =»—  a—:  pbfl J t=ra  — * p —  1  [131  [121  V  4 -4 (  -^H  JH  f  -/=r* •l.  0  -  ————•  0  V*  -•  -. —f  There  i s a middleground  structure  primary melody and b a s s - l i n e p i t c h e s ,  i n mm.  with the PC  ted by s u c c e s s i o n s o-f c e r t a i n prominent ICs 1 and 2 ( i . e . , G2-F2-Fb3-Eb4-D4) . al  p i t c h i n mm.  1-6 i n v o l v i n g both 1ines—sugges-  pitches"* — descending by  F4-E4-Eb4-D4 i n the primary melody, and Ab2D4 i n -fact remains  6-13.  In mm.  as an important  5-13, a middleground  structur-  progression  o-f G5-G86-G84-G4, i n v o l v i n g both primary melody and upper ter  pitches,  pitches  i n mm.  an apparent these  i s apparent. 6-13 ( i . e . ,  descending  pitches.  regis-  A similar structure  involves  D4-G#3-A2-G#2-G2).  Again, t h e r e i s  tendency  i n the PC l i n e  bass  suggested by  136 Melodic  Additionally,  fragments.  t h e r e a r e c e r t a i n melodic  fragments c h a r a c t e r i z e d by s i m i l a r s u c c e s s i v e suggest another dimension of u n d e r l y i n g 3-6) .  IC sequences  that  l i n e a r s t r u c t u r e (Ex.  Some o-f the p i t c h e s a r e n o t a t e d an octave h i g h e r t o show  similarities  i n IC sequence  (numbers above the p i t c h e s ) . A l l  noteheads a r e beamed t o g e t h e r to i d e n t i f y melodic fragments, labelled  with lower case  Example 3-6. (11  letters.  M e l o d i c fragments of mm. (21  ••'  (21  [31  "B"  (41  (51  "o*  1-5 and 10-13 of (101  (121  *p' (TRANSPOSED)  IC PATTERN  (  5—2—2—1—2—1—2  5—2—1—2  "I"  5-2~3"2-3  5-2-1-2  (4-51  (10-131  )  3E 11-21  (2-31  is-10]  3 There i s an antecedent-consequent r e l a t i o n s h i p fragments m and n  f  between  and o and p i n that consequent fragments n  and p, t r a n s p o s i t i o n s of each o t h e r , cadence by step t o f i n a l p i t c h e s of t h r e e q u a r t e r v a l u e s i n d u r a t i o n , w h i l e the a n t e c e dent m and o fragments a r e c h a r a c t e r i z e d by l a r g e r moving i n d i s j u n c t motion.  intervals  Hence, as t h e r e i s a c o n n e c t i v e PC  137 (F#)  between -fragments m and  tween -fragments o and and  the  initial  ity  i n mm.  6-8  Example 3-7.  i s a connection  G** o-f p.  The  This progression  involves pitch  PC p r o g r e s s i o n G-G*»/Ab i n mm. (8)  T  * 7 —  f—  *»*—  (91  (101 (M. 5-10)  -4*  i*  4  i  •  ;  G**/Ab are prolonged,  i n a sense, in mm.  thus emphasizing the G-to-G8/Ab p r o g r e s s i o n i e s o-f PC -frequency n i f i c a n c e o-f G and  6-8.  »  *»  Both G and  and  i n mm.  5-10.  Gtt/Ab in " I " .  such sequences are s i g n i f i c a n t  ground pitches  linear  3-8).  which  o-f such melodic  se-  1 and/or 2), i n d i c a t e  i n " I " , perhaps m o t i v i c .  structures.  i n d i c a t o r s of both (Ex.  sig-  in these measures.  quences (IC 5 -followed by a s e r i e s o-f ICs  ins  Stud-  In a d d i t i o n , there are t o n a l  In g e n e r a l , the -frequent o c c u r r e n c e  Bass-I  6-8,  d u r a t i o n have i n d i c a t e d the general  i m p l i c a t i o n s of t h i s G-Gtt/Ab s u c c e s s i o n -for Eb t o n a l i t y , i s a l s o prominent  activ-  . • .-  (71  T  be-  p, a p r o g r e s s i o n between the -final G o-f o  (Ex. 3-7) .  (61  ft  n, so too t h e r e  Eb and  There are midd1eground/backG tonalities  i n the  bass-1ine  138 Example 3-8. <a)Eb  B a s s - l i n e s t r u c t u r e o+ " I " .  tonality: 111  121  (3)  [41  [31  [61  ±  3!  17)  i—  1  1  — *— 1  1  4* 4-.  3 «Kia-TPT. tft-3-RBwrej>  > i  >  '  —' ^  77«—  [101  (81  till  (121  [131  3  (b)Q  tonality: (11  (31  14)  (31  (61  (71  (81  (10,111 (121  2 g :  V7  1  V-—bVI—V  bll  1  (131  V  139 The r e i t e r a t e d A2-G*t/Ab2 (mm. (mm.  1-4), the prominence o-f D4  pitch  (mm.  (Ex.  3-8b).  mm.  10-11), the Ab2-G2  (mm.  6-7), and the -final G bass  12-13) might i n d i c a t e a tendency towards G t o n a l i t y  12-13  In a d d i t i o n ,  r e i n f o r c e s G.  the r e i t e r a t e d primary melody D4 i n However, t r i t o n e s i n the background  s t r u c t u r e suggest Eb t o n a l i t y i n the f i n a l Eb minor with Gb r e p l a c e d  measures.  by G i s suggested by T-O  t h i s harmony i n d i c a t i n g both G and Eb  harmonic s t r u c t u r e s of " I "  Besides s t r u c t u r e s  i n d i c a t i v e of Eb, G, and D  the most s i g n i f i c a n t T - l e v e l s of the p i e c e o c c u r r e n c e and t o t a l and T - 7 ) ,  1 0  time-spans ( i . e . ,  tonalities,  as to f r e q u e n c y of  and "balanced" o c c u r r e n c e s of I C - 3 - r e l a t e d 3-0,  3-1, 3-2,  (m. 13),  T-0, T - l l , T-4, T-3,  families  (i.e.,  nificant  f a c t o r s of midd1eground/background  3-9).  PCs  Of c o u r s e ,  tonalities.  Midd1eground/background  (Ex.  succession  3-1, and 3 - 0 )  1 1  T-9,  T-level  would a l l be  s t r u c t u r e of " I "  sig-  140 Example 3-9.  Midd1eground/background "I" .  [11  (21  T-0  T-3  [31  T-10  (41 T-10  T-4  T-ll  Tonality  S u r f a c e Tonal  harmonic s t r u c t u r e of  (31 T-3  (61 T-ll  T-0  in " I I "  Features  As i n " I " , r e f e r e n c e s  to t o n a l i t y i n " I I " are f l e e t i n g , ob-  s c u r e d by n o n - d i a t o n i c PCs and the absence of t e r t i a n s t r u c tures.  However, of a l l i n f e r a b l e t o n a l  the most s i g n i f i c a n t .  The ICC at T-0,  centers,  F appears to be  although s i m i l a r to the D  minor s c a l e ,  a c t u a l l y resembles the r e l a t i v e F s c a l e more c l o s e -  ly:  "1" (D, T-O)  element  ment "11"  i s a variant  (C), the dominant  element, and because e l e -  degree of F, i s i n c l u d e d  i n the ICC  141 of  " I I " (Ex. 3-10).  Indeed,  PC o c c u r r e n c e and t o t a l  t h e PC h i e r a r c h y o-f " I I " (based on  time-spans)  most s i g n i f i c a n t PCs a r e d i a t o n i c and  i s i n d i c a t i v e b-f F as the  t o F, with dominant,  tonic,  subdominant PCs at the top of t h e h i e r a r c h y .  Example 3-10.  ICC of " I I " and i t s resemblance  t o F.  ICC of "II"  ELEMENTS  0  1  3  n  o  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 t o n i c chord of the major t o n a l i t y level.  t a  harmony w i l l suggested  T-0 i s t h e most s i g n i f i c a n t  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 rence and t o t a l  time-spans).  Other  resemble the  by the harmony's T-  T-level  i n " I I " as i n d i c a -  (based on T - l e v e l  occur-  significant T-levels  (from  g r e a t e r t o l e s s e r ) a r e T-5, T-3, T-IO, T-8, and T-7, w i t h the o t h e r T - l e v e l s each o c c u r r i n g o n l y once. c h a r a c t e r i s t i c of T-0 (m. 13) i s such progression Although  The t e m p o r a l - t e x t u r a l  that  i t suggests a I-V-I  i n F (Ex. 3-11)5 the Fs a r e doubled  the t h i r d  and f i f t h  of t h e F chord  and r e i t e r a t e d .  (i.e.,  are p a r t of t h e T-0 s i m u l t a n e i t y , the temporal  A5 and C6)  and t e x t u r a l  sep-  a r a t i o n of the s i m u l t a n e i t y and i t s s h o r t d u r a t i o n make i t poss i b l e t o p e r c e i v e i t as a V7 chord  i n F s i t u a t e d between the  142 doubled F a n d * i t s r e c u r r e n c e ( i m p l i e d T-0  I).  In comparison,  other  harmonies do not have such a 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  that - f a c i l i t a t e s  Example 3-11.  the p e r c e p t i o n o-f F s t r u c t u r e s  T-0  harmonies i n mm.  (131  111  110-121  T-0  T-0  T-0  some sense,  the T-5  In  13,  1, and  (Ex. 3-11).  10-12.  harmonies a d j a c e n t t o those T-0  monies i n mm.  10-12  suggest a u x i l i a r y  the seven T-0  p i t c h e s proceed by s t e p t o those o-f T-5.  har-  harmonies s i n c e -five o-f  t o n a l s u r f a c e f e a t u r e s are p r e s e n t e d i n Ex.  3-12.  Other  143 Example 3-12. til T-0  (21 T-3  Sur-face t o n a l f e a t u r e s (31 T-10  (41 T-3  T-10  T-3  in "II".  (31  (61  T-6  T-2  T-5  HARMONIES  Eb: I  tbll)-—I-  (bll)—-I  Bb: viI7  I-V7-I  144 Example 3-12 c o n t i n u e d . C71  [81 T-10  T-3  T-ll  T-8  T-4  [91  (10-121  T-7  T-O  113] T-O  T-5  5  r +  §  >  V9 , I b#  T<" . ^ f e c  /I  L  r* ,1,=  l TV  -9—9  ft:  3 T Ab: vi7—(VJ—I-V7-I  F: I-V7-I E: vii7  The  I-V7-I  same t e x t u r a l - t e m p o r a l c o n f i g u r a t i o n 0+ T-O (m.  13)  c h a r a c t e r i z e s T-5 (m. 6 ) , T-3 (m. 7 ) , and T - l l (m. 8 ) , with each harmony s u g g e s t i n g a t o n a l tonality pitches  (i.e.,  tertian  chord  and c o n c e i v a b l e  Bb, Ab, and E, r e s p e c t i v e l y ) .  T - l l (m. 8 ) , immediately  plied  The doubled E  (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) p r o l o n g the E chord and t o n a l i t y . and  local  tonalities  And with T-5 (m.  p r e c e d i n g chords  rein-force the im-  (Bb and E, r e s p e c t i v e l y ) because lower  o-f the p r e c e d i n g T-2 and T-8 harmonies suggest t i o n i n g t e r t i a n chords  (Ex. 3-13).  6)  pitches  dominant-func-  145 Example 3-13.  Harmonies o-f mm. 6-9 and t h e i r implications.  161  171  T-2  T-S  5  2  f  lb/ i  3  I K  /  T-3  !  T-8  VP  —I--V7--I  »  *  1  •6-  E: vii7 (V)-I--V?--I  i n v a r i a n t PCs o-f t o n a l  (31 T-10  T-3  T-10  T-3  (SI T-6  a3i  2  +  ( s i m i l a r t o that implication  Eb i n mm. 3-5. (41  *  I--V7--I  3-14).  Example 3-14.  T-7  9^1  >  Another harmonic s u c c e s s i o n  (Ex.  T-4  ^  »b: wl7  involving  (91 T-ll  ft*  3! Bb: vii7  (8)  T-10  tonal  T-9  o-f mm. 8-9)  o c c u r s i n mm. 3-5  146 The emphasis on Eb T-10,T-3 s u c c e s s i o n . o-f the T-10  harmonies, and  in part  "roots"  bll).  to t h e i r v e r t i c a l  Hence, i t may  than s p e c i f i c a l l y  voices  (T-3) suggest  an upper T-10  e s p e c i a l l y G and  configuration),  the o c c u r r e n c e s of Eb p i t c h e s rather  i n the o u t e r  Although most of the  the E b - t r i a d PCs,  scured by these other PCs. describe  t o the r e i t e r a t i o n of the  the E2 p i t c h e s  (i.e.,  are d i a t o n i c to Eb,  (due  in part  E b - t r i a d PCs occur  1 3  l e a d i n g - t o n e t o Dtt/Eb PCs  i s due  Bb  are p a r t i a l l y  ob-  be more a c c u r a t e to  i n the bass  describing  l i n e as Eb  the chords as Eb  t r i ads.  Midd1eground/background Diminished-seventh  l i n e a r s t r u c t u r e s of " I I " structures  ground /background s t r u c t u r e s , t y , e s p e c i a l l y F. tures F5  An  important  Certain  harmonic,  p i t c h e s are h i g h l i g h t e d  6-9.  while a t h i r d  the d i m i n i s h e d - s e v e n t h  i s a component, s o l i d  tonali-  (m. 6)  and  (m. 8 ) , whose melodic  diminished-seventh  In Ex. 3-15a, these  noteheads d e n o t i n g components of the For example, i n T-2  diminished-sev(m. 6) and  p i t c h e s form C-D#/Eb-F*»/Gb-A.  d i m i n i s h e d - s e v e n t h chord D-F-Gtt-B i s prominent and T-7  (mm.  open note-  chord of which the melody  enth chord C-D**/Eb-Ftt/Gb-A i s prominent  i n T-4  imply  Between F6  by beams, w h i l e i n Ex. 3-15b  o t h e r d i m i n i s h e d - s e v e n t h chords.  and  middle-  component of the l i n e a r s t r u c -  i s formed by b a s s - l i n e p i t c h e s .  heads comprise  6-9.  a l t e r n a t i n g d i m i n i s h e d - s e v e n t h chords are formed  by primary melody p i t c h e s ,  pitch  l i n e a r and  i n " I I " i s the segment i n mm.  (m. 9 ) , two  chord  in mm.  8-9).  Example 3-15c  T-8  Likewise,  i n T-10  (m. 7 ) ,  suggests the essen-  147 tial mm•  chord p r o g r e s s i o n governing the p r i m a r y melody p i t c h e s o-f 6 — 9•  Example 3-15.  A r p e g g i a t e d d i m i n i s h e d - s e v e n t h harmonies i n the primary melody o-f mm.  (a)Primary melody and b a s s - l i n e (61  171  6-9.  pitches:  181  191  b0  I?  -0—±7J Q  r [  <b) Dimi n i shed-seventh T-2  T-5  T-10  -?—  components o-f harmonies i n mm. T-3  T-8  T-ll  T-4  6-9:  T-7  <c)Background harmonic s u c c e s s i o n suggested by d i m i n i s h e d seventh chords -formed by melody p i t c h e s :  148 These melodic chords initial  F86-F6 melodic  expansion  imply a harmonized  "expansion"  o-f the  s u c c e s s i o n <m. 6) o-f t h i s s e c t i o n , an  i n v o l v i n g a p r o g r e s s i o n o-f two s e m i t o n a l l y d i s p l a c e d  d i m i n i s h e d - s e v e n t h chords whose uppermost p i t c h e s a r e F# and F, respectively. -first  The C-D*t/Eb-F#/Gb-A d i m i n i s h e d - s e v e n t h  i n t h i s middleground  component o-f i n i t i a l  harmonic p r o g r e s s i o n , i s i n -fact a  harmonies i n mm.  the D-F-G#/Ab-B d i m i n i s h e d - s e v e n t h ny)  i s a component o-f the -final  The  third  the bass  IC-6-related T-levels T-ll,  6-8.  6 <T-2) and 8 (T-S), w h i l e  chord  (the consequent  harmonies i n mm.  d i m i n i shed-sevent h chord l i n e o-f mm.  chord,  8-9  harmo-  (T-4,T-7).  (C**/Db-E-G-A#/Bb) o c c u r s i n  A l s o , note the c o i n c i d e n c e between  i n mm.  6-9 (e.g., T-2 and T-3, T-5 and  T-IO and T-4) and the d i m i n i s h e d - s e v e n t h chords (Ex.  3-15). The midd leground/background well mm.  as s u r f a c e t r i t o n e s ,  r e s o l u t i o n s o-f s t r u c t u r a l as  some i n c l u d i n g the melody p i t c h e s o-f  6-9, i n d i c a t e the s i g n i f i c a n c e of c e r t a i n  cially  F.  tonalities,  An a n a l y s i s of l i n e a r s t r u c t u r e s a r t i c u l a t e d  primary melody and bass  line  by the  (Ex. 3-16) i n c o r p o r a t e s these p r e -  v i o u s o b s e r v a t i o n s with a study of midd1eground/background structures.  espe-  tonal  149 Example 3-16. HI  12)  131  Midd1eground/background "II". [4]  [51  [61  17)  [81  191  l i n e a r s t r u c t u r e s of [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 r e s o l u t i o n s suggested by the l o c a l (mm.  tonal  8-9), and "exposed" p i t c h e s * 1  "root"  (mm.  (e.g.,  mm.  resolut ion.  1  regions  strongly  3-5), as well as o u t e r - v o i c e 6, 7, 8 ) , a c t as a p r e p a r a t i o n  Bb  (m. 6) and E  imply F.  The Eb  o c c u r r e n c e s o+ Eb -for the E-F s t r u c t u r a l  ISO Mi dd 1 eground/background Example 3-17  Example 3-17. til T-:  0  p r e s e n t s these  structures.  Midd 1 eground/background "II".  121 13,41 5  harmonic s t r u c t u r e s o-f " I I "  10  The i n t e r v a l  151 [61 3  2  171 5  10  18) 3 8  19] 11 4 7  harmonic s t r u c t u r e s o-f [10-121 -0  [13]  5 0 0  5 c y c l e o-f T - l e v e l s u n d e r l y i n g the harmonic  sequence o-f " I I " would not i t s e l f m i dd 1 eground/background  suggest a  s t r u c t u r e , were i t not -for c y c l e  -fragments taken out o-f sequence and repeated, as w e l l c o i n c i d e n c e o-f c e r t a i n T - l e v e l s with -formally t ime-points.  as the  important  151 Tonality S u r f a c e Tonal Of i s the  the  Features  three  pieces,  " I I I " represents  l e a s t t o n a l , p a r t i a l l y because of  c l e a r t e r t i a n tonal Even the  notation  the c h o i c e the  harmonies and  of PCs  of the  tonal  ICC  of  PC  the  " I " and  " I I " , i s not  t e r p r e t a t i o n although the PCs form a minor s c a l e  <Ex.  Example 3-18.  ICC  The  of  organization infrequent  harmonic  that  use  specifically  unlike  those of  r e a d i l y conducive to t o n a l the  ICC  of  of  progressions.  " I I I " <i.e.,  of a c c i d e n t a l s used with the PCs),  ICCs of  ICC  in " I I I "  in-  " I I I " themselves  do  3-18).  of  "III".  of " I i r  ELEMENTS  0  1  3  6  4  8  9  10  11  61/Ab MINOR SCALE  Yet, not 3-19  despite  the apparent t o n a l  clearly exploited shows a few  dures and  ICC,  as a " t o n a l " r e s o u r c e in " I I I " . " *  surface  structures.  nature of the  1  features  t h a t do suggest t o n a l  it is Example proce-  152 Example 3-19. (41  (31 T-I  Surface tonal s t r u c t u r e s T-2  T-ll  T-8  [91  (81  171  (5-61 T-5  in " I I I '  T-6  T-9  (10-111 T-2  HARMONIES  E  fa  1  3/  1/  TONAL FEATURES OF HARMONIES  1± 77  S C*a,*.JL*J!l^A _ _ _ _ i "si^ 1  A : V---I ' . j . v7  D: i—v  T-O  T-3  F : I--V7  Eb: I Bb: v  [14-151  [131  [121 T-5  g: v - i - i v — - V 7 - - I 1  T-O  T-4  T-7  T-O  Db: I or Gb: V  In mm.  3-7, t h e r e i s a s e r i e s o-f I C - 5 - r e l a t e d PCs with most  o-f the component tral  p i t c h e s approached  (at times with  c o n n e c t i o n s ) as t o n i c s , by upper and lower  inter-regis-  semitonal  153 1 ead i n g - t o n e s s u g g e s t i v e o-f an augmented-sixth chord on •flattened s u p e r t o n i c degree  (Ex. 3-20).  Long stems and  the beaming  at the bottom o-f the system i n d i c a t e these t o n i c p i t c h e s . limited vidual tem)  extent,  4 dyads -formed between p i t c h e s o-f i n d i -  harmonies ( i s o l a t e d by b r a c k e t s  suggest  tonal  IC 3 and  To a  t o n a l chords  i n Ex.  3-20,  second s y s -  i n a " t o n i c i z i n g V-I" sequence;  these  i m p l i c a t i o n s are i n d i c a t e d .  Example 3-20. 131  Only  I C - 5 - r e l a t e d PC s u c c e s s i o n s i n mm.  (41  (5-61  Fl  B  L-fJ  il  171  11-  6 C  Jl  i n such PC s u c c e s s i o n s o-f mm.  r e s e n t e d with any  clarity,  o-f " I I I  (81  0  II—*Lil  3-7  1  l  5-7  1  are t o n a l i t i e s  e i t h e r because o-f the PC  or because PC c o n f i g u r a t i o n suggests  tertian  rep-  successions  harmonies.  154 Midd leground/background  linear  s t r u c t u r e s o-f " I I I "  Example 3-21 i l l u s t r a t e s the l i n e a r  Example 3-21. Ill  ,  Mi dd 1 eground/background "III". 121  131  [41  s t r u c t u r e s o-f " I I I " .  linear  13-61  s t r u c t u r e s o-f  171  — — ff— -J-  r *"  1  —  J  tf——  .4-— .4-  [81  (11  [91  [31  [10-111  [41  (5)  (121  [71  [131  [81  [91  [14-151  [101  [121  [141  —  «!  ^  :  M  I  <X£-  — —  :  =  ——yL.  —  155 There  i s a c l e a r midd1eground/background  linear  i n v o l v i n g a PC a s c e n t " o-f primary melody p i t c h e s , 1  registrally  h i g h e s t p i t c h e s i n mm.  1-4.  structure  i n c l u d i n g the  I t c o n t i n u e s t o Cx4 (m.  7) and c o u l d be p e r c e i v e d t o c o n t i n u e t o Eb5 (m. 12). such c o n t i n u i t i e s have no speci-f i c t o n a l a-f-fect one's p e r c e p t i o n o-f melodic motion e s t a b l i s h a p e r c e p t i b l e path through  While  i m p l i c a t i o n , " they do 1  and i n t h i s  sense  the p i e c e .  A PC that o c c u r s -frequently i n the primary melody p r o x i m i t y t o p i t c h e s o-f t h i s Gb.  Ftt/Gb may  in fact  p a t t e r n o-f o c c u r r e n c e line,  "ascending" s t r u c t u r a l  r e p r e s e n t a secondary  in c l o s e  line  i s F#/  tonal center.  This  i s shown i n Ex. 3-22, where the s t r u c t u r a l  r e p r e s e n t e d by beamed p i t c h e s , a r e separated -from o c c u r -  rences o-f Ftt/Gb.  Interestingly,  such exposed o c c u r r e n c e s o-f  F#/Gb do not occur a-fter m. 7, the apparent "ascending" s t r u c t u r a l  Example 3-22. tl]  h— c  j—  (2)  Ftt/Gb and the l i n e a r s t r u c t u r e s o-f " I I I " . 131  141  15-61  17)  (8)  1/  -  191 HO) (121  (141  -  -p  -  »<  -J—Mu— ^ — f=  -4  it  K  Fi/5t: I  o-f the  line.  X*  hi  terminus  -in—  fr  '  y+  \-»  «7  156 A possible explanation  o-f t h i s F#/Gb i n v o l v e s i n t e r p r e t i n g  the -final T-O (mm. 14-15) as a dominant although  (<J) harmony o-f F4*/Gb,  the t o n i c harmony n e i t h e r precedes nor -follows i t . I t  does however appear i n the l i n e a r s t r u c t u r e a s s o c i a t e d with the primary melody with  i n mm.  the Att/Bb ( t h i r d  the PC ascent  1-7, with  the r e c u r r e n c e s  o-f the t o n i c t r i a d ) and Ctt/Db (-fi-fth) o-f  o-f the s t r u c t u r a l  Bass-line  o-f Ftt/Gb, and  line  (Ex. 3-22).  l i n e a r s t r u c t u r e s a r e shown i n i s o l a t i o n  i n Ex.  3-23.  Example 3-23. (11  (21  Bass-line structure in "III". (31  ski-)  (41  (5-61  [7]  [8]  (91  r — ^ - * » —  *'£ *>  *  *t Bb: IEb: V-  (10-111  [12]  [131  [14-15]  3! Cl/Db  Bb: IV Eb:  I  In mm. on C*»/Db.  12-15, t h e bass l i n e  i s centered  A middleground p r o g r e s s i o n  of Eb2 (mm. 10-11) t o Db2  (mm. 12-15), preceded by an e n h a r m o n i c a l l y Bb two  triad  spelled,  ( s u g g e s t i v e of a V-I PC p r o g r e s s i o n  phrases.  In mm.  around and cadences  arpeggiated  i n Eb),  1-7, however, the bass l i n e  links  these  i s not as  c l e a r l y d e f i n e d as i t i s i n mm. 8-15 (given the s h o r t  duration  157 of many bass p i t c h e s ) , which c o m p l i c a t e s the d e r i v a t i o n of a mi dd1eground/background s t r u c t u r e . tial  bass l i n e could  shown i n Ex. 3-23. mm.  be p e r c e i v e d  On the o t h e r hand, an essento begin with G#2  As a r e s u l t , i t may  t r a n s p o s i t i o n of mm.  midd1eground/background to c e r t a i n s a l i e n t PCs Interestingly, i n v o l v e s mm.  1-7,  1-2  structural  lines,  (C3), and Bb  between mm.  (Ex. 3-23,  last  the a s c e n d i n g PC  (A#2).  This  1-7 and 8-15,  i n mm.  perceive  because of Hence, the reducible  staff).  line  (Bb-Cx) e s s e n t i a l l y  bridge  i n c l u d e s mm.  between  8-  the two  i n v o l v i n g a descending PC s u c c e s s i o n  D  (Cx4>,  i n d i c a t e s some formal d i s t i n c t i o n  highlighted  5-11), and the p a r t i a l  succession  1-11  12-13.  w h i l e the b a s s - l i n e s t r u c t u r e  as reduced tempo and g e n e r a l l y l y mm.  i n mm.  to  b a s s - l i n e s t r u c t u r e would be  15, with m. 7 as an i n t e r - r e g i s t r a l  C  be p o s s i b l e  12-15 as a "summary" of the PC e v e n t s i n mm.  the m o d i f i e d  (m. 1), as  by p a r a m e t r i c changes such  slower harmonic rhythm t r a n s p o s i t i o n of mm.  (especial-  1-2's  T-level  8-9.  Midd1eground/background  harmonic s t r u c t u r e s of  "III".  The harmonies forming the middleground/background harmon i c structures  i n " I I I " are shown i n Ex.  3-24.  158 Example 3-24.  Midd1eground/background "III" .  [11  (21  [4]  T-O  T-7  T-7  T-O  T-5  harmonic  15,61  [81  [101  (121  T-8  T-2  T-2  T-5  s t r u c t u r e s o-f  h  T-O  (21  (41  T-7  T-7  [121 T-O  T-5  T-5  [141 T-O  3 i  i  3*  —  The u n d e r l y i n g symmetrical s t r u c t u r e based on c y c l i c c e s s i o n s o-f T - l e v e l s  (indicated e a r l i e r  i n Chapter Two)  the main component o-f a midd leground/background  suc-  -forms  s t r u c t u r e , wh i  159 also  i n c l u d e s c a d e n t i a l and  n i e s not none 0+  p a r t o-f the c y c l e s .  qualities, cession.  tuant  c o n f i g u r a t i o n or  above,  there  a sense of p r o c e e d i n g to a f o l l o w i n g t o n a l i t y i n a f l u c -  context,  whether suggested by  monies, except f o r T-0 T-7,  and  so on.  lection coincident As three  tonal  in harmonic suc-  l i n e a r s t r u c t u r e s discussed  harmony, with no apparent r e t u r n  T-2,  however,  harmonies takes on e x p l i c i t l y  e i t h e r in v e r t i c a l As with the  s t r u c t u r a l l y important harmo-  With -few e x c e p t i o n s  1 0  these s i g n i f i c a n t  i s only  other  has  and  teristics.  In a d d i t i o n , t h e r e  i s no  in the p r e v i o u s  seems to r e p r e s e n t  three  pieces,  recurrent  analyses  two  linear structures  T-8, PC  col-  1-7. of  pieces  the  in i t s  melodic  charac-  the more mature, or  experi-  i n v o l v i n g fewer obvious  harmonic s t r u c t u r e s and  tertian  f o r T-5,  with the r e c u r r i n g Ftt/Gb i n mm.  " I I I " d i f f e r s from the other  "Ill"  a  to or emphasis of c e r t a i n har-  midd1eground/background harmonic and  mental, of the to t o n a l  or by  to a l e s s e r extent,  been e s t a b l i s h e d  pieces,  surface  and,  a s i n g l e PC  references  procedures w h i l e u s i n g more  i n a more c o n t r a p u n t a l  texture.  Cone 1 us ion The  three pieces  e x h i b i t some important f e a t u r e s  tional  tonality.  piece,  t o n a l s t r u c t u r e s and  in the p i e c e s ,  From the  ICC  are e v i d e n t l y t o n a l ,  procedures are d e r i v e d  system  (e.g.,  and  employed  "II".  In f a c t ,  the PC  content of the  i n d i c a t i n g that the system i s  upon t o n a l p r o c e d u r e s .  conven-  ICCs which are the b a s i s of each  e s p e c i a l l y i n " I " and  a c t e r i s t i c s of the  of  However, t o n a l m a n i f e s t a t i o n  some charICCs)  contingent takes d i f -  160 f e r e n t -forms, and sic  to h i g h l i g h t  six  to e i g h t  i s dependent upon c e r t a i n -features in the the t o n a l a s p e c t s .  (and more) d i f f e r e n t  n o n - d i a t o n i c PCs,  PCs  and  (both s u r f a c e melodic  f e a t u r e s and  t o n a l i t i e s through PC In " I " , Eb, nificant,  G,  suggested  tonal conventions  reiteration  and  agogic  D t o n a l i t i e s are most obvious  linear structures.  f e a t u r e s do not as c l e a r l y  imply  the e x c e p t i o n  and  given  sig-  f e a t u r e s , and  harmony.  Likewise,  tonality, other  i m p l i e d by t r a n s p o s i t i o n s of the  l i n e a r s t r u c t u r e s , both  also  In " I I " , s u r f a c e  the p i e c e ' s p r i n c i p a l  of the f i n a l  t o n a l i t i e s are The  of  to some degree by c l e a r t e r t i a n chord s t r u c -  by midd1eground/background  nal harmony.  ascending  accentuation.  by s u r f a c e melodic  subordinate  (e.g.,  dominant PCs  t u r e s of these t o n a l i t i e s ,  F, with  PCs  midd1eground/background  emphasize t o n i c and  and  ter-  d i s t r i b u t i o n of  r e s o l u t i o n , p i t c h s u c c e s s i o n s such as  i n t e r v a l 5 c y c l e s ) and  the many  In a d d i t i o n , l i n e a r s t r u c t u r e s  s t r u c t u r e s ) need to adhere to c e r t a i n dissonance  the  to p e r c e i v e t o n a l  registral  of such chords.  thing, given  per harmony, and  i t i s often d i f f i c u l t  t i a n chords u n l e s s v e r t i c a l h i g h l i g h t s PCs  For one  mu-  s u r f a c e and  fi-  middle-  ground/background, are r e s p o n s i b l e f o r conveying  the  of F.  In " I I I " ,  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  s o c i a t e d with the 12-15) but  but  i s at best f l u c t u a n t .  5-7;  i n d i c a t i o n s of any  harmonies of " I " and  sonorities  (e.g., A, D,  i n t e r v a l 5 PC s u c c e s s i o n , mm.  no r e c u r r i n g , c l e a r  l i k e the T-0 ential  tonality  impression  and  C#/Db,  tonality.  " I I " t h a t are not o n l y  i n the sense of b e i n g  G,  hierarchically  asmm. Un-  referimportant  a l s o i n c o r p o r a t e t o n i c t r i a d s of the r e s p e c t i v e 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 t o n i c  triad  •for any t o n a l i t y . " 1  Certainly, duced t o e x p l a i n tonal and  tonal  s t r u c t u r e s and p r o c e d u r e s cannot be ad-  a l l PC o c c u r r e n c e s and -functions.  system does, however, allow  one t o p e r c e i v e  An i n f e r r e d musical  r e l a t i o n s h i p s between musical e v e n t s with r e s p e c t  motion  t o ves-  t i g e s of -familiar t o n a l procedures and s t r u c t u r e s .  Notes 1. R o s l a v e t s ,  "Roslavets"-^,  397.  2. Gojowy, "Hal-f Time," 212. Elsewhere, Gojowy i n d i c a t e s the n o n - f u n c t i o n a l nature of harmonies i n R o s l a v e t s ' s music, d e s p i t e t h e i r correspondence t o romantic chord s t r u c t u r e s . (Gojowy, Neue  sowjetische  3. Gojowy, Neue  4.  Berry s t a t e s :  Musik,  sovijetische  196.)  Musik,  146; my  translation.  " T o n a l i t y may be thus b r o a d l y  conceived  as a formal system in which pitch content is perceived as functionally related to a specific pitch-class or pitch-classcomplex of resolution, o f t e n p r e e s t a b 1 i s h e d and p r e c o n d i t i o n e d ,  as a b a s i s f o r s t r u c t u r e a t some understood l e v e l of p e r c e p t i o n . The tonal system c o n s i s t s of a h i e r a r c h i c o r d e r i n g of PC f a c t o r s , with the t o n i c ( f i n a l , a x i s , c e n t e r , e t c . ) t h e u l t i m a t e p o i n t of r e l a t i o n s h i p which t o n a l s u c c e s s i o n s a r e c o n t r i v e d t o "expect." . . . In more recent s t y l e s i n which t o n a l i t y i s r e l e vant a system may (but need not) c o n s i s t of s p e c i f i c s c a l a r f o r m u l a t i o n s (PC c o l l e c t i o n s ) of these or other k i n d s , with d e r i v a t i v e melodic and harmonic c o n f i g u r a t i o n s disposed i n such a way as t o e x p r e s s and g i v e primacy t o a p a r t i c u l a r " t o n i c " o r , i n f l u c t u a n t c o n t e x t s , p a r t i c u l a r " t o n i c s . " Often such t o n a l cont e n t i s r e m i n i s c e n t of c o n v e n t i o n s of t h e t o n a l p e r i o d . ( B e r r y , Structural  5.  Ibid.  Functions,  27-28.)  162 6. In t h i s t h e s i s , "middIeground/background" i n d i c a t e s some u n d e r l y i n g or non-foreground aspect or s t r u c t u r e . Although the combination o-f the two Schenkerian terms may be con-fusing and c o n t r a d i c t o r y , and although the p i e c e s a r e not t o n a l (hence, a r a t h e r loose a p p l i c a t i o n o-f the two Schenkerian c o n c e p t s t o the p i e c e s ) , t h e i r use t o g e t h e r i s a p t , c o n s i d e r i n g t h a t t h e r e i s o f t e n t i m e s more than one non-foreground l e v e l . Moreover, i t i s d i f f i c u l t t o d i f f e r e n t i a t e the "middleground" from the "background" i n t h i s music; hence, the more general d e s i g n a t i o n "midd1eground/background" t o i n d i c a t e any or a l l non-foreground s t r u c t u r e s or a s p e c t s , r a t h e r than one term or the o t h e r . 7. E x c e p t i o n s t o 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 a r e : 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 a r e a d i s t i n c t formal u n i t . 8. T h i s i s s i m i l a r t o the i d e a of p i t c h a x i s as expounded by R i c h a r d Chrisman i n h i s Ph.D. d i s s e r t a t i o n "A Theory of A x i s T o n a l i t y f o r Twentieth-Century Music" (Ph.D. d i s s e r t a t i o n , Y a l e U n i v e r s i t y , 1969), 2 2 f . To quote Chrisman, a p i t c h a x i s i s "a l i n e or s e r i e s of p o i n t s about which other p i t c h s t r u c t u r e s a r e arranged." T h i s term i s , a c c o r d i n g t o Chrisman, r e l a t i v e l y -free of a s s o c i a t i o n s with tonic-dominant t o n a l i t y and f r e e of s p e c i f i c f u n c t i o n a l a s s o c i a t i o n s (p. 2 2 ) . Some of Chrisman's a n a l y t i c a l p r o c e s s e s (e.g., d e t e r m i n i n g s i g n i f i c a n t PCs and T - l e v e l s through c a l c u l a t i o n of o c c u r r e n c e s and t o t a l time-spans through a g i v e n p i e c e ) a r e employed i n 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 s u c c e s s i v e PCs, i n t h i s case r e p r e s e n t i n g a c t u a l p i t c h e s i n the music, although the p i t c h e s are not l o c a t e d w i t h i n one r e g i s t e r or octave, and need not be adjacent t o each o t h e r . 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, r e p r e s e n t ing bass p i t c h e s ) . A "prominent p i t c h " i s one t h a t i s u s u a l l y t e m p o r a l l y and/or r e g i s t r a l l y i s o l a t e d (e.g., i n the outer v o i c e s of the t e x t u r e ) , o f t e n having m e t r i c a l and/or agogic a c centuation. In " I " , the s i n g l e i n i t i a t i n g p i t c h e s a r e examples of prominent p i t c h e s . 10. The h i e r a r c h y of T - l e v e l s , i n descending h i e r a r c h i c o r der, i s : 0, 11, 4, 3/9, 7, 2, 5, 6/10, 1. T-8 i s not used i n "I " . T-9; T-5,  11. The 3-0 f a m i l y of T - l e v e l s i n c l u d e s T-O, T-3, T-6, and 3-1 i n c l u d e s T-1, T-4, T-7, and T-10; and 3-2 i n c l u d e s T-2, T-8, and T - l l .  163 12. As s t a t e d e a r l i e r , two t o n a l t e r t i a n chord components as the lowest p i t c h e s and another component as the h i g h e s t p i t c h would - f a c i l i t a t e t o n a l i n t e r p r e t a t i o n s o-f more complex harmonies. Such harmonies a r e : 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 c o r r e s p o n d s to the Eb-major scale. T h i s a l s o suggests the reason why T-10 and T-3 were r e moved -from the i n t e r v a l 5 c y c l e t h a t i s the b a s i s o-f T - l e v e l successions in " I I " . 14. To r e i t e r a t e , "exposed" p i t c h e s r e f e r to those that occur i n outer v o i c e s of a homophonic t e x t u r e , or t h a t are r h y t h m i c a l l y or t e m p o r a l l y i s o l a t e d i n some manner. For example, A#/Bb in mm. 1, 4, 5, 8, and 10-12; and E i n mm. 3, 4, and 5. 15. I n t e r e s t i n g l y , the PC content of the ICC of " I I I " does suggest a p o t e n t i a l approach to u n d e r s t a n d i n g PC o r g a n i z a t i o n . T h i s i n v o l v e s s u b d i v i d i n g the ICC i n t o subsets, based on the a c c i d e n t a l s of the PCs as n o t a t e d . In other words, G, Bb, and Db (elements "O", "3", and "6", r e s p e c t i v e l y ) form one subset w h i l e Gtt, B, and D# (elements "1", "4", and "8", r e s p e c t i v e l y ) form another. In f a c t , the G-Bb-Db subset forms a v i i - i r e l a t i o n s h i p to the Gtt-B-Dtt subset, when one of the two i s enharmoni c a l l y understood. There are some i n s t a n c e s where twoand t h r e e - p i t c h s u b d i v i s i o n s of harmonies, produced by temporalt e x t u r a l c o n f i g u r a t i o n s of p i t c h e s (such as dyads formed by simu l t a n e o u s l y a t t a c k e d p i t c h e s ) , i n v o l v e PCs of one subset or another. T h i s p r i n c i p l e of PC l o c a t i o n i s however not c o n s i s t e n t l y a p p l i e d 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 e x p l o i t e d in the t e m p o r a l - t e x t u r a l configurations of i n d i v i d u a l harmonies. 16. Ascending PC l i n e r e f e r s t o a n o n - l i t e r a l ascent i n the sense t h a t t h e r e i s no constant ascent w i t h i n 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. tonic  17. Each t w o - p i t c h s u c c e s s i o n succession.  suggests a  1eading-tone-to-  18. To r e i t e r a t e , t h i s s t r u c t u r e i n c l u d e s the T-7-centered c y c l e (3-1, mm. 2-4), T-O (m. 4 ) , and the T-5-centered c y c l e (3-2, mm. 4-13), with an i n i t i a l T-0,T-5 s u c c e s s i o n (m. 1) and f i n a l T-7,T-0 s u c c e s s i o n (mm. 13-15). Both T-5 and T-7, I C - 5 - r e l a t e d to T-0, have a somewhat symmetrical or "opposing" relationship. These T - l e v e l s T-O, T-5, and T-7 have a s s o c i a t i o n s with t o n a l i t y at l e a s t on a s u p e r f i c i a l b a s i s ( i . e . , T-O being " t o n i c " , T-5 being "subdominant", and T-7 b e i n g "dominant"). The h i e r a r c h y of T - l e v e l s i n " I I I " , based on frequency of o c c u r r e n c e 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 - l e v e l s of t h i s h i e r a r c h y would be i n c l u d e d in the middleground/background harmonic s t r u c t u r e .  164  19. As suggested by Ex. 3-22, hand, the dominant o-f Ftt/Gb.  i t c o u l d be, on the other  I  <b5"  CHAPTER FOUR  OTHER SYSTEMS OF PITCH-CLASS ORGANIZATION IN TROIS  Our a t t e n t i o n that  COMPOSITIONS  i s now turned t o systems of PC  a r e t o some degree apparent i n the t h r e e p i e c e s ,  octatonicism,  sified  be c o n s i d e r e d f i r s t ,  can be c l a s  as a form of t o n a l i t y i n the g e n e r a l 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. poraries  of R o s l a v e t s  and S c r i a b i n )  applicability  1  i n Trot's  Because R u s s i a n contem  (e.g., N i k o l a i Rimsky-Korsakov,  used the o c t a t o n i c  some of t h e i r m u s i c ,  the  namely  and s e r i a l i s m .  O c t a t o n i c i s m , which w i l l  sky,  organization  we need  c o l l e c t i o n as a b a s i s f o  to i n v e s t i g a t e  Compositions.  the e x t e n t of i t s  Example 4-1  resemblance of the ICCs of the t h r e e p i e c e s  c o l 1 e c t i ons.  Stravin-  illustrates  to o c t a t o n i c  166 Example 4-1.  ICCs o-f Trois Compositions octatonic collections.  ICC OF "I" AT T-O  ICC OF - i r AT T-O  m  OCTATONIC (1 - 2! D)  Jo  "bo  OCTATONIC (1 - 2; CI)  3*=  h  OCTATONIC 12 - 1! 0)  0 cr  compared with  OCTATONIC 12-11  CI)  _ o  V  —  OCTATONIC (2 - If Ob)  h  0  OCTATONIC (2 - i i CI  *> IT ICC OF 'III'  AT T-O  ltd  OCTATONIC (1 - 25 6)  OCTATONIC 12 • 1} 61  OCTATONIC (2 - li 6bI  HE The ICC o-f " I " c l o s e l y resembles o c t a t o n i c c o l l e c t i o n 1 (i.e.,  semitone-tone) while that o-f " I I " resembles both octa  tonic collections  1-2 and 2-1, with each ICC having s i x o-f  e i g h t PCs common to those o-f the r e s p e c t i v e o c t a t o n i c  collec  167 tion.  With the ICC of " I I I " ,  octatonic collection  there  a r e f i v e PCs matching the  1-2.  D e l i b e r a t e use of the o c t a t o n i c c o l l e c t i o n might be i n d i cated  by some c o n s i s t e n c y  i n the t e m p o r a l - t e x t u r a l  location  and/or f u n c t i o n of ICC elements not b e l o n g i n g  t o the c l o s e s t  octatonic collection.  elements u s u a l l y  occur  Although n o n - o c t a t o n i c  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  t e r n s of occurrence strongly  are s t i l l  the i d e a t h a t R o s l a v e t s  p o s i t i o n s of harmonies.  and " q u a s i - i n v a r i a n t " PCs i n T - l e v e l f a m i l i e s  ance i n IC-3-Related T - L e v e l s , "  in Roslavets's  Taruskin's  and f n . 40 i n Chapter Two)  While some s i m i l a r i t i e s c o u l d  be ob-  music and t h a t of S c r i a b i n , based on  d e s c r i p t i o n s of o c t a t o n i c i s m  (see Chapter Two, f n . 40), t h e r e  i n the l a t t e r ' s music  i s no r e a d i l y apparent  t e r n of l o c a t i o n or f u n c t i o n of n o n - o c t a t o n i c family.  "PC I n v a r i -  1-2 c o l l e c t i o n s w h i l e those of " I I " form an oc-  t a t o n i c 2-1 c o l l e c t i o n . served  inner-  used the system at a l l . A l l e l e -  " I " and " I I I " <see Chapter Two s e c t i o n e n t i t l e d  form o c t a t o n i c  pat-  PCs of a T - l e v e l  Hence, the o c t a t o n i c system does not appear  signifi-  c a n t l y a p p l i c a b l e t o PC events assessed as t o f u n c t i o n and pos i t i o n .  3  that  harmonies would seem t o r u l e  ments appear i n n e a r l y a l l v e r t i c a l  of  pat-  The f a c t  elements a r e components, a l b e i t  v o i c e components, of the v a r i o u s  Invariant  such  2  not c o n s i s t e n t enough t o be  i n d i c a t i v e of d e l i b e r a t e o c t a t o n i c i s m .  these n o n - o c t a t o n i c  out  situations,  168 Serial  PC  Organization  In the p e r t i n e n t l i t e r a t u r e , flict  r e g a r d i n g the e x t e n t  dodecaphonic t h i n k i n g . a "Russian  to which R o s l a v e t s ' s music  In f a c t  have regarded  a s p e c t s of  Roslavets's  These are, f o r example:  reference  sowjet  i n Gojowy's Neue  i n " I I " of " a l l twelve  p e r c e i v a b l e methodical  as  Gojowy's e a r l i e r w r i t i n g s  works to be dodecaphonic.  use  reflects  Some w r i t i n g s r e f e r to the composer  Schoenberg."**  i n d i c a t e t h a t he may  t h e r e seems to be some con-  ische  Musik  l e v e l s of one  to  complex  ordering;""* an e a r l i e r  a  Roslavets's  . . . in a  reference in  t h i s same t e x t 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  u n d e r l i e s the twelve-tone Gojowy e n t i t l e d  p r i n c i p l e that l i k e w i s e  row;"** and  " N i k o l a j Andreevic  an e a r l i e r a r t i c l e  Roslavec,  by  ein fruher  Zwo 1 f tonkompon i e r t . '"* P e r l e q u a l i f i e s h i s use of the terms " s e t " and with regard to the music of S c r i a b i n and  Roslavets.  "series" Initially  he d e f i n e s the term " s e t " as c o m p r i s i n g  " a l l 12 notes of  semitonal  l i n e a r o r d e r " and  s c a l e , arranged  in a s p e c i f i c  "Cno3 note appears more than once w i t h i n the set."°  the that  Later,  states: In a s t r i c t sense the term " s e r i e s " denotes an o r dered s u c c e s s i o n of elements, such as the Schoenbergian 12-tone s e t . Hauer*s " t r o p e s " are o n l y p a r t i a l l y ordered, w h i l e i n the works of S c r i a b i n and some other composers the s e t i s a c o l l e c t i o n of p i t c h e s the s p e c i f i c o r d e r i n g of which i s p u r e l y c o m p o s i t i o n a l . The term " s e r i a l c o m p o s i t i o n " i s used i n the p r e s e n t study as a g e n e r a l d e s i g n a t i o n f o r music based on any of these types of sets.**  he  169  will  In a d d i t i o n , P e r l e s t a t e s :  "[The] term unordered  d e s i g n a t e such a c o l l e c t i o n  . . . employed  a s i n g l e aspect [ i . e . ,  not a p p l i c a b l e  s p e c i f i e d succession  . . . only i n  in inverted  r e t r o g r a d e f o r m s ] , as i n the works of S c r i a b i n ;  set  and  for . . .  a  of the notes [ i s not] assumed to be a  defining characteristic  of the  set."  l o  R e c e n t l y , Gojowy has suggested t h a t R o s l a v e t s ' s music not i n t e n t i o n a l l y  was  dodecaphonic.  Through s y s t e m a t i c a p p l i c a t i o n of such t r a n s p o s i t i o n s [ 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 t h i n k i n g as e a r l y as 1914-15 i n the works mentioned above. For t h i s reason, George P e r l e 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 R o s l a v e t s ' s system, t o g e t h e r with that of S c r i a b i n , as "nondodecaphonic s e r i a l c o m p o s i t i o n . " I cannot e n t i r e l y agree with t h i s d e s i g n a t i o n , s i n c e i t seems to imply that the R u s s i a n system amounted merely t o a kind of p r e - f i g u r i n g of the f u l l y developed twelve-tone system. In r e a l i t y , the R u s s i a n system, which had a l r e a d y been i d e n t i f i e d as such i n S c r i a b i n ' s work by the P o l i s h m u s i c o l o g i s t Z o f i a L i s s a i n the 1930's, s t a n d s 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 d e f i n e d by the i n v a r i a b l e o r d e r of i t s members. But i n the tone complex, as used by S c r i a b i n and R o s l a v e t s , the order of i t s elements remains f r e e ; the complex i s d e f i n e d o n l y by i t s i n t e r v a l l i c s t r u c t u r e . Composition based on the m a n i p u l a t i o n of tone complexes may at times approach the t e c h n i q u e of twelve-tone w r i t i n g , as happens o c c a s i o n a l l y i n R o s l a v e t s as a consequence of h i s p a r t i c u l a r c h o i c e s of s c a l e degree f o r t r a n s p o s i t i o n of a tone complex. T h i s , however, o c c u r s f o r t u i t o u s l y , not out of n e c e s s i t y . The method may a l s o g e n e r a t e o t h e r s t r u c t u r e s u n r e l a t e d to twelve-tone p r o c e dures . *• 1  While t h e r e i s no apparent use of i n v a r i a n t PC c h a r a c t e r i s t i c of s e r i a l  music  ordering  as p r e v i o u s l y e s t a b l i s h e d i n  170 s t u d i e s of element o r d e r i n g , t h e r e are a s p e c t s o-f R o s l a v e t s ' s music t h a t approach s e r i a l organization  i s not c o n s i s t e n t l y  c o n s c i o u s use o-f s e r i a l nonetheless matic  and  dodecaphonic o r g a n i z a t i o n .  important,  a p p l i e d , thus r e f l e c t i n g  techniques.  Yet,  i t s existence i s  s t y l e s prevalent  post-Romantic e r a at the time of Trois  Compositions.  examination  certain  s u c c e s s i o n s and  segments of the t h r e e p i e c e s w i l l and/or dodecaphonic  Serial  sequences.  serial"  i n the An  melodic  i l l u s t r a t e such  serial  1 2  O r d e r i n g of T - L e v e l s and  The  of PCs  in T-Levels  s u c c e s s i o n of T - l e v e l s i n the t h r e e p i e c e s i s " q u a s i i n the sense t h a t a l l or most T - l e v e l s are used  t h r e e p i e c e s i n d i v i d u a l l y w h i l e c e r t a i n T - l e v e l s are ted.  no  symptomatic perhaps of the h i g h l y c h r o -  sometimes a t o n a l m u s i c a l  of T - l e v e l  Such  i n the  reitera-  Moreover, t h e r e appears to be some c o i n c i d e n c e between  the completion important first  of the s e r i e s of twelve  time-points.  occurrence  sequence of  F i g u r e 4-1.  T - l e v e l s and  T h i s i s shown i n F i g . 4-1,  of each T - l e v e l  with  the  g i v e n s e p a r a t e l y below  the  T-levels.  Serial  o r d e r i n g of T - l e v e l s i n  Trois  Compositions. •I" MEASURE: 1 2 3 4 3 6 T-LEVEL: 0-3-10 1-4 7-10-4 11-9-2 5 11-0 T-LEVEL*S FIRST O C C U R R E N C E : 0-3-t0--l-4--7 tl-9-2-3-  formally  7 11-2  8 10,11 7 3-6  12 9-4-9  (T-8 6 lissing)  13 0  171 F i g u r e 4-1 c o n t i n u e d . •II" MEASURE: 1 2 3 4 5 6 7 8 9 10,11 12-13 T-LEVEL: 0-5 8-1 10-3 10-3 6-9 2-5 10-3 8-11-4 7 0-5 0 T-LEVEL*S FIRST O C C U R R E N C E : 0-5--8-1-10-3 6-9-2 11-4--7  •nr MEASURE: 1 2 3 4 3,6 7 8 9 10,11 12 1 3 14 T-LEVEL: 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-LEVEL'S FIRST 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  the f i r s t final In  T-level  (T-7, m. 9) precedes  (T-6, m. 10) o c c u r s i n In " I I " , the s e r i e s -  the r e c a p i t u l a t i o n  i n m. 10.  " I I I " , the s e r i e s - f i n a l T-9 (m. 9) forms with T-2 (mm. the r e c a p i t u l a t i o n  D e s p i t e the s i x t o e i g h t  ies.  T-level  measure of the r e c a p i t u l a t i o n .  the cadence which precedes  is  1 3  no t r u e PC complementarity  i n m. 12.  d i f f e r e n t PCs per harmony, t h e r e i n v o l v i n g PCs of a d j a c e n t harmon-  At l e a s t one and u s u a l l y more PCs a r e not p a r t of two ad-  j a c e n t harmonies, with c o m p l e t i o n of a PC s e r i e s i n v o l v i n g or more a d j a c e n t harmonies. in  lO-ll)  Moreover, t h e r e i s no c o n s i s t e n c y  o c c u r r e n c e s and c o m p l e t i o n s of such PC s e r i e s ,  registral  or temporal  three  location.  i n terms of  172 S e r i a l Ordering  o-f Melodic  Pitches  C e r t a i n primary melody and b a s s - l i n e segments of the three p i e c e s e x h i b i t l i m i t e d -forms o-f s e r i a l o-f i n t e r e s t i s the c o i n c i d e n c e important time-points. r i e s are stated  ordering.  o-f s e r i e s - f i n a l PCs with  -formally  A d d i t i o n a l l y , many PCs o-f i n d i v i d u a l s e -  in i n i t i a l  measures o-f the r e s p e c t i v e p i e c e s , a  s i g n o-f the chromatic nature o-f these melodies. presents  Again, what i s  Example 4-2  the primary melodies and bass l i n e s o-f the p i e c e s , and  i n d i c a t e s the PC s e r i e s involved with each. designated  Melodic p i t c h e s are  both by s t a f f n o t a t i o n and by PC numbers.  T-levels  are a l s o i n d i c a t e d f o r the purposes of comparison.  Example 4-2.  S e r i a l o r d e r i n g of primary melody and b a s s - l i n e PCs.  •r N.: T-:  (11 0  3  r—to 5  f  10  » ' 0 !  (21 1  10  "° — 1  3  4  6  11  «.: T-:  [6] 11  0  1  *  •  »  6  (71 11  "  (51 92 5  i .....  l» ' - 1 1 1 • i  1 1  I 9  141 II  4  „  9  1 1  ~n—^  8  (31 7 10  i  :  2  4  2  (8)  r*  rT>  0  3  t  1  2  [81 7  7  5  bo  4 1 0 (11 NISSIN6)  (101 3 6 (T-8 NISSIN6)  8  173 Example 4-2 continued. •II* M. (11 [21 T- 0 3 8  131 10 3  1  H 0  2  3  (41 10  3  10  1  151 161 6 9 2  171 10  3  [81 3 8 11 (T-4,7 IN M. 8-9)  — r 6  7  8  11 (4 NISSIN6).  *> 'ft Ibo 10  9  BSE  1  6  3  3  4  0  8  4  (41 7  1 (11 NISSIN6)  •nr N. (11 T- 0  (21 8  3  to  az 4  5  6  7  10  (31 1  1  8  9  i_  3  3*  2  1  11  7  TT ZZ =  •*c—  N. 13-61 T- 8  x  jfa±  8  0  • ^ V far 1° I I  !E 10  3  4  11 10  2  (81 2  (7) 11  6  (91 9  (10-11)  9  (12)  N— 0  6  7  3  1  5  174 The "III"  primary  m e l o d i e s o-f " I " and " I I I " and t h e bass l i n e o-f  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 e l e v e n PCs each. In a d d i t i o n , t h e r e tween the s e r i e s - f i n a l at  least  <Bb,  PCs and f o r m a l l y s i g n i f i c a n t  i n " I " and " I I " .  m. 5) o c c u r s  series-final T-level  i s a c e r t a i n amount o-f c o i n c i d e n c e be-  p i t c h climax  the r e c a p i t u l a t i o n .  significant  occurrence  in the piece.)  relative  o t h e r , and with f o r m a l l y important  the s e r i e s - f i n a l final tion),  primary  in "III",  pri-  b a s s - l i n e PC (Db) occur T-level  (T-7),  In " I " and " I I " , t h e r e  c o i n c i d e n c e of s e r i e s - f i n a l  dence i s not as e v i d e n t  i s how-  the s e r i e s - f i n a l  t o m. 9 and the s e r i e s - f i n a l  which precedes the r e c a p i t u l a t i o n .  (There  of G# CG#6, m. 73, the  In " I I " , both  mary melody PC (A) and t h e s e r i e s - f i n a l i n m. 8, a d j a c e n t  The  melody PC (G*», m. 10) and the s e r i e s - f i n a l  c o i n c i d e with  ever, an e a r l i e r  b a s s - l i n e PC i n " I "  i n the cadence of t h e second phrase.  primary  (T-6)  The s e r i e s - f i n a l  time-points,  PCs and T - l e v e l s with  time-points.  Such  is a each  coinci-  however, with d i s j u n c t i o n of  melody PC (C#, mm.  5-6), t h e s e r i e s -  b a s s - l i n e PC (Ctt, m. 12, c o i n c i d i n g with the r e c a p i t u l a and the s e r i e s - f i n a l  T-level  does, however, form a cadence with preceding  the r e c a p i t u l a t i o n .  (T-9, m. 9 ) . The l a t t e r the T-2 harmony  (mm. 10-11)  In a l l t h r e e p i e c e s , t h e r e a r e no  apparent r e p e t i t i o n s of numerical  sequences r e p r e s e n t i n g the s e -  r i e s of PCs or T - l e v e l s , or of IC p a t t e r n s u n d e r l y i n g such PC and  T-level  series  (although  there are limited  s i m i l a r i t i e s un-  der  i n v e r s i o n i n t h e IC p a t t e r n u n d e r l y i n g the T - l e v e l  series).  175 It  is difficult  p a r t i a l l y or f u l l y deliberate.  The  t d determine whether completions  of  dodecaphonic s e r i e s are c o i n c i d e n t a l  r e c u r r e n c e s of T - l e v e l s , T - l e v e l  or  i n " I " (mm.  (mm.  of such m a t e r i a l w i t h i n  the r e i t e r a t i o n  are  successions,  and melodic-harmonic f i g u r a t i o n s 10-13), and  such  10-13) and " I I " these  r e c a p i t u l a t i v e measures, i n d i c a t e a complete use of a l l o r i g i n a l p i t c h and  rhythmic  sense then,  m a t e r i a l by m.  p l e t i o n of PC or T - l e v e l  t i m e - p o i n t , the r e c a p i t u l a t i o n , series.  d e l i b e r a t e dodecaphonic s e r i a l ism (particularly  those  Whether these s e r i e s  one  and comrepresent  i s q u e s t i o n a b l e s i n c e some of  i n v o l v i n g T - l e v e l s ) are based  non-dodecaphonic, n o n - s e r i a l t e c h n i q u e s  (e.g., the i n t e r v a l  c y c l e of T - l e v e l s which i n c l u d e s a l l twelve such  In  t h e r e should be some manner of c o i n c i d e n c e between  t h i s f o r m a l l y important  the s e r i e s  9 of both p i e c e s .  T-levels).  on 5  However,  s e r i e s , whether d e l i b e r a t e or not, are m a n i f e s t a t i o n s of  the h i g h l y chromatic  nature of R o s l a v e t s ' s music.  Notes 1. Some w r i t i n g s t h a t examine o c t a t o n i c i s m i n e a r l y 20thc e n t u r y Russian music are: A r t h u r Berger, "Problems of P i t c h O r g a n i z a t i o n i n S t r a v i n s k y , " Perspectives on Schoenberg ana" Stravinsky, ed. Benjamin Boretz and Edward T. Cone (New York: W. W. Norton, 1972), 123-154; P i e t e r C. van den Toorn, The Music of Igor Stravinsky (New Haven: Y a l e U n i v e r s i t y P r e s s , 1983); and more r e c e n t l y , R i c h a r d T a r u s k i n , "Chernomor to K a s h c h e i : Harmonic S o r c e r y ; o r , S t r a v i n s k y ' s 'Angle'," Journal of the American MusicologicaI Society, 38/1 ( S p r i n g 1985): 72-142. 2. In g e n e r a l , n o n - o c t a t o n i c elements occur i n l e s s s i g n i f i c a n t s i t u a t i o n s more than 50% of the time. In " I " the non-oct a t o n i c element i s "8"; i n " I I " , "1" (the v a r i a n t element) and "4"; and i n " I I I " , "8" and "11" (one of the t h r e e v a r i a n t e l e ments). In the case of element "8" i n " I " , 17 of 25 o c c u r r e n c e s of the element can be d e s c r i b e d as f u n c t i o n a l l y l e s s s i g n i f i cant, t h a t i s , i n a r e l a t i v e l y c o n c e a l e d inner v o i c e , or on a  176 r e l a t i v e l y weaker m e t r i c t i m e - p o i n t , sometimes with a c o r r e spondingly short duration. (6 of these 17 o c c u r r e n c e s are i n the primary melody, on weaker m e t r i c t i m e - p o i n t s and with s h o r t durations.) O-f the 24 i n d i v i d u a l harmonies or T - l e v e l s i n " I I " , the n o n - o c t a t o n i c element "1" o c c u r s o n l y t h r e e times ( i n the bass l i n e ) w h i l e element "4" o c c u r s -fourteen times i n more exposed o u t e r v o i c e s although o n l y e l e v e n o-f these can be des c r i b e d as - f u n c t i o n a l l y s i g n i f i c a n t s i t u a t i o n s a c c o r d i n g to the c r i t e r i a s t a t e d above. On the o t h e r hand, i-f one were to cons i d e r the o c t a t o n i c 1-2 s c a l e 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 n o n - o c t a t o n i c . Element "8" o c c u r s 75% of the time ( i . e . , i n 75% of element "8"'s o c c u r rences) as an i n n e r - v o i c e p i t c h although i t o c c u r s i n h a l f of the T - l e v e l s as the second h i g h e s t p i t c h i n the harmonies (and seven times i n the o u t e r v o i c e s ) . Element "11" o c c u r s 60% of the time as an inner v o i c e p i t c h a l t h o u g h i t o c c u r s 40% of the time as the second h i g h e s t p i t c h i n the harmonies (and ten times in the outer v o i c e s ) . In " I I I " , element "8" o c c u r s 66% of the time as a l e s s s i g n i f i c a n t o u t e r - v o i c e p i t c h or an i n n e r - v o i c e p i t c h , w h i l e element "11" o c c u r s o n l y twice i n the p i e c e , each of these as a l e s s 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 o b s e r v a t i o n s made by T a r u s k i n conc e r n i n g o c t a t o n i c i s m i n S c r i a b i n ' s l a t e r music ( T a r u s k i n , " S t r a v i n s k y ' s 'Angle'," 99, f n . 47) have i m p l i c a t i o n s f o r R o s l a v e t s ' s music: the t h r e e o c t a t o n i c s e t s (or I C - 3 - r e l a t e d Tl e v e l f a m i l i e s ) a c t 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 a k i n to keys i n the t r a d i t i o n a l sense; a sense of t o n a l motion achieved by modulations from one o c t a t o n i c g r o u p i n g t o another, or, i n the case of the t h r e e p i e c e s , t r a n s f e r e n c e from one Tl e v e l f a m i l y to another; and the r e t u r n t o the same o c t a t o n i c key ( T - l e v e l ) with which the p i e c e began. There may be some b a s i s f o r the a p p l i c a t i o n of o c t a t o n i c t h e o r y and s t r u c t u r e s to the music of R o s l a v e t s , i f not to the t h r e e p i e c e s i n p a r t i c u lar. However, one p o i n t 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 t h a t , i n S c r i a b i n ' s l a t e r music, the o c t a t o n i c c o l l e c t i o n "does not i n t e r a c t with d i a t o n i c harmony or emphasize t r i a d i c cognates" ( T a r u s k i n , " S t r a v i n s k y ' s 'Angle,'" 99, f n . 47), w h i l e d i a t o n i c harmonies and t r i a d i c cognates are observed to e x i s t , a l b e i t i n a l i m i t e d way, i n the t h r e e p i e c e s . 4. One Life  in  such  Soviet  reference occurs  Russia,  i n Schwarz, Music  and  Musical  86.  5. Gojowy, Neue sowjetiscAe Musik, 171-2, i n a s e c t i o n e n t i t l e d "Fruhe Ansatze von Zwd1ftontechnik b e i Roslavec und Lourie: Z w o l f t o n t e c h n i k und Zwo1ftonkomp1exe." 6.  Ibid.,  140.  7. Gojowy, " N i k o l a j Andreevic Roslavec, ZwoIftonkomponist," Die Musikforschungt 22/1 1969): 22-38.  ein friiher (January-March  177 8. P e r l e , Serial  Composition,  2.  9. I b i d . , p. 40, f n . 1, i n a c h a p t e r e n t i t l e d phonic S e r i a l Composition." 10. I b i d . , 11. Gojowy,  "Nondodeca-  46. "Hal* Time," 212.  12. Some o-f Gojowy's a n a l y s e s o-f R o s l a v e t s ' s works l i k e w i s e 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 nondodecaphonic s e r i e s . 13. ser i es.  " S e r i e s - f i n a l " means the f i n a l  PC or T - l e v e l  of a  176  CHAPTER FIVE CONCLUSION The  What can we conclude niques  i n Trois  nization, levels,  ICC System  about R o s l a v e t s ' s c o m p o s i t i o n a l  Each p i e c e has a complex PC orga-  Compositions'?  i n v o l v i n g a b a s i c ICC r e a l i z e d  whose content  tech-  as a PCC a t v a r i o u s T-  can be v a r i e d w i t h i n c e r t a i n  limitations.  T r a n s p o s i t i o n and element v a r i a n c e 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  pressed  vertically,  d i v i d e d i n t o s p a r s e r harmonies made up of  ICC  subsets,  and, i n a few i n s t a n c e s , l i n e a r i z e d .  the t h r e e p i e c e s d i f f e r One T - l e v e l given piece,  i n PC and element  s o n o r i t y -for the  i n the sense t h a t the s o n o r i t y begins  greater t o t a l  important  The ICCs of  content.  (T-O) a c t s as a r e f e r e n t i a l  the p i e c e , and i s most s i g n i f i c a n t rence,  i n a g i v e n p i e c e , ex-  as t o frequency  and  concludes  of o c c u r -  time-span, and c o i n c i d e n c e with f o r m a l l y  time-points.  A l l T - l e v e l s can i n f a c t be h i e r a r -  c h i z e d , as t o these c r i t e r i a , of each i n a g i v e n p i e c e .  i n assessment of the s i g n i f i c a n c e  T-5, T-3, and T-8, a s i d e from T-O,  are s i g n i f i c a n t T - l e v e l s i n the t h r e e p i e c e s . Successions interval  o-f T - l e v e l s a r e g e n e r a l l y based on  3 and 5 c y c l e s .  Particularly  or f o u r T - l e v e l s of an i n t e r v a l cending  ascending  i n " I " and " I I I " ,  3 c y c l e a r e employed  s u c c e s s i o n , b e f o r e y i e l d i n g t o another  three  i n an a s -  interval  3 cycle  179 or component (s) t h e r e o f .  PC i n v a r i a n c e i n al'l f o u r  (or even  t h r e e or two) T - l e v e l s o-f a -family o-f I C - 3 - r e l a t e d T - l e v e l s , and t r a n s f e r e n c e s from one f a m i l y  (or component) t o another, a r e  somewhat analogous t o the PC c o l l e c t i o n s of t o n a l keys and modul a t i o n s between such keys. from one i n t e r v a l volve  In f a c t , many of the t r a n s f e r e n c e s  3 T-level family  IC-5-related T - l e v e l s .  (or component) t o another i n -  Since the three d i f f e r e n t  3 T - l e v e l c y c l e s can be mapped onto the i n t e r v a l  interval  5 c y c l e , as  shown i n Chapter Two, i t i s p o s s i b l e t o view t h e i n t e r v a l level  f a m i l i e s as components of t h e i n t e r v a l  3 T-  5 cycle.  There a r e no r e a d i l y apparent c o n s i s t e n c i e s of PC and e l e ment o c c u r r e n c e  and o r d e r i n g , w i t h i n  or through adjacent trol.  collections,  i n d i v i d u a l PC c o l l e c t i o n s  i n d i c a t i v e of d e l i b e r a t e con-  Because most T - l e v e l s u c c e s s i o n s  i n v o l v e IC-3- or 5-  r e l a t e d T - l e v e l s , t h e r e a r e on average t h r e e or f o u r i n v a r i a n t PCs  i n a given succession,  ity.  Likewise,  evolved  l e a d i n g or p i t c h s u c c e s s i o n ,  i n d i c a t i o n t o t h e c o n t r a r y , although  with  (i.e.,  despite these may have  tendencies  i n element  i n the primary m e l o d i e s and bass l i n e s of the  t h r e e p i e c e s , and i n ranges of v e r t i c a l (i.e.,  continu-  l a t e r works.  There are, however, c e r t a i n l i m i t e d occurrence  involving pitch  t h e r e a r e no apparent, c o n s i s t e n t l y a p p l i e d  p r i n c i p l e s of v o i c e Roslavets's  one of these  p o s i t i o n s ) and o r d e r i n g  similarities  in vertical  element o r d e r i n g s of harmonies,  as w e l l as f r e q u e n t  occurrences  of c e r t a i n element a d j a c e n c i e s ) ,  tendencies  suggesting  terminants  of chord  t h a t elements, and not j u s t PCs, a r e de-  structures.  180 T o n a l i t y , O c t a t o n i c i s m , and S e r i a l ism  The ICC system and v a r i o u s s t i t u t e an "expanded"  tonal  p r i n c i p l e s discussed  system, which can be manipulated to  produce d i f f e r e n t t y p e s of s t r u c t u r e s , tures.  including tonal  In a sense, two systems a r e employed  etical  above con-  struc-  at once:  a  theor-  ICC system, and a more p e r c e p t i b l e t o n a l system.  ICCs resemble t o n a l tonal e x p l o i t a t i o n .  s c a l e s , and have consequent p o t e n t i a l f o r In " I " , t h r e e  t o n a l i t i e s - - D minor,  (major/minor), and G minor — are e v i d e n t , i s evident  in " I I " .  fluctuant,  involving references  is d i f f i c u l t  The  Tonality  midd1eground-background  w h i l e one t o n a l i t y , F,  i n " I I I " i s best to v a r i o u s  t o i d e n t i f y any p e r v a s i v e structures  Eb  described  tonalities,  centricity.  in f a c t reveal  as  since i t  Studies  of  large-scale  t o n a l s t r u c t u r e s and p r o c e d u r e s i n " I " and " I I " , which a r e not r e a d i l y apparent i n " I I I " .  Moreover,  of harmonic r e s o u r c e s of a g i v e n may  piece  while tonal e x p l o i t a t i o n i s dependent  upon, and  be l i m i t e d by, p r i o r d e c i s i o n s c o n c e r n i n g the ICC system and  T-level  successions,  there  s t r u c t u r e s and s u c c e s s i o n s cations 3-43,  (one example  are i n s t a n c e s  where ICC  are a l t e r e d t o allow  system-based  f o r tonal  impli-  b e i n g the r e p e t i t i o n of T-10,T-3 C " 11",  f o r emphasis on Eb t r i a d Both o c t a t o n i c i s m ,  mm.  components of T-10).  which can be a b a s i s of t o n a l i t y i n the  broad sense of the term, and s e r i a l ism (both dodecaphonic and non-dodecaphonic) Compositions.  are a p p l i c a b l e to a l i m i t e d extent  Such i n c o n s i s t e n t use of o c t a t o n i c  and  in  Trois  serial  methods, q u i t e u n i i k e the d e l i b e r a t e use of t o n a l s t r u c t u r e s  and  181 procedures  i n the p i e c e s , i s t y p i c a l  o-f the music o-f the com-  poser's e r a .  I m p l i c a t i o n s o-f " I I I " Concerning Matters L a r g e - S c a l e Form As  little  compositional  i s known about d e t a i l s o-f R o s l a v e t s ' s  li-fe, h i s  a c t i v i t i e s and p r a c t i c e s , i n f l u e n c e s upon  music, and h i s p e r s o n a l  this  and p r o f e s s i o n a l c o n t a c t s , t h e r e  upon which one can s p e c u l a t e . sent study,  o-f S t y l e and  One matter, a r i s i n g  i s much  i n the p r e -  upon which one can make some i n t e r e s t i n g and impor-  t a n t s p e c u l a t i o n s , i s the c i r c u m s t a n c e  of pronounced d i f f e r e n c e s  between " I " and " I I " on the one hand, and " I I I " on the o t h e r . P l a u s i b l e reasons  f o r such d i f f e r e n c e s c o u l d be:  between the c o m p o s i t i o n intervening  of the f i r s t  r e d i r e c t i o n s in Roslavets's compositional  represent  and/or d e l i b e r a t e  techniques.  Whatever  f o r these d i f f e r e n c e s , " I I I " would seem t o  the more experimental  and, perhaps, mature of t h e  t h r e e p i e c e s , one i n v o l v i n g fewer r e f e r e n c e s t o t o n a l dures,  lapse  two p i e c e s and the t h i r d ,  i n f l u e n c e s from v a r i o u s s o u r c e s ,  the a c t u a l reasons  a time  proce-  more l i n e a r s t r u c t u r e s , and a more c o n t r a p u n t a l  texture.  On the other hand, t h e r e a r e 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 " t h a t perhaps suggest  even s u g g e s t i n g  t h e i r formal a s s o c i a t i o n ,  a l a r g e - s c a l e t e r n a r y form i n Trois  Compositions  as a whole. T h i s study  has e s t a b l i s h e d some b a s i c p r i n c i p l e s of  Roslavets's compositional tions,  which belong  technique,  based on Trois  Composi-  t o an e a r l y phase of the composer's c a r e e r .  182 It  i s hoped  that  i t will  c o n t r i b u t e t o a deepened u n d e r s t a n d i n g  and a p p r e c i a t i o n o-f R o s l a v e t s ' s music, which and w i l l  i s l a r g e l y unknown,  encourage -further study and performance o-f t h i s music.  With such study, the composer and h i s music w i l l position musical  be accorded a  of deserved importance i n t w e n t i e t h - c e n t u r y R u s s i a n development.  IS2>  SELECTED BIBLIOGRAPHY  Abraham, G e r a l d . "The R e a c t i o n A g a i n s t Romanticism: 18901914." In New Oxford History of Music, e d i t e d by M a r t i n Cooper, v o l . IO, 80-144. Toronto: Ox-ford U n i v e r s i t y P r e s s 1970. Asa+iev,  Boris.  teenth  Russian  Century.  M i c h i g a n : J . W.  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Gojowy, D e t l e f .  "Das  Musik-Konzepte isten, edited  144.  Musik  der  t r a n s m e n t a l e Sprache  32/33.  Aleksandr  Skrjabin  20er  Jahre.  Laabe  der Neuen Musik." und  die  Skrjabin  by H e i n z - K l a u s Metzger and Rainer Riehn, Munich: E d i t i o n Text + K r i t i k , 1983.  127  Gojowy, Detle-f. "Hal-f Time -for N i k o l a i R o s l a v e t s (1881-1944): A Non-Love S t o r y with a Post-Romantic Composer." In Russian and Soviet Musi a Essays for Boris Schwarz. Edited by Malcolm Hamrick Brown, 211-220. Ann Arbor, M i c h i gan: U n i v e r s i t y M i c r o f i l m I n t e r n a t i o n a l Research P r e s s , 1984. Goldstein, Michael. " S k r j a b i n und d i e S k r j a b i n i s t e n . Das S c h a f f e n S k r j a b i n s und s e i n e r Nach-folger — I n d u k t i o n und Deduktion." T r a n s l a t e d from Russian by P. Ruhl. In Musik Konzepte  32/33.  Aleksandr  Skrjabin  und  die  e d i t e d by H e i n z - K l a u s Metzger and Rainer Riehn, Munich: E d i t i o n Text + K r i t i k , 1983.  Skrjabinisten,  178-190.  184 Montagu-Nathan, Montagu. Contemporary Russian Composers. London: C e c i l Palmer and Hayward, 1917; Westport, Connect i c u t : Greenwood, 1970. P e r l e , George. Serial Compos i t i on and Atonality. 4 t h rev. ed. B e r k e l e y , L o s Angeles: U n i v e r s i t y of C a l i f o r n i a P r e s s , 1977. P e r l e , George. "Scriabin's Self-Analyses." 3/2 ( J u l y 1984): 101-124. Riemann  Musiklexikon:  £rg'anzungsband,  "Rosslawets, N i k o l a j Roslavets,  Music  1975 ed.  Analysis.  S.v.  Andrejewitsch."  "Nik. A. R o s l a v e t s o sebe i svoem t v o r c h e s t v e . "  Sovremennaia  muzyka  Gojowy, Neue  sowjetische  Laabei—Verlag,  5 (1924): Musik  132-138. der 20er  Translated in J afire  (Laaber:  1980), 395-400.  Sabaneyeff CSabaneevJ, L e o n i d . Modern Russian Composers. T r a n s l a t e d by Judah J o f f e . New York: I n t e r n a t i o n a l P u b l i s h e r s , 1927; Da Capo, 1975. Salzman, E r i c . Twentieth-Century Music: An Introduction. 2d ed. Englewood C l i f f s , New J e r s e y : P r e n t i c e - H a l l , 1974. Saminsky, Lazare. Music of Our Day: Essentials and Prophecies. New York: I n t e r n a t i o n a l P u b l i s h e r s , 1927; Da Capo, 1975. Samson, Jim. Music and Atonality,  Schibli,  Sigfried.  uberschre  itungen  in Transition: 1900-1920.  A Study  of Tonal  Expansion  London: J . M. Dent and Son, 1977.  Alexander Skrjabin eines prometheischen  und seine Geistes.  Z u r i c h : R. P i p e r and Co. V e r l a g , 1983.  Musik. GrenzMunich,  S c h o l e s , Percy A^ ed. The Oxford Companion to Music. New York, Toronto: Oxford U n i v e r s i t y P r e s s , 1955. Schwarz, B o r i s . Enlarged  Indiana:  Music and Musical Edition 1917-1981.  Life  in Soviet  9 t h ed.  Russia:  2d. en 1. ed. Bloomington, I n d i a n a U n i v e r s i t y P r e s s , 1983.  Slonimsky, N i c h o l a s , ed. Baker's Biographical Dictionary Musicians, 7th ed. S.v. " R o s l a v e t z , N i c o l a i . " Taruskin, Richard. "Chernomor t o Kashchei: Harmonic or, S t r a v i n s k y ' s 'Angle'." Journal of the American logical Society 38/1 ( S p r i n g 1985): 72-142. The  New  Grove  Dictionary  of Music  and Musicians,  " R o s l a v e t s , N i k o l a y Andreyevich,"  of  Sorcery;  6 t h ed.  by D e t l e f Gojowy.  Musico-  S.v.  185" APPENDIX A Chronological L i s t  o-f Works by R o s l a v e t s  T h i s c h r o n o l o g i c a l l i s t i n g of works by R o s l a v e t s , -followed by a c l a s s i f i c a t i o n by genre, -following  listings:  r e p r e s e n t s an amalgamation o-f t h e  Gojowy, Neue  sowjetische  Musik,  327-329;  Gojowy, "Half Time," 217-219} Gojowy, "Roslavec," Die forschung,  22/1:  "Roslavets" watrt  36-38; Grove  CMGG3, s.v. "Roslawetz"  listing  6th ed., s.v.  Dictionary,  (by Gojowy); and Die Musik  Musik-  in Geschichte  (by Guido Waldmann).  und  T h i s present  i s the most complete of any p u b l i s h e d , t o date.  with square  Gegen-  Dates  b r a c k e t s i n d i c a t e approximate dates of c o m p o s i t i o n ;  in some cases, o n l y the decade has been e s t i m a t e d . of c o m p o s i t i o n  i s not known or cannot  of p u b l i c a t i o n  (e.g., pub. 1925) i s i n d i c a t e d .  name of t h e poet  be approximated,  i s given i n parentheses,  ment i s assumed. extant m a n u s c r i p t s  F o r most u n p u b l i s h e d  I f the date t h e date  With songs, the  and a piano  accompani-  works, an i n d i c a t i o n of  i s g i v e n , with t h e S o v i e t l i b r a r y  i n which  these a r e l o c a t e d ( i . e . , C e n t r a l S t a t e A r c h i v e f o r L i t e r a t u r e and  A r t CCSALA3; G l i n k a Museum of M u s i c a l C u l t u r e CGMMC3; Moscow  Conservatory  Library  CMCL3; L e n i n L i b r a r y , Moscow CLLM3).  186 1907  -for S t r i n g Q u a r t e t .  nenuet  -for V i o l i n  Reverie  1908  Romance, Gavotte,  Reverie, Elegie,  piano.  CSALA.  and O r c h e s t r a .  Morgenstimmung, Serenade, etc.  CSALA.  1909  Serenada  -for Two V i o l i n s .  19091910  3 Poemes  and Romance-arabesque  Score.  CSALA.  Sonata ( b e g i n n i n g ) , P i e c e s f o r v i o l i n and  CSALA. -for V i o l i n  and Piano.  CSALA.  C 1910s] 1/ chasy novoluniia CIn the Hours o-f the New Moon]. phonic poem -for l a r g e o r c h e s t r a . Score with p a r t s . CSALA. Liricheskaia  poemaJPoeme  lyrique  CSALA. 1910  S t r i n g Quartet. Symphony  1912  belykh  Heaven  and  1913  Premier  Score.  dev/Danses  and Piano.  apparently  Earth.  lost  and Piano.  GMMC.  i n C Minor.  Tantsy  Violin  -for V i o l i n  CSALA.  des  CSALA. vierges  blanches  -for  C a n t a t a , a f t e r Byron. Unpublished, ( i n c l u d e d i n MGG and Gojowy l i s t i n g s ) .  a cordes; a l s o Quartet/Quatuor p a r t , a t CSALA.)  Ouatuor  •first v i o l i n  Sym-  No. 1,  Tri sochineniia CThree C o m p o s i t i o n s ] . Songs: 1."Sumrak t i k h i i " (V. B r i u s o v ) ; 2."Ty ne u s h l a " (A. B l o k ) ; 3.-Vetere n a l e t i t e " (A. B l o k ) . peizazhy CPaysages t r i s t e s ] ( V e r l a i n e ) . Songs: 1. " O s e n n i a i a p e s n i a " (Russian t r a n s . N. M i n s k i i ) ; 2. "Zakat" (Russian t r a n s . V. B r i u s o v ) ; 3."B1agos1ovennyi chas."  Grustnye  Noktiurn/Nocturne.  ce1lo. 1913-  Sonate  pour  violon  Harp, oboe, two v i o l a s , et  violon-  piano.  1914 sochineniia [Four C o m p o s i t i o n s ] . Songs: 1 . " M a r g a r i t k i " ( I . S e v e r i a n i n ) 1914; 2."Vy n o s i t e l i u b o v " (K. Bol'shakov) 1913; 3."Volkovo k l a d b i s h c h e " (D. B u r l i u k ) 1913; 4."Kuk" (V. Gnedov) 1914.  Chetyre  1914  Trois  compositions  pour  piano.  187 1914  Tri  Et iuda/Tro  1915  D\/a sochineni  prelude,"  is Etudes ia/Deux  "Quasi  pour  piano.  compositions  pour  piano.  poeme."  Prelude  pour  piano.  Poema.  Violin  and p i a n o .  Pesenka  Arlekina  "Quasi  Pub. 1915.  [Harlequin's L i t t l e  Song] (E. Guro).  Song. 1916  Q u a r t e t , second score. CSALA.  1917  Sonata No. 2 -for V i o l i n  19191922  and t h i r d  movements.  and Piano.  Q u a r t e t No. 2.  Incomplete  Five Preludes.  Piano.  score.  Score;  piano  CSALA. CSALA.  [1920s] 7 Pieces f a r V i o l i n and Piano: Etude mortelIe, Etude i n Eb Major, Canon, Pugar Adagio, Pre Iiud i i a, Pomant i cheskai a poema [Romantic poema]. CSALA. [1920s O r c h e s t r a l work, without t i t l e . -1930s] s c o r e . CSALA. O r c h e s t r a l work, without t i t l e . CSALA. 1920  Dve  Poemy/Deux  Third  Unfinished  Unfinished score.  Piano.  Quartet.  T r i o No. 2. 1921  Poemes.  Lento.  CSALA.  Sonata. V i o l o n c e l l o and piano; a l s o , Sonata f o r V i o l o n c e l l o and Piano at GMMC. Trois  Danses.  Paxdum'e/  Violin  Meditation.  Third Trio.  Violin,  and p i a n o . V i o l o n c e l l o and p i a n o . violoncello,  piano.  Man and Sea. Symphonic poem, a f t e r B a u d e l a i r e . Unpublished, a p p a r e n t l y l o s t ( i n c l u d e d i n MGG l i s t i n g ) . 1922  Symphony i n f o u r movements. Without b e g i n n i n g and ending. Score. CSALA. (Grove Dictionary, 6th ed., s.v. " R o s l a v e t s , " i n d i c a t e s u n p u b l i s h e d symphony, 1922.)  188 1922  Sonata  No. 2 -for V i o l o n c e l l o and Piano.  CSALA.  End. Symphonic poem, a f t e r L a f o r g u e . Unpubl i s h e d , a p p a r e n t l y l o s t ( i n c l u d e d i n MGG l i s t i n g ) .  World's  1923  Symphony No. 2 -for O r c h e s t r a and Chorus. s c o r e and s k e t c h e s . CSALA. Sonata  1924  No. 5.  Piano.  Fourth Sonata.  V i o l i n and p i a n o .  Piano Q u i n t e t f o r Two V i o l i n s , Piano. Score. CSALA. 1925  Unfinished  V i o l i n Concerto.  Arranged  (Pub. 1924.)  V i o l a , V i o l o n c e l l o , and  for violin  and piano.  chudo (A. Andreev). A g i t - p r o p , song (baritone voice). (Pub. 1925.) LLM.  Poslednee  C o n t r i b u t i o n s t o a g i t a t i o n - p r o p a g a n d a song c y c l e s (pub. 1925-26) Song c y c l e Pesni rex/oliutsii [ R e v o l u t i o n a r y Songs! : l."Na pervoe maia" (P. O r e s h i n ) . ( B a r i t o n e v o i c e . ) (Pub. 1925); 2. "Na p o l i a c h " (P...Oresh i n) . C h o i r a c a p p e l l a . (Pub. 1925); 3 . " O k t i a b r ' " (S. Rodov). C h o i r a c a p p e l l a . (Composed 1924.) LLM. Song c y c l e Poeziia rabochikh professii [Poetry of the workers' c a l l i n g ] : l . " T k a c h " ( L i t k o v s k y ) . (Middle v o i c e . ) (Pub. 1925); 2."Shveia" (G. Korenev). (Pub. 1926.) LLM. 3 . " T o k a r i a " (A. T v e r d y i ) . C h o i r a c a p p e l l a . (Pub. 1926.) Song c y c l e Pesni o 1905 gode [Songs of the year 19053: 1. " S m o l k l i z a l p y . . . " (E. T a r a s o v ) . (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 D e c e m b r i s t s ] : 1 . " P o s l a n i e v S i b i r ' dekabristam" (A. P u s h k i n ) . (Pub. 1925.) MCL; 2."Otvet' na p o s l a n i e v S i b i r ' " (F. O d o e v s k i i ) . (High v o i c e . ) (Pub. 1925.) LLM. 1926  Chamber Symphony. U n f i n i s h e d piano s c o r e with notes f o r orchestration. CSALA. Sonata  f o r V i o l a and Piano.  CSALA.  189 1926  Gimn  sovetskoi raboche-krest' ianskai militsii [Hymn of the S o v i e t workers' and p e a s a n t s ' m i l i t i a ] (ViatichBerezhnich). Wind band and chorus, o r c h e s t r a ad. l i b .  1927  Trio.  Violin  and v i o l a p a r t s .  CSALA.  Concerto -for V i o l i n and O r c h e s t r a , i n -four movements. Without b e g i n n i n g . Piano s c o r e . CSALA. 1928  Concerto No. 1 -for V i o l i n and O r c h e s t r a . v i o l i n - p i a n o s c o r e . CSALA. KomsomoI'skaia.  and Piano S o l o .  Symphonic Poem -for O r c h e s t r a , Chorus, Sketches -for s c o r e . CSALA.  Sonata No. 1 -for V i o l a 1929  19291931  and Piano.  (P. D r u z h i n i n ) .  Bab'ia  dolia  Kon'ki  <A. S h i r i a e v e t s ) .  Quartet.  Sketches -for  LLM.  LLM.  CSALA.  Piano s c o r e with  Unfinished score.  Pakhta [Cotton peasant]. "Half Time," 215) .  CSALA.  CSALA.  and Piano.  Uzbekistan. Symphonic Poem. •for o r c h e s t r a t i o n . CSALA. O r c h e s t r a l work.  A g i t - p r o p . song.  A g i t - p r o p . song.  Fragments o-f s c o r e .  C 1930s! Sonata No. 2 -for V i o l a  Incomplete.  Ballet.  notes  CSALA. (Listed  i n Gojowy,  1930  S t u c h i t e ! KOMSOMOL [Communist Youth Group] March (I. Utkin).  19321933  Geroi'a [Song of the H e r o ] . orchestra. CSALA.  19341935  Quartet f o r Four Domras, on themes of Chechen songs. Score. CSALA.  folk  1935  Invention  and Piano.  CSALA.  and Piano.  GMMC.  and Nocturne  Dance f o r V i o l i n Kolybel'naia Scherzo Valse  Song arranged f o r  for Violin  and P i a n o .  GMMC.  [Lullaby] f o r V i o l i n for Violin  for Violin  and Piano.  and Piano.  GMMC. GMMC.  190 1936  Concerto f o r V i o l i n Score. CSALA.  1939  Quartet No. 4.  and O r c h e s t r a , i n t h r e e movements.  Unfinished score.  CSALA.  Potpou.fr-f-Fantasie, on themes of S o v i e t p o p u l a r f o r Xylophone and Piano. CSALA. 1940  Legends  1941  Quartet No. 5 i n Eb Major.  19411942  24 P r e l u d e s f o r V i o l i n  1942  Tabachok  n.d.  Rondo  songs,  f o r V i o l i n and P i a n o . CSALA; a l s o Legenda f o r V i o l i n and Piano i n D minor, n.d., a t GMMC.  and Piano. \  (A. P r i s h e l e t s ) .  and Polonaise  GMMC. GMMC.  A g i t - p r o p song.  for Violin  and Piano.  LLM. GMMC.  191 Listing  o-f Works by Genre  A . O r c h e s t r a l Works -for V i o l i n  Reverie  Symphony  and O r c h e s t r a .  i n C Minor.  1/ c/tasy novoLun t1910s.3  i ia.  1907.  1910. Symphonic poem -for l a r g e o r c h e s t r a ,  nan and Sea. Symphonic poem, a f t e r B a u d e l a i r e . Unpublished, a p p a r e n t l y l o s t . Symphony World's  i n -four movements. End.  Unpublished,  1922.  Without b e g i n n i n g ,  Symphonic poem, a f t e r J u l e s L a f o r g u e . apparently lost.  Symphony No. 2 f o r O r c h e s t r a and Chorus. Violin  Concerto.  Chamber  1926.  Concerto No. 1 f o r V i o l i n v i o l i n - p i a n o score. Solo.  and O r c h e s t r a .  1928.  Symphonic Poem f o r O r c h e s t r a , 1928. Sketches f o r the s c o r e . title.  Lento.  O r c h e s t r a l work, without  title.  C1920s-1930s.3  Uzbekistan.  Ballet.  Unfinished. 192S.  1927.  Sketches f o r Chorus, and  C1920s-1930s.3 Unfinished.  C1930s.3  Symphonic Poem.  O r c h e s t r a l work.  1922.  i n f o u r movements.  O r c h e s t r a l work, without Unfinished.  Pakhta.  ending.  Unfinished.  Concerto f o r V i o l i n and O r c h e s t r a , Without b e g i n n i n g .  Piano  1923.  Arranged f o r v i o l i n and piano.  Symphony.  KomsomoI'skaia.  1921.  C1930s.3  C1930s.3 Unfinished.  Geroia.  Arranged f o r o r c h e s t r a .  Concerto  for Violin  and O r c h e s t r a ,  1932-33. i n t h r e e movements.  1936.  192 B.Solo and Chamber Works 1.Works -for S o l o Piano. Trots  Compositions  Tri  Etiuda/Trois  Dva  sochineniia  Prelude  pour  piano.  Etudes IDeux  pour  piano.  1914.  Compositions  piano.  Five Preludes.  pour  1914.  pour  piano.  1915.  1915.  1919-1922.  fli/e Poemy/Deux  Poemes.  Sonata No.  1923.  5.  1920. (No i n d i c a t i o n s o-f other p i a n o  sonatas.)  2.Sonatas f o r V i o l i n  and Piano. 6th ed., s.v. " R o s l a v e t s , " i n d i c a t e s t h a t -five v i o l i n sonatas were w r i t t e n . )  (Grove  Sonate  Dictionary,  pour  violon  Sonata No.  et  piano.  2 -for V i o l i n  F o u r t h Sonata.  Pub.  t  piano. 3  and Piano.  and  Reverter Morgenstimmung Sonata ( b e g i n n i n g ) , E leg ie, Serenade, e t c . P i e c e s -for v i o l i n and f  1908.  and Romance-arabesque 19O9-1910.  Liricheskaia  for Violin  poema/Poeme  lyrique  C1910s.3 belykh  and Piano.  Poema. 7  Pub.  dev/Danses  des  1912.  and  for Violin  vierges  Piano.  and  blanches  Piano.  for Violin  1915.  Pieces -for V i o l i n and Piano: Eb Major, Canon, Fuga Adagio, t  poema.  1917.  Piano.  Poemes  Tantsy  1913-1914.  1924.  3.Other Works -for V i o l i n Pomance Gavotte,  c.  C1920s.3  Etude mortelle, Pre Iiudiia,  Etude i n Romanticheskaia  193  7rot's  Dansss.  1921.  and Nocturne  Invention  Dance -for V i o l i n Ko lyt>e I'nsi's  and Piano.  -for V i o l i n  -for V i o l i n  Scherzo  -for V i o l i n  i/alse  Violin  and Piano  Rondo  Sonata f o r V i o l a  1935. 1940.  i n D minor.  (Also Legends  n.d.; l i k e l y  and Piano.  for Violin  4.Sonatas f o r V i o l a  1935.  1935.  and Piano.  and Polonsise  1935.  1935.  and Piano.  24 P r e l u d e s f o r V i o l i n  and Piano.  and Piano.  and Piano.  -for V i o l i n  Legends  for Violin  for  the same work)  1941-42.  and Piano.  n.d.  and Piano.  and Piano.  1926.  Sonata No. 1 f o r V i o l a  and Piano.  1928.  Incomplete.  Sonata No. 2 f o r V i o l a  and Piano.  C1930s.3  5.Sonatas and Other Works f o r V i o l o n c e l l o and Piano. Sonata.  1921.  Sonata f o r V i o l o n c e l l o and Piano. Pszdum'et  Ned i tst i on.  1921.  1921.  Sonata No. 2 f o r V i o l o n c e l l o and Piano.  1922.  6.Piano t r i o s . Trio  No. 2.  Third Trio. Trio.  Violin  1920. For v i o l i n ,  violoncello,  and v i o l a p a r t s .  1927.  and piano.  1921.  194 7.String Nenuet  Quartets.  f o r S t r i n g Quartet.  S t r i n g Quartet.  1910.  Quartet/Quatuor  No.  Premier  a  Quatuor  1.  and  Quartet No.  1919.  Third Quartet. Quartet.  First  cordes.  Q u a r t e t , second 2.  1907.  v i o l i n part.  1913.  1913.  t h i r d movements.  1916.  Incomplete.  1920.  1929-1931.  Fragments of s c o r e .  Q u a r t e t No.  4.  1939.  Unfinished.  Quartet No.  5 i n Eb Major.  1941.  8.Other M i s c e l l a n e o u s Chamber Works Serenada  f o r Two  Violins.  1909.  Harp, oboe, two  NoktiurnJNocturne.  1913.  Piano Q u i n t e t f o r Two 1924. Quartet f o r Four 1934-1935.  Violins,  violas,  violoncello.  Viola, Violoncello,  Domras, on themes of Chechen f o l k  and  Piano.  songs.  P o t p o u r r i - f a n t a s i ' e , on themes of S o v i e t popular songs, f o r Xylophone and Piano. 1939. C.Vocal  Works  1.Choral Heaven  and  Works. Earth.  apparently  lost.  Cantata,  From song c y c l e Pesni Choir a cappella. a c a p p e l l a . 1924.  a f t e r Byron.  Revo I iutsi  (Pub.  i'.  1925)5  1912.  Unpublished,  "Na p o l i a k h " (P. O r e s h i n ) . " O k t i a b r * " (S. Rodov). Choir  195 From song c y c l e Poeziia rabochikh Tverdyi). Choir a cappella. Simn  sox/etskoi  ianskoi militsii (ViatichWind band and chorus, opt. o r c h e s t r a p a r t s .  raboche-krest'  Berezhnich). 1926.  2.Songs f o r V o i c e and  Piano.  Tri sochineniia. 1913. l."Sumrak t i k h i i " ne u s h l a " (A. B l o k ) ; 3."Vetere n a l e t i t e " Srustnye  (Verlaine). 3."B1agos1ovennyi  peizhazy  2."Zakat".  " T o k a r i a " (A.  professii'.  1926.  (V. B r i u s o v ) ; (A. B l o k ) .  2.  1913. l."Osenniaia pesnia"; chas."  soch inert iia. 1913-1914. 1. "Margar i tk i " ( I . S e v e r i a n i n ) . 1914J 2."Vy n o s i t e l i u b o v " (K. B o l ' s h a k o v ) . 19135 3."Volkovo k l a d b i s h c h e " (0. B u r l i u k ) . 1913; 4."Kuk" (V. Gnedov). 1914.  Chetyre  Pesenka  ArZekina  (E. Guro).  3.Agitation-propaganda Poslednee  chudo  1915.  songs.  (A. Andreev).  Baritone voice.  (Pub.  From song c y c l e Pesni Pewo I i utsi i'. "Na pervoe maia" Oreshin). Baritone voice. (Pub. 1925.) From song c y c l e Poeziia rabochikh professii'. (Litkovsky). Middle voice. (Pub. 1925); Korenev). (Pub. 1926.)  "Tkach" "Shveya"  1925.  (P.  (G.  From song c y c l e Pesni o 1905 gode: " S m o l k l i z a l p y . . ." <E. Tarasov). (Pub. 1925); "Mat' i Syn" (G. G a l i n a i a ) . (Pub 1926.) From song c y c l e Dekabristy. " P o s l a n i e v S i b i r ' dekabristam" (A. P u s h k i n ) . (Pub. 1925); " O t v e f na p o s l a n i e v S i b i r ' " Odoevskii). High v o i c e . (Pub. 1925.) Bab' ia dolia  Kon'ki Stuchite.' Tabachok  (A.  (P.  Druzhinin).  Shiriaevets).  1929.  1929.  (KOMSOMOL-March) ( I . U t k i n ) . (A. P r i s h e l e t s ) .  1942.  1930.  ^t.  i  APPENDIX B  T h i s appendix p r o v i d e s a b r i e f examination o-f issues o f content t a n g e n t i a l  T-level  \  .  in Chapter  Two.  Harmonies in " I " , Measures  6-8  •  6-8  of  c o n c e i v a b l e e x p l a n a t i o n of T - l e v e l  " I " involves  of most s i m i l a r PC to the 6,  discussions  I d e n t i t i e s o-f I n d i v i d u a l  A further, mm.  to the  PC  7,  d e s i g n a t i n g each harmony with a T - l e v e l  content, with  i n d i v i d u a l harmonies conforming  T-O,T-2,T-7 t r a n s p o s i t i o n a l and  8,  Example 6-1.  i d e n t i t y in  respectively Collections 1 eveIs.  (Ex. in mm.  relationship  assumed f o r  6-1). 6-8  and  the most s i m i l a r T-  (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)  mm.  197 Example 6-1 continued. 171 4TH 7-TIHF.-SPMII  5TH J'-TIflE-SPAHl  is  6TH /-TIME-SPAR  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|  )  1  T-7 (3)  210 J'-TIK-SPAMJ  J-  L  3RD ^-TIRE-SPAN  o rz—i bo  T-8 (5)  a ° °\  T-7 (51  tt»** T - l l (31  T-4 (31  T-2 (61  Note:. PCs i n T - l e v e l s that match the c o l l e c t i o n ' 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 l i k e w i s e of m. 7, second  h a l f , and of m. 8) have four  PCs out of s i x i n common, as do t h e second  and t h i r d .  Because  of these common PCs and because t h e middle c o l l e c t i o n of each group of three tends to f u n c t i o n collection of  (a f u n c t i o n t h a t  as an a u x i l i a r y , d e c o r a t i v e  i s e a s i l y perceived s i n c e many PCs  these middle c o l l e c t i o n s a r e 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 t h r e e are d e s i g n a t e d  as  the same T - l e v e l . The T - l e v e l  s u c c e s s i o n thus adduced -for mm.  T-ll,T-0,T-l/T-9,T-0 T-7, T-8/T-4, T-7  (m. 6 ) , T-11,T-2,T-3/T-11,T-2 (m. 7 ) ,  (m. 8 ) .  Such a s u c c e s s i o n o-f T - l e v e l s 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 an e n l a r g e d mm.  c o l l e c t i o n s r a t h e r than  s u b s e t s o-f  ICC; the T-0,T-2,T-7 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 o-f  6, 7, and 8; a c o n s i s t e n c y o-f T - l e v e l  measures;  6-8 i s :  sequence  and the s i m i l a r i t y o-f the - f i r s t and t h i r d  o-f each time-span, as noted  i n the t h r e e collections  above.  Gojowy's A n a l y s i s o-f T - L e v e l s  in " I I I "  Gojowy's -four ICCs o-f " I I I " i n c l u d e the -four most -frequentl y o c c u r r i n g PC c o l l e c t i o n s or t r a n s p o s i t i o n s t h e r e o f . sequence of ICCs and t h e i r T - l e v e l s i s i l l u s t r a t e d  His  i n F i g . 6-1.  199 F i g u r e 6-1. (a)ICCs  T-level successions analysis.  in "III",  as g i v e n  i n Gojowy'5  of " I I I " :  7  •b-  (b)T-level  successions  in "III":  MEASURE  111  [21  13)  ICC, T-LEVEL  i,0—a,3  c,0—c,7—c,ll—e,2  IRRE6ULAR—b, 1—b,4 (a,l/b,l)  H.  (41  15-61  ICC, T- b , 7 — b , 0 ™ b , 3  171  181  (91  (10-111  4 , 0 - — c , 3 - — c , 6 — * , ( )—4,1 (a,5) <d,10)  N. (121 113) ICC, T- a,3—IRRE6ULAR—-c,9—c,4—c,8—c,ll (•,0 TIMERS'*)  c,6  (14-131 c,4  There i s , however, a compromise of Goj owy's system of f o u r ICCs t h a t i s more p r a c t i c a l . and  The s i m i l a r i t i e s between ICCs "a"  "b", and between ICCs " c " and "d" ( i n e i t h e r case with  only  one PC t h a t d i f f e r s ) , a r e such t h a t two of the ICCs c o u l d be cited  i n s t e a d of f o u r ;  6-2a p r e s e n t s given  "a" and "d" a r e more i n c l u s i v e .  the two ICCs; the a l t e r e d  i n F i g . 6-2b.  Figure  sequence of T - l e v e l s i s  200 Figure  6-2.  ICCs "a" and "d" i n " 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 aO":  Db-Dtt-E-F-G-G**- (Bb) -B  "new dO":  Eb-E-Gb-G-Bbb-B-(Db)  ICAs:  2—1-1-2-1  3 2 +1)  (2  1-2—1-2  2  4 + 2)  (2  ( b ) T - l e v e l s o-f ICCs "a" and "d":  n.  [1]  (21  ICC, T- a,0 a,5 M.  (71  (31  d,0 4,7  (81  4,1  a,l  f  [9] [10,111  ICC, T- 4,3 4,6 4,10  (c)T-level  d 11 4,2  (41 a,l  (121  4,6  a,4 [131  a,5 4,0  al  a4  a5  a7  a( I  OCCURRENCES  2  2  1  3  1  9  TOTAL TINE-SPAN (8TH VALUES):  4  5  1  8  2  20  40  41  3  1  TOTAL TINE-SPAN 14  6  OCCURRENCES  42 1 1  43 1  d4 2  9  9  4,8 4,11  46  47  48  2  1  1  10  1  49 1  2  410 1  2  T h i s system o-f two ICCs r e p r e s e n t s Gojowy's -four  (i.e.,  4,4  time-spans:  aO  ICC, T-  4,0  (14,13]  4,9 4,4  o c c u r r e n c e s and t o t a l  ICC, T-  (5,6]  a,7 a,0 a,5  3  dll  d( I  2  16  3  60  a compromise between  t h e most -frequently o c c u r r i n g PC c o l l e c -  t i o n s and t r a n s p o s i t i o n s t h e r e o f ,  with no v a r i a n t elements), and  P e r l e ' s use o-f a s i n g l e ICC with t h r e e v a r i a n t elements not o c c u r r i n g with every An  examination o-f l o c a t i o n s and -functions o-f v a r i a n t  ments ( i . e . , "d",  collection.  represented  ele-  by the b r a c k e t e d PCs i n ICCs "a" and  F i g . 6-2a) e s t a b l i s h e s no c o n s i s t e n t  r e l a t i o n s h i p between  201 these elements and t h e i r  l o c a t i o n and f u n c t i o n i n the music.  F i g u r e 6-2c shows t h e o c c u r r e n c e s and t o t a l T-levels  i n order t o 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  c o n s i d e r e d more s i g n i f i c a n t . "d6" of  time-spans of ICC  (and t o a l e s s e r e x t e n t  In t h i s  light,  T-levels  "dO" and  "d3" and "d4") can be i d e n t i f i e d as  greater significance.  An A n a l y t i c a l  A l t e r n a t i v e : A S i n g l e ICC f o r " I " , " I I " , and " I I I "  S i m i l a r i t y of content makes i t p o s s i b l e t o a n a l y z e t h e harmonic s u c c e s s i o n s of t h e t h r e e p i e c e s i n terms of a s i n g l e ICC i n c l u d i n g elements "0", "3", "4", "6", and "8". T-level  of t h i s common ICC, o c c u r r i n g as the f i r s t  "I",  were t o be d e s i g n a t e d  "II"  would be T - l l ,  as T-O, then  and the f i r s t  There a r e obvious a n a l y t i c a l ICC;  I f the i n i t i a l  the f i r s t  T-level  harmony of T - l e v e l of  of " I I I " would be T-5.  advantages i n u s i n g a s i n g l e common  however, t h e r e a r e some problems with t h i s method.  The use  of  a s i n g l e common ICC i m p l i e s t h a t i n i t i a t i n g  of  the t h r e e p i e c e s a r e somehow s u b o r d i n a t e t o t h a t of the p i e c e  whose i n i t i a l differences  T-level  i s designated  as T-O.  harmonies i n two  And s i n c e t h e r e a r e  i n v a r i a n t elements a s s o c i a t e d with each p i e c e  (e.g., element "IO" i n " I " , "1" i n " I I " , and "9", "IO", and "11" in  "III"),  in  the n o t a t i o n a l orthography  ticularly  and i n the e x t e n t of t h e i r use, and a l s o  that of " I I I " ,  of ICC T - l e v e l s  three i n d i v i d u a l  basis f o r analyses in t h i s  thesis.  differences  i n t h e music,  par-  ICCs a r e taken as a  202 P r o l o n g a t i o n o-f T - L e v e l s  Reiterated occurrences,  T - l e v e l s , with o n l y a -few harmonies s e p a r a t i n g  imply  sequent, s p e c i a l  a p r o l o n g a t i o n of the T - l e v e l s and t h e i r  significance.  c o n t i n u i t y can p l a y a r o l e  PC i n v a r i a n c e and p i t c h - c l a s s  i n the p e r c e p t i o n o-f p r o l o n g a t i o n ,  t h i s perception being f a c i l i t a t e d  when:  t h e r e a r e no more than  t h r e e or f o u r i n t e r p o l a t i n g T - l e v e l s ; 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 p i t c h e s remains the same i n both ances of the T - l e v e l ; also ster;  con-  p i t c h e s i n the r e c u r r i n g T - l e v e l  appearappear  i n the i n t e r p o l a t e d T - l e v e l s , p r e f e r a b l y i n the same r e g i the r e i t e r a t e d  T - l e v e l s appear on s t r a n g e r m e t r i c  p o i n t s , and/or have s i m i l a r rhythmic ances of the r e i t e r a t e d T - l e v e l  p a t t e r n s ; and both  appear-  a r e g i v e n s i m i l a r forms of  emphasis, exposure, a c c e n t u a t i o n ,  or a r t i c u l a t i o n .  p r e s e n t s prolonged  the musical  illustrating  time-  T - l e v e l s , with  Example 6-2  n o t a t i o n of these  i n v a r i a n t PCs and p i t c h c o n t i n u i t y .  203 Example 6-2.  Prolonged  T-levels  i n Trois  Compositions.  204 Example 6-2 c o n t i n u e d . (101 T-3  T-6 5(2)  (ill  [121  T-3  T-9  5(2)  T-4 4(2)  T-9 412)  —en—  r-jr-e-  1  1_  1  0—\ 1  1 1  0—| i  OS*?  !  1 »>• 1 i " I V l l  1  • .  n  MEASURE  3  4  T-LEVELS  10-3  1 0 - 3 . . . . 10-3  PROLONGED [10 10 LEVELS: [33  — — -  1 I  7  1  1  101  10 31  10  0-5....0-5 0 (5.......5  11  12 13  0-3  0  0  0—0J 31  0  20S Example 6-2 c o n t i n u e d . •Ill* MEASURE  2  T-LEVELS  8—3—7—10 1-4  PROLONGED LEVELS  3 [7  4  8  9 10 12  13  14-15  7-0-3  2-6  9 2  5-0-4-7  0  71  12——21 15....  5-0 (0 5  0 51  01  206 Nate: L i n e s i n the - f i r s t a-f two s t a v e s with each example o-f p r o l o n g a t i o n connect i n v a r i a n t PCs i n a d j a c e n t harmonies. The unbracketed and b r a c k e t e d numbers above each harmonic s u c c e s s i o n i n d i c a t e the number o-f i n v a r i a n t 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 s t a v e s , h o r i z o n t a l l i n e s i l l u s t r a t e i n v a r i a n c e o-f PCs o-f the prolonged T - l e v e l s through i n t e r p o l a t e d T - l e v e l s . Given the above-stated T-3 (mm.  and  T-6  3-4),  (mm. and  10-11), and T-0  and  " I I I " are p a r t i c u l a r l y levels  c o n d i t i o n s , T - l e v e l s T - l l (mm.  less easily  T-5  T-9  (mm.  (m.  in " I " , T-10  10-11), and  convincing,  interrelated  12)  as  T-2  w h i l e other  (mm.  and  T-3  8-11)  in  reiterated  prolongations.  6-7),  T-  

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