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Form and process in Morton Feldman’s Spring of Chosroes Paynter, Terrence Jack 1996

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FORM AND PROCESS IN MORTON FELDMAN'S SPRING OF CHOSROES  (1977)  by TERRENCE JACK PAYNTER B.Mus., U n i v e r s i t y of Saskatchewan, 1978 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES (Department of Music) We accept t h i s t h e s i s as conforming to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA August 1996 ©  Terrence Jack Paynter, 1996  In presenting this thesis in partial fulfilment of the  requirements for an advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholariy purposes may be granted by the head of my department  or by his  or her representatives.  It is  understood  that  copying or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  - 1 1 -  ABSTRACT  The  music of Morton Feldman has  s t a s i s and  been noted f o r the sense of  l i n e a r d i s c o n t i n u i t y i t p r o j e c t s . However,  analytic studies  recent  have shown t h a t l i n e a r processes d i r e c t  h o r i z o n t a l dimension. T h i s t h e s i s i n v e s t i g a t e s process form i n Feldman's Spring piece  s t r u c t u r a l features  r e l a t i o n s h i p s . The  and  of Chosroes (1977) by segmenting  i n t o d i s c r e t e u n i t s c a l l e d modules that are  by c o i n c i d e n t  the  interconnected  and  the  affiliated  by developmental  modules, p a r t i c u l a r l y those  t h a t share aspects of p i t c h , rhythm, and  register, articulate  form. The  formal p l a n of the p i e c e  i s ABA':  the modular s t r u c t u r e of s e c t i o n A, and section B create  s e c t i o n A'  engages  parallelisms  p a l i n d r o m i c r e l a t i o n s h i p s . Two  in  sets  of  modules, each of which are connected by developmental processes, comprise l a r g e - s c a l e  frameworks t h a t r e f l e c t  ternary  the p a l i n d r o m i c d e s i g n of  s e c t i o n a l s t r u c t u r e and  s e c t i o n B. Processes of rhythmic d e c e l e r a t i o n and  in sections  A' r e i n f o r c e the s e c t i o n a l d e s i g n i n that the  modules i n each s e c t i o n generate momentum that slowed by t r a n s f o r m a t i o n s of t h e i r rhythm The  is  initial gradually  central  modules. Each module b i s e c t s a set of p a l i n d r o m i c a l l y together they b i s e c t the piece  A  patterns.  music i s s t r u c t u r a l l y weighted toward i t s two  modules, and  the  related  as a whole.  -  I l l  -  Organic and inorganic processes unite a l l levels of form and they connect local and large-scale structures. Effects of disconnectedness, then, are seen to be surface phenomena that arise from the interaction of disparate, ordered structures.  - iv -  TABLE OF CONTENTS Abstract  i i  Table of Contents  iv  L i s t of Examples  v  L i s t of F i g u r e s  vii  Acknowledgement  viii  INTRODUCTION Chapter One  1 Patterns  and Modules  Module A n a l y s i s Chapter Two  Chapter Three  Form  9 32 45  Section B  46  S e c t i o n s A and A'  67  Large-scale  84  Large-scale  Structure  Rhythmic Pulse  105  Section A  106  Section B  115  S e c t i o n A'  121  Summary and Conclusions  129  Endnotes  137  Bibliography  148  Appendix  Segmentation of S p r i n g of Chosroes  150  - v -  LIST OF EXAMPLES 1 - M a t e r i a l Overlapped i n Adjacent Modules  13  2 - V a r i e d R e p e t i t i o n i n a Module  17  3 - Various Orderings of Elements i n a P a t t e r n  19  4 - "Modular C o n s t r u c t i o n " and "Module"  20  5 - Beginning and End P o i n t of a Module  23  6 - Delayed Rhythm P a t t e r n i n a Module  25  7 - Development of a P a t t e r n  30  8 - Development of the Rhythm of a P a t t e r n  31  9 - P i t c h e s of a Chromatic T r i c h o r d D i v i d e d Among the Piano and the V i o l i n  34  10 - Delayed R e p e t i t i o n of a Module  35  11 - Lengthy Delay i n the R e p e t i t i o n of a Module...  36  12 - Gradual I n t r o d u c t i o n of P i t c h C l a s s e s  37  i n a Module  13 - Overlapped Elements of PM I and PM II  39  14 - J u x t a p o s i t i o n of P i t c h C l a s s e s from Four Adjacent Modules 15 - P i t c h C l a s s e s Extended t o a Module from Previous  40  Modules  42  16 - Overlapped R e g i s t e r s i n Adjacent Modules  43  17 - Comparison of the D i s t r i b u t i o n of Modules i n S e c t i o n s A and A' 18 - P a l i n d r o m i c  Design of S e c t i o n B  45 47  19 - I s o l a t i o n of Modules VI/1 and VI/2 Showing 20 - Palindromic I s o l a t i o n ofR Module VII elations h i p sShowing R e g i s t r a l I n v e r s i o n ....51 49  - vi-  21 - Graphic I l l u s t r a t i o n  of R e g i s t r a l I n v e r s i o n  i n Module VII  52  22 - R e g i s t r a l Spans of Modules i n S e c t i o n B  54  23 - Expansions of Magnitude i n Modules VIII/1 and VIII/2....55 24 - I s o l a t i o n of Modules IX/1 and IX/2 Showing C o n t r a c t i o n s of Magnitude 25 - I s o l a t i o n of Modules X / l and X/2 Showing Duration  57  Inversion  60  26 - I s o l a t i o n of Module XI and VM I I ' '  63  27 - P i t c h - C l a s s Connections Among S e c t i o n B Modules  64  28 - Contour R e l a t i o n s Among VM II and I t s V a r i a n t s  65  29 - S t r u c t u r a l Roles of VM II and I t s V a r i a n t s  66  30 - I s o l a t i o n of Modules VI/2, X I I , and XIII  .  68  31 - S p a t i a l D i s p o s i t i o n of Modules VI/1, VI/2, X / l , X/2, and  XII  32 - Instrument and R e g i s t e r  69 Inversion  i n Module XII  33 - Segmentation of VM I and Module XIII 34 - Comparison of Lengths of Segments i n VM I and Module XIII 35 - R e g i s t r a l Expansion i n the F i r s t Segment of VM I and Module XIII  69 ...72 75 76  36 - Rhythmic Connections Between PM I and PM XIV  77  37 - Comparison of the S p a t i a l Formations of Module I I I and Module XV  78  38 - Rhythmic Connection Between PM IV and Module XV 39 - P i t c h and R e g i s t e r Expansion i n Modules V and XVI 40 - I s o l a t i o n of Module XVI, VM I I ' , and the Coda 41 - P i t c h - C l a s s Connections Between VM I, and Modules XI and XVI -. 1 , 1  80 ..81 82 85  -  VI 1  -  42 - Large-Scale R e g i s t r a l Arch Formed by VM I, Modules XI and XVI, and the Coda  89  43 - Comparison of the Rhythm P a t t e r n s of VM I, and Modules XI and XVI  91  44 - P i t c h - C l a s s Connections among VM II and I t s V a r i a n t s . . . . 9 2 45 - Rhythmic Connections Among VM II and I t s V a r i a n t s  93  46 - Large-Scale R e g i s t r a l Arch Formed by VM II and Its Variants  94  47 - P o i n t s of Coincidence Between the Two L a r g e - s c a l e Arches  96  48 - Graphic R e p r e s e n t a t i o n of the R e g i s t r a l Arch Formed by the Uppermost P o i n t s of C o i n c i d e n c e .  96  49 - D e t a i l of the Spans of VM I, VM I I ' , I I ' , I I " * , and Module XI  97  50 - D e t a i l of P i t c h and R e g i s t e r Connections VM I I , I I ' ' ' ' , Modules XIII and XVI  99  1  Between  51 - R e g i s t r a l Arch Formed by Modules VI/1, X / l , XI, X/2, VI/2, and VM II • •  102  52 - R e g i s t r a l Formations of PM I, Module XI, and VM I I " . . . 110 53 - R e g i s t r a l Expansion i n Modules V and VI/1  114  54 - Comparison of the Attack P a t t e r n s of VM I, PM I, and Module V I I I / 2 . .  119  55 - Rhythmic Connections Between Module XIII and VM I I ' ''..124 56 - Comparison of the Spans of VM II • ' ' and PM XIV, and Module XV  125  LIST OF FIGURES 1 - Segmentation  of "Durations 3, I I I " (DeLio)  2 - Ordered L i s t of Modules i n S p r i n g of Chosroes 3 - Rhythmic Connections Between VM I, PM I, and A l l Subsequent Modules  2 33 128  - vi i i  ACKNOWLEDGEMENT I wish t o thank my a d v i s o r , John Roeder, f o r h i s kind p a t i e n c e , and f o r h i s i n v a l u a b l e comments from which I learned much. I a l s o wish t o thank W i l l i a m Benjamin f o r h i s grace, and f o r g u i d i n g the i n i t i a l development of the concepts t h a t are c e n t r a l t o t h i s t h e s i s .  P o r t i o n s of the score are r e p r i n t e d with the express permission of European American Music D i s t r i b u t o r s Corporation.  - 1 -  INTRODUCTION Much has been w r i t t e n about the v e r t i c a l dimension and seeming l i n e a r d i s c o n t i n u i t y i n the music of American composer Morton Feldman (1926-1987). The composer himself emphasized these f e a t u r e s i n some of h i s essays and lectures,  1  but there i s a growing body of evidence t h a t  disposes us to regard these as merely  superficial  c h a r a c t e r i s t i c s of the music, and t h a t exposes u n d e r l y i n g l i n e a r processes that a r t i c u l a t e formal s t r u c t u r e s . T h i s study r e p r e s e n t s a step i n the development of an a n a l y t i c approach to Feldman that i s concerned  with process and form.  Since i t i s hoped t h a t the ideas that emerge w i l l provide a point of departure f o r f u t u r e s t u d i e s , i t i s a p p r o p r i a t e to begin by acknowledging two e a r l i e r analyses concerned  with  l i n e a r i t y and form i n t h i s music. In "Toward an a r t of Imminence, Morton Feldman's Durations 3  f  III."  2  Thomas DeLio t r a c e s the t r a n s f o r m a t i o n of a  v e r t i c a l t e x t u r e i n t o a p u r e l y l i n e a r one (Figure 1 ) . In gesture 1, three p i t c h c l a s s e s , Ftt, G and A , are combined i n to  four d i s t i n c t v e r t i c a l s p a c i n g s , each of which d i s t r i b u t e s i t s p i t c h e s among upper and lower middle  r e g i s t e r s and leaves the  r e g i s t e r empty. A suggestion of rhythmic momentum  e x i s t s i n that a l l four chords are repeated but the second, t h i r d , and e s p e c i a l l y the f o u r t h are repeated l e s s o f t e n than the f i r s t .  In t h i s way chord formations change more  FIGURE 1 (reproduced from D e l i o p.468)  Durations  Gesture 1  &  v La  -QJ i  m  A  ** ** •  m  3  4  5  6  Gesture 2  7  8  11  12  13  14  s  0  *  t  put  »*  «  •  m  A  «  t  *.  V  «-  **= 16  17  18  19  20  21  22  24 25  23  Gesture 4 *>  31  *•  7-  26  27  ID  -•  30  32  33  34  35  36  15  pizz  arco  »  £  *«~— * r -  10  9  *  Gesture 3  f~ i —  f  —*c-  —  ka. *»"—*•  1 2  u  W  37  28  29  i  -  frequently Gesture three  as  the  passage  2 contains  pitch classes  attack. register  proceeds.  a series  of  c h o r d s made w i t h t h e  whose s p a t i a l  No p i t c h c l a s s  appears  and p r e v i o u s l y v a c a n t  change  with  consecutively  i n the  same  registral  2 retains  p i t c h and r e g i s t e r  gesture  1 b u t has  a degree  new,  were  More  to  associations  textural  3 new p i t c h c l a s s e s importantly,  more i n d e p e n d e n t  starts  fragment"  formed by a l l  and 4 p i t c h e s (virtually  violin  "the  roles  (474). three  all  instruments  as  a result  In g e s t u r e s  instruments  At the  new o n e s )  against  tetrachords  the  together.  and p i a n o .  generated  the  with makes  it  DeLio d i v i d e s  and shows t h a t  from t h e  initial  o r i g i n a l three  f o r e g r o u n d as  their  the  take  of which the 1 and 2,  but  simultaneities  in gesture  3  the  v a r i o u s l y p l a y i n g 2, the  tuba's  a foregrounded  tuba l i n e  of  unfolds  the an  f o r m a t i o n " (476)  v e r t i c a l texture  on  texture  linear  into  piece.  3  pitches  the  two  i n t e r v a l l i c structures  trichord  note c l u s t e r  the  as  original  begin to  same t i m e ,  emerge  the  v e r t i c a l b a c k g r o u n d p r o v i d e d by  highly structured linear the  utilized.  f l u i d i t y that  a r e added t o  p i a n o assumes a l a r g e r v e r t i c a l r o l e ,  construct  spaces are  each  "static."  In g e s t u r e three.  of  same  formations  Gesture  seem l e s s  3 -  "Thus,  are from  independent, that  recedes  projects into  into  the  background. In g e s t u r e connections  4,  the  exist  t u b a melody i s  between  its  unaccompanied.  tetrachords  and t h e  Intervallic foreground/  -  background s t r u c t u r e s i n gesture and  3, the o r i g i n a l  the low r e g i s t e r notes i n gesture  4 not only extends the music before d i r e c t i o n and with gesture DeLio has  provides  4  -  trichord,  1. In t h i s way,  gesture  i t , i t expands i n a  new  c l o s u r e by v i r t u e of i t s a s s o c i a t i o n  1. shown us a four-stage process  i n which an  e s s e n t i a l l y s t a t i c , v e r t i c a l t e x t u r e l o s e s cohesion,  and  is  r e l e g a t e d to the background by an emerging melodic l i n e t h a t u l t i m a t e l y supersedes i t . T h i s would suggest t h a t the i s l i n e a r l y conceived,  and  piece  t h a t v e r t i c a l i t y e x i s t s as a  t e x t u r a l phenomenon whose s h a p e — i n d e e d whose very  existence-  - i s determined by u n d e r l y i n g l i n e a r f o r c e s i n much the same way  that the s u r f a c e f e a t u r e s of a r i v e r are a l t e r e d by  u n d e r l y i n g c u r r e n t s . Disconnectedness appears as a s u r f a c e e f f e c t caused by l o c a l p e r t u r b a t i o n s instrumentation,  in r e g i s t e r ,  etc.  In an unpublished  paper e n t i t l e d ,  Music of Morton Feldman,"  3  "Organic  Stephen Johnson takes exception  the "overemphasis on the s t a t i o n a r y " i n the Instead,  Construction in  he seeks to uncover l i n e a r and  i n the domains of t e x t u r e , timbre,  to  literature.  organic  connections  harmony, and  p i t c h space  i n some s e c t i o n s of For Frank O'Hara (1972). Johnson's choice of segments i s based on e x h i b i t e d d i f f e r e n c e s i n t e x t u r e , timbre,  and  He begins  p o s i t i o n i n the p i t c h  field.  by examining harmony i n s e c t i o n 1 and  points  out  -  that chord r e p e t i t i o n s generate u n i t y while organicism  is  demonstrated i n a s e r i e s of s i x chords, the  of  first  five  which are subsets of the s i x t h . V a r i a t i o n procedures applied  to some aspects of c h o r d s - - f o r  pitches  of a chord are arranged  In i t s v a r i a n t form, the c l u s t e r s and but  example, the  i n a given  5  -  are clustered  s p a t i a l formation.  i n t e r v a l l i c r e l a t i o n s h i p s i n the  t h e i r r e l a t i v e v e r t i c a l p o s i t i o n s are  preserved  the s i z e s of the spaces between them are changed. In  Johnson's example 3 we formation and spacing  see an  i n v e r s i o n a l l y symmetrical  example 4 shows the r e t u r n of an  " j u s t beyond the halfway p o i n t " of the  Feldman was p a i n t i n g and  keenly i n t e r e s t e d i n a b s t r a c t appears to have incorporated  earlier piece.  expressionist  at l e a s t one  p r i n c i p l e s i n t o h i s music--"the p r i n c i p l e of p o s i t i v e  of i t s and  negative space." Simply put,  the o b j e c t s  represent  the areas t h a t separate them,  p o s i t i v e space and  in a picture  negative space. In h i s a n a l y s i s , Johnson t r e a t s p i t c h e s p o s i t i v e space and  the v e r t i c a l and  as  h o r i z o n t a l spans between  them as negative space. He goes on to say that  negative  spaces do not remain so f o r long; they soon become f i l l e d - i n p o s i t i v e spaces and  v i c e versa  i n l o c a l and  extended  passages. I t seems that Feldman, " l i k e a true  abstract  e x p r e s s i o n i s t , obeyed the b a s i c laws of balance." In h i s d i s c u s s i o n of s e c t i o n two,  Johnson  describes  " c r y s t a l l i z a t i o n , " a process by which the enmeshed elements of e a r l i e r m a t e r i a l  become d i s t i n c t , t a k i n g  on a "sharper  -  f o c u s . " In h i s example 6,  -  he shows that three d i s t i n c t  timbres are a s s o c i a t e d with three s p e c i f i c  harmonic  formations: "What has happened, i n e f f e c t ,  i s that  timbres  which have mainly blended together a t the beginning coagulate i n t o d i s t i n c t , non-blended  suddenly  groups."  The process of " c r y s t a l l i z a t i o n " demonstrates approach  6  Feldman's  to o r g a n i c i s m . "The stages progress from an i n i t i a l  s t a t e of f l u x ,  i n which the m a t e r i a l has not f u l l y  taken  shape; through a c e n t r a l , prolonged moment of c l a r i t y , i n which the m a t e r i a l c r y s t a l l i z e s  into d i s t i n c t  relationships;  to a f i n a l stage of d i s i n t e g r a t i o n . " Although the " c r y s t a l l i z e d " r e l a t i o n s h i p s i n stage two begin to break down in  the f i n a l stage, they r e t a i n aspects of e a r l i e r  spatial,  t i m b r a l and harmonic s t r u c t u r e s . Johnson demonstrates  that the emergence of t i m b r a l  s t r u c t u r e s i n s e c t i o n 2 i s prepared by chords e a r l y i n s e c t i o n 1.  The f i r s t  three chords of the p i e c e blend  timbres  that e x h i b i t d i f f e r i n g r a t e s of decay, but a few measures l a t e r , the timbres are d i s e n t a n g l e d to form chords that decay uniformly. Regarding  the t h i r d and f o u r t h s e c t i o n s , Johnson  observes  that "incremental a l t e r a t i o n s " i n the repeated m a t e r i a l of a passage do not d i s r u p t i t s c o n t i n u i t y . As w e l l , he i d e n t i f i e s i n a " v e r t i c a l " passage some " l i n e a r - f u n c t i o n " p i t c h e s that are d i r e c t l y l i n k e d to an e v o l v i n g melody l i n e . In the f i n a l s e c t i o n , the foregrounded  melody forms a harmonic, t e x t u r a l  -  and  timbral  "point of c u l m i n a t i o n "  set  type i n the piece  (set c l a s s 4-1)  p r e v i o u s l y vacant s p a t i a l a n a l y s i s presents  that unfolds  area.  and  fills  a  7  -  prevalent  in a  In summary, Johnson's  a v a r i e t y of processes and  r e l a t i o n s that  b e l i e the view that Feldman's music i s made from v e r t i c a l , random events. Two  procedures i n Durations 3  f  e s p e c i a l l y important to form. The generates a s e c t i o n a l t h r e e - p a r t supported by d i s t i n c t  I I I and  For Frank O'Hara are  crystallization  s t r u c t u r e i n 0'Hara t h a t i s  changes i n t e x t u r e . Durations may  understood to begin i n the second, " c r y s t a l l i n e " t h e r e f o r e e x h i b i t s two each piece contains  types of v e r t i c a l  stage  texture.  Durations,  be and  Secondly,  a l i n e t h a t emerges from the t h i r d  i n which v e r t i c a l s t r u c t u r e s " d i s i n t e g r a t e , " and p o i n t of focus  process  stage,  becomes a  f o r the e n t i r e p i e c e . In the f i n a l passage of  the l i n e i s unaccompanied and  the d i s i n t e g r a t i o n  of v e r t i c a l t e x t u r e complete. In these two s t r u c t u r e s are more s t r o n g l y d e f i n e d  and  pieces  vertical  linear structures  are g r a d u a l l y eroded as the music proceeds. Feldman has  c h a r a c t e r i z e d h i s approach to composing h i s  l a t e r works as " c o n t i n u a l l y r e a r r a n g i n g same room."  4  If the  of compositional  the  f u r n i t u r e i n the  " f u r n i t u r e " i s analogous to a r e p e r t o i r e  techniques,  h i s statement i m p l i e s t h a t  he  uses the same procedures i n h i s pieces  to v a r i o u s s t r u c t u r a l  ends. Thus, i n 0'Hara and  see two  formal  Durations we  s t r u c t u r e s generated by c r y s t a l l i z a t i o n ,  distinct and  two  -  c u l m i n a t i n g melodic l i n e s with d i f f e r e n t  8  -  structural  a s s o c i a t i o n s to the t e x t u r e s from which they emerge. Feldman was g e n e r a l l y enigmatic when d i s c u s s i n g h i s music but implied l i n e a r way.  i n some statements that he conceived i t i n a s  By " l i n e a r  i n f o r m a t i o n " he seems to mean  m a t e r i a l with inherent d i r e c t i o n a l dissonant  tendencies such as  i n t e r v a l s , seventh chords e t c . e x h i b i t  i n tonal  music. Although h i s i n f o r m a t i o n may not be p r e c o m p o s i t i o n a l l y l i n e a r , the two s t r u c t u r e s we have seen here that were b u i l t with t h a t " i n f o r m a t i o n " have profound  linear  dimens i o n s . DeLio and Johnson r e c o g n i z e the importance of the v e r t i c a l aspect of Feldman's music but they show us p e r v a s i v e evidence of l i n e a r process as w e l l . That Feldman implied the e x i s t e n c e of both supports t h i s  view.  - 9 CHAPTER PATTERNS AND  ONE  MODULES  In h i s w r i t i n g s Feldman r e l a t e s process concepts of " p a t t e r n " and  "module." We  and  form to the  s h a l l see  that  p a t t e r n s are the b a s i c s t r u c t u r a l u n i t s i n Feldman's music. A passage generated by r e p e t i t i o n s of a p a t t e r n i s a "module." The  purpose of t h i s chapter  i s to d e f i n e p a t t e r n s and  and  examine the ways t h a t Feldman t r e a t e d them, u s i n g , as  example, Spring of Chosroes (1977) f o r v i o l i n and Feldman was  deeply  drew a n a l o g i e s  i n h i s w r i t i n g s and  the p a t t e r n was  i n s p i r e d by the h i g h l y c o l o r f u l ,  of T u r k i s h  and  l e c t u r e s between  rug designs  an  piano.  i n f l u e n c e d by the v i s u a l a r t s and  of p a i n t i n g and  designs  modules  often  aspects  h i s music. His conception  of  asymmetric  rugs.  The c o l o r - s c a l e of most nonurban rugs appears more extensive than i t a c t u a l l y i s , due to the great v a r i a t i o n of shades of the same c o l o r ( a b r a s h ) — a r e s u l t of the yarn having been dyed i n small q u a n t i t i e s . As a composer, I respond to t h i s most s i n g u l a r aspect of a rug's c o l o r a t i o n and i t s c r e a t i o n of a microchromatic o v e r a l l hue. My music has been i n f l u e n c e d mainly by the methods i n which c o l o r i s used on e s s e n t i a l l y simple d e v i c e s . I t has made me q u e s t i o n the nature of musical m a t e r i a l . What could best be used to accommodate, by e q u a l l y simple means, musical color? Patterns. 1  He goes on i n t h i s passage to d i s c u s s p a t t e r n s compos itions--Why  P a t t e r n s , S t r i n g Quartet,  and  of Chosroes. In h i s comments r e g a r d i n g the f i r s t  i n three Spr ing he  i n d i c a t e s that s l i g h t v a r i a t i o n s i n a p a t t e r n do not its  identity;  i n s t e a d , they generate s u r f a c e  alter  asymmetries  - 10 -  analogous  to the i r r e g u l a r i t i e s of shape and c o l o r  i n rug  patterns. Why P a t t e r n s i s a composition f o r f l u t e , g l o c k e n s p i e l , and piano c o n s i s t i n g of a l a r g e v a r i e t y of p a t t e r n s . The work i s notated s e p a r a t e l y f o r each instrument and does not c o o r d i n a t e u n t i l the l a s t few minutes of the composition. T h i s v e r y c l o s e , but never p r e c i s e l y synchronized, n o t a t i o n allows f o r a more f l e x i b l e pacing of three d i s t i n c t c o l o r s . M a t e r i a l given to each instrument i s i d i o m a t i c a l l y not interchangeable with that of the other instruments. Some of the p a t t e r n s repeat e x a c t l y — o t h e r s , with s l i g h t v a r i a t i o n e i t h e r i n t h e i r shape or rhythmic placement. At times, a s e r i e s of d i f f e r e n t p a t t e r n s are l i n k e d together on a c h a i n and then juxtaposed by simple means. 2  Feldman i m p l i e s that p a t t e r n s are independent  entities  which, when strung t o g e t h e r , have equal s t r u c t u r a l  importance.  The most i n t e r e s t i n g aspect f o r me, composing e x c l u s i v e l y with p a t t e r n s , i s t h a t there i s not one o r g a n i z a t i o n a l procedure more advantageous than another, perhaps because no one p a t t e r n ever takes precedence over the o t h e r s . The c o m p o s i t i o n a l c o n c e n t r a t i o n i s s o l e l y on which p a t t e r n should be r e i t e r a t e d and f o r how long, and on the c h a r a c t e r of i t s i n e v i t a b l e change i n t o something e l s e . 3  One  may  t h e r e f o r e expect to f i n d a " f l a t " s t r u c t u r e , v o i d of  hierarchical relationships,  i n a composition made  " e x c l u s i v e l y with p a t t e r n s . " I t w i l l be shown t h a t t h i s i s , i n f a c t , not the case. The design of a given p a t t e r n i s not i n and  of i t s e l f predisposed to any s t r u c t u r a l  however, some p a t t e r n s share p i t c h c l a s s e s , elements,  r e g i s t e r , contours  purpose;  rhythmic  ( e t c . ) and are t h e r e f o r e  "connected." Larger passages formed by repeated p a t t e r n s are c a l l e d modules. L o c a l and  l a r g e - s c a l e connections between modules  d e f i n e formal s t r u c t u r e s . We  w i l l see t h a t l a r g e - s c a l e  - 11 -  connections, e s p e c i a l l y those that are made with two c o n n e c t i v e elements, local  or more  have deeper s t r u c t u r a l meanings than  connections.  Feldman goes on to d e s c r i b e two  types of p a t t e r n s .  I enjoy working with p a t t e r n s t h a t we f e e l are symmetrical (patterns of 2, 4, 8, etc.) but present them i n a p a r t i c u l a r context:  Example 1 i s c h a r a c t e r i s t i c of a v e r t i c a l p a t t e r n framed by s i l e n t beats; i n t h i s i n s t a n c e the r e s t s on e i t h e r end are s l i g h t l y unequal. L i n e a r p a t t e r n s are n a t u r a l l y more ongoing, and c o u l d have the "short b r e a t h " r e g u l a r i t y of example 2 or a n t i c i p a t e a s l i g h t staggered rhythmic a l t e r a t i o n such as i n example 3. Another d e v i c e I use i s to have a l o n g i s h s i l e n t timeframe that i s asymmetrical; i n t h i s i n s t a n c e , with a q u i x o t i c four-note f i g u r e i n the middle:  or a symmetrical measure:  silent  frame around a s h o r t asymmetric  4  R e p e t i t i v e c h o r d a l p a t t e r n s might not progress from one another, but might occur at i r r e g u l a r time i n t e r v a l s i n order to d i m i n i s h the c l o s e - k n i t aspect of p a t t e r n i n g ; while the more evident rhythmic p a t t e r n s might be mottled  -  12  at c e r t a i n junctures to obscure t h e i r p e r i o d i c i t y . For me p a t t e r n s are r e a l l y s e l f - c o n t a i n e d sound-groupings t h a t enable me to break o f f without p r e p a r a t i o n i n t o something else. 3  The  p i t c h e s i n v e r t i c a l p a t t e r n s are combined i n v e r t i c a l  formations repeated,  (dyads, t r i c h o r d s , etc.) t h a t are u s u a l l y and  i n l i n e a r p a t t e r n s the p i t c h e s are  disposed  h o r i z o n t a l l y . In Spring of Chosroes, f o r example, v e r t i c a l p a t t e r n s are found i n the piano (measures 58-63), and  aspects  and  violin  measures 219-228 c o n t a i n a l i n e a r  p a t t e r n . Most p a t t e r n s other of these two  (measures 1-27)  i n t h i s piece f a l l  i n t o one  or  the  c a t e g o r i e s but some p a t t e r n s embody  of both; f o r example, i n measures 1-12  v e r t i c a l s o n o r i t i e s are i n c o r p o r a t e d predominantly l i n e a r  i n t o an  (violin), otherwise  design.  Feldman's c h a r a c t e r i z a t i o n of p a t t e r n s as " s e l f - c o n t a i n e d sound-groupings t h a t can break o f f i n t o something e l s e " a p p r o p r i a t e l y d e s c r i b e s abrupt patterns 146  and  changes between some  i n Spring of Chosroes ( f o r example, measures 155-156) but other p a t t e r n s c o n t a i n "borrowed"  elements t h a t prepare f o r the a r r i v a l Example 1 shows how overlapped.  Measures 340  and  {C2,  D2,  adjacent  to  from the D f l a t s  modules i s  to  v i o l i n p i t c h of module  measure 340  we  as i t s p a t t e r n a d i s c r e t e , b r i e f  E 4, E7}.  patterns  342-347 c o n t a i n D 5 i n the  In the measures surrounding  XV which has  of subsequent  the m a t e r i a l of two  v i o l i n which a n t i c i p a t e s the i n i t i a l XVI.  145-  I n i t i a l l y r e s t s separate  i n the v i o l i n , but  see module  tetrachord  this tetrachord  i n measures 344  and  346  -  13  -  EXAMPLE 1  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n of E u r o p e a n A m e r i c a n Music D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n  - 14 -  appear two p i t c h e s and occupies  chords that have the rhythm of module XV and r e g i s t r a l d i s t r i b u t i o n of the hexachord t h a t  measure 357  i n module XVI.  temporal space occupied t h e i r rhythm and  by two  i n the v i o l i n ;  In t h i s way,  the  but  initial  does "break o f f i n t o something e l s e "  i t does not do so "without  the  thus,  s p a t i a l o r g a n i z a t i o n extends module XV  (module XV)  but  preparation."  Regarding S t r i n g Quartet. that contains  These chords cohabit  D flats  t h e i r p i t c h e s prepare module XVI. pattern  the  Feldman d i s c u s s e s a passage  four juxtaposed  patterns.  In S t r i n g Quartet there i s an almost obsessive r e i t e r a t i o n of the same c h o r d — d i s p e r s e d i n an o v e r l a y of four d i f f e r e n t speeds:  3  Jff  h  8  h  m  —  m  , |. ......  t  3  —  .  ti i i h¥- i- i- r~ 3  \  L  j  j  ]  wwvuw •r r rifffffi  The rhythmic s t r u c t u r e of the block c o n s i s t s of four uneven bar lengths with four permutations t h a t i n c o r p o r a t e the i n s t r u m e n t a t i o n of the q u a r t e t . I must c a u t i o n the reader not to take the b a r l i n e s here at face v a l u e . T h i s  - 15 passage becomes r h y t h m i c a l l y obscured by the complicated nonpatterned syncopation t h a t r e s u l t s . Only a f t e r r e h e a r s a l s , and by f o l l o w i n g the s c o r e , c o u l d I c a t c h an i n d i v i d u a l [rhythmic] p a t t e r n as i t c r i s s c r o s s e d from one instrument to a n o t h e r . 6  A s t r i k i n g f e a t u r e of t h i s design i s the t r a n s f e r of rhythmic  p a t t e r n s between the four instruments, an u n d e r l y i n g  order t h a t Feldman sought the passage. In t h i s  to d i s c e r n i n repeated hearings of  instance he was not concerned  with  disconnected events but with ordered events which, when juxtaposed, generate Regarding  the e f f e c t of randomness.  Spring of Chosroes Feldman s t a t e s the f o l l o w i n g :  In Spring of Chosroes f o r v i o l i n and piano, the " p a t t e r n " of one s e c t i o n c o n s i s t s of h e i g h t e n i n g the e f f e c t of the plucked v i o l i n f i g u r e (encompassing three p i t c h e s ) by not e s t a b l i s h i n g any c l e a r - c u t rhythmic shape except f o r i t s constant displacement w i t h i n the q u i n t u p l e t . T h i s allows f o r f i v e permutations, which are then juxtaposed i n a h e l t e r - s k e l t e r f a s h i o n as the s e r i e s c o n t i n u e s . The use of three p i t c h e s a g a i n s t f i v e uneven beats c r e a t e d , i n my ears, a c r i p p l e d c o n s t e l l a t i o n of " e i g h t " as I was w r i t i n g i t . Against the v i o l i n ' s p a t t e r n , the piano has an independent rhythmic s e r i e s of the same three p i t c h e s , played i n a symmetric u n i t of four equal beats to a measure. T h i s f u n c t i o n s as s t i l l another d e t e r r e n t to the n a t u r a l p r o p u l s i o n of the q u i n t u p l e t .  - 16 -  A modular c o n s t r u c t i o n such as the above could be a b a s i c device f o r organic development. However, I use i t to see that p a t t e r n s are "complete" i n themselves, and i n no need of d e v e l o p m e n t — o n l y of e x t e n s i o n . My concern i s : what i s i t s s c a l e when prolonged, and what i s the best method to a r r i v e at i t ? 7  Feldman's view t h a t the passage encompasses three (G#,A,B ) assumes octave equivalence to  pitches  given t h a t they appear  i n three d i s t i n c t r e g i s t e r s . T h i s seems to c o n t r a d i c t a statement made i n h i s Darmstadt l e c t u r e , "Instead twelve-tone as a concept, I'm notes."  8  i n v o l v e d with a l l the  In Spring of Chosroes he  12 p i t c h c l a s s e s , not  88  the 88  i s evidently involved  with  pitches.  S l i g h t v a r i a t i o n s i n a p a t t e r n do not a l t e r because they do not a l t e r  of  i t s identity  i t s r e l a t i o n to other  measures 33-48 (Example 2), two  patterns  patterns.  that c h a r a c t e r i z e a  passage i n the piano e x h i b i t changes i n d u r a t i o n . these changes the d u r a t i o n s  In  Despite  of p a t t e r n 1 are c o n s i s t e n t l y  " f a s t " r e l a t i v e to p a t t e r n 2; thus, s p e c i f i c changes do  not  a l t e r the broad, " g e n e r i c " r e l a t i o n s h i p t h a t e x i s t s between the two  p a t t e r n s . Small f l u c t u a t i o n s i n r e g i s t e r , p i t c h and  t e x t u r e s i m i l a r l y do not change the l a r g e r , u n d e r l y i n g  - 17 EXAMPLE 2  iJ  pattern 1  pattern 2  *  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n of E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n .  - 18 -  s t r u c t u r e of the passage. The  order  of events i n a p a t t e r n may be v a r i e d somewhat  without t h r e a t to i t s u n i t y . In measures 291-300, f i v e permutations of a s i n g l e p a t t e r n are used t o generate a module i n the v i o l i n  (Example 3). Within  each p a t t e r n ,  rhythmic events (three q u i n t u p l e t s i x t e e n t h d u r a t i o n s  five and two  q u i n t u p l e t s i x t e e n t h r e s t s ) are arranged four ways, three of which c o n t a i n two dyads and one d i s c r e t e p i t c h while the fourth contains  a d i s c r e t e p i t c h , a dyad and a t r i c h o r d . The  p i t c h e s of a l l four permutations are d i s t r i b u t e d among two r e g i s t e r s . The f i f t h  permutation has the rhythm of the f i r s t  but the p i t c h e s of i t s three dyads are d i s t r i b u t e d i n three r e g i s t e r s . Thus, the more c o n s i s t e n t aspects of the passage (durational values, provide  r a t i o of a t t a c k s versus r e s t s e t c . )  a coherence that o f f s e t s the d e s t a b i l i z i n g e f f e c t of  the changing  order.  P i t c h c l a s s and rhythm are the most important aspects of a pattern's  i d e n t i t y because they are the ones that are v a r i e d  least; therefore,  i n t h i s analysis a pattern  be a s e t of p i t c h c l a s s e s a s s o c i a t e d  i s understood to  with a s e t of one or  more rhythmic elements. These p i t c h c l a s s e s w i l l be c a l l e d " c o n s t i t u e n t p i t c h c l a s s e s . " A p a t t e r n may a l s o c o n t a i n c l a s s e s that are "borrowed" from other  patterns;  increase the number of p i t c h c l a s s e s of a passage  pitch  these may containing  a p a t t e r n but do not i n c r e a s e the number of the p a t t e r n ' s c o n s t i t u e n t p i t c h c l a s s e s . Other aspects of a p a t t e r n such as  - 19 -  EXAMPLE 3  k  -I  ft,  ^  7 -f<-  s  ry: -V-  J=2 £ L  ±fc:  duration,  — i ^ *—*  gl133 . 1—  r e g i s t e r , the order  and number of events, e t c . , may  be v a r i e d , but not to an extent  that threatens  the p a t t e r n ' s  identity. Let us now t u r n to the concept of a "module." Feldman r e f e r s to measures 291-300 as a "modular c o n s t r u c t i o n . " I t i s apparent from Example 4 that these measures are part of a  EXAMPLE 4  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n of E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l Ed  - 22 -  l a r g e r c o n s t r u c t that extends to measure 329--permutations of the v i o l i n p a t t e r n are extended to measure 305 but i t s p i t c h c l a s s e s are extended to measure 329, and the rhythm of the piano ( d i s c r e t e s i x t e e n t h - n o t e  d u r a t i o n s v a r i o u s l y placed on  one of four beats i n each measure) a l s o extends to the l a t t e r measure. The measures c i t e d by Feldman  are the minimum  necessary to demonstrate the f i v e permutations of the v i o l i n p a t t e r n . A c c o r d i n g l y we w i l l r e f e r to any passage i n which a pattern  i s repeated as a "modular  construction."  The two e s s e n t i a l elements of a p a t t e r n , and t h e r e f o r e of a module, are i t s p i t c h c l a s s content and rhythm. In g e n e r a l , a module begins when both elements have r e p l a c e d those of the previous  module and ends when each i s r e p l a c e d by a f o l l o w i n g  module or when each i s extended to i t s f u r t h e s t p o i n t . Thus, when the p i t c h c l a s s e s but not the rhythm of a p a t t e r n A are r e p l a c e d by those of a subsequent p a t t e r n B, i t i s the f u r t h e s t extension  of the rhythm of p a t t e r n A t h a t  defines  the end p o i n t of the module to which p a t t e r n A belongs. Similarly,  i f the rhythm but not the p i t c h c l a s s e s of a  p a t t e r n A i s r e p l a c e d by t h a t of a subsequent p a t t e r n B, i s the f u r t h e s t extension  it  of the p i t c h c l a s s e s of p a t t e r n A  that d e f i n e s the end p o i n t of the module to which p a t t e r n A belongs. This p r i n c i p l e i s demonstrated by Example 5. Measures 339347 c o n t a i n a module c o n s i s t i n g of a p a t t e r n A i n which p i t c h c l a s s e s C,D,E ,E are combined to  four  with a rhythm c o n s i s t i n g  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n of E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n  - 24 -  of d i s c r e t e s i x t e e n t h d u r a t i o n s  p o s i t i o n e d at the ends of  measures i n 5/16 and 7/16 time. Each statement of p a t t e r n A i s followed  by at l e a s t one measure of r e s t i n the p i a n o .  9  In measures 344 and 346, the p i t c h c l a s s e s F#,G,A ,A,B ,B 13  13  from measure 357 i n p a t t e r n B r e p l a c e those of p a t t e r n A, but the rhythm of p a t t e r n A i s extended t o measure 347. In measure 348, the rhythm of p a t t e r n B begins;  thus,  the end  p o i n t of the module to which p a t t e r n A belongs i s measure 347. Returning the v i o l i n  b r i e f l y to Example 4 we see t h a t the rhythm of i s replaced  sixteenth-note concurrent durations  i n measure 307 by detached q u i n t u p l e t  durations  t h a t are borrowed from the  p a t t e r n of the piano.  These a l t e r n a t e with  longer  t h a t a n t i c i p a t e those of the f o l l o w i n g c o n s t r u c t  (measures 330-338). The p i t c h c l a s s e s G#, A, and B are 13  extended i n both instruments to measure 329; thus, f u r t h e s t extension  i t i s the  of i t s p i t c h c l a s s e s that d e f i n e s the end  point of the module. In Example 6, the rhythm i n the piano t h a t i d e n t i f i e s a module B begins i n measure 65 but the p i t c h c l a s s e s of the module are introduced  i n measures 59-64 with d u r a t i o n s  those of an e a r l i e r , non-adjacent  like  pattern--specifically,  measures 36 and 41. The rhythm created by these r e p l a c e s the rhythm of the previous  durations  p a t t e r n A; thus, the  endpoint of the module c o n t a i n i n g A i s measure 58. Although the rhythm of module B does not begin  u n t i l measure 65, the  - 25 EXAMPLE 6  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n o f E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n .  -  module c o n t a i n i n g p a t t e r n B i s understood 59.  to begin  26  -  i n measure  Thus, a module begins when the p i t c h c l a s s e s but not  the  rhythm of i t s p a t t e r n r e p l a c e those of the previous module i f the commencement of i t s rhythm i s delayed  by  rhythmic  elements that are l i k e those of a non-adjacent module. The  terms " p a t t e r n " and  "module" are used  interchangeably  by Feldman. In t h i s a n a l y s i s , however, "module" r e f e r s to a complete modular c o n s t r u c t and a " p a r t i a l module" i s any segment of a module. A " p a t t e r n " i s that unique  combination  of f e a t u r e s t h a t determines the i d e n t i t y of a module, or a p a r t i a l module, i n r e l a t i o n to other modules. Modules are favored by Feldman as a c o m p o s i t i o n a l  raw  m a t e r i a l p r e c i s e l y because they do not presuppose a compositional  process. A module must c o n t a i n a r e c o g n i z a b l e  p a t t e r n of p i t c h and  rhythm but  s t r i c t u r e s of p r e - c o m p o s i t i o n a l  i t i s otherwise  f r e e of the  l o g i c . In t h i s way  the  composer i s able to d e v i s e the s t r u c t u r e of a piece a c c o r d i n g to any c r i t e r i a  i n c l u d i n g t h a t of a s p e c i f i c  process. F u r t h e r , any musical dimension may used i n a s t r u c t u r a l way;  thus, any  compositional be  imaginable  i s p o s s i b l e . Pieces composed with modules may  isolated formal  and  design  t h e r e f o r e be  widely d i s p a r a t e i n t h e i r u n d e r l y i n g and s u r f a c e s t r u c t u r e s . Feldman d i s c u s s e s h i s "modular" approach to composing i n Anecdote XXII. I work very modularly, I don't work i n a c o n t i n u i t y ; I work modularly. And many times I l i k e to work modularly  -  27  -  because then I turn i t around! I f I j u s t think i n terms of a module, I could take t h i s i n another p l a c e l i k e F r a n k e n s t e i n , and I could put i t over here...(draws)  I got t h i s idea when I was a young man not from John Cage, not from modern a r t , not from Miro. I got t h i s from from T o l s t o i . In a marvellous book that h i s daughter wrote (about) him w r i t i n g "War and Peace." What they d i d was t h i s : on an o l d - f a s h i o n e d t y p e w r i t e r , and I suppose the l e t t e r s were small i n Russian, they wrote these long l i n e s - - i n the house they were c a l l e d noodles. What he then would d o . . . i s cut up every sentence, you put the sentence on the t a b l e and l i k e a f i l m e d i t o r would rearrange--and i t ' s a marvellous book about the w r i t i n g of War and Peace. I work the same way now. And Burrough's "Naked Lunch", he worked the same way you see, i t s very much l i k e a f i l m . 1 0  In h i s l e c t u r e at Darmstadt,  Feldman a p p l i e s the term  "assemblage" to a composition made i n t h i s m a n n e r Anecdote  XXII e x p l a i n s the advantage  of t h i s  11  and i n  approach.  I don't work i n a c o n t i n u i t y , the c o n t i n u i t y comes l a t e r . In other words, I'm not involved i n l i n e a r i n f o r m a t i o n .  - 28 And so, very q u i c k l y , I see p o s s i b i l i t i e s i n new t h i n g s . I could assemble...I have i t a l l , a l l together, marvelously visual." 1 3  Earlier  i n the passage Feldman e x p l a i n s t h a t he uses  retrograde  "to b r i n g back a kind of fake a s s o c i a t i o n . " He  f u r t h e r s t a t e s , "I have p i e c e s where I don't repeat r e t r o g r a d e , but  I repeat  the tones  the whole module r e t r o g r a d e " . I t  w i l l be seen that r e t r o g r a d e  and  i n v e r s i o n r e l a t i o n s between  modular c o n s t r u c t s are h i g h l y s i g n i f i c a n t to c o n t i n u i t y and form i n the second s e c t i o n of Spring of Chosroes. Thus, a t y p i c a l Feldman piece i s an assemblage of modular c o n s t r u c t i o n s , each of which i s an assemblage of r e p e t i t i o n s of a p a t t e r n . The  ordered  arrangement of p a t t e r n s w i t h i n a  modular c o n s t r u c t generates l o c a l u n d e r l y i n g l i n e a r i t y which may  or may  not be d i s c e r n e d  i n the r e s u l t a n t s u r f a c e  effect.  Connections between c o n s t r u c t s d e f i n e formal s t r u c t u r e s and t h e i r ordered  arrangement generates l a r g e - s c a l e c o n t i n u i t y .  In " C r i p p l e d Symmetry" Feldman s t a t e d : "A modular c o n s t r u c t i o n could be a b a s i s f o r organic development. However, I use i t to see t h a t p a t t e r n s are "complete" i n themselves, and i n no need of development-only of e x t e n s i o n . " 7  It may  be  i n f e r r e d t h a t r e p e t i t i o n and  e q u i v a l e n t procedures.  extension  In f a c t , extension  are  i s a somewhat  g e n e r a l i z e d n o t i o n of r e p e t i t i o n that d e s c r i b e s both and  literal  v a r i e d r e p e t i t i o n ; however, any v a r i a t i o n must be  so that i t does not a l t e r the Although the "extension"  small  i d e n t i t y of the module.  of an o b j e c t i s normally  attached  the o b j e c t , i n t h i s a n a l y s i s the s t r u c t u r a l components  to  - 29 -  that connect two non-contiguous modules are s a i d to be "extended" to the l a t e r module from the e a r l i e r one. Implicit  i n the d e f i n i t i o n of extension  i s the d e f i n i t i o n  of "sameness." A module's i d e n t i t y i s determined by i t s s t r u c t u r a l components, p a r t i c u l a r l y those components that are l e a s t v a r i e d . When a l l of the i d e n t i f y i n g elements of a module are extended to a l a t e r module, the l a t e r segment i s s a i d to be a r e t u r n of the f i r s t the  first.  1 3  and t h e r e f o r e the "same" as  The concept of sameness may be a p p l i e d to  complete modules or to each of the v a r i o u s domains w i t h i n modules; thus two modules may share the "same" p i t c h c l a s s e s or rhythmic p a t t e r n while  retaining their  independent  identities. Some p a t t e r n s repeated  are a l t e r e d s t r u c t u r a l l y when they are  and may t h e r e f o r e be seen to be "developed." For  example, i n the i n i t i a l rhythmic p a t t e r n of the v i o l i n (measures 1-12 of example 7) q u i n t u p l e t s  containing  a l t e r n a t i n g e i g h t h notes and e i g h t h r e s t s are separated by sixteenth t r i p l e t s . values.  Some d u r a t i o n s  In measures 13-16, detached longer d u r a t i o n s  p a t t e r n that i s a slower, simpler pattern  are d i v i d e d i n t o smaller form a  v e r s i o n of the f i r s t  (Example 8 ) , and i n measures 17-20 the p a t t e r n i s  further s i m p l i f i e d l a t t e r two p a t t e r n s  to connected d u r a t i o n s . Although the are v a r i a n t s of the f i r s t  the changes  they undergo are h a r d l y " s l i g h t " and may t h e r e f o r e be considered  "development," not " v a r i a t i o n . "  -  30  -  EXAMPLE 7  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i q h t s R e s e r v e d . Used by p e r m i s s i o n of E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n .  -  31 -  EXAMPLE 8  VM  I 5  5  1-12  5 v 7 ^  r  "  -  £_  f  v  r .  1*1*1  i  i  M  i  1  1  l  i—  13-16  3.  J.  sZ-A  v  1  f  1  J  1  v J/ I J  J J  V  1  J  7  J  1  1  7  i  17-20  3  1  1  J  e>  f 1  1  1  .1  J J  1  1  J  1  i  ^  -  J  T  J~"  I  J  i  If a theory i s a means by which the p r o p e r t i e s , and t h e r e f o r e the d i r e c t i o n a l p o s s i b i l i t i e s ,  of a given musical  system are d e f i n e d , there w i l l never be a "theory of modular composition."  Modules are a p r e - c o m p o s i t i o n a l ,  raw m a t e r i a l that may be conceived  structureless  i n order to c r e a t e a new  system, or t o adapt to any e x i s t i n g system, or t o be unsystematic. found,  The substance  of a c o n v e n t i o n a l composition i s  f o r example, i n the development of i t s themes and i n  r e s u l t a n t c o n t i n u i t i e s . Feldman chose not to u t i l i z e developmental but  procedures  as a means of g e n e r a t i n g c o n t i n u i t y  i n s t e a d "extended" h i s p a t t e r n s to form modules; thus, i t  i s i n p a t t e r n s and the c o n n e c t i v i t i e s between them t h a t we f i n d the substance  of Feldman's music.  - 32 As the foundation of h i s new a r t , Feldman proposed a language of pure p r o c e s s . Rather than r e p r e s e n t form as o n t o l o g i c a l l y p r i o r to process Feldman... t r e a t e d process as o n t o l o g i c a l l y p r i o r t o form. In h i s a r t , the work and the a c t of c r e a t i o n became i n d i s t i n g u i s h a b l e . For him, the act of c r e a t i n g a p i e c e becomes the very substance of t h a t piece — i t s form i n a r i c h new sense of the word. To experience a r t such as t h i s i s q u i t e l i t e r a l l y t o experience the a c t of c r e a t i o n " i n medias r e s " and the work i n the a c t of being born. What the p e r c e i v e r witnesses i s the very emergence of order; the artwork organizing i t s e l f into e x i s t e n c e . 1 4  MODULE ANALYSIS The  first  step i n a n a l y z i n g a work of Feldman's i s t o segment  it  i n t o modules. A l i s t  of the c o n s t i t u e n t modules of S p r i n g  of  Chosroes i s shown i n F i g u r e 2. Modules designated PM and  VM belong to the piano and v i o l i n  r e s p e c t i v e l y , and the  c e n t r a l column l i s t s modules i n which the v i o l i n and piano are combined. V i o l i n those  modules are numbered independently  from  i n the piano and the c e n t r a l column. Each module  c o n t a i n s a t l e a s t two p i t c h c l a s s e s .  X B  (The d e s i g n a t i o n s  VI/1, VI/2 e t c . w i l l be e x p l a i n e d i n chapter 2 ) . In  the modules that i n c o r p o r a t e both  instruments i n  s e c t i o n s 1 and 3 (excepting modules XII and XIII) a s i n g l e v i o l i n p i t c h c l a s s i s added to a piano dyad to c o n s t r u c t a chromatic t r i c h o r d , a s e t type t h a t i s used throughout  consistently  the p i e c e . For example, we see i n module I I I  (measures 52-56, Example 9) t h a t a s u s t a i n e d A violin  to  i n the  i s combined with the lower piano dyad to form the  t r i c h o r d F#,G,A . to  - 33  FIGURE 2  MODULES Section 1  Measures 1 33  Piano  Violin  PM I PM II  VM I  53 59 90 2  3  146 156 158 163 165 174 192 201 210  V VI/1 VII/1 VIII/1 VII/1 IX/1 X/l IX/1 X/l XI  228 237 247 265  X/2 IX/2 VIII/2 VI/2  282 291 330 339 348  XII XIII  380  PM XIV  1  VM II  III PM IV  Measures  VM I I I  49 53 58  VM I I '  90 141 146 156 158 163 165 174 192 201 210 219 228 237 247 265  VM I I "  VM I I ' ' 1  XV XVI XVI  VM I I ' ' ' (coda)  1  282 291 330 339 348 369  - 34 EXAMPLE 9  module I I I 53  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n o f E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n .  Some measures i n VM-I and VM-III c o n t a i n p i t c h c l a s s e s  that  a l s o belong to the piano modules adjacent to them--measures 23-28 (F#), measure 64 (B), and measures 65 and 72 ( D ) . F# b  doubles G  b  i n the piano and each of the l a t t e r two p i t c h  c l a s s e s forms a chromatic t r i c h o r d with the upper dyad i n the piano that immediately  precedes i t .  A p a t t e r n must be repeated to generate a module; however, i t need not be repeated immediately. (Example 10) c o n t a i n the i n i t i a l its repetition  Measures 156-157  statement  of module VII but  ( i n a v a r i e d form) i n measure 163 i s  i n t e r r u p t e d by module VIII/1 i n measures 158-162. In each module the p a t t e r n i s repeated only once; t h e r e f o r e , each i s the s h o r t e s t p o s s i b l e m o d u l e .  16  >  •x i—• o  Ul >-> 11 rr rr fi ?o o M* 3 C7i£> C 3- •*] rr rr m o Ul  n  a  Ul 33 3 n> 01 n Ul 3 O n> H CO  •a < 13 0  M  01 rr  a > c  50 i—(  Z Q  o Ul O . 3 n> TI  a  n  Ul cr X  o K o CO n> •o ro O IS  C H M • 3 CO CO •  o 3 o XI  m x >  n  T3  flj  a  Ul  n  3 ><  o o 01rti  3 3" Hi W rr  a c  h" i01 O kD 3 •a -j (D U>  01  ro  3 > rr 3  i-n o H  c  3  < n  i—• m a  c  3  <  o in  01 H 3 Ul  OJ  t~*  C Ul M  Ul o  fti  CT  a  rr  °T  QJ  ifl 3  1  3 >  r  •g aanseaui ut „D pue S amseaui UT  pue  pappe  S T  a  U 9 U 3  '#a sassexo q o ^ T d I-WA UT usas aqq.  U T  puno?  S T  'saanseaui xe-t^fUT aq} aaaqq.  qoTqM  U T  uaas aae a  axduiexa oq. l a j a a )  U T (i  ssaooad a A T ^ r p p e OTijeuiejrp ssax v  S T « , V  ' U T X O T A  ssexo qoq.Td qq.UTU e frXT aartseaui  'pappe 3 i e ajtoui anoi zoi aanseaui  U T 'XOT-06  papua^xa d i e sassexo qoq.Td 21:103 ill  U T  pue  saartseaui qbrtoaqq.  axduiexa) A axnpoui u i  • A"xienpe;i6 paonpoa^uf aq A"eui axnpoui e go sassexo q o ^ T d a q j ,  t e s j s A T u n J O J 311361= U B i p e u e o pue " S T l s t 'uoi^BiodioD s3o;nqinsta o-tsnw u e o T j a u i y u e a d o a n a 30 u o T s s r u i a a d Aq p s s n ' p s A i s s s j j s ^ u f c T j j TTV •uoT^xpa i B S i a A T u n 6LSI ^nbT^Adoo ' S a O H S O H O .30 DNIHdS ueuip-[sj U O ^ T O W  •uoi^Tpa  o  s  IT aidHvxa ' (cO) ssexo qo^Td pappe ue q } T pue (sq.a>pe:r.q M  e  U T  apejBoj^aj q.ou  axduiexa)  -  9Z -  S T  U T  q.nq  U T T O T A  saeadde  U T a i a q  ^ T uaqM  saanseaui aqq. U T  uaas  U T  uwoqs) aa^stbaa  ifri annseaui X ! 3 pa^e^s  ^ S J T J  S T U O T ^ d n u a q u T  S T  u n  l a q b j q  ps^eadaa  n-WA '(TT  amaa^xa aaoui v  - 37  D  >  m  Z  h" ( < O UI I— M rr rr H 33 o »-»• 3  coco  tr >a c 3-  rt rr re o ui  a. H 3 UI a>70 01 O re H n Ui TJ < T3 O re 50 m  OJ  rt- z o i- c o» o 3ro*l  - a  o  m a x o o CO  M  re 'a JO O  re m n Ui Ui 3  M  ui  OJ Ul O 3 O o n a 3  n  >  TJ  r w  o H~  01 l-n id 3 D QJ Rl rt -  a  t-o  c  3 TO D --1  01  re ua  01  a  Qj 3 a  >  3 G  re 3 n v— i- < n re  < c re ui  H  — I  ui n  "TOT  o  3  - 38 -  Feldman employs techniques that b l u r p o i n t s of change between modules. I t has been shown, f o r example, that p i t c h may  be "borrowed" from a subsequent module  classes  (Example 5) or  may be introduced with a rhythm that i s extended from a non-adjacent module  (Example 6). In measures 29-41  (Example  13) elements of PM I and PM II are overlapped. Measure 36 c o n t a i n s one of the two c h a r a c t e r i s t i c elements of PM I I , a chord c o n t a i n i n g a low r e g i s t e r dyad and a m i d - r e g i s t e r t r i c h o r d . The p i t c h c l a s s e s that form the lower t r i c h o r d of PM I i n measure 26 (G, A ,and A) are c l u s t e r e d to  register are  i n a low  i n measures 29 and 31. This grouping and r e g i s t e r  "borrowed" from PM II and prepare the lower r e g i s t e r dyad  i n measure 36. In PM I I , r a p i d l y a r t i c u l a t e d p a i r s of upper r e g i s t e r C's i n measures 33-35 are followed by a contrasting v e r t i c a l .  registrally  When the high C's are repeated i n  measures 39-40 they are followed i n measure 41 by the lower register cluster vertical,  found i n measures 29 and 31 r a t h e r than the  but with a d u r a t i o n more c l o s e l y a s s o c i a t e d with  PM I I . S i m i l a r l y , Example 14 shows the o v e r l a p p i n g of p i t c h c l a s s e s from modules IV and V, VM I I I , and by e x t e n s i o n , VM I i n measures 81-88 module V .  1 7  immediately p r i o r to the beginning of  P i t c h c l a s s e s from VM I I I (measure 82) and the  extension of VM-I piano t r i c h o r d  (measure 81) are combined to form the upper  i n measure 84. The p i t c h c l a s s e s of the upper  t r i c h o r d of module  IV are extended to the lower piano  - 39 -  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n of E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n .  - 41 -  trichord  i n measure 84, and the lower t r i c h o r d of module IV  forms the lower t r i c h o r d of measure 86. The p i t c h c l a s s e s E, F, and G  to  that form the upper piano t r i c h o r d of measure 86,  and the lower t r i c h o r d of measure 88, are borrowed measure 102 of module V. The upper r e g i s t e r A  to  from  i n the v i o l i n  seen throughout measures 84-88 i s found i n module V i n measures 114-139. In measures 114-138 (Example  15) p i t c h c l a s s e s unique to  modules III and IV (B*=, D , and D) are extended to module V to  and mixed with i t s c o n s t i t u e n t p i t c h c l a s s e s . At l e a s t four of the s i x p i t c h c l a s s e s i n each hexachord are common to module V, and v a r i a t i o n s i n other parameters texture,  (rhythm,  e t c . ) are s l i g h t ; thus, the number of p i t c h c l a s s e s  i n the passage has i n c r e a s e d ,  but the number of c o n s t i t u e n t  p i t c h c l a s s e s i n module V has not. The extended p i t c h c l a s s e s do not r e p l a c e the p i t c h c l a s s e s of module V; r a t h e r , they commingle with them. In t h i s way,  the added  pitch material  masks but does not change the i d e n t i t y of the module. A l a s t example of b l u r r e d modular  boundaries appears i n  measure 263 of module VIII/2 (Example t e x t u r a l l y and r e g i s t r a l l y exposed  16). C n a t u r a l i s  i n a way  that a n t i c i p a t e s  the lower r e g i s t e r of the dyad A,B ' i n module VI/2 t  272-281).  (measures  - 42 -  3  o a c O > 2 t- o tn H* N  rr M  33  rr o  ty iO C 3" >*) rt rr rt> O UI H UI PO3 01 01 n ui 3 o n> CO  <  ro pa Qj  •  c  o  M  Z  o  01 O a  o ui cr ac o CO  rti *D PO fB O C « w CO CO 3 UI  to oo  3 o "a a 3 i< H 0 O QJ r* 3 3" 01 PJ rr  CO X rr (5 3  a QJ  TJ  rt O rr  01  l3 TJon u > ~J a  c  K  H  a> ID  0i 01 <0 3  CT  rr 3 C m 3 i-ti H  <  3  I-  1  c  nun  a ui n >-• oi rr H  a  03  or  M X >.  TJ  r m  - 43 -  EXAMPLE 16  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n o f E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n .  -  44  -  Module manipulations such as these tend to s o f t e n the t r a n s i t i o n s between s u c c e s s i v e modules and generate v a r i e t y w i t h i n modules. Feldman v a r i e s and o c c a s i o n a l l y develops aspects of modules but h i s a l t e r a t i o n s are never taken to such an extreme that the i d e n t i t i e s of modules cease to be recognizable. Thus f a r we have observed connections that e x i s t  largely  near the musical s u r f a c e . In chapter 2 we w i l l examine deeper connections that generate  form.  - 45 -  CHAPTER TWO FORM Spring of Chosroes may be d i v i d e d  i n t o three  s e c t i o n s ; A (measures 1-145), a c o n t r a s t i n g  large  section B  (measures 146-290), and A', a r e p r i s e t h a t engages the modular s t r u c t u r e of s e c t i o n A. In Example connect modules  17, l i n e s  that  i n d i c a t e t h a t aspects of the c o n s t i t u e n t  modules of s e c t i o n A are extended to modules  in section A in  an order which l a r g e l y p a r a l l e l s that of the f i r s t  1  section;  t h e r e f o r e , some processes that u n i f y s e c t i o n A are reproduced i n s e c t i o n A'. EXAMPLE 17  -  The  unity  of  each s e c t i o n a r i s e s from the  m o d u l e s . Some modules u n f o l d formal  coherence  m o d u l e s , as  was  i n a d e v e l o p m e n t a l way  i s l a r g e l y created defined  i n Chapter  by 1,  share  not,  as  one  a r u l e , grow out  configurations an  Organicism  will  that  involves within  motivic  are  repeated  structure  of  portion  therefore,  another  at the  i n ways t h a t  of  we  of  will  way  chapter  inorganic  form. first rise  involves to  these define  a  t h e y a l s o show t h a t  The  second  aspect  unfold over  modules. P a r a l l e l i s m s d e f i n e  b e g i n by  various  developmental  m o d u l e s , or  are  say,  surface.  developments t h a t  f o r m and  do  that,  (the  this  give  and  s e c t i o n A.  they  in this  But  f o r m . The  between a d j a c e n t  in repeated  substantive  of  latter).  i n s e c t i o n B,  is a variant  modules or  SECTION  later  articulate large-scale aspects  i n the  of  by  one  fragments  i n some b r o a d e r ,  c o n t i n u i t i e s and  time spans  its  two  another  parallelisms. Specifically,  palindromic s e c t i o n A'  resemble  module I I d i s c u s s e d  examine two  structural  One  one  i s most commonly f o u n d  modules t h a t  B;  or  i s revealed  connections We  of  of  a r g u a b l e example o f t h e  connectivity  than  of i t s  but  extension  or more c h a r a c t e r i s t i c e l e m e n t s b u t  a theme grows f r o m one  are  the  rather  d e v e l o p m e n t a l p r o c e d u r e s . Modules may and  connection  -  46  most o b v i o u s  discussing  those  locally larger the  in section measures.  B: the  p r i n c i p a l s t r u c t u r a l features  palindromic  design  (Example  18).  of  In t h i s  this  section  example,  the  is  -  47  -  EXAMPLE 18  MODULE  MEASURES  - VI/1 VII  146-155 —  156-157  - VIII/1  158-161  VII  —  163  - IX/1 —  165-173  - X/l — i  174-191  IX/1  192-200  X/l — '  201-209  xi  210-218  "---i 1  II"-  219-227  1  228-236  - X/2  237-246  - IX/2  247-264  - VIII/2  265-281  - VI/2  labels first  VI/1, VI/2 e t c . denote corresponding modules i n the and second h a l f  of the palindrome.  Brackets to the l e f t  of the "module" column l i n k modules with t h e i r r e t r o g r a d e s and those t o the r i g h t  i d e n t i f y modules t h a t are merely  extended. Modules XI and I I ' are connected 1  bracket t o i n d i c a t e t h a t they share s e v e r a l f e a t u r e s but are i n f a c t d i s t i n c t modules.  with a dotted characteristic  -  The  palindrome  repeated varied  i n the  i s asymmetric; first  half  when r e p e a t e d ,  at a l l .  Feldman  and  but  that not  there  i s , modules IX  the  i s no  and  48  X  s e c o n d , modules  -  are  are  " m i r r o r " of module  VII  explains,  "I'm v e r y i n t e r e s t e d a l s o i n r e t r o g r a d e . And I have p i e c e s where I d o n ' t r e p e a t t h e t o n e s r e t r o g r a d e , but I r e p e a t t h e whole module r e t r o g r a d e " . He t h e n s u g g e s t s ways i n w h i c h r e t r o g r a d e modules may be v a r i e d , and c o n t i n u e s , "The r e a s o n i s t h a t I want t o b r i n g back a k i n d o f fake a s s o c i a t i o n . " 1  Feldman's a p p r o a c h t o r e t r o g r a d e treatment  of module VI  verticality  composed  stated  times  five  pizzicato  central  of a low  a single  register  contraction pitch  central  pitch  i n the  incremental  i n the  t o an  prior  t e x t u r e and  and  length are  variation,  expansion t o an  of bar  violin.  seven times  and  bar  but 2  statements in  lengths  both ends  in  module VI/2  the  has  Thus,  of module  VI--  lengths—but  the m e t r i c  repetition  in  incremental  module V I / 1 .  v a r i e d and  and  of  s i x t e e n t h s s i t u a t e d at the  i s unchanged. T h i s s e l e c t i v e  retrograde,  of t h e  to seven  i n module VI/2,  register,  a  number  A l l durations  i s a p p l i e d t o some a s p e c t s  instrumentation  equal  register  piano.  i s reversed  violin  his  d i s t a n t dyads i s  is articulated  violin  by  In module V I / I ,  prior  c l a s s e s i n common w i t h  retrograde  durations  piano  module a r e  i n module VI/1  19).  registrally  of t h e  dyad  of t h e  of m e a s u r e s . The  no  i n the  register  statements  piano  of two  G n a t u r a l s i n the  In module V I / 2 , the  (Example  is typified  pitch,  position  of  a p p l i c a t i o n of i s used  to b r i n g  about  -  3 > i—' o UI N rf rt H JO O — t 3  49  -  o  cr c rt o  o*>  ICWO  id  3" "rj rt re U) I-I  H a Ul JO 3 n> Oi n CO 3  o re H M co •o < 13  3  o a c  'trft 5*"  JO t~i w 01 • 2 rt Q t~" C o U) O 3 ro "J  ^ a  |o*°!  O  cr X o tCO JO re"a ID o C rt Pi• 3 co  o  CO •  1  o»!  •  UI CO o  01 t— o 3 o •D a 3  I OXJ  H  n o H" 01 rti id 3 3" 01 M rt a C I—* 01 tt o <o 3 •a -J  01 kO 01 01 <a 3 CT ID »< 3 > rt 3 G £j Ml f HD 1 — < o M n re OJ H c 3 co 3 0l i-< < C C O re w H a UI n 01 rt  1  x > TJ  r <J3 Or*  Or-  oM 5<o  3W>  o &  re <  Or5  O  5*° i  H>  5H  3 •  rt — t  o 3  oH  o>w  I  - 50 -  palindromic  a s s o c i a t i o n s . Feldman has d e s c r i b e d  i n the f o l l o w i n g  the  process  way:  "You can do two t h i n g s with music, you could be i n v o l v e d with v a r i a t i o n , which i n simple terms means o n l y vary i t , or you could be i n r e p e t i t i o n . R e i t e r a t i v e . What my work i s , i s a s y n t h e s i s between v a r i a t i o n and r e p e t i t i o n . However, I might repeat t h i n g s t h a t , [are] v a r y i n g [themselves] on one aspect. Or I could vary r e p e t i t i o n . " 3  Retrograde ( r e p e t i t i o n i n reverse) " s y n t h e s i s , " and  i s one  aspect  of  this  i s t h e r e f o r e a means by which small  l a r g e - s c a l e c o n n e c t i v i t y and  or  s t r u c t u r a l coherence may  be  generated. As example 18 shows, modules i n s e c t i o n B are arranged p a l i n d r o m i c a l l y , so r e t r o g r a d e form. The  i s important to l a r g e s c a l e  modules t h a t are a s s o c i a t e d  i n t h i s palindrome,  however, are not always r e t r o g r a d e - r e l a t e d Rather, the palindromic  in  content.  s t r u c t u r e of s e c t i o n B i s l a r g e l y  d e f i n e d by i n v e r s i o n r e l a t i o n s of modules. I n v e r s i o n i s rarely l i t e r a l , oppositions  however, and  instead involves  of r e g i s t e r , d u r a t i o n , t e x t u r e ,  instrumentation.  general  and  I n v e r s i o n r e l a t i o n s are a l s o generated  by  extreme d i f f e r e n c e s of magnitude ( s h o r t e s t to l o n g e s t , widest to narrowest, etc.) r e l a t i v e to other For example, although module VII  modules.  (measures 156-157) does  not reappear i n the second h a l f of the palindrome, i t i s extended to measure 163.  In the extension,  the  relative  r e g i s t r a l p o s i t i o n s of i t s p i t c h c l a s s e s are the the o r i g i n a l 156,  (Example 20)  i n v e r s e of  i n the f o l l o w i n g sense: i n measure  the p i t c h c l a s s e s of module VII are disposed  in  two  - 51 -  o > Ox UI rr r\  rt rr 50 3o  c ET ra  rr rr ro 0 CO >-•  MI a U 50 3 ro CO 3ai o O ro n rt CO  •0o ro < 5> 0o n  01  rr  •  z  o c o U I o 3 ra N ro a o UI cr x o »-» i-<; COo roT3 50 ro o c H ra 3 co CO • to  ui n  Qj H- O 3 O •O a 3 ^< rt  0o 3 01  =r ra rr  ac r-rtf-* ll o « 3 13 -J  ro vo  01 01  ua 3 cr ro »<  3" c ro 3 i-n M i o n n ro c;013 rtto rr  H- <  3  c  a>  ui ra  ra a  o 3  M X  s TJ  r w O  -  registral central  areas;  to  register  low r e g i s t e r . retains  D 4, E 4,  its  the  central register  rise  register  to  trichord  pitches  inversion is from t h e  157  is  but  i n a low  measure  register  of  in this  E7. Also  o c c u p i e d by t h e  i n v e r s i o n takes  of  is  j o i n e d to  it  a high  register.  trichord  to  i n measure 163  m o d u l e , F#4  module V I I I  where  to  and C#5 e x t e n d  D 4, E 4 , to  place. EXAMPLE 21  t o  156  toward  (Example 2 1 ) .  E6 i m m e d i a t e l y p r i o r  trichord  163,  a  p r e p a r e d by two p i t c h c l a s s e s D  lower  extended  to  E5 and E 6 . The uppermost p i t c h i n measure  extends the  area  of  extended  -  in a  F l , D2, E2 o c c u p i e s  o c c u p i e d by E7 i n measure  D5 i n measure joined  trichord  When module V I I i s  registral  and E t h a t  and C5 form a t r i c h o r d  and a s e c o n d  E7 r a t h e r t h a n a s e t This  t o  52  the the  it  the  is  162,  D 6, to  arrival spatial  C5 a r o u n d w h i c h  the  - 53 -  The  palindromic  r e p r i s e of a l l modules i n s e c t i o n B  than modules VII and  XI s i m i l a r l y i n v o l v e s other  other  general  r e l a t i o n s of i n v e r s i o n . In the r e p r i s e of module V I I I , magnitude of some domains i s expanded i n a way palindromic  that  the  creates  a s s o c i a t i o n s with the o r i g i n a l statement. Module  VIII/1 i s the s h o r t e s t module i n the  first  h a l f of  the  palindrome and  i n the second h a l f , module VIII/2 i s the  longest;  thus,  the d i f f e r e n c e i n i t s length r e l a t i v e to that  of other  modules c o n s t i t u t e s an  S i m i l a r l y , module VIII/1 has in the  first  "inversion" relation. the narrowest r e g i s t r a l  h a l f of the palindrome and  widest i n the second h a l f (Example 22).  span  module VIII/2 has I t i s true that  the  the  incomplete r e p e t i t i o n of module X / l (measures 173-191) i n measures 201-209 extends a s i n g l e p i t c h and narrower span, but  these measures are not  r a t h e r , they are the extension  of an  t h e r e f o r e has  a  a d i s c r e t e module;  " i n t e r r u p t e d " module the  combined span of which i s wider than that of module  VIII/1.  Thus, the d i f f e r e n c e i n the r e g i s t r a l spans of modules VIII/1 and  VIII/2 r e l a t i v e to other  forms an The  modules (narrowest to widest)  inversion relation.  magnitudes of domains are v a r i o u s l y expanded i n module  V I I I . Extreme changes generate i n v e r s i o n r e l a t i o n s while s l i g h t l y smaller  changes form "incomplete" i n v e r s i o n  r e l a t i o n s . Connections that c o n t r i b u t e to l a r g e s c a l e form are generated by extreme expansions while smaller r i s e to l o c a l i z e d form. For  example, an  ones give  "incomplete"  - 54 -  EXAMPLE 2 2 REGISTRAL  SPANS OF MODULES  V  : VI/1 f\ •  hr  #rt VII  IX/1  x/l  —  it  VIII/1  VIII/2  X/2  IX/2  VI/2  1  i n v e r s i o n r e l a t i o n i s formed by changes of i n s t r u m e n t a t i o n i n module VIII i n that module VIII/1 i s the only module with one instrument i n the f i r s t  h a l f of the palindrome but i s one of  two modules with two instruments i n the second h a l f (module VI/2  i s the o t h e r ) .  Module VIII i s the o n l y module i n the palindrome i n which the  number of p i t c h c l a s s e s i n c r e a s e s , from 4 i n module  VIII/1 t o 7 i n module VIII/2 (Example 23). The change i n t h i s case i s not from " l e a s t " to "most" and i s t h e r e f o r e not i n v e r s i o n a l ; r a t h e r , i t i s a f e a t u r e that i s unique to t h i s module. Marginal expansions of magnitude i n module VIII decorate  - 55 -  EXAMPLE 23 PITCH CLASS CONTENT OF MODULES VIII/1 AND VIII/2  module  VIII/1  module  {C# D E F#}  {  B  VIII/2  c C# D D# E F )  the s u r f a c e of the music. Module VIII/2 has two rhythmic and r e g i s t r a l configurations  (measures 247-254 and 255-264) and  module VIII/1 has one. As w e l l , module VIII/2 has three d i s c r e t e meters; module VIII/1 has two. L i k e expansion, c o n t r a c t i o n s of magnitude produce  complete  or incomplete " i n v e r s i o n " r e l a t i o n s . In module IX c o n t r a c t i o n s e x i s t but not t o the extent that r e l a t i o n s are formed.  In the f i r s t  inversion  h a l f of the palindrome,  module IX/1 i s s t a t e d twice (measures 165-173 and 192-200) and c o n t a i n s a s e r i e s of v e r t i c a l t e t r a c h o r d s that are d i s t r i b u t e d between both instruments (Ex.24). Module IX/2, on the other hand, i s s t a t e d once i n measures 237-246 and c o n t a i n s a s e r i e s of v e r t i c a l dyads i n the v i o l i n . Thus, the  - 56 -  chord s i z e , number by the number are h a l f  of instruments, and t o t a l  length (measured  of a t t a c k s and measures) of the l a t t e r module  (or n e a r l y h a l f ) that of module  IX/1.  4  I n v e r s i o n r e l a t i o n s a r e formed i n another way a t the p o i n t s of  t r a n s i t i o n from modules IX/1 t o X / l , and IX/2 t o VIII/2.  In  the f i r s t case, measures 171-174 i n Example 24, £ ^ 5 f a l l s  to  D 5 twice, then there i s an abrupt r i s e to a high C7. The to  neighbouring E  to  and D  b  generate a sense of r e g i s t r a l  d i r e c t e d n e s s i n each of measures 172 and 173. When these two p i t c h e s appear i n other measures of module IX/1 t h e i r i m p l i c a t i o n s are obscured  by t h e i r t e x t u r a l  linear  context—each  p i t c h i s combined with three other p i t c h c l a s s e s to form a v e r t i c a l t e t r a c h o r d . In measure 172 however, they o b t a i n a degree  of rhythmic  independence from the three v e r t i c a l  p i t c h e s i n the measure and are thereby p e r c e i v e d as h o r i z o n t a l l y r e l a t e d , and i n measure 173 t h i s sense of pairing  i s r e i t e r a t e d when they appear without other p i t c h e s .  The sudden r i s e t o C i n measure 174 i s t h e r e f o r e a l l the more pronounced. By c o n t r a s t , the e s s e n t i a l l y r i s i n g contour of module IX/2 (measures 237-245) maintains a d i r e c t e d c h a r a c t e r , ascending most s t e e p l y i n i t s f i n a l of  instead  r i s i n g t o the i n i t i a l septachord of module VIII/2. In  these same passages IX/1 X/l  three measures, then f a l l s  the r e l a t i v e l y f u l l t e x t u r e of module  i s r e p l a c e d by the t h i n n e s t of the palindrome  i n module  while the r e l a t i v e l y t h i n t e x t u r e of module IX/2 i s  - 57  - 58  0> 3 h" l-J O 1 01 (— H rt rt N P3 O K"  cr  3 o a  0=Ol I  c  3  H»  C  3 " •*) rr rr ID  O N  «  a  H '3  OJ  ui pa 3 ID  O H oi CO  0 (D 'O TJ 0 K  M < 01 ID  »  rr •  H"  O  3  3  o a. c  z  3  o. a c  o  c  UI O ID •*)  > a  X  o  ui cr ac  o><o  CO  ID TJ P3 ID C H CO  w  3  • 3 CO I— n • 01 01 01 3 O TJ  ID  01 01  c M ID  a Ml 3 ^< lO  w  0) W rt  ac  H. H 101 O 3  IX  -a < ID u:  01 01 iQ 3 cr ID  ><  rr | " C ID  3  Mi l i i -  o  n ID 0i C ; 3 01 3 01  3  < C ID 01 H H CO  01  -a  > ro to  it rr 01 O co  IE  - 59  replaced  by the t h i c k e s t of the palindrome i n module  Although these two  VIII/2.  t e x t u r a l t r a n s i t i o n s are not r e l a t e d by  i n v e r s i o n i n the s t r i c t sense, the  latter  i s the  nevertheless  the r e c i p r o c a l of the former i n that a t h i c k t e x t u r e to a t h i n one  -  i n the  first  proceeds  h a l f of the palindrome and  second h a l f , a t h i n t e x t u r e moves to a t h i c k one.  i n the  Thus, the  magnitude of some aspects of module IX i s c o n t r a c t e d  but  not  to a degree t h a t generates i n v e r s i o n r e l a t i o n s . The d i r e c t i o n of r e g i s t r a l change at the p o i n t s of t r a n s i t i o n between modules IX/1  and  X / l , and  IX/2  and  VIII/2,  is inverted,  and  t e x t u r a l changes demonstrate a somewhat g e n e r a l i z e d p r i n c i p l e of i n v e r s i o n but do not c r e a t e a palindromic We  relationship.  see another kind of i n v e r s i o n i n connection  X (Example 25).  Its f i r s t  statement  (measures 174-191)  f e a t u r e s a sudden s h i f t of meter and notes i n 5/32,  7/32  and  9/32  to s i x t e e n t h notes i n 5/16, (the l a t t e r values  7/16,  and  9/16  measures (183-191)  are uniform but the  (measures  c o n t r a c t i o n i n that each measure  l e s s beat than the one  previous  to i t . Durations  length of the r e s t s s e p a r a t i n g  r e g u l a r l y decrements. Thus, greater module X / l are combined with greater s h o r t e r r e s t s i n module X/2 There are other  thirty-second  measures (174-182) are changed  In c o n t r a s t , module X/2  228-236) e x h i b i t s a metric one  durations:  are extended to measures 201-209 i n which  module X / l i s repeated).  contains  with module  measure lengths  in  p i t c h durations,  r e s u l t from metric  contractions  attacks  while  contraction.  as w e l l i n module X.  The  - 60  EXAMPLE 2 5  module X / l 201  (repeat)  - 61 -  module  X/2  228  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n of E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n .  - 62  length of module X/2  i s h a l f that of the  first  statement of  module X / l (measures 174-191). Module X / l c o n t a i n s c l a s s e s , C and  A* , 3  that are s t a t e d  c l a s s e s of module X/2, the  C and  B,  two  pitch  i n i s o l a t i o n but the p i t c h  form a v e r t i c a l dyad;  "merging" of p i t c h elements i n module X/2  thus,  reduces i t s  l e n g t h . A l s o , the number of instruments i s reduced from in module X / l to one  i n module X/2;  r e l a t i o n s h i p e x i s t s with regard contractions  thus,  an  of o v e r a l l length and  instrumentation  but do  to the two XI and  not  modules.  s t r u c t u r e of s e c t i o n B. Let us t u r n our s i n g u l a r modules at the c e n t r e  VM  II"  that the  (Example 26). We  of the  r e l a t e d and Module XI  palindrome,  i n t e r n a l s t r u c t u r e s of modules XI and  t h e r e f o r e as the centre  the two  of the  VM  i n the II''  modules as  palindrome.  i s d i s t i n g u i s h e d on the s u r f a c e by the  change i n the dynamic l e v e l of the piece  (PPP  first  to PPPPP). But  i t p r o j e c t s some c o n t i n u i t y as w e l l because i t c o n t a i n s pitch class material and  the  attention  s h a l l see s i m i l a r i t i e s  u n f o l d , s i m i l a r i t i e s t h a t support hearing  27)  the  p a r a l l e l i s m s i n the modules c i t e d above help d e f i n e  palindromic  way  two  inverse  to measure l e n g t h s ,  produce i n v e r s i o n r e l a t i o n s r e l a t i v e to other The  from each module i n s e c t i o n B  some  (Example  occupies an upper r e g i s t e r c l o s e to that of i t s  neighbouring module VI/1  and  near-neighbour X/2.  (In t h i s  example, p i t c h c l a s s e s that are added to the modules i n the second h a l f of the palindrome are letters) .  3  -  i n d i c a t e d by lower case  63  -  03-J  x > TJ  r m  01 n 3 o c o 3 o c Ml 01 rt a rt 01 n> TJ  M  a  >  c o to 3 0 Tl TJ PO  <  c o o n C pa rt z 3 0l li H cr H* ro li o 3 01 o O lO 01 iQ 3" 01 3" o < 01 rr r— Tj a H" 01 til Tl rr i—• rr ro O rr 01 ID 01 n 01 01 3 rt 3 rt M n a <D 01 3 V— 3 PO ro I-J or > h— CD H" -J o QJ 01 c 01 01 rr JXI CO o rr m 01 ro r— JO a (D O H H" H o cr o 3 ro rt O < 3 ro rr rr 01 n 3 ro CO c a 01 • • o 3 3 10  Jr. III,  - 64 -  EXAMPLE 27 VM I I "  {D# E F  G} b  module XI  {D D# E F G  module VI  {D D# E  b  b}  F# G g# A B  b  B}  module VIII  {C C# D d# E f F#}  module IX  {C c# D E  module X  {C  b  fa  a b  {C D  to  G A} G  module VII  b  D E  to  E F}  e  A  b}  b  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 s of module XI are extended i n VM I I ' ' (measures 219-227). The s t r o n g e s t exist  connections  i n the domains of p i t c h , rhythm and r e g i s t e r ; f o r  example, four of the seven p i t c h c l a s s e s of module XI, D#, E, F, and G , are extended to VM I I to  1 1  to form i t s s e t of  c o n s t i t u e n t p i t c h c l a s s e s . The p i t c h c l a s s e s of module XI are distributed  i n two d i s c r e t e r e g i s t e r s - - V M  I I ' extends the 1  lowermost r e g i o n . Each module u t i l i z e s a common pool of d u r a t i o n a l values  that are f r e q u e n t l y separated  from one  another by r e s t s . However, aspects of r e g i s t e r , instrumentation,  contour and  s t r u c t u r a l f u n c t i o n i n VM I I ' ' r e v e a l a connectedness to VM II and i t s v a r i a n t s  (Example 28) that i s deeper than that of  module XI, r e i n f o r c i n g the d i s t i n c t i v e n e s s of module XI and VM I I ' ' . The repeated four-note VM I I ' (transposed 1  "motive" G 6, to  F6, D#6, E6 i n  to octave 4 i n t h i s example) has the  - 65 -  EXAMPLE 28  pitch classes  module  II  1  reverse  contour  II  II  3 reverse order  I I , II • • '  reverse  contour of the  141-145) and  first  four p i t c h e s  the second, t h i r d , and  repeated "motive" (F6, D#6, contour as VM  E6)  p i t c h e s of VM All  i n VM  the  I I ' have the same 1  VM  II''''  (measures  contour of the f i r s t  three  I I ' ' ' i n measures 330-338.  f i v e versions  structural divisions  of VM  II are  " b r i d g e " modules that span  (Example 29). T h i s example shows t h a t  modules nearer the center We  I I ' (measures  f o u r t h p i t c h e s of  II (measures 49-52) and  369-379) as w e l l as the reverse  i n VM  of the piece  join larger sections.  w i l l see that these modules are more important to l a r g e -  s c a l e form and  to the s t r u c t u r e of the p i e c e as a whole than  modules nearer the beginning and  end.  - 66  -  EXAMPLE 29  MODULE  MEASURES  II  STRUCTURAL ROLE  49-52  Bridges two  modules  II '  141-145  Bridges two  sections  II ' *  219-227  Bridges two halves of palindrome and the piece  II ' •  330-338  Bridges two  369-379  Bridges the f i n a l module and the "coda"  1  II ' ' '  1  To summarize our Feldman has and  modules  i n v e s t i g a t i o n of s e c t i o n B, we  combined i n v e r s i o n and  v a r i e d r e p e t i t i o n to c r e a t e  see  r e t r o g r a d e with  that  literal  palindromic r e l a t i o n s h i p s .  Extreme changes i n the magnitude of some domains generate i n v e r s i o n r e l a t i o n s r e l a t i v e to l e s s e r changes i n other modules. Modules t h a t c o n t a i n  extreme changes a l s o  contain  l e s s e r changes that produce "near" i n v e r s i o n a l r e l a t i o n s h i p s and  other d i s t i n g u i s h i n g c h a r a c t e r i s t i c s .  Palindromic structure  i s commonly understood to be  shaped". Here, modules XI and palindrome represent the  I I ' ' at the c e n t r e of  II'  than those f u r t h e r  1  the  "peak" of the arch. V a r i a n t s  module II that are s i t u a t e d more c l o s e l y to the modules XI and  "arch-  central  are more important to l a r g e - s c a l e from the c e n t r e .  between module II and  form  Developmental connections  i t s v a r i a n t s , and  bind module I I ' ' to module XI and  of  the c o n t i n u i t i e s t h a t  therefore  to  the  - 67 -  palindrome, serve to extend p a l i n d r o m i c s t r u c t u r e beyond the formal boundaries of s e c t i o n B i n t o the temporal r e g i o n s of s e c t i o n s A and A'.  SECTIONS A AND  A':  Non-palindromic p a r a l l e l i s m s between s e c t i o n s A and A' r e v e a l the l a t t e r s e c t i o n to be a v a r i a n t of the former. Before d i s c u s s i n g these however, l e t us f i r s t XII  examine module  (measures 282-290, Example 30) which f a c i l i t a t e s the  t r a n s i t i o n between the d i s p a r a t e c o n s t r u c t s of the f i n a l module of the s e c t i o n B palindrome module of s e c t i o n A  1  (VI/2) and the f i r s t  (XIII) by i n c o r p o r a t i n g aspects of both  modules. Module VI/2, l i k e the previous r e l a t e d modules VI/1, X/l  and X/2  (Example 31), i s extended by the w i d e l y spaced  dyads of module XII and by the alignment of s p e c i f i c r e g i s t e r s with one instrument or the other i n measures 282286. Extreme high and low r e g i s t e r notes, the l a t t e r n e c e s s a r i l y , are played by the piano, and m i d - r e g i s t e r p i t c h e s are given to the v i o l i n . A l l f i v e modules c o n t a i n s h o r t , d i s c r e t e d u r a t i o n s and a l l v i o l i n a r t i c u l a t i o n s a r e pizzicato. Instrumental and r e g i s t r a l demonstrated  i n v e r s i o n i n module X I I ,  i n Example 32, a l s o c o n t r i b u t e s to the  t r a n s i t i o n to s e c t i o n A'. In measures 287-289 the extreme upper and lower piano r e g i s t e r s merge i n piano events that occupy the c e n t r a l r e g i s t e r of the v i o l i n and thereby prepare  - 68 -  EXAMPLE  r — module  30  XIII  M o r t o n F e l d m a n SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n of E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n .  - 69  EXAMPLE  vi/2  VI/1  31  XII  X/l  X/2  piano  violin  piano * 5  EXAMPLE  mm.  282-286  32  287-289  290 ^ — v l n  # —*— pno 1  ^  '  _^  0  vln  ' \ /"pno/vln  * \  pno  - 70 -  the compressed s p a t i a l  focus of the e a r l y measures of module  X I I I . In measure 290, the v i o l i n departs from i t s c e n t r a l r e g i s t e r to occupy the upper  one l e f t vacant by the piano as  the c e n t r a l space l e f t vacant by the v i o l i n  is filled  by the  piano. The p i t c h c l a s s e s i n the low r e g i s t e r of the piano r i s e t o the upper the upper dyad  r e g i s t e r of the v i o l i n  i n measure 290 and  of the piano moves t o the c e n t r a l r e g i s t e r but  does not proceed t o the low r e g i s t e r of measure 290. At t h i s p o i n t i n module X I I , then, each instrument has exchanged i t s p i t c h space f o r that of the other; we can suppose t h a t the low r e g i s t e r remains  i n measure 290 "belongs" t o the v i o l i n but  u n f i l l e d because  t h a t instrument cannot p l a y so low.  Thus, module XII a t the end of s e c t i o n B i s not t r e a t e d p a l i n d r o m i c a l l y with r e s p e c t t o a module p r i o r t o s e c t i o n B, but there i s an echo of i n v e r s i o n i n i t s p a t t e r n . T h i s l o c a l i n v e r s i o n r e c a l l s the l a r g e r r e l a t i o n s h i p s of s e c t i o n B that i t concludes. Another of  t r a n s i t i o n a l f e a t u r e of module XII i s that aspects  i t s rhythm and p i t c h extend module VI/2 and prepare module  X I I I . The rhythm of each instrument i s c h a r a c t e r i z e d by i n f r e q u e n t , r e l a t i v e l y s h o r t d u r a t i o n s that extend the rhythmic e f f e c t of module VI/2. Heard  t o g e t h e r , however,  these rhythms generate a sense of i r r e g u l a r i t y that prepares the rhythm of module X I I I . Piano d u r a t i o n s i n module VI/2 do not o v e r l a p those of the v i o l i n , but i n modules XII and XIII piano and v i o l i n d u r a t i o n s are d i s p e r s e d w i t h i n the same time  - 71 -  span. C o n s i d e r i n g p i t c h : G#  i s exposed throughout module XII  as the upper p i t c h of a repeated of  each instrument  dyad, and  i s the f i r s t  i n module X I I I . Thus, the aspects  of  module XII that extend  module VI/2  generate  organic c o n n e c t i v i t y i n a r e l a t i v e l y  l i n e a r i t y and  and/or prepare  pitch  module XIII  s h o r t but s t r u c t u r a l l y s t r a t e g i c passage. We  recognize module XIII as the beginning  of a v a r i e d  r e p r i s e of s e c t i o n A because of i t s s i m i l a r i t i e s to VM example, aspects of rhythm and  I. For  a r t i c u l a t i o n d i v i d e both VM I  and module XIII i n t o three segments as shown i n Example The  first  33.  segment i n both modules c o n t a i n s r a p i d , s h o r t  d u r a t i o n s . The  second c o n t a i n s longer, l e s s frequent  each t h i r d segment e s s e n t i a l l y l i n e a r designs  ones. In  transmute to  e s s e n t i a l l y v e r t i c a l ones. Both segments c o n t a i n e x a c t l y four vertical chords—the divided In VM  i n t o two  fifth  chord  consecutive  of VM  dyads.  I, i n measure 46, i s  s  I, segment 1 c o n t a i n s p i z z i c a t o and  a r t i c u l a t i o n s , while  i n segment two,  arco  a l l d u r a t i o n s are bowed.  In module X I I I , the i n v e r s e i s t r u e — w e see only bowed d u r a t i o n s i n segment one segment two.  and  p i z z i c a t o and  arco markings i n  In each t h i r d segment, a l l chords are  played  pizzicato. The  r e l a t i v e lengths of segments are shown i n Example  Each f i r s t  segment i s roughly the same length but  r e l a t i v e lengths of segments two is,  i n VM  I, segment two  34.  the  and three are r e v e r s e d ; t h a t  i s r e l a t i v e l y s h o r t and  segment  -  72  EXAMPLE 33  segment 1 0  o  _  o  i—tfV-  y  VM I  f  ,| f f  ^ f  J f  n  ppp  »rco i  7*  1  "Tp  (J)-  \ ' f  — segment 2 -<S)  1  •v  it » 1  »  *— L_°  J  1  J  L _ - l  U . . . 1 . . . S  1  -  74  -  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n of E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n .  - 75 -  EXAMPLE 3 4 SECTION  MODULE  MEASURES  LENGTH IN MEASURES  1  VM  I  1-12  12  2  VM  I  13-20  8  3  VM  I  29-46  20  1  XIII  291-305  15  2  XIII  306-325  20  3  XIII  326-329  4  three r e l a t i v e l y long but longer. The  TOTAL — 40  TOTAL--39  i n module XIII segment two  i s the  combined length of a l l three segments i n each  module i s n e a r l y i d e n t i c a l . that were seen i n chapter  (Measures 21-28  c o n t a i n F sharps  1 to be c o n s t i t u e n t members of  piano module I. These measures are t h e r e f o r e excluded from this  summation).  In each module, segment one expansion (Example 35) of VM  e x h i b i t s a process  of  registral  i n that the c o n s t i t u e n t p i t c h c l a s s e s  I are r e d i s t r i b u t e d i n measures 7 and  8 to form a b i -  l e v e l e d s t r u c t u r e t h a t spans 14 semitones, then a t r i - l e v e l e d one  spanning 26 semitones. Module XIII c o n t a i n s b i - and t r i -  l e v e l e d c o n s t r u c t s and  a nearly identical  spatial  expansion  from 14 to 25 semitones. P a r a l l e l i s m s i n the domain of rhythm deepen the bond  - 76 -  EXAMPLE 3 5  module I  m  -Ifr-  measures  1-6  span i n s e m i t o n e s  3  7  8  14  26  module X I I I  '  /  i  4 Ji- o  h  —" J-  measures 291-298 span  i n semitones  between s e c t i o n s A and (as w e l l as other explores  A'  299-304  14  25  in general,  and  modules I and  these i n some depth, some connections are  relevant  chapter.  i n s t a n c e , Example 36 demonstrates that PM  XIV  (four  measures of which are shown i n t h i s example) contains same p i t c h c l a s s e s as PM formations, the  last  and  I and  the  first  of i t s two  the  trichord  that i t s rhythm i s c l o s e l y r e l a t e d to that of  few measures of PM  that the two  XIII  p a i r i n g s ) i n p a r t i c u l a r . Although chapter 3  to the d i s c u s s i o n of form i n t h i s For  <¥• • '  I (29-32). In chapter 1 we  most c o n s i s t e n t aspects of a m o d u l e — p i t c h  saw and  -  EXAMPLE  77  -  36  PM I  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n o f E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n .  - 78 -  rhythm—define  i t s p a t t e r n ; thus,  i t seems that PM XIV i s a  v a r i a n t of PM I r a t h e r than a d i s t i n c t module; but the rhythm p a t t e r n of PM I i s contained  i n measures 1-27, not measures  29-32. The l a t t e r measures may t h e r e f o r e be seen to c o n t a i n a rhythmic "seed" that emerges at the corresponding p o i n t i n the r e p r i s e , PM XIV. (The n o t i o n that the rhythms of l a t e r modules have t h e i r g e n e r a t i v e f u l l y explored  o r i g i n s i n e a r l i e r ones i s more  i n chapter 3 ) .  Elements of the next two modules i n s e c t i o n A ( I I I and IV) are contained  i n the next module i n s e c t i o n A , module 1  XV.  P i t c h c l a s s e s i n module XV are d i s t r i b u t e d i n a v e r t i c a l arrangement that i s e s s e n t i a l l y the same as the arrangement of p i t c h c l a s s e s i n module I I I but occupies a l a r g e r s p a t i a l area  (Example 37). That i s , a low dyad, a s i n g l e EXAMPLE 37  1-36  1-15  module  III  module  XV  mid-level  - 79 -  p i t c h and a s i n g l e u p p e r - l e v e l p i t c h are arranged such that the lower segment of each chord i s s l i g h t l y l e s s than h a l f the span of the upper  segment. Moreover, s h o r t , widely spaced  d u r a t i o n s i n the i n i t i a l measures of module IV (59-63: Example 38) are extended In modules V and XVI  to form the rhythm of module  (Example 39), which  XV.  occupy  corresponding p o s i t i o n s i n s e c t i o n s A and A',  an expansion of  p i t c h and r e g i s t e r takes p l a c e such t h a t t r i c h o r d s i n the piano i n module V become septachords at measure 102, t r i c h o r d s i n module XVI  are expanded to hexachords  (and  septachords) i n measures 355-356. (A second s p a t i a l occurs i n module V at measure  114).  expansion  7  Example 12 has shown that module V may three segments that d i f f e r  and  be d i v i d e d  into  i n p i t c h c l a s s content, t e x t u r e ,  and s p a t i a l d i s t r i b u t i o n ; the t h i r d segment c o n t a i n s nine p i t c h c l a s s e s to which are added three others that are extended  from e a r l i e r modules, and that complete  the  chromatic gamut ( r e f e r to example 15). The corresponding module XVI  i n s e c t i o n A'  (measures 348-368) l i k e w i s e c o n t a i n s  a l l twelve p i t c h c l a s s e s but none of them are borrowed. Rather, chords are transposed to form chromatic descending l i n e s t h a t u l t i m a t e l y i n c o r p o r a t e a l l twelve p i t c h Module XVI may  classes.  t h e r e f o r e be understood to c o n t a i n twelve  c o n s t i t u e n t p i t c h c l a s s e s that are g r a d u a l l y introduced by means of transposed chords.  -  EXAMPLE  80  -  38  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n o f E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n agent f o r U n i v e r s a l E d i t i o n .  - 81 -  o> 01 H ft rr rr M JD O h" — t 3 c rr rr rt u o » H rt a in » 3 it cu n ui 3  o ro H  "O < 13 0 IH 33 01 • Z rr O i- G O Ul o 3 a> -  a  o  ui cr x  o >< o  co IH TJ 33 IT) O  I-"  c * w • 3 CO  co • • in  x >  ui n m p- o  3 O TI a 3 > < H 0 O >-• 01 HiiO 3 J 01 M rr a C — i « to 01 o 3 >a tr~ J ro (T> 0 01 3) > rr 3 3 ID < n i» 01 C h- 3 l-* < C re ui rfl n M - ex  in n >-• pa  U3  CXKjl  - 83  -  M o r t o n Feldman SPRING OF CHOSROES. C o p y r i g h t 1979 by U n i v e r s a l E d i t i o n . A l l R i g h t s R e s e r v e d . Used by p e r m i s s i o n of E u r o p e a n A m e r i c a n M u s i c D i s t r i b u t o r s C o r p o r a t i o n , s o l e U.S. and C a n a d i a n a g e n t f o r U n i v e r s a l E d i t i o n .  - 84 -  The t h i r d segment of module XVI (measures 380-388) extends the second one but i s separated I  I  i  n  measures 369-379  saw that the s u r f a c e  from i t by a bridge  module,  (Example 40). In Example 27 we  features  of VM I I  1 1  connect i t to module  XI but i t s s t r u c t u r a l r o l e more deeply connects i t to VM II and  i t s v a r i a n t s . I f we consider  "coda" that r e t a i n s s u r f a c e distinct  formal  measures 380-388 to be a  features  of module XI but has a  r o l e , module XVI ends at measure 386 and  thereby r e v e a l s another p a r a l l e l i s m between modules V and X V I — e a c h i s followed  by a v a r i a n t of VM I I .  In t h i s d i s c u s s i o n of form we have shown that p a r a l l e l i s m s between modules generate formal  connections between s e c t i o n s  A and A' and d e f i n e palindromic  s t r u c t u r e i n s e c t i o n B. The  s e c t i o n a l s t r u c t u r e i s augmented, however, by recurrences module II that have s p e c i a l formal  f u n c t i o n s . Connections  between module II and i t s v a r i a n t s extend r e l a t i o n s h i p s beyond the formal  of  palindromic  boundaries of s e c t i o n B i n t o  s e c t i o n s A and A' with i m p l i c a t i o n s to form that w i l l be addressed i n the f o l l o w i n g d i s c u s s i o n .  LARGE SCALE STRUCTURE The connections that a r t i c u l a t e l a r g e - s c a l e form are found i n the domains of p i t c h , rhythm, and r e g i s t e r . Each of two s e t s of modules—{VM and  I, module XI and module XVI, and VM II  i t s variants}—form  a d i s c r e t e framework: together  these  - 85 -  comprise the u n d e r l y i n g  s t r u c t u r e of the p i e c e . We w i l l see  that the frameworks c o i n c i d e  i n some ways--that i s , modules  i n one framework are connected to modules i n the other but  first  one—  l e t us examine each s e t i n t u r n .  Example 41 i l l u s t r a t e s the p i t c h c l a s s e s that connect VM I, module XI and module XVI as w e l l as the coda. The f i v e c o n s t i t u e n t p i t c h c l a s s e s of VM I are extended to module XI which a l s o contains  two a d d i t i o n a l p i t c h c l a s s e s , G and A .  Module XVI c o n t a i n s  a l l twelve p i t c h c l a s s e s and i s t h e r e f o r e  to  connected to a l l modules i n t h i s domain, but i t s connection  EXAMPLE 41 VM I module XI  {D D# E F  G} b  v l n {D D# E F G  A}  b  b  pno {D D# E F G* G} module XVI (mm. 357-362)  {D E  b  E F F#}  to VM I i s e s p e c i a l l y strong because the f i v e p i t c h c l a s s e s of t h a t module are exposed i n the upper v o i c e of a s e r i e s of descending hexachords i n measures 357-362 ( r e f e r to Examples 39 and 4 0 ) . Several  B  f a c t o r s cause us to p e r c e i v e  the s e r i e s of  hexachords as coherent. They are u n i q u e l y that each i s contained the preceding  orchestrated i n  i n the piano, but one p i t c h i n each of  t r i c h o r d s i s played  by the v i o l i n , and, a f t e r  - 86 -  measures 357-360, a high s u s t a i n e d G i n that  instrument  overlaps the hexachords i n measures 365-367. The  hexachords  i n measures 357-360 are u n i q u e l y a r t i c u l a t e d as w e l l . Although the rhythm of these chords and that of the preceding t r i c h o r d s i s i d e n t i c a l , they are s u s t a i n e d through the e i g h t h r e s t s that separate them while i d e n t i c a l r e s t s i s o l a t e t r i c h o r d . Likewise, each of the subsequent measures 361-364 are i s o l a t e d by More important to the exposure  each  septachords i n  rests. of measures 357-360 are the  rhythmic, r e g i s t r a l , and t e x t u r a l punctuations that are c r e a t e d by the two  septachords that frame them i n measure  355  and measure 361. P r i o r t o measure 355,  t r i c h o r d s are s t a t e d  i n which the p i t c h e s are evenly spaced  i n three r e g i s t e r s .  Although the p i t c h e s of the f o l l o w i n g septachord i n measures 355-356 are l i k e w i s e disposed at three l e v e l s , are packed  f i v e of them  i n t o the c e n t r a l octave space. Moreover, the  t r i c h o r d s span a range  from E 6 i n measure 348 to A 3 i n to  to  measure 354 but the f o l l o w i n g septachord i n h a b i t s a lower space between B2 and G5,  thus adding to i t s weight.  After  measures 357-360, the s p a t i a l formation of the septachord i n measures 361-364 extends  that of the preceding hexachords but  the r e p e t i t i o n of t h i s chord forms a r e g i s t r a l p l a t e a u that i n t e r r u p t s the steady descent of the module. Regarding  rhythm, the i n i t i a l  septachord i n measures  355-  356 c o n t a i n s three p i t c h e s that extend the d u r a t i o n a l values of the preceding t r i c h o r d s and prepare those of the  following  - 87 -  hexachords, but i t s four other p i t c h e s have v e r y short d u r a t i o n s . One  of these s h o r t notes i s given a p i z z i c a t o  a r t i c u l a t i o n that i n c r e a s e s our sense of i t s d u r a t i o n a l c o n t r a s t . The subsequent septachord i n measures 361-364 s i m i l a r l y c o n t a i n s s i x s u s t a i n e d d u r a t i o n s i n the piano and one s h o r t , p i z z i c a t o note i n the v i o l i n . The d u r a t i o n a l value of the f i n a l three hexachords i n measures 365-367 i s h a l f t h a t of the s e t of hexachords i n measures 357-360. These s h o r t e r values are prepared by the first  statement of the septachord i n measures 361-362, but  when t h i s chord i s repeated i n measures 363-364, i t has a s l i g h t l y longer d u r a t i o n t h a t i s p r e c i s e l y three s i x t e e n t h s s h o r t e r than the hexachords  i n measures 357-360 and three  s i x t e e n t h s longer than the hexachords  i n measures 365-367.  Each septachord i s preceded by a r e s t that i s twice the length of that which precedes each t r i c h o r d 354 and each hexachord  i n measures  348-  i n measures 357-360.  Each septachord completes at l e a s t one of the descending l i n e s i n the stream of chords that precedes i t .  In measures  348-354 the l i n e i n the v i o l i n that f a l l s  b  culminates at the p i z z i c a t o F#4  from D 5  i n measure 355. The  to G4 spatially  exposed upper l i n e of the piano descends c h r o m a t i c a l l y from E^S to A5 then leaps two semitones r a t h e r than one to G5--the expected G#  i s t r a n s f e r r e d to an inner v o i c e . G5 then a c t s as  an upper neighbour to the f i r s t  of the f i v e exposed  c l a s s e s that connect t h i s module to VM  pitch  I, and the second  -  septachord i n measures 361-364 contains that completes the s e t . The perceive  the upper v o i c e  r e p e t i t i o n of D5  i t as a terminus and,  as we  causes us  halts  D5 to  have seen, c r e a t e s  moment of r e g i s t r a l s t a s i s that t e m p o r a r i l y descending path of the  88  a  the  line.  Thus each septachord i s a punctuation that completes some aspects of the events before i t and  prepares other events  that f o l l o w . Each septachord i s h i g h l i g h t e d by durations  and  by the  module i s t h e r e f o r e chords, and  lengthy divided  r e s t t h a t precedes i t . The i n t o three descending s e r i e s of  i t i s the second s e r i e s that f e a t u r e s  c l a s s e s of VM  first  s t a t e d three  times; thus, three  E  pitch classes  is therefore  to  the  the  I--F#,  first  the v i o l i n plays  the  the  i n the descending l i n e , D and  and  the  E  to  last v i o l i n pitch class in  piece.  Let us t u r n our  a t t e n t i o n to the r e g i s t r a l d i s p o s i t i o n s of  the p i t c h c l a s s e s of VM and  p i t c h c l a s s e s from VM  are  exposed i n the upper v o i c e . In  measures of the p i e c e ,  remaining two  pitch  (measures  three chords of t h i s second s e r i e s  E--are r e p e a t e d l y  l a s t two  the  I. In the coda, shown i n example 40  380-388) the  F, and  short  XVI.  I that are p r o j e c t e d  to modules XI  These comprise an arched s t r u c t u r e that i s  illustrated  i n Example 42.  In measures 1-6,  constituent  p i t c h c l a s s e s of VM  four of the  five  I occupy a narrow high  r e g i s t e r , which i s made s l i g h t l y wider by the a d d i t i o n of in measure 8. This r e g i s t e r comprises one  of three  G  to  strata in  - 89  EXAMPLE  measures 8-12 then D and  but  -  42  i n measures 13-20, three p i t c h c l a s s e s ,  E, are r e l o c a t e d to a higher  E , to  r e g i s t e r that  prepares the upper l e v e l of module XI. Measures 29-48 c o n t a i n a t r i - l e v e l e d s t r u c t u r e that i s d e r i v e d measures 8-12;  thus,  from the one  the upper r e g i s t e r of VM  octave 6 to octave 7 and  in  I moves from  back to octave 6 forming a l o c a l  arch t h a t r e f l e c t s the shape of the  l a r g e - s c a l e arch  by the upper r e g i s t r a l l e v e l s of VM  I, module XI, and  formed module  XVI. Although there are four d i s t i n c t s t r a t a i n VM defines  the s t a r t i n g p o i n t of the  i s the only l e v e l  I, octave 6  l a r g e - s c a l e arch because i t  i n t h a t module that contains  a l l five pitch  c l a s s e s . In module XI, these f i v e p i t c h c l a s s e s appear simultaneously  i n two  r e g i s t e r s , octave 6 and  l a t t e r of which i s the highest and  i n module XVI,  point of the  they are placed  at the  octave 7,  large-scale  the arch,  lowest r e g i s t e r of  -  90  -  the arch--octave 5. In the coda, four p i t c h c l a s s e s , D, E, F, and F#, extend octave 5, but E 7 i n the v i o l i n echoes the to  upper l e v e l of module XI and of VM I. Thus, a process of r e g i s t r a l change that generates a l o c a l arch i n VM I i s p r o j e c t e d across the e n t i r e length of the p i e c e , although the f i n a l l e v e l of the l a r g e - s c a l e arch i s lower than t h a t of the l o c a l one. In the domain of rhythm, the second and t h i r d stages of the three-stage process of rhythmic s i m p l i f i c a t i o n  i n VM I ( r e f e r  to Example 7a) are p r o j e c t e d to modules XI and XVI r e s p e c t i v e l y . Example 43 shows the r a p i d , d u r a t i o n s that t y p i f y measures 1-12 rhythms below and to the l e f t  irregular  (VM I) and the two  i l l u s t r a t e the second and t h i r d  stages of the process. The rhythm of module XI i s a v a r i a n t of measures 1-12 that i s analogous to the rhythm of stage two i n measures 13-16. In module XVI, s u s t a i n e d , r e g u l a r d u r a t i o n s are the analog of the rhythm of stage t h r e e . Thus, a process of rhythmic change i n VM I i s p r o j e c t e d to modules XI and XVI i n such a way that the second and t h i r d each of which f i l l e d  stages,  only a few measures i n the l o c a l  process, are expanded to comprise an e n t i r e module. Now  l e t us examine the l a r g e - s c a l e s t r u c t u r e formed by VM  II and i t s v a r i a n t s . T h i s framework extends p a l i n d r o m i c r e l a t i o n s h i p s beyond s e c t i o n B and c o i n c i d e s i n some ways with the s t r u c t u r e generated by VM I and modules XI and XVI.  - 91 -P- w  -1  i  -J  o  i  -1  ~ in -c riai -J ID  -J  (f  rr It  I  01 03 (D  rr o  01 rr g Qi 3 < iQ 3 fD t-> I M  O 3  n>  3  3  CL C  QJ  o  o  C  w >  X  <  r w  a*. -1  -if ti-  ckle  I  5  -  92  -  EXAMPLE 4 4  i—  VM II  {G# A B }  VM II '  {G# A B  VM I I "  {  b  L_ VM II ' ' ' VM II  b  B> D# E F G } to  {G# A B  B C D  to  to  D E } to  {G# A B }  i i i i  b  Example 44 shows p i t c h - c l a s s a s s o c i a t i o n s  between VM II and  i t s v a r i a n t s . P a l i n d r o m i c r e l a t i o n s h i p s , symbolized by square brackets i n the example, are produced G#, A, and B  b  by the p i t c h  classes  that are common t o VM II and VM I I ' ' ' , 1  and by  the p i t c h c l a s s e s G#, A, B , and B that are common to VM I I ' to  and VM I I ' " ' . VM I I ' ' c o n t a i n s a d i s c r e t e s e t of p i t c h c l a s s e s , D#, E, F and G . to  Some p i t c h connections are not p a l i n d r o m i c ; f o r example, VM II"'  begins with Gff, A, B , and B i n measures 330-332, then to  C, D , D and E to  b  are added. The l a s t of these, E , i s common b  to VM I I " . When they are viewed  as a s i n g l e s e t , the p i t c h  c l a s s e s of VM I I ' and VM I I " do not form a chromatic s e t ; however, the p i t c h space between B and D# that separates them is f i l l e d classes  by the C, D , and D i n VM I I ' " . Each s e t of p i t c h b  i n each of the f i v e modules i s a chromatic s e t , and  the union of these forms a s i n g l e , l a r g e a l l - a d j a c e n t s e t . The p a r a l l e l i s m s  i n the domain of rhythm shown i n Example  -  93  -  EXAMPLE 4 5  45 e x h i b i t aspects of palindrome. VM II and VM I I sustained  durations  contiguous d u r a t i o n s only s l i g h t  that are separated  , , ,  '  contain  by r e s t s , and the  of VM I I ' are extended to VM I I  1 1  ' with  changes. VM I I ' ' may be seen t o embody aspects of  both p a i r s of modules i n that i t c o n t a i n s a d j o i n i n g notes, and has d u r a t i o n a l values  some r e s t s and some i n common with a l l  four modules. The  number of a t t a c k s  i n each module are t a b u l a t e d  column to the l e f t of t h i s palindromic  i n the  example. These f i g u r e s demonstrate  a s s o c i a t i o n s i n that VM II and VM II  1 , 1  ' have  fewer a t t a c k s  than VM I I ' and VM I I ' ' , which i n turn have  fewer a t t a c k s  than VM I I ' ' . Furthermore, the magnitudes of VM  1  II and VM I I are expanded when they are r e s t a t e d as modules 1  - 94 -  VM I I '  11 1  and VM I I ' ' r e s p e c t i v e l y , 1  9  a process that  generated i n v e r s i o n r e l a t i o n s and a r t i c u l a t e d palindromic s t r u c t u r e i n s e c t i o n B. Among VM II and i t s v a r i a n t s , however, expansions do not c r e a t e  i n v e r s i o n r e l a t i o n s and t h e r e f o r e  have o n l y l o c a l meaning. Example 46 i l l u s t r a t e s the r e g i s t r a l f i v e modules. Palindromic  arch c r e a t e d  by these  a s s o c i a t i o n s are formed by the  common low r e g i s t e r of VM II and VM II '•»' and by the shared upper r e g i o n of VM I I ' and VM I I ' ' . VM I I ' ' i s s i t u a t e d i n a 1  range that i s s l i g h t l y lower than t h a t of i t s neighbouring modules. EXAMPLE 46  r—f —A  M  ^  VM  y  ^  s  VM I I '  II  VM I I '  VM I I " '  1  Although the p i t c h c l a s s e s G#, A, B , and C to  same high s p a t i a l module contains  level  other,  VM  to  occupy the  i n VM I I ' and VM I I ' ' ' , the l a t t e r higher  p i t c h e s that form the uppermost  p o i n t of the arch. We have seen, however, i n Example 29 that VM I I ' ' has a p i v o t a l s t r u c t u r a l r o l e among the f i v e modules; thus,  the r e g i s t r a l  high p o i n t does not c o i n c i d e with the  - 95 -  underlying s t r u c t u r a l  one.  Thus f a r , our d i s c u s s i o n of l a r g e r s t r u c t u r e has shown us that the piece c o n t a i n s two  frameworks,  each formed by a  d i s c r e t e s e t of modules. Although we have i n v e s t i g a t e d these s t r u c t u r e s as d i s t i n c t u n i t s , they share some common a t t r i b u t e s of p i t c h , rhythm,  and r e g i s t e r , and are t h e r e f o r e  s a i d to c o i n c i d e . At the same time however, each s t r u c t u r e retains i t s individual  i d e n t i t y . The frameworks are t h e r e f o r e  fastened to one another at p o i n t s of c o i n c i d e n c e such that they are p e r c e i v e d to be two segments of a s i n g l e , more complex s t r u c t u r e . Let us c o n s i d e r p o i n t s of c o i n c i d e n c e i n the domain of r e g i s t e r , represented i n Example 47. We have seen that the r e g i s t e r of measures 1-7  i n VM  I i s extended to module XI and  forms the lower of i t s two d i s c r e t e r e g i s t e r s . The module VM  subsequent  I I ' ' i n h a b i t s t h i s space; thus, i t s r e g i s t e r i s  extended to i t by VM  I. A more d e t a i l e d r e p r e s e n t a t i o n of  t h i s r e l a t i o n s h i p i s g i v e n i n Example 49. This example shows that each of two processes of expansion cause the span of a module i n one framework to o v e r l a p the span of a module i n the other one. The span of VM to 6 semitones  I expands from 4 semitones  (1-6) when i t i s extended to the lower  of module XI, and VM  I I ' expands from 1-3  to 1-7  i n VM  Thus, we see t h a t A 6 i n module XI c o i n c i d e s with G#6 to  I I ' and VM  I I ' ' ' , and that D7 and E 7  with the upper s t r a t a of module XI.  b  i n VM  II'''  (1-4)  strata II'''. i n VM  coincide  - 97 -  EXAMPLE 49  G7 E 7 b  D7  C 6 to  G#6  A* 6  G 6  D6  D6 VM I  G 6  G#6  to  to  VM I I '  XI  D#6  VM I I ' '  VM I I  ,  ,  !  Example 49 e x h i b i t s a broader process of expansion such that the span of VM I widens t o the extent that i t incorporates  both s t r a t a of module XI. Each of VM I, VM I T  and the upper s t r a t a of module XI occupy d i s c r e t e , p r o g r e s s i v e l y r i s i n g spaces that may be seen t o widen the span of VM I from 1-4 t o 1-10 i n VM I I ' , and 1-17 i n module XI. Thus, while the span of VM I I ' does not c o i n c i d e with t h a t of VM I, i t c o n s t i t u t e s a s t e p i n the expansion process of VM I. Thus, the r e g i s t e r s of the two frameworks c o i n c i d e i n module XI and VM I I " such that the space of VM I I ' '  is  contained w i t h i n that of module XI. By c o n t r a s t , r e g i s t e r s  - 98 -  c o i n c i d e more s e l e c t i v e l y by way  of d i s c r e t e processes of  expansion i n two p a i r s of modules—VM I and XI, and VM I I ' and VM  I I ' ' . Although the r e g i s t e r s of VM 1  I and VM  I I ' do  not c o i n c i d e , the span of the l a t t e r module i s encompassed by the r e l a t i v e l y dramatic expansion process of the former. In the same way  that the r e g i s t e r of VM  1 1 ' may 1  be seen to  emerge from w i t h i n that of module XI, the span of VM derives  of module XVI  11 ' ' ' ' i n a low one but the descending l i n e s  f a c i l i t a t e the s p a t i a l t r a n s i t i o n between the  l e v e l s . In module XVI  ( r e f e r to Example 39 and 40), we see  three g r a d u a l l y descending l i n e s , the highest from E 6 to G5 to  (measures  p i t c h c l a s s e s of VM these p i t c h e s  of which moves  348-356) then s t a t e s the c o n s t i t u e n t  I i n measures 357-364 (the r e g i s t e r of  i s i s o l a t e d i n Example 47). Three  subsequent  (D 5, C5, and B4) complete the d e s c e n t . to  x o  In measures  352-354, the lower v o i c e a r t i c u l a t e s the p i t c h e s of VM but  1  from module XVI. VM I I ' " i s s i t u a t e d i n a high  r e g i s t e r and VM  pitches  II' ''  i n the measures t h a t f o l l o w , the widened  II''''  span of module  XVI envelopes t h e i r narrow r e g i s t e r . The descending hexachords and F#5; may  i n measures 357-367 i n h a b i t a space between E 2  thus, the p i t c h e s of VM  to  II''''  (G#3,  A3, and B 3) to  be seen to emerge from about i t s midpoint.  The descending l i n e s of module XVI t h e r e f o r e  ensure that  the t r a n s i t i o n from the v e r y high r e g i s t e r of VM low r e g i s t e r of VM I I ' ' ' ' i s p e r c e i v e d  I I " ' to the  as a g r a d u a l one.  Although the s p a t i a l locus of the l a t t e r module c o i n c i d e s  - 99 -  with that of module XVI II''  and  seems to be extended from i t , VM  remains more s t r o n g l y connected to VM  1 1  e x a c t l y repeats  that module's r e g i s t e r and  II i n t h a t i t  pitch classes.  Let us t u r n f o r a moment to the domain of p i t c h . In Example 26 we  saw  that VM  I I ' ' contains  four of the c o n s t i t u e n t p i t c h  c l a s s e s of module XI r a t h e r than the expected p i t c h c l a s s e s G#,  A, and  B  13  that connect VM  II with i t s other  three  v a r i a n t s . These are i n s t e a d d i s p l a c e d to module X I I I . Example 50 between VM and two,  B  fa  i l l u s t r a t e s p i t c h and  I I , modules XIII and  r e g i s t e r connections  XVI,  and  occupy a s i n g l e r e g i s t e r i n VM  then three  takes place  c l a s s e s of VM module XVI  i n h a b i t s the  I are exposed at the h i g h e s t  constituent  s t r a t a of module XIII  foreshadow the  large-scale r e g i s t r a l  arch.  pitch  of these l e v e l s i n  i n the coda. VM  lower l e v e l . In t h i s way,  A,  (An analogous process  I--see Example 35). The  (measures 357-362) and  I I ' ' ' ' . G#,  II that i s expanded to  l e v e l s i n module X I I I .  i n VM  VM  II'''  the upper and  1  lower  f i n a l r e g i s t e r of each  EXAMPLE 50  VM  1;  II  XIII  XVI  VM  11 ' * ' '  - 100 -  Example 48 d e p i c t s the arch formed by the uppermost p o i n t s of  r e g i s t r a l c o i n c i d e n c e between the two l a r g e - s c a l e  s t r u c t u r a l frameworks. Each s t r u c t u r e begins at a d i s c r e t e r e g i s t e r - - t h e s e converge a t octave  6 i n VM I I ' and r i s e to  octave  7 i n module XI. A f t e r VM I I ' ' ' ' the arch f a l l s to  octave  5 i n module XVI and the two s t r u c t u r e s d i v i d e - - o c t a v e  5 i s extended to the coda and the r e g i s t e r of VM II i s recovered  i n VM II ' ' ' ' .  Most p o i n t s of c o i n c i d e n c e i n the p i e c e are r e g i s t r a l ; however, there are two p o i n t s of rhythmic w i l l now c o n s i d e r . The f i r s t  occurs  c o i n c i d e n c e t h a t we  i n module XI and VM II "  and the second takes place between module XVI and VM Regarding  the f i r s t ,  II''''.  Example 43 demonstrated that each of  the second and t h i r d stages of a three-stage process of rhythmic  simplification  i n VM I were p r o j e c t e d to modules XI  and XVI r e s p e c t i v e l y . Example 45 r e v e a l s t h a t p a l i n d r o m i c r e l a t i o n s h i p s among VM II and i t s v a r i a n t s were c r e a t e d by a d i f f e r e n t type of rhythmic  p r o c e s s . These d i s c r e t e  procedures  produced rhythms i n the two c e n t r a l modules XI and VM I I ' ' that c o i n c i d e ; t h a t i s , they are e s s e n t i a l l y the same i n t h a t the rhythm of VM I I ' ' sounds l i k e a c o n t i n u a t i o n of the rhythm of module XI. At the second p o i n t of c o i n c i d e n c e , module XVI and VM II'''*  share common rhythmic  contiguous  attributes.  Sustained,  d u r a t i o n s comprise the t h i r d stage of rhythmic  simplification  i n VM I (measures 17-20, Example 43) but the  -  d u r a t i o n s of VM II and VM I I ' (Example 4 5 ) .  1 , 1  101  -  are separated by r e s t s  The rhythm of module XVI, the l a r g e - s c a l e  analog of the t h i r d stage of VM I, i n c o r p o r a t e s t h i s  aspect  of VM I I ; t h a t i s , i t s d u r a t i o n s are separated by r e s t s . But the d u r a t i o n s of VM II  1 , 1  ' are more widely spaced  than  those  of module XVI and t h e r e f o r e proceed more s l o w l y ; thus, while the rhythm of module XVI e x h i b i t s elements of VM I and VM I I , the rhythm of VM I I '  1 , 1  extends  the process of rhythmic  s i m p l i f i c a t i o n t h a t i s p r o j e c t e d from VM I to module XVI. We w i l l c o n s i d e r one l a s t example of c o i n c i d e n c e that takes place o u t s i d e the domains of p i t c h , rhythm, and r e g i s t e r ; s p e c i f i c a l l y , module XI and VM I I * share the same s t r u c t u r a l 1  f u n c t i o n . P a l i n d r o m i c r e l a t i o n s h i p s u n i f y each of two s e t s of modules--VM comprise  II and i t s v a r i a n t s , and the modules t h a t  s e c t i o n B. The c e n t r a l module i n each s e t (VM I I ' 1  and module XI r e s p e c t i v e l y ) i s not repeated, nor i s i t s own p a t t e r n p a l i n d r o m i c ; i n s t e a d , i t f u n c t i o n s as a b r i d g e module t h a t connects  the two halves of i t s palindrome. But  the c o n n e c t i v e purpose of module XI has a deeper meaning. VM I, module XI, module XVI and the coda, s c a l e framework that extends  form a l a r g e -  from the f i r s t measure of the  p i e c e t o the l a s t . I t s c e n t r a l module t h e r e f o r e b i s e c t s not only the palindrome  i n s e c t i o n B but the p i e c e as a whole.  The framework made with VM II and i t s v a r i a n t s begins i n measure 49 and ends i n measure 379;  thus, while i t s c e n t r a l  module VM I I ' b i s e c t s a l a r g e - s c a l e s t r u c t u r e t h a t i s i t s e l f 1  - 102 -  palindromic,  i t does not, s t r i c t l y speaking,  d i v i d e the  e n t i r e p i e c e . But module XI and VM I I ' are contiguous and 1  share  s e v e r a l a t t r i b u t e s such that we p e r c e i v e the l a t t e r  module t o be a c o n t i n u a t i o n of the f i r s t ; be seen to embody the deeper connective  thus, VM I I ' ' may  meaning of module XI  as w e l l . Module XI and VM I I * ' c o i n c i d e i n three  domains—pitch,  rhythm, and r e g i s t e r , and they share a common s t r u c t u r a l purpose; thus the p i e c e i s weighted so t h a t i t s s t r u c t u r a l focus  i s l o c a t e d at i t s c e n t r e . As Example 51 shows, a  secondary r e g i s t r a l arch created by the spans of modules VI/1,  X / l , X/2, and VI/2 frames the c e n t r a l modules. (In t h i s EXAMPLE 51  VI/1  X/l  X/l  XI  II•'  X/2  VI/2  - 103 -  example, the upper and lower p i t c h e s of module XI and VM I I are bracketed  to show t h a t other p i t c h e s are contained  i n the  space between them). Although  there are few p i t c h - c l a s s  connections  four modules share  among them, these  n e a r l y i d e n t i c a l rhythms and together  1 1  distinctive,  they i n h a b i t three  widely spaced r e g i s t e r s . Module VI/1 c o n t a i n s a l l three spatial and  l e v e l s , while module X / l r e t a i n s only the upper two,  the h i g h e s t l e v e l i s extended to the repeat of module  X / l . The r e g i s t r a l immediately  f l o o r t h e r e f o r e r i s e s to i t s highest p o i n t  p r i o r to module XI. The downward s l o p e of the  arch i s s t e e p e r - - a f t e r VM I I , each r e g i s t r a l presented  level is  i n t u r n from h i g h e s t to lowest. The p i t c h e s of  module X/2 are c l u s t e r e d i n the high r e g i s t e r , then, i n module VI/2, a c e n t r a l p i t c h i s followed by a low r e g i s t e r dyad. The b i s e c t e d peak of the r e s u l t a n t arch r i s e s above module XI and VM I I ' ; t h e r e f o r e , Example 51 p r o j e c t s a r e g i s t r a l 1  p r o f i l e t h a t resembles t h a t of the l a r g e - s c a l e arch  generated  by VM II and i t s v a r i a n t s (Example 46). The c e n t r a l modules of each formation are lower than the modules t h a t surround i t but t h e i r s t r u c t u r a l meanings are deeper. One of the modules of the secondary arch, VI/1, i s connected to module XI and VM I i n that a l l of i t s f i v e p i t c h c l a s s e s are contained  within  the former module and four of them are shared with the l a t t e r one. In t h i s way, the secondary arch c o i n c i d e s with the framework whose c e n t r a l modules i t surrounds.  - 104 -  In the f i r s t  part  of t h i s chapter, we saw that s t r u c t u r a l  p a r a l l e l i s m s between modules gave r i s e t o an ABA' formal and that  that the second of these segments c o n t a i n s a palindrome i s i t s e l f a two-sided s t r u c t u r e . VM II and i t s v a r i a n t s  project  p a l i n d r o m i c r e l a t i o n s h i p s , and t h e r e f o r e  s t r u c t u r e , across a l a r g e d i s t a n c e . a whole i s b i s e c t e d the  plan  large-scale  two-part  Furthermore, the piece as  by i t s s t r u c t u r a l p i v o t , module XI, but  framework to which i t belongs p r o j e c t s  stage processes i n the domains of rhythm and r e g i s t e r  threethat  are analogs of l o c a l ones w i t h i n VM I. Thus a v a r i e t y of formal processes generate juxtaposed formal shapes that a r t i c u l a t e l o c a l and l a r g e - s c a l e s t r u c t u r e .  In the f o l l o w i n g  chapter, we w i l l examine another process that a r t i c u l a t e s the ABA' plan of the piece — l a r g e - s c a l e rhythmic  pulse.  - 105 -  CHAPTER 3 LARGE-SCALE RHYTHMIC PULSE Let us begin by examining two important and  concepts—"pulse"  "rhythm stream." In some recent l i t e r a t u r e , the term  " p u l s e " r e f e r s t o a r e g u l a r s e r i e s of equal d u r a t i o n s .  1  David  E p s t e i n presents the c o n t r a s t i n g view t h a t the s p e c i f i c d u r a t i o n s of pulses are c o n t r o l l e d by the performer and t h e r e f o r e may or may not e x h i b i t r e g u l a r i t y .  2  He contends  t h a t beats and pulses r e s i d e i n d i s c r e t e temporal One of these, the dimension comprised  of "chronometric  dimensions.  time," i s  of beats, measures and hypermeasures t h a t together  form an u n d e r l y i n g , p e r i o d i c m e t r i c g r i d . I t s c o u n t e r p a r t , " i n t e g r a l time," c o n t a i n s p u l s e s , motives and phrases  that  may or may not e x a c t l y c o i n c i d e with the m e t r i c s t r u c t u r e ( i n rubato passages f o r example). Pulses are t h e r e f o r e c o n s i d e r e d to be a u r a l l y d i s c e r n i b l e , t e m p o r a l l y f l e x i b l e a t t a c k p o i n t s t h a t correspond  t o beats but may not s p e c i f i c a l l y a l i g n with  them. In the present a n a l y s i s , a q u i t e d i f f e r e n t concept  of p u l s e  i s l i n k e d t o the n o t i o n of " a u d i t o r y stream" as i t i s d e f i n e d i n the psychoacoustic  literature.  3  In t h i s c o n c e p t i o n , a  pulse i s d e f i n e d as a span of time w i t h i n which momentum i s generated  then d i s s i p a t e d  i n a more or l e s s gradual way. I t s  length i s demarcated by the attack p o i n t t h a t begins  i t and  - 106 -  by the c u l m i n a t i o n of the d u r a t i o n t h a t ends i t . Momentum i s generated and maintained  by a stream of r e l a t e d rhythmic  events t h a t n e v e r t h e l e s s d e c e l e r a t e the pulse over time. Spring of Chosroes c o n t a i n s two such p u l s e s : the length of the f i r s t  equals  the l e n g t h of s e c t i o n A and the second i s  the l e n g t h of s e c t i o n A'. The rhythm of s e c t i o n B p r o j e c t s s t a s i s , t h a t i s , i t generates no momentum, but s u r f a c e processes  of d e c e l e r a t i o n may be found i n the f i r s t  h a l f as  w e l l as i n the c e n t r a l modules XI and VM I I ' , and there are 1  processes  of a c c e l e r a t i o n i n the second h a l f . In t h i s way,  the gradual decay of rhythmic momentum i n s e c t i o n A reverberates  on the s u r f a c e of s e c t i o n B, and the  a c c e l e r a t i o n s t h a t f o l l o w prepare us f o r the a r r i v a l of the second pulse i n measure 291. S e v e r a l f a c t o r s c o n t r i b u t e t o the d e c e l e r a t i o n of momentum i n each p u l s e ; among them, lengthened  durations,  registral  expansion, d i s p a r a t e r e g i s t e r s , wide temporal s p a c i n g , a t t a c k s , e t c . Conversely,  each pulse i s prolonged  fewer  by rhythms  that d e r i v e from VM I or PM I. We w i l l begin our d i s c u s s i o n by examining these and other  f e a t u r e s i n s e c t i o n A.  SECTION A The  first  pulse i s comprised of two d i s c r e t e , simultaneous  rhythm streams. The more powerful begins  i n the piano while  and longer  i t s counterpart  l a s t i n g of these  i n the v i o l i n  d i s s i p a t e s partway through the s e c t i o n . Our i n i t i a l w i l l be toward the s h o r t e r stream.  focus  - 107  In VM  I, measures 1-6  (see Example 33), momentum i s  generated by a l i n e a r p a t t e r n comprised of r a p i d , v a r i o u s l y articulated,  i r r e g u l a r l y spaced d u r a t i o n s t h a t are  w i t h i n a narrow r e g i s t e r . The module begins i n measures 7 and to 1-27.  8 when i t s s p a t i a l  field  contained  to d e c e l e r a t e expands from  1-2  Because the expansion u n f o l d s a lower space, the  module becomes more weighted, and s i n c e there  i s no  compensatory i n c r e a s e i n the attack frequency  i n these  measures to support  the added weight, the momentum begins  slow down. In measures 8-10, measures i s recovered  to  the narrow span of the opening  but the a t t a c k s are l e s s frequent  and  they are more r e g u l a r ; t h e r e f o r e , the momentum does not r e t u r n to i t s i n i t i a l Durations 12, and  intensity.  are longer  i n measures 13-16  than i n measures 1-  a t t a c k s are more widely spaced. Three p i t c h c l a s s e s  are d i s t r i b u t e d  i n two  span t h a t separates the widest  r e g i s t e r s — o c t a v e 5 and  these two  levels  7.  The  (1-25) i s l a r g e r than  u n f i l l e d space i n measures 8-12  module i s at once higher and  octave  (1-13);  thus,  the  l e s s dense. In measures 16-20,  s u s t a i n e d , l e g a t o d u r a t i o n s are p o s i t i o n e d i n the uppermost of these two  registers.  As the rhythm of VM  I d e c e l e r a t e s i n measures 13-20, i t  i n c r e a s i n g l y resembles the p a t t e r n of PM  I; t h a t i s , i t s  d u r a t i o n s are longer and more u n i f o r m l y spaced, and measure 20, s h o r t p i z z i c a t o chords t h a t are i s o l a t e d lengthy r e s t s p r o j e c t s t a s i s .  after by  -  - 108  Although the energy of the f i r s t d i s s i p a t e s i n measures 13-20 to t h a t of the piano, VM  the  12 measures of VM  -  I  as i t assumes a p r o f i l e c l o s e r  interlocked patterns  of PM  II  and  I i n measures 33-49 (Example 2) ensure the continuance of  i t s rhythm stream. For example, the p a t t e r n d i s p l a y s three p a i r s of s h o r t d u r a t i o n s  i n measures 33-35  t h a t are spaced  by  i n the v i o l i n  that  e i g h t h r e s t s ( i n the t h i r d p a i r , a chord  a r t i c u l a t e s three d i s c r e t e r e g i s t e r s precedes a high C7 i n the p i a n o ) . T h i s i s l i k e the f i r s t  two  measures of VM  I and  measures 10-11, where p a i r s of s i x t e e n t h s are followed e i g h t h r e s t s ; i n f a c t , most a t t a c k s  i n measures 1-12  i s o l a t e d by e i g h t h r e s t s . In measures 8 and  by  are  10-12, the  violin  d i s t r i b u t e s four v e r t i c a l p i t c h e s i n the three  general  s p a t i a l areas t h a t are demarcated by the chord  i n measure  but each v i o l i n t e t r a c h o r d means of two  consecutive  precedes the higher two  one.  i n measures 10-12  i s stated  by  dyads such t h a t the lower dyad The  s p a t i a l r e l a t i o n s h i p of these  dyads i s echoed i n measure 35 by the t e t r a c h o r d  subsequent high C7  35,  i n measure 35, and  and  by the r a p i d  a r p e g g i a t i o n of the p i t c h e s of t h a t chord  from lowest to  highest. Each of the two  s u c c e s s i v e statements of the measure 33-35  p a t t e r n i n measures 39-46 i s modified impetus of VM set  i n a way  t h a t slows the  I. In measures 39-42, each p a i r of a t t a c k s i s  o f f by quarter  r e s t s r a t h e r than by e i g h t h s . In measures  41-42, a low c l u s t e r e d t r i c h o r d precedes the  mid-register  - 109 -  v i o l i n c h o r d — t h e i r combined span (1-59) i s wider and lower than t h a t of the corresponding p a i r of a t t a c k s i n measure 35 (1-45). Measures 43-48 c o n t a i n three p a i r e d C7's as i n measure 33, but here the notes are d i v i d e d by a b r i e f In  rest.  measure 46, the p i t c h e s of the v i o l i n chord are arranged  as c o n s e c u t i v e dyads: the d u r a t i o n s of the dyads and the r e s t that d i v i d e s them i s twice that of the preceding C7's. Thus, the p a t t e r n of VM I d i s s i p a t e s i n measures 13-20 but the momentum i t generated  i n measures 1-12 i s extended by  the p a t t e r n of PM I I . In VM II and module I I I , the l a s t few d u r a t i o n s i n the rhythm stream are passed to  the v i o l i n In  from the piano back  ( r e f e r t o Examples 11 and 9 ) .  VM II and module I I I the momentum of VM I ceases.  Three  m i d - l e v e l s u s t a i n e d d u r a t i o n s i n VM II g i v e way t o a s i n g l e , very long A 6. I t i s supported by a repeated s u s t a i n e d chord te  i n the piano t h a t occupies a r e l a t i v e l y high s p a t i a l area and t h e r e f o r e has l i t t l e weight. PM IV c o n t a i n s a few s h o r t notes and p a i r s of notes t h a t remind  us of the rhythm of VM I, but  these a r e i s o l a t e d events that do not r e v i v e i t s momentum. Let  us t u r n t o the s t r o n g e r , more enduring rhythm stream  that begins with a repeated two bar p a t t e r n i n the piano i n measures 1-1.8. (The f i r s t isolated  occurrence of t h i s p a t t e r n i s  i n example 36). Each p a i r of measures c o n t a i n s two  chords, the p i t c h e s of which are disposed as t r i c h o r d s  that  together r e s i d e i n seven octaves as shown i n Example 52. The first  chord i n each p a i r i n h a b i t s the upper and lower  strata  - 110 -  EXAMPLE 52  •  T_ Span  and  / 1-70  •  =  1-32  the subsequent chord  1-17  occupies  1-11  1-3  four of the c e n t r a l l a y e r s .  Because the d u r a t i o n of the upper t r i c h o r d i n the second chord  of each p a i r i s s u s t a i n e d , the span of the p a t t e r n  c o n s t r i c t s from 1-70 t o 1-32, then t o 1-11. At the same time, the d u r a t i o n a l r e l a t i o n s h i p between the two chords ( s h o r t long) c r e a t e s c l o s u r e . In t h i s way, a wide span compresses t o a narrow one to c r e a t e p r o p u l s i o n t h a t d i s s i p a t e s somewhat d u r i n g the l e n g t h of the long t r i c h o r d i n each p a i r , but the pattern  i s repeated  s e v e r a l times and t h e r e f o r e generates  enduring momentum. Measures 19-27 c o n t a i n s u s t a i n e d r e i t e r a t i o n s of the second chord  of the p a t t e r n — t h e  i n t e n s i t y t h e r e f o r e eases somewhat.  - Ill -  (Measures  23-27 are shown i n Example 13). A f t e r a measure of  r e s t , PM I culminates with two chords w i d e l y separated i n time, i n measures 29 and 31 (Example 2). As we have seen, the rhythm of PM II subsequently i n t e r a c t s with t h a t of VM I and prolongs the l a t t e r module's rhythm stream thereby i n t e r r u p t i n g the rhythm of PM I; however, two chords i n PM II e x h i b i t c h a r a c t e r i s t i c f e a t u r e s of the second chord of each two-bar p a t t e r n i n PM I . In measures 36-37, a r e l a t i v e l y s h o r t , r e g i s t r a l l y d i s p e r s e d chord i n the piano i s combined with a s u s t a i n e d v i o l i n p i t c h the span of i t s upper  (D5) t h a t i s contained w i t h i n  t r i c h o r d . In measures 47-48, a  s i m i l a r l y d i s p o s e d piano chord repeats the d u r a t i o n a l p a t t e r n of the f i r s t but more c l o s e l y r e f l e c t s the formation of PM I i n t h a t i t s upper t r i c h o r d  i s s u s t a i n e d . These two chords  connect PM I t o PM II and t h e r e f o r e extend not o n l y i t s rhythm but the deeper momentum that i t generated. A f t e r VM II and module I I I , the p a t t e r n of VM I I I (measures 58-87) extends some aspects of PM I . P a i r s of v i o l i n dyads i n measures 58-62 are separated by complete  measures of r e s t ,  and a f t e r measure 63 they a r e more w i d e l y separated i n time. In c o n t r a s t t o PM I however, the span of each p a i r widens from 1-6 t o 1-11 and thereby g r a d u a l l y reduces the energy of the u n d e r l y i n g momentum. In measures 58-64 (Example 6) i s o l a t e d s i x t e e n t h notes i n the piano r e c a l l the rhythm of VM I (measures 29-48) but the d i s p e r s i o n of these p i t c h e s i n chromatic dyads a t extreme  - 112  high and  low r e g i s t e r s not only extends the  formation the  of the  first,  Example The  initial  chord of PM  i t anticipates VI/l--see  19).  p a t t e r n of PM  IV i n measures 56-73 (Example 6) e x h i b i t s spatial  configuration  d u r a t i o n a l r e l a t i o n s h i p of each p a i r of chords i n PM  are echoed i n the p a i r s of a t t a c k s and  registral  s t a t i c module of s e c t i o n B (module  elements of both rhythm streams. The and  I, but  72  -  i n measures 65,  68,  i n that the span of each p a i r c o n t r a c t s , and  second attack  i s longer  than the f i r s t .  each p a i r of a t t a c k s d e r i v e s measures 1, 2, and  10-11  The  I 70,  each  c l o s e spacing  from the p a i r e d s i x t e e n t h s  i n VM  of  in  I, but these do not r e v i v e  the  momentum of that module; r a t h e r they decorate the s u r f a c e  of  an otherwise l a r g e l y s t a t i c passage that extends the rhythm of PM  I.  In measures 84-89 elements from three modules are intermingled  (Example 14). Each of the chords i n the  r e f l e c t s the formation  of the second chord of each p a i r i n PM  I i n that each forms two longer  than the  values  t r i c h o r d s , the higher  lower. But  pitch; therefore,  of which l a s t s  each chord i s u n i t e d with a v i o l i n  i t s instrumentation  and  exact  durational  s p e c i f i c a l l y r e i t e r a t e the f i n a l chords of VM  I i n measures 26-27 and  piano  I and  measures 29-31. However, i n these  PM the  lower t r i c h o r d i s s u s t a i n e d . Module V e x h i b i t s a p a t t e r n of long, repeated chords that is derived  from measures 19-26  i n PM  I ( r e f e r to Example  12).  - 113 -  In module V, s p a t i a l expansions i n measures 102 and 114,  and  i n c r e a s e d d e n s i t y i n measure 102, add weight t o the module that decreases the momentum. S e v e r a l f a c t o r s r e i n f o r c e our p e r c e p t i o n that the chords after 16).  measure 114 u n f o l d w i t h i n that wide span  (I-66)(Example  Although they are more d e n s e l y packed than any p r e v i o u s  chords i n the module, they sound  l e s s weighted because  their  lowest p i t c h e s are higher than t h a t of the repeated chord i n measures 102-113, and because  they p r o j e c t some i n s t a b i l i t y  s i n c e no two adjacent chords are the same. G5 and A 6 to  comprise a t w o - t i e r e d r e g i s t r a l c e i l i n g such that each chord a f t e r measure 114  i s suspended  from the lower t i e r . The  trichord  i n measure 114  exposed,  and i t i s d i s t i n c t i v e f o r i t s d e n s i t y and  Furthermore,  i s r e g i s t r a l l y and  low  texturally weight.  i t occupies a d i s c r e t e octave space below the  chords t h a t surround i t ; thus, i t resonates i n our h e a r i n g and so comprises the r e g i s t r a l f l o o r of the passage. N e v e r t h e l e s s , t h e r e i s another s p a t i a l expansion i n the f i n a l measures of the module (Example 53). A repeated piano hexachord the  i n measures 129-133 spans 1-20  p i t c h e s of the two subsequent  from B3 and G5,  and  chords i n measures 136  and  138 are wider, more bottom-heavy v e r t i c a l s spanning between C2 and  1-43  G5.  Although the f i r s t  rhythmic p u l s e d i s s i p a t e s e n t i r e l y  after  measure 139, the s p a t i a l expansion c r e a t e d by the a r r i v a l of the  first  chord of module VI/1 p r o v i d e s f i n a l  closure.  - 114  -  EXAMPLE 53  mm.  129  136  146  4^ module V  module  VI/1  L o c a l l y t h i s chord completes the expansion from 1-20 i n measures 129-138, but more broadly, 1-22  to 1-40  i n measure 102  i n module VI/1. by the  The  span. Thus, the first  1-66  the span widens from  i n measure 114  i s very s h o r t and  at the upper and  initial  l a r g e s c a l e pulse and  patterns  1-75  that i t s  s i g n a l s the  by PM  stasis.  I i n measures 1-27  that are d e r i v e d  end  the beginning of s e c t i o n B  In s e c t i o n A then, the momentum t h a t i s c r e a t e d and  then  lower extremes of i t s  chord of module VI/1  p r e c i s e l y because i t p r o j e c t s  measures 1-12  1-43  c l o s u r e t h a t i t generates i s strengthened  f a c t that i t s d u r a t i o n  p i t c h e s are disposed  of the  and  to  from one  by VM  i s extended  module or the  I in by  other.  Modules that d i s p l a y f e a t u r e s of both are more h e a v i l y disposed  toward one  source or the other. E s s e n t i a l l y ,  the  - 115  rhythm of PM  II i n measures 33-48 extends  the rhythms of VM Because PM  I I I , PM  that of VM  IV, and module V extend PM  II more s t r o n g l y r e f l e c t s  two modules t h a t f o l l o w — V M  I, and I.  the rhythm of VM  II and module I I I — s o u n d  -  I, the like a  continuance of that rhythm stream and t h e r e f o r e r e p r e s e n t i t s endpoint. Thus, although the rhythm stream of VM t r a n s f e r r e d to the piano i n PM  I is  I I , i n i t s f i n a l measures i t  i s r e t u r n e d to the v i o l i n . The p a t t e r n of PM n e v e r t h e l e s s , two prolong i t s deeper derive their  II i n t e r r u p t s the p a t t e r n of PM I;  i n t e r m i t t e n t chords are s u f f i c i e n t impulse. Conversely, VM  rhythm from PM  I I I and PM  I but e x h i b i t elements  to IV  of VM  I;  however, these do not r e v i v e the momentum of i t s rhythm stream.  SECTION B In s e c t i o n A, l a r g e - s c a l e rhythmic p u l s e was the opening measures of VM stasis  I and PM  i s c r e a t e d by module VI/1  generated i n  I — l i k e w i s e , a context of  i n the f i r s t measures of  s e c t i o n B (see Example 19). P r i o r to module X/2,  surface  processes of d e c e l e r a t i o n augment the u n d e r l y i n g calm. For example, i n the opening subsequent  f i v e measures of module VI/1,  each  measure i s longer than the one t h a t precedes i t .  Although these f i v e measure lengths are then r e o r d e r e d , the module n e v e r t h e l e s s d e c e l e r a t e s i n t h a t measures 153 and are longer than measures 151 and  152,  and measure 155 i s  154  - 116  longer than each of the previous In s e c t i o n A we  saw  -  four.  t h a t r a p i d i s o l a t e d a t t a c k s i n PM  momentarily a g i t a t e d the s u r f a c e rhythm but d i d not  IV  affect  the u n d e r l y i n g momentum. S i m i l a r l y , r a p i d p a i r s of a t t a c k s i n module VIII/1 a way  (Example 20, measures 158-161) are  t h a t preserves  the u n d e r l y i n g calm. Three c l o s e l y  spaced a t t a c k s a r t i c u l a t e the p i t c h e s of two 162  chords.  c o n t a i n s a d i s c r e t e s e t of a t t a c k s i n the  however, each s e t i s d i s t a n c e d s u s t a i n e d d u r a t i o n s , and chords i n module VII Measure lengths  isolated in  Measure  violin;  from i t s neighbour  by  the passage i s framed by the  (measures 156-157 and  long  163).  i n module X / l (Example 25, measures  174-191) are i n i t i a l l y 5/32,  7/32,  and  9/32  5/16,  7/16,  and  9/16.  demarcated by meter s i g n a t u r e s of  but these are subsequently The  doubled to  c o n t r a s t e d r e g i s t e r s of each  passage c o n t r i b u t e to the module's d e c e l e r a t i o n i n t h a t high C8's register  g i v e way  i n measure 183  to more weighted  to  (Example 26, measures 210-218) echoes the  of d u r a t i o n a l expansion demonstrated by VM  i n the f i r s t  first  7 and  more widely  f o u r . Furthermore, the module  p r o j e c t s l i t t l e weight because i t s p i t c h e s are i n octaves  process  I such that  i n i t s l a s t 4 measures are longer and  spaced than those  disposed  mid-  A 3's.  Module XI  durations  very  8. The  seven measures of VM I I ' ' .  process  linearly  i s extended to the  - 117 -  In c o n t r a s t to the processes of d e c e l e r a t i o n d i s p l a y e d i n the f i r s t h a l f of s e c t i o n B, s u r f a c e a c c e l e r a t i o n i n the second h a l f prepares us f o r the a r r i v a l of the second  large-  s c a l e rhythmic p u l s e . We have seen t h a t the d u r a t i o n s of module XI and VM I I  1 1  expand; however, the r e l a t i v e spans of  these modules r e f l e c t the process of r e g i s t r a l compression i n PM I that was c r u c i a l t o the formation of the rhythmic pulse i n s e c t i o n A (Example  52). R e c a l l that i n PM I, a span t h a t  extended from octave 1 to octave 7 was compressed  into a  narrow space w i t h i n octave 6; thus, the d i s t a n c e t h a t the low t r i c h o r d rose was g r e a t e r than the d i s t a n c e the upper trichord f e l l .  The much narrower span of module XI (1-17)  l i k e w i s e compresses resultant profile  to a space w i t h i n octave 6 (1-3) but the  i s the i n v e r s e of the shape of PM I i n t h a t  the upper r e g i s t e r f a l l s Module X/2 (Example  f a r t h e r than the lower one r i s e s .  25, measures 228-236) demonstrates a  decrementing of measure length i n that each s u c c e s s i v e measure i s s h o r t e r than the one t h a t precedes i t . f o l l o w i n g module IX/2 (Example  In the  24, measures 237-246) a s l i g h t  momentum i s c r e a t e d by the r e g u l a r s p a c i n g of i t s d u r a t i o n s , the r e l a t i v e l y narrow spans of i t s dyads, and by i t s r i s i n g contour. These f e a t u r e s do not produce deeper momentum because the d u r a t i o n s a r e slow moving and detached, and the module r e s i d e s i n r e l a t i v e l y high octave s p a c e s — o c t a v e s 4, 5, and 6. In f a c t , t h i s rhythm a n t i c i p a t e s that of module XVI and the coda a t the c u l m i n a t i o n of the second  large-scale  - 118 -  pulse. By c o n t r a s t , the next module, VIII/2, d e n s e l y packed septachords  begins  with  repeated,  t h a t a r e a l t e r n a t e l y spaced by  e i g h t h and quarter r e s t s (Example 24). In measures 255-260 however ( r e f e r t o Example 16), the p a t t e r n i s changed so t h a t the lower t r i c h o r d  i n the piano  and the s i n g l e p i t c h i n the  v i o l i n a r e m e t r i c a l l y d i s p l a c e d , and B 3 i n the v i o l i n to  to  rises  D 7 thereby widening the span from 1-15 t o 1-36. At f i r s t to  glance,  these a l t e r a t i o n s seem t o d i f f u s e the impact of the  weighted p u l s a t i o n c r e a t e d by the chords i n measures 246-254; however, they i n s t e a d c r e a t e a p a t t e r n t h a t d e r i v e s from VM I (See example 54). Furthermore, the d i s p a r a t e r e g i s t e r s of the piano 262)  hexachord and the high D 7 i n the v i o l i n to  (measures 255-  echo the s p a t i a l r e l a t i o n s h i p between the low t r i c h o r d  t h a t begins  each p a i r of chords i n PM I and the subsequent  s u s t a i n e d upper t r i c h o r d  i n the second chord  of t h a t p a t t e r n .  Example 54 i s o l a t e s r e g i s t e r changes and attack p a t t e r n s i n VM I , PM I , and module VIII/2. The rhythm of the f i r s t  three  p i t c h e s i n VM I i s r e i t e r a t e d by the d i s p l a c e d a t t a c k s i n module VIII/2.  In VM I , the f i r s t and t h i r d attack a r e  emphasized by v i r t u e of t h e i r c l o s e alignment t o the f i r s t two  chords i n PM I . Thus, module VIII/2 i n c o r p o r a t e s a  v a r i a n t of the d i s t i n c t i v e rhythm of the f i r s t  three  pitches  of VM I and of the r e g i s t r a l and d u r a t i o n a l r e l a t i o n s h i p of the two chords t h a t form the i n i t i a l p a t t e r n of PM I. Thus, a l t e r a t i o n s t o the p a t t e r n of module VIII/2 do not  EXAMPLE  54  T —J —*  VIII/2  J* 5  it  m -4  1  x 7f  - 120 -  d i f f u s e the impetus of measures 247-254; r a t h e r , they augment i t by i n c o r p o r a t i n g d i s t i n c t i v e aspects of PM I and VM I that contributed  to the formation  of the f i r s t  large scale  rhythmic p u l s e . In t h i s way, the energy of the p a t t e r n of module VIII/2 i n c r e a s e s as i t progresses and thereby threatens not low,  the u n d e r l y i n g  s t a s i s ; however, these f e a t u r e s are  extended to l a s t 3 measures of the module.  In f a c t , the  exposed CI i n measure 263 adds weight to i t and widens  i t s span, and t h e r e f o r e helps it  4  to d i s p e r s e  the momentum that  created. In module VI/2 (Example 19, measures 265-281) we r e t u r n t o  a s t a t i c pattern; s t i l l ,  measure lengths  repeatedly  decrease  by two beats i n measures 265-272, from 19 to 17 to 15 e t c . In t h i s way, the rhythmic p a t t e r n a c c e l e r a t e s a t twice the r a t e of the analogous p a t t e r n  i n module X/2. Thus, modules t h a t  are p o s i t i o n e d nearer to s e c t i o n A* and t h e r e f o r e to the second rhythmic p u l s e , a c c e l e r a t e more i n t e n s e l y than those nearer to the f i r s t h a l f of s e c t i o n B. S e v e r a l aspects of module XII (Example 30, measures 282-290) that prepare us f o r the a r r i v a l of module XIII been d i s c u s s e d  i n chapter 2.  c l a s s e s are disposed  s  have  In measures 282-286, i t s p i t c h  among three widely spaced r e g i s t e r s , but  i n the three measures t h a t f o l l o w , these converge a t midl e v e l and t h e r e f o r e r e c a l l the s p a t i a l compression i n the i n i t i a l measures of PM I. At the same time, the v e r t i c a l l y d i s p l a c e d dyads i n measures 282-286  inhabit discrete linear  - 121  -  planes that e x h i b i t d i f f e r e n c e s of i n s t r u m e n t a t i o n , p i t c h c l a s s content and timbre. Although each of measures 282-286 c o n t a i n two d i s c r e t e a t t a c k s , they are d i s t r i b u t e d among the s t r a t a so t h a t each l e v e l c o n t a i n s one a t t a c k i n each measure. When the s p a t i a l  l e v e l s converge  i n the  following  three measures, the a t t a c k frequency t h e r e f o r e seems t o i n c r e a s e . In t h i s way,  module XII u t i l i z e s aspects of VM I  and PM I t o generate an i n t e n s i t y t h a t prepares us f o r the r e g i s t r a l l y focused, a g i t a t e d rhythm of module X I I I . S e c t i o n B as a whole p r o j e c t s a context of rhythmic  stasis  but i t s s u r f a c e rhythm p e r i o d i c a l l y d e c e l e r a t e s p r i o r to module X/2.  Beginning i n modules XI and VM  I I ' , processes of 1  a c c e l e r a t i o n are more i n t e n s e i n modules that are c l o s e r to the beginning of the second  l a r g e s c a l e rhythmic p u l s e ,  e s p e c i a l l y modules VIII/2 and XII. Processes of d e c e l e r a t i o n and a c c e l e r a t i o n o v e r l a p i n module XI and VM each module demonstrates  I I ' ' such t h a t  d u r a t i o n a l expansion while a broader  process of r e g i s t r a l compression  i n c o r p o r a t e s both of t h e i r  spans. SECTION A' We have seen t h a t the rhythmic pulse i n s e c t i o n A comprised  of two simultaneous, c o n t r a s t i n g rhythm  was  streams  t h a t are d i v i d e d between the piano and v i o l i n . L i k e w i s e , at the beginning of A', module XIII d i s p l a y s two rhythms but they share the same p i t c h c l a s s e s ,  discrete registral  - 122 -  space and some d u r a t i o n s  thereby forming a s i n g l e stream that  i s analogous t o t h a t generated by VM I . Each of module XIII and VM I has an ordered w i t h i n which s u b t l e v a r i a n c e  structure  generates i r r e g u l a r i t y (see  Example 33). VM I i s comprised of a l t e r n a t i n g s e t s of q u i n t u p l e t eighths attack  and s i x t e e n t h t r i p l e t s ,  p a t t e r n of the t r i p l e t s ,  subdivided  but changes i n the durations  etc.,  obscure t h e i r r e g u l a r i t y . The i n i t i a l p a t t e r n of module XIII i s comprised of four d i s c r e t e orderings sixteenth durations one  of q u i n t u p l e t  ( r e f e r t o Example 3) each of which  measure. In the piano, each measure c o n t a i n s  attack  fills  a single  that f a l l s on one of four beats but does not c o i n c i d e  with the q u i n t u p l e t a t t a c k s  i n the v i o l i n . The r e s u l t a n t  i r r e g u l a r i t y a r i s e s from the f a c t t h a t no two orderings  consecutive  i n the v i o l i n are the same and that o n l y two  consecutive  piano a t t a c k s are l o c a t e d on the same beat. Thus,  each module d i s p l a y s u n d e r l y i n g  order  but p r o j e c t s  irregularity. R e c a l l t h a t the momentum of VM I began t o decrease when the r e g i s t e r span expanded from 1-3 t o 1-15 i n measures 7 and 8. Likewise,  the momentum of module XIII begins t o d e c e l e r a t e i n  measure 299 when i t s span widens from 1-14 to 1-26. In measures 299-305, a g l i s s a n d o t h a t u n i t e s each p a i r of c h r o m a t i c a l l y r e l a t e d dyads c r e a t e s the e f f e c t of a s i n g l e , " b l u r r y " dyad. In t h i s way, the p e r c u s s i v e  c l a r i t y of the  p a t t e r n that was brought about by the p i z z i c a t o a r t i c u l a t i o n s  - 123  i n measures 291-298 and  t h e r e f o r e h i g h l i g h t e d the  i r r e g u l a r i t y of i t s a t t a c k s , i s d i m i n i s h e d . 325,  -  In measures  306-  each s u s t a i n e d dyad r e i t e r a t e s , or i s d e r i v e d from,  one  or the other of the u n i t e d dyads. The  p a t t e r n of measure 299  each of measures 301-304 and measure 305.  The  i n the v i o l i n  i s repeated  in  a v a r i a n t of t h i s i s extended to  r e g u l a r i t y of the passage r e l a x e s  the  i n t e n s i t y of the p r o p u l s i o n i n a manner t h a t i s analogous to measures 19-27  i n which a s i n g l e repeated  the p a t t e r n of PM 316  and  I. T h i s process  chord  "stabilized"  i s echoed i n measures  i n measures 326-329 i n which three of four  a t t a c k s are e q u a l l y spaced, and  both piano a t t a c k s  313-  violin are  a l i g n e d with the l a s t beat of a measure.® The  pace of the rhythm d e c e l e r a t e s a f t e r each s t a b l e  passage. In measures 306-316, the p a t t e r n of the v i o l i n i s d e r i v e d from the concurrent  p a t t e r n of the piano  each measure c o n t a i n s a s i n g l e a t t a c k , although  in that some d u r a t i o n s  i n the v i o l i n are s u s t a i n e d . In measures 317-325, most v i o l i n d u r a t i o n s are s u s t a i n e d ; then, II '' 1  a f t e r measures 326-329, VM  a r t i c u l a t e s a s u s t a i n e d , l e g a t o l i n e , and  measures, the p a t t e r n of PM Although VM disposition contour  i n the same  XIV p r o j e c t s s t a s i s .  I I ' ' ' r e s i d e s i n a very high r e g i s t e r , i t s  w i t h i n a narrow span demonstrates a  that d i r e c t s  i t s forward  l i n e are i r r e g u l a r l y s p a c e d — i n  motion. The  rising  a t t a c k s of  the  f a c t , the rhythms of some  measures are d e r i v e d from rhythms i n the v i o l i n  i n module  - 124 -  XIII  (Example 5 5 ) — b u t  i t s slow pace ensures that i t does not  p r o j e c t the a g i t a t i o n of the e a r l i e r  module.  EXAMPLE 55  293  291  5"  sr i  s 1  i  s  , i  ftl  u l ew XIII modu* ** ^  8  i  294  ,  , c 5  The  l i n e a r i t y of VM  I I ' " i s c o n t r a s t e d with the v e r t i c a l ,  s t a t i c p a t t e r n of PM XIV  (Example 33). Together however,  these modules encompass a v e r y wide span that g r a d u a l l y widens as VM  II  ,  ,  ,  r i s e s . Although the p a t t e r n of VM I I '  prolongs the momentum of module X I I I , the s p a t i a l i t c r e a t e s and the r e l a t i v e l y  expansion  low, weighted chords i n PM  XIV  c o n t r i b u t e to i t s d e c e l e r a t i o n . In measures 339-347 (see Example 1), module XV extends the rhythm, and t h e r e f o r e the s t a s i s , c o n s t i t u e n t chords (measures  of PM XIV although i t s  339 and 341) are v e r y s h o r t , and  they occupy a wider, higher s p a t i a l  a r e a . The h e a v i e r chords  i n measures 344-346 a n t i c i p a t e module XVI as they extend the rhythm of module XV.  Similarly,  irregularly  spaced D 5's i n to  - 125 -  the v i o l i n extend the rhythm of VM I I ' 1  1  but t h e i r  durations  more c l o s e l y p r e d i c t those of module XVI. Furthermore, a n t i c i p a t e the f i r s t we p e r c e i v e  they  v i o l i n p i t c h of t h a t module; t h e r e f o r e ,  them t o be l i n e a r l y d i r e c t e d events.  Example 56 compares the spans of VM I I ' ' ' and PM XIV, and module XV. We have seen t h a t r e g i s t r a l c o n t r a c t i o n s n o r m a l l y generate momentum but the f a c t o r s i n the passage d i m i n i s h the s t r e n g t h  of the pulse  offset this  that  effect.  EXAMPLE 56  VM II ' ' ' PM XIV  I  In module XVI (measures  XV  348-368—refer  t o Example 40)) the  weight of the c h r o m a t i c a l l y descending streams of chords i n c r e a s e s as the module proceeds; t h e r e f o r e , the u n d e r l y i n g momentum g r a d u a l l y d e c e l e r a t e s . r e g i s t r a l l y dispersed heavier  hexachords  In measures 354-355,  t r i c h o r d s are transformed t o denser,  t h a t extend the lower l i m i t of i t s span.  - 126  Although the d u r a t i o n s of module XVI are r e l a t i v e l y  -  long,  they e x h i b i t a r e g u l a r s p a c i n g t h a t perpetuates the u n d e r l y i n g momentum—in the subsequent  module (VM  II  , , , ,  )  these d u r a t i o n s are more w i d e l y spaced and t h e r e f o r e reduce the s t r e n g t h of the In s e c t i o n A, VM  impulse. II and module I I I were the end p o i n t of  the rhythm stream that began i n VM  I. VM  and the Coda  f u n c t i o n a n a l o g o u s l y at the end of the second p u l s e ; however, the s t a t i c e f f e c t of VM  of VM  I I " " i s more pronounced than that  II because i t s d u r a t i o n s are more w i d e l y spaced,  and  i t s pattern i s longer. The p a t t e r n of the coda  (measures 380-388) e x h i b i t s  processes of d u r a t i o n a l and r e g i s t r a l  expansion. The  first  three s e t s of descending hexachords i n the piano extends d u r a t i o n of VM  of  the  but the f o l l o w i n g s e t of chords i s h a l f  as long as the f i r s t  s e t . In the t h i r d s e t , d u r a t i o n s are  more than double those of the f i r s t s e t ; thus, the s l i g h t l y f a s t e r rhythm of the second  s e t c o n t r a s t s with and t h e r e f o r e  accentuates the very slow speed of the t h i r d s e t . Because they are repeated, these s e t s of chords d i s p l a y a s t a t i c r e g i s t r a l p r o f i l e a g a i n s t which three p i t c h e s i n the v i o l i n — C 4 , D5,  and E 7 — a r t i c u l a t e a s t e e p l y r i s i n g t o  contour.  C4 and D5 are contained w i t h i n the span of the concurrent piano chords; thus, the hexachords and the v i o l i n l i n e may understood  to occupy d i s c r e t e s p a t i a l  planes such that  overlaps the o t h e r . N e v e r t h e l e s s , the descending  chords  one  be  - 127  i n t e r a c t with the concurrent widened i n the  l i n e such t h a t the span i s  l a s t measure of the p i e c e . C l o s u r e  is  t h e r e f o r e produced by processes of d u r a t i o n a l and expansion, and We  by the  registral  f a c t that each s e t of chords descends.  have seen that the two  l a r g e - s c a l e pulses  a r t i c u l a t e 3-  p a r t form because they a l i g n with s e c t i o n s A and palindromic  -  A'.  The  s t r u c t u r e of s e c t i o n B i s r e f l e c t e d by the  that surface decelerations  fact  i n the f i r s t h a l f transmute t o  a c c e l e r a t i o n s i n the second h a l f - - t h e p i v o t a l c e n t r a l modules XI and  VM  I I ' ' e x h i b i t both  Chapter 2 r e v e a l e d  processes.  that p a l i n d r o m i c  from s e c t i o n B to s e c t i o n s A and  s t r u c t u r e was  A' by VM  radiated  II and i t s  v a r i a n t s . In the domain of rhythm, processes of d e c e l e r a t i o n are extended to s e c t i o n B from s e c t i o n A, and  processes of  a c c e l e r a t i o n , though not extended to s e c t i o n B from s e c t i o n A*,  nevertheless  Surface  help to prepare us f o r i t s a r r i v a l .  continuity i s exhibited  i n s e v e r a l ways; f o r  example, the p i t c h c l a s s e s of most chords d e s c r i b e  a  chromatic c l u s t e r that i s normally disposed  i n t r i c h o r d s that  span about an octave. Furthermore, VM  PM  I and  I  together  demonstrate v i r t u a l l y a l l subsequent octave spaces i n the p i e c e . The  highest  48);  nearly a l l r e g i s t r a l  thus,  point  (C8)  appears i n PM  II (measures  33-  l e v e l s are prepared by these  three source modules. Rhythmic c o n t i n u i t y i s generated by the aspects of PM VM  I t h a t are extended to a l l subsequent modules. F i g u r e  I and 3  - 128  shows t h a t a l l modules d e r i v e t h e i r rhythm p a t t e r n e i t h e r from VM I or PM I, or from both. In f a c t , these connections l a r g e l y o b t a i n f o r other f a c t o r s i n each p a t t e r n  except  p i t c h . Thus, on the s u r f a c e , the e n t i r e p i e c e may be seen t be a p r o j e c t i o n of VM I and PM I.  FIGURE 3  MODULE  RHYTHM SOURCE VM I  PM II VM II III VM I I I PM IV V VM II ' VI/1 VII VIII/1 IX/1 X/l XI VM I I " X/2 IX/2 VIII/2 VI/2 XII XIII PM XIV VM I I • ' ' XV XVI/Coda VM I I ' ' ' •  X X X X X X X X X X X X X X X X X X X X  PM X X X X X X X  X  X X  - 129 -  SUMMARY AND CONCLUSIONS In S p r i n g of Chosroes  r  form a r i s e s from the processes t h a t  c r e a t e and u n i f y p a t t e r n s and generate connections between modules. Two p r o c e s s e s — e x t e n s i o n and development—produce l o c a l and l a r g e - s c a l e s t r u c t u r e s . When p i t c h c l a s s e s and rhythms are extended, they generate coherent p a t t e r n s t h a t determine  the i d e n t i t i e s of modules. Connections  between  adjacent modules c r e a t e l o c a l c o n t i n u i t i e s , and l a r g e r  formal  r e l a t i o n s h i p s a r i s e when s t r u c t u r a l f e a t u r e s of modules are extended  t o other, non-contiguous  modules. Three-part  form  a r i s e s when aspects of modules i n s e c t i o n A a r e extended to t h e i r c o u n t e r p a r t s i n s e c t i o n A'. In s e c t i o n B, on the other hand, p a r a l l e l i s m s a r t i c u l a t e p a l i n d r o m i c r e l a t i o n s h i p s . Developmental processes c r e a t e o r g a n i c u n i t y and l i n e a r i t y w i t h i n some modules and connect  the two s e t s of modules t h a t  form l a r g e - s c a l e frameworks—modules VM I and modules XI and XVI; and VM II and i t s v a r i a n t s . Some modules a r e connected t h e i r boundaries  by other processes t h a t make  l e s s t r a n s p a r e n t and t h a t smooth the  t r a n s i t i o n s between modules. The m a t e r i a l s of some modules o v e r l a p (Examples 13 and 14), and i n one case, aspects of a module precede  i t sarrival  (Example 1 ) . On a l a r g e r  scale,  module XII c o n t a i n s elements of the modules that precede and follow i t ;  t h e r e f o r e i t not o n l y f a c i l i t a t e s t h e t r a n s i t i o n  between i t s d i s p a r a t e neighbouring modules VI/2 and X I I I , but  - 130  it  l i n k s s e c t i o n B to s e c t i o n A The  1  well.  s e c t i o n B palindrome, a two-part s t r u c t u r e ,  w i t h i n the  larger, three-part  ABA'  r e l a t i o n s h i p of these s t r u c t u r e s frameworks formed by VM II and  as  I and  i t s v a r i a n t s . The  comprises a t h r e e - p a r t  p l a n . The  resides  nested  i s echoed by the  modules XI and  first  -  large-scale  XVI,  and  by  VM  of these s e t s of modules  s t r u c t u r e t h a t extends from  beginning of the p i e c e to the end.  VM  II and  the  i t s variants, a  p a l i n d r o m i c a l l y r e l a t e d s e t , l i e w i t h i n these temporal extremes. The  c e n t r a l module of each s e t  b i s e c t s a palindrome, and s t r u c t u r a l focus of the  (XI and  VM  II'')  together these modules form the piece.  Organicism i s demonstrated by l o c a l and  large-scale  developmental p r o c e s s e s . Some l o c a l processes are  projected  to modules t h a t a r t i c u l a t e l a r g e - s c a l e r e l a t i o n s h i p s . In VM  I  f o r example, a process of rhythmic development proceeds through three  stages (Example 8). The  are p r o j e c t e d  to modules XI and  expanded and  developed  p i t c h content of VM  XVI  (Example 43).  second and  third  i n which rhythms are In the p i t c h domain, the  I i s expanded i n module XI by  A* ,  classes increases  to twelve. Thus, the process t h a t binds  I to modules XI and  XVI  i n module XVI,  the  a d d i t i o n of G and  3  and  stages  derives  the number of p i t c h  from a process w i t h i n VM  Organicism i s a l s o produced by the t r a n s f o r m a t i o n s rhythmic f e a t u r e s  of VM  I and  PM  I that d e c e l e r a t e  of each  l a r g e - s c a l e rhythmic p u l s e . Although s e c t i o n B p r o j e c t s  VM I.  the  - 131 -  s t a s i s , organic  processes a t the musical  surface  create  s u b t l e e f f e c t s of d e c e l e r a t i o n and a c c e l e r a t i o n : these processes a r e d e r i v e d  from the preceding  local  l a r g e - s c a l e ones.  Since a l l the rhythms of the p i e c e a r e t o some extent  like  those of VM I and PM I, they c o n t r i b u t e  to i t s f l a t  Other important f e a t u r e s  i n c l u d e slow tempi,  i n t h i s regard  surface.  s o f t dynamics and muted a t t a c k s . Furthermore, most chords are made with chromatic p i t c h c l a s s s e t s t h a t are u s u a l l y dispersed  i n t r i c h o r d s that combine a dyad and a s i n g l e note  i n adjacent  octaves.  Thus, a t most l e v e l s , form i n Spring of Chosroes i s generated by organic  and i n o r g a n i c processes.  r i c h a r r a y of h o r i z o n t a l connections,  Despite  the p a t t e r n s  this  of many  modules p r o j e c t a sense of randomness and s t a s i s . In what sense, then, can the music be considered  t o be " v e r t i c a l " and  "disconnected?" R e c a l l t h a t a passage i n S t r i n g Quartet e x h i b i t e d ordered rhythms t h a t , when juxtaposed, c r e a t e d  four  the e f f e c t of  randomness (see pages 14-15). Module XIII demonstrates t h i s p r i n c i p l e i n that four ordered rhythms i n the v i o l i n a r e combined with the c o n t r a s t i n g rhythm of the piano. In VM I , juxtaposed p a t t e r n s durations  incorporate  p i t c h formations.  The  i n measures 1-12 are subsumed under a l t e r n a t i n g  s e t s of q u i n t u p l e t eighths  and t r i p l e t s i x t e e n t h s . In  measures 1-7, the p i t c h e s p a r t i t i o n demonstrate palindromic  i n t o three segments that  a s s o c i a t i o n s and i n v e r s i o n a l  - 132  symmetry. patterns  x  In the f i r s t  and  second segments, d u r a t i o n a l  a l i g n with these s t r u c t u r e s but they do not a l i g n  with the r e g u l a r t r i p l e t and the two  -  disparate patterns  q u i n t u p l e t groupings; thus, when  c o i n c i d e , they c r e a t e a sense of  disorder. Most modules demonstrate d u r a t i o n a l asymmetry and Each of the two  variety.  modules that have r e g u l a r rhythms--IX/2 and  X V I — c o n t a i n a r e l a t i v e l y l a r g e s e t of p i t c h c l a s s e s t h a t are presented g r a d u a l l y i n v a r i o u s combinations. Module contains  IX/2  nine p i t c h c l a s s e s that are d i s t r i b u t e d among nine  dyads as shown below. E C# * b  D A *  to  A# B *  C# E  to  D A  b  G# A *  E A# *  C D *  to  A E  b  Dyads t h a t are marked with an a s t e r i s k c o n t a i n newly s t a t e d p i t c h m a t e r i a l . Thus, s i n c e we dyads, and  hear new  pitches  i n most  most p a i r i n g s are unique, the p i t c h content of  the  module, normally the l e a s t f l u c t u a n t element, sounds "unfixed." In module XVI, introduce  descending streams of chords g r a d u a l l y  a l l twelve p i t c h c l a s s e s : the  c o n t a i n p r e v i o u s l y unstated the module c o n t a i n s  first  ten  p i t c h m a t e r i a l , and  verticals  each chord i n  a unique combination of p i t c h c l a s s e s .  Thus, the v a r i o u s p i t c h e s and  combinations of p i t c h e s i n  these modules c r e a t e a sense of d i s o r d e r r e g u l a r i t y of the rhythm p a t t e r n .  that o f f s e t s the  - 133 -  Asymmetries o b t a i n a t a l l l e v e l s of s t r u c t u r e . For example, s e c t i o n A* c o n t a i n s fewer modules than s e c t i o n A, and t h e r e i s no r e t r o g r a d e of module VII i n the second h a l f of the s e c t i o n B palindrome. P a r a l l e l i s m s t h a t d e f i n e t h r e e - p a r t form a r e r a r e l y l i t e r a l , and the connections they generate u t i l i z e some but not a l l aspects of modules. The l a r g e - s c a l e r e g i s t r a l arches a r e l i k e w i s e asymmetrical  (Examples  42 and  46) as a r e the s p e c i f i c l e n g t h s of the p a l i n d r o m i c a l l y r e l a t e d modules among VM II and i t s v a r i a n t s  (Example 45). Thus, i n  the same way t h a t modules r e t a i n t h e i r  i d e n t i t i e s when t h e i r  components are v a r i e d , these l a r g e r asymmetries  do not  d e s t r o y the form of the p i e c e . When the elements of a module a r e extended, t h e i r  surface  f e a t u r e s may be v a r i e d , but t h e i r s t r u c t u r a l ones are n o t . By c o n t r a s t , developmental processes generate  linear  r e l a t i o n s h i p s because each developmental s t e p i s d e r i v e d the one that precedes i t and engenders  the one that  from  follows;  thus, developed p a t t e r n s p r o g r e s s . The s t a t i c e f f e c t i n Feldman's music t h e r e f o r e a r i s e s when the components of a module a r e extended but not developed: i n Feldman's words, " I t ' s f r o z e n , a t the same time i t s v i b r a t i n g . " 1, Note 1 ) . Module V demonstrates  (see Chapter  both processes (Example  12). Each of i t s t h r e e segments p r o j e c t s s t a s i s — i n  segments  one and two, chords are repeated without v a r i a t i o n , and i n segment three they " v i b r a t e . " However, each new segment expands the r e g i s t e r of the module and adds t o i t s s e t of  - 134 -  p i t c h c l a s s e s ; t h e r e f o r e , s i n c e these elements are developed, the module progresses.  The i r r e g u l a r s u r f a c e rhythm of most  modules c o n t r i b u t e s t o the s t a t i c e f f e c t ; thus, modules are most s t a t i c when t h e i r elements are most f i x e d and t h e i r s u r f a c e rhythms are i r r e g u l a r . In summary, disconnectedness i s a s u r f a c e e f f e c t generated by juxtaposed,  d i s p a r a t e s t r u c t u r e s and by the v a r i e d  surface  f e a t u r e s of modules. S t a s i s a r i s e s when the s t r u c t u r a l f e a t u r e s of a module a r e extended but not developed. Modules t h a t e x h i b i t developmental processes  are t h e r e f o r e l e s s  s t a t i c than those modules t h a t are merely extended. These s u r f a c e e f f e c t s mask the u n d e r l y i n g order t h a t u n i t e s the piece as a whole. The  a n a l y t i c approach presented  i n t h i s study i s most  s u i t e d t o Peldman's l a t e r works ( a f t e r 1969) because they are h i s most patterned  ones. In these f u l l y notated  no domains a r e indeterminate;  thus, a l l aspects  scores,  of modules  can be examined. Not a l l l a t e p i e c e s are, s t r i c t l y speaking, "modular." "Madame Press contains  Died Last Week a t Ninety"  (1970)  n i n e t y c o n f i g u r a t i o n s of a s i n g l e chord, and  t h e r e f o r e comprises a s i n g l e module. In many e a r l i e r p i e c e s , p a r t i c u l a r l y those from the 1960's, durations  are u n s p e c i f i e d ; and s i n c e the i d e n t i t i e s of  modules are determined by t h e i r p i t c h c l a s s e s and rhythm, the works are not modular i n the s t r i c t sense. Many of these  - 135  pieces are, however, s e c t i o n a l . In F i g u r e saw  t h a t Durations 3  r  1 f o r example,  I I I comprises four "gestures"  demarcated by d i f f e r e n c e s of t e x t u r e , and by d i f f e r e n c e s of p i t c h . However, i f we  that  -  we are  to a l e s s e r degree  generalize  the  d e f i n i t i o n of a module such that the determiners of i t s i d e n t i t y are i t s p i t c h c l a s s e s and (in  t h i s case, t e x t u r e )  A ,  G, and  t o  than rhythm  the p i e c e p a r t i t i o n s somewhat  d i f f e r e n t l y . Consider t h a t the F#,  a domain other  initial  three p i t c h c l a s s e s ,  are extended from gesture 1 through gesture 3  in a r e g i s t r a l l y r i g i d v e r t i c a l pattern that gradually i t s cohesion;  that i n gesture 4 ,  and  texture contains  seven new  previewed i n gestures  2 and  d i s t i n c t i o n s d e l i n e a t e two which embodies gestures gesture 4 . II  Several  intermingle  its  1-3  a contrasting  loses  linear  p i t c h c l a s s e s , f i v e of which are 3. These p i t c h and generalized  texture  modules, the f i r s t  of  while the second c o n s i s t s of  of the c o n s t i t u e n t p i t c h c l a s s e s of module  with those of module I thereby a n t i c i p a t i n g  a r r i v a l . In gesture 3, F i s added to the set of p i t c h  c l a s s e s but  i t i s not  extended to module I I ; thus,  i t may  be  seen to expand the number of p i t c h c l a s s e s i n module I from three to four and chromatic The  to combine with F#,  G,  and  A" to form a  tetrachord.  d e f i n i t i o n of a module may  Chosroes and  Durations.  be f u r t h e r g e n e r a l i z e d .  the domain of p i t c h i s the  primary  determiner of each module's i d e n t i t y . I f t h i s f u n c t i o n i s t r a n s f e r r e d to other domains, a module may  be  In  recognized,  - 136  say, by i t s c o n s t i t u e n t r e g i s t e r s , or by the v a r i o u s it  textures  contains. In S p r i n g of Chosroes, Feldman uses secondary elements,  register  i n p a r t i c u l a r , to a r t i c u l a t e form. In e a r l y works  t h a t do not e x h i b i t f i n d formal  g e n e r a l i z e d modules we  processes  w i t h i n these domains.  may  -  expect to  - 137 -  ENDNOTES INTRODUCTION 1. The f o l l o w i n g q u o t a t i o n s are taken from Morton Essays  f  Feldman  Ed. by Walter Zimmerman, Kerpen: Beginner P r e s s , 1985.  "I'm i n v o l v e d i n s t a s i s . I t ' s f r o z e n , a t the same time i t ' s v i b r a t i n g . " (168) "I work v e r y modularly, I don't work i n a c o n t i n u i t y . "  (166)  "Many years ago I got a l e t t e r from F r e d e r i c k Rzewski; he s a i d , "Was a piece of mine a v a i l a b l e ? " He says, "You know, that canon f o r two p i a n o s . " Canon? Me, w r i t e a canon! Oh yeah, t h a t f r e e d u r a t i o n a l p i e c e . . . i t ' s a CANONl T e l l you the t r u t h , i f I thought i t was a canon...I would have committed s u i c i d e . " (108) " I t [ e a r l y 20th c e n t u r y a t o n a l i t y ] was s t i l l another o r g a n i z a t i o n a l p r o c e s s , and one that adapted i t s e l f p e r f e c t l y to the o l d forms. Only by " u n f i x i n g " the elements t r a d i t i o n a l l y used to c o n s t r u c t a p i e c e of music c o u l d the sounds e x i s t i n t h e m s e l v e s — n o t as symbols, or memories which were memories of other music to begin w i t h . " (48-49) 2. Thomas DeLio, "Toward an A r t of Imminence, Morton Feldman's Durations 3. I I I . " I n t e r f a c e 12  (1983):465-480.  3. T h i s paper was d e l i v e r e d at the Annual Meeting of the S o c i e t y f o r Music Theory i n Montreal, Canada, (November I o f f e r my g r a t i t u d e t o Dr. Johnson gave t o me. and Rothko's  1993).  f o r the copy he g r a c i o u s l y  His more recent a r t i c l e e n t i t l e d Chapel" ( P e r s p e c t i v e s of New  "Rothko Chapel  Music 32/2  (Summer  1994):6-53) e x p l o r e s o r g a n i c i s m i n a p i e c e t h a t i s i n many ways a t y p i c a l of Feldman. W r i t t e n to commemorate  Rothko,  c h a r a c t e r i s t i c s of the p a i n t e r ' s s t y l e are i n c o r p o r a t e d the music. Johnson examines some of these and  uncovers  into  - 138 -  f e a t u r e s that are p e c u l i a r to the piece as w e l l as techniques that have wider a p p l i c a t i o n s i n Feldman's  music.  4. Essays. "The A n x i e t y of A r t , " 94. 5. " I , i n s t e a d of f i g u r i n g out s e r i e s ' , I do my s e r i e s underneath on the music paper, i n s t e a d of making s e r i e s , because I don't work i n a c o n t i n u i t y , the c o n t i n u i t y comes l a t e r . In other words, I'm not i n v o l v e d i n l i n e a r i n f o r m a t i o n . " (Essays, 167) " I f the a r t i c l e [ i n an i s s u e of Tempo magazine! accused me of k i l l i n g melody, I would hang my head. But p i t c h r e l a t i o n s h i p s ? I can't get that e x c i t e d about p i t c h r e l a t i o n s h i p s . " (Essays. "Conversations Without S t r a v i n s k y , " 64) CHAPTER ONE:  PATTERNS AND MODULES  1. Morton Feldman, Essays  r  " C r i p p l e d Symmetry," i n Morton  Feldman  ed. Walter Zimmerman (Cologne: Beginner P r e s s ,  1985),  128. 2. I b i d .  129.  3. I b i d . 4. The term "timeframe" appears to r e f e r to the empty measures on e i t h e r s i d e of the measures i n each example that c o n t a i n s notes. In the second i n s t a n c e , the timeframe i s symmetrical because the empty measures are of equal l e n g t h . The f i r s t  i n s t a n c e , l i k e the second, has a symmetrical  timeframe that Feldman  c l a i m s i s asymmetrical. I f our  understanding of the meaning of the term "timeframe" i s accurate we must assume that the meter s i g n a t u r e of one the  - 139 -  outer measures i n the f i r s t 5. I b i d .  129-130.  6. I b i d .  130.  example has been m i s p r i n t e d .  7. I b i d . 131. 8. Morton Feldman, "Darmstadt L e c t u r e , " i n Essays. 195. 9. The upper p i t c h C i n measure 341 i s absent from the r e c o r d i n g used i n t h i s study (Spring of Chosroes, 1979: Paul Zukofsky, v i o l i n , and U r s u l a Oppens, p i a n o ) . 10. Morton Feldman, "Lecture XXII," i n Essays  r  166.  11. "Darmstadt L e c t u r e , " 184. 12. "Lecture XXII," 167. 13. Consider, f o r example, module IX/1 i n measures 165-172 and 192-200. Although the r e t u r n i s not i d e n t i c a l to the f i r s t statement, i t r e i t e r a t e s the f e a t u r e s of the f i r s t . 14. DeLio,  466-467.  15. I t i s c o n c e i v a b l e t h a t a module c o u l d be made with one p i t c h c l a s s . Feldman used a minimum of two and n o r m a l l y two to seven. 16. Aspects of p i t c h and r e g i s t e r connect modules VII and VIII/1 so that they seem to be a s i n g l e c o n s t r u c t (Examples  - 140 -  20, 21, and 27); however, d i s t i n c t i v e f e a t u r e s i n t h e i r rhythms i s o l a t e t h e i r  i d e n t i t i e s . On the s u r f a c e , the r a p i d  a t t a c k s i n module VIII/1 c o n t r a s t with the r e l a t i v e l y l e i s u r e l y ones i n module V I I . More s i g n i f i c a n t l y however, the rhythms of these modules are d e r i v e d from d i f f e r e n t  source  modules, PM I (module VII) and VM I (module V I I I / 1 — s e e F i g u r e 3, page 127), and t h e r e f o r e e x h i b i t d i f f e r e n t  f u n c t i o n s i n the  process of l a r g e - s c a l e rhythmic d e c e l e r a t i o n t h a t i s d i s c u s s e d i n chapter 3. F i g u r e 3 r e v e a l s that the rhythm of module VIII/2 a r i s e s from VM I and PM I, but rhythms that  emanate  from both sources tend to r e f l e c t one source more s t r o n g l y than the o t h e r . In the case of module V I I I / 1 , the r a p i d a t t a c k s more c l o s e l y a s s o c i a t e i t with VM I. 17. The i s o l a t e d t r i c h o r d s  {G, A, B } to  and {D, D , to  A}  r e s i d e e x c l u s i v e l y i n the modules from which they are drawn. The t r i c h o r d s {B, C, D }  and {E, F, F#} are r e s t a t e d  to  i n the  f i n a l module, XVI, i n measures 350 and 359 r e s p e c t i v e l y . (In measure 359, D i s m i s p r i n t e d — s e e Chapter trichord  {E, F, Fjf} a l s o appears  tetrachord  {D#, E, F, G } b  2, Note 8 ) . The  i n the context of a l a r g e r  i n VM I (measures 29-46). In t h i s  example, the source modules f o r t r i c h o r d s are t h e r e f o r e those nearest t o module V. A**" i s extended 7  from module I I I ( r e f e r  to example 9) to measures 84-88 immediately preceding module V. Since A 7 b  t h e r e f o r e a n t i c i p a t e s module V, i t i s shown to be  "borrowed" from i t .  - 141 -  CHAPTER TWO: FORM 1. "Lecture XXII," 167. 2. The l a b e l s VI/1, VI/2 e t c . imply that the two modules that make up each corresponding p a i r i n s e c t i o n B are understood  to be two v e r s i o n s of the "same" module. As we  have seen i n chapter 1, two modules are the "same" i f they share a l l of the same i d e n t i f y i n g c h a r a c t e r i s t i c s . We w i l l see t h a t p a l i n d r o m i c p a i r s of modules are not, s t r i c t l y the same; however, they do s t r o n g l y resemble  speaking,  one another i n  t h a t some of the i d e n t i f y i n g c h a r a c t e r i s t i c s of the one are extended VI/2  to the o t h e r . For example, although modules VI/1 and  share no common p i t c h c l a s s e s , they do share a v i r t u a l l y  i d e n t i c a l rhythm p a t t e r n and r e g i s t r a l s p a c i n g . These two d i s t i n c t i v e aspects of t h e i r s t r u c t u r e c r e a t e a powerful connection between the two modules. Thus, the n o t i o n of sameness t h a t i s i m p l i e d by the module l a b e l s i s somewhat generalized. We w i l l a l s o see that VM II and i t s v a r i a n t s I I ' , I I " , II'",  and I I " " do not e x p l i c i t l y conform  t o the n o t i o n of  "sameness" as i t i s d e f i n e d i n chapter 1, although a case may be made i n favor of sameness between VM's II and I I " " , and I I ' and I I "  1  . C h a r a c t e r i s t i c f e a t u r e s of VM II are passed on  to VM I I ' e t c . but not without s t r u c t u r a l changes. I argue that these modules a r e d e v e l o p m e n t a l l y r e l a t e d such t h a t  VM's  I I ' to I I " " are not merely extensions of one another but  - 142  -  n e i t h e r do they have d i s c r e t e s t r u c t u r e s . They are, i n a sense, the "same" but not i n the l i t e r a l way  the concept  has  been d e f i n e d ; thus, the n o t i o n of "sameness" t h a t i s implied i n the l a b e l l i n g of VM  II and  to i n c o r p o r a t e developmental  i t s v a r i a n t s has been enlarged connections between modules.  3. "Lecture XXIV," 169. The penultimate sentence paraphrase  exact meaning of Feldman's  i s u n c l e a r — t h e brackets indicate  my  of i t . The o r i g i n a l reads: "However, I might repeat  t h i n g s t h a t , as i t ' s going around, i s v a r y i n g I t s e l f on aspect." No reason  one  i s g i v e n f o r the d i s t i n c t i o n made between  the terms " v a r i a t i o n " and  " v a r i e d r e p e t i t i o n " although we  may  s p e c u l a t e t h a t the former, by means of i t s h i s t o r i c a l usage, r e t a i n s an i m p l i c a t i o n of developmental  process t h a t the  l a t t e r does not. 4. In chapter 1 we saw t h a t a module begins when i t s p i t c h c l a s s e s and rhythm r e p l a c e those of the previous module. Measure 246  i s a measure of r e s t with a m e t r i c a f f i l i a t i o n to  module VIII/2; thus, the p o s s i b i l i t y e x i s t s t h a t module VIII/2 i s introduced by i t s metre, not i t s p i t c h and rhythm. But i f we a l l o w domains other than p i t c h and rhythm to a r t i c u l a t e modular boundaries, we  open a pandora's box  of c r i t e r i a t h a t  tend to obscure p o i n t s of d i v i s i o n r a t h e r than c l a r i f y them. Measure 246 may  t h e r e f o r e be seen t o extend module IX/2 with a  metre t h a t a n t i c i p a t e s module VIII/2.  - 143  -  5. Some p i t c h c l a s s e s i n the second h a l f of the palindrome are the enharmonic e q u i v a l e n t s of ones i n the f i r s t h a l f .  In  the "Darmstadt L e c t u r e , " Feldman c h a r a c t e r i z e s m i c r o t o n a l [enharmonic] s p e l l i n g as "the hardening between a minor second." He goes on to  of the d i s t a n c e ,  say  say:  "When you've been working with a minor second as long as I've been, i t ' s very wide. So t h a t p e r c e p t i o n of hearing i s a very i n t e r e s t i n g t h i n g . Because, c o n c e p t u a l l y you are not hearing i t , but p e r c e p t u a l l y , you might be able to hear i t . I hear t h a t pitch...coming to me very s l o w l y , and there's a l o t of s t u f f i n t h e r e . But I don't use i t c o n c e p t u a l l y . That's why I use the double f l a t s . But I use i t because I think i t ' s a very p r a c t i c a l way of s t i l l having the focus of the p i t c h . And a f t e r a l l , what's sharp? I t ' s d i r e c t i o n a l , r i g h t ? And a double sharp i s more d i r e c t i o n a l . But I d i d n ' t get the idea c o n c e p t u a l l y from music at a l l . I got the idea from "Teppishe," rugs. One of the most i n t e r e s t i n g t h i n g s about a b e a u t i f u l o l d rug i n n a t u r a l vegetable dyes i s t h a t i t has "abrash." "Abrash" i s that you dye i n s m a l l q u a n t i t i e s . You cannot dye i n b i g bulks of wool. So i t ' s the same, but yet i t ' s not the same. I t has a kind of m i c r o t o n a l hue. So when you look at i t , i t has t h a t kind of marvellous shimmer which i s that s l i g h t g r a d a t i o n . " (Morton Feldman Essays, pp.192-193) Feldman's use of m i c r o t o n a l s p e l l i n g i s intended the "microtonal  hue"  of "abrash"  to emulate  by c r e a t i n g "shades" of a  p i t c h r a t h e r than d i s c r e t e p i t c h e s ; t h a t i s , to explore  the  space around a p i t c h but not draw our focus from i t . 6. The d i s t i n c t i o n between l i n e a r and l e s s obvious i n module XIII than i n VM 318, and  321,  and  e s p e c i a l l y 322  v e r t i c a l designs  is  I. Chords i n measures  a n t i c i p a t e the t e x t u r e , rhythm,  a r t i c u l a t i o n of segment t h r e e , and dyads predominate the  t e x t u r e i n module XIII but seldom occur  i n VM  I.  Nevertheless,  the t h i r d segment of each module i s the more v e r t i c a l  one.  - 144 -  7. In measure 102, the span  i n the piano embodies  seven p i t c h e s and i t e n g u l f s the v i o l i n A3 i n i t s middle r e g i s t e r . Conversely, the p i t c h e s of VM I I  , , , ,  emerge from i t s  analog—module XVI — i n the same middle r e g i s t e r near the centrepoint hexachords 8.  of the space  i n h a b i t e d by the descending  piano  i n measures 357-368.  The score  that was used f o r t h i s a n a l y s i s c o n t a i n s  D5  i n measure 359 r a t h e r than the expected E5; however, the e n t i r e module i s c o n s t r u c t e d  with p a r a l l e l descending chromatic  and D5 i s the only p i t c h t h a t departs from t h i s Furthermore, Chapter  on the r e c o r d i n g used  lines  pattern.  f o r t h i s study (Endnote  14,  1) E5 r a t h e r than D5 i s heard i n measure 359. I t i s  t h e r e f o r e assumed that D5 i s a m i s p r i n t . 9.  The term " r e s t a t e d " i m p l i e s t h a t VM II and VM I I " "  are the "same," a concept that i s addressed 10.  Although i t i s not, s t r i c t l y speaking, a p o i n t of  coincidence, II"".  i n Note 2 above.  a c o n t i n u i t y nonetheless l i n k s module XVI and VM  The upper  l i n e i n measures 348-356 begins with the  f i r s t v i o l i n p i t c h of the piece  (E 6) and completes i t s to  chromatic descent at B n a t u r a l i n measure 367. VM I I " " begins with the next expected p i t c h , B , but i n the same te  r e g i s t e r that i t appears a t the beginning of VM I I . In t h i s way, the upper v o i c e descent leads us from the f i r s t one l a r g e - s c a l e framework t o the f i r s t  p i t c h of  p i t c h of the other one.  - 145 -  CHAPTER 3: LARGE SCALE RHYTHMIC PULSE 1. See, f o r example, Wallace B e r r y ' s d e f i n i t i o n of " p u l s e " i n S t r u c t u r a l F u n c t i o n s i n Music  (New  York:  Dover  P u b l i c a t i o n s Inc., 1987):305. J o e l L e s t e r uses the terms "beat" and " p u l s e " i n t e r c h a n g e a b l y i n The Rhythms of Tonal Music  (Carbondale and E d w a r d s v i l l e : Southern  Illinois  U n i v e r s i t y P r e s s , 1986):45-46; however, i n The S t r u c t u r e of Music  Rhythmic  (Chicago: The U n i v e r s i t y of Chicago P r e s s ,  1960):3-4, Grosvenor Cooper and Leonard Meyer d i f f e r e n t i a t e the meanings of the terms and conceive p u l s e s t o be u n i n t e r p r e t e d beats. John Roeder d i s c u s s e s the i n t e r s e c t i o n of simultaneous d u r a t i o n a l s t r a t a , each of which  i s comprised of  a s e r i e s of r e g u l a r p u l s e s , i n " I n t e r a c t i n g P u l s e Streams i n Schoenberg's  A t o n a l Polyphony." Music Theory Spectrum  (1994):231-249.  In Phrase Rhythm i n Tonal Music  (New  16/2, York:  Schirmer Books, 1989) W i l l i a m R o t h s t e i n g e n e r a l i z e s the term " p u l s e " to i n c l u d e r e g u l a r d u r a t i o n s that are longer than beats. 2. David E p s t e i n . Shaping Time (New  York: Schirmer Books,  1995):22-40. 3. The term " a u d i t o r y stream" i s d e f i n e d i n A l b e r t Bregman. A u d i t o r y Scene A n a l y s i s  (Cambridge  Massachusetts: The  MIT  P r e s s , 1990):9-10. An a u d i t o r y stream i s our p e r c e p t u a l grouping of the p a r t s of the n e u r a l spectrogram that go t o g e t h e r .  - 146 -  The stream serves qualities. 4.  We recognize  o n l y to the a t t a c k s  the purpose of c l u s t e r i n g r e l a t e d  however t h a t t h i s o b s e r v a t i o n  i n these measures and that D7 i s s u s t a i n e d  through measure 262, having  begun i n the previous  5.  Chapter 2, pp. 66-70.  6.  Although measure 329 c o n t a i n s  meter s i g n a t u r e  applies  only 3 s i x t e e n t h s , i t s  i s 4/8. T h i s bar l i n e should  a l i g n e d with the 4/8 meter s i g n a t u r e  measure.  t h e r e f o r e be  i n the v i o l i n at measure  330. SUMMARY AND CONCLUSIONS 1. In measures 1-7 ( r e f e r t o Example 7) p i t c h e s  partition  n e a t l y i n t o three segments t h a t d i s p l a y d i s c r e t e p a t t e r n s . These a r e reproduced below as segments A, B, and C. P i t c h and rhythm i n segment A are p a l i n d r o m i c .  In segment C, the inner  7 p i t c h e s form a palindrome. Although each p a i r of bracketed notes i s the transposed palindromic  retrograde  of the other, the  contours of- the passage are preserved.  r e v e a l s a c o n t r a s t i n g s t r u c t u r e i n t h a t the l a s t are the r e t r o g r a d e - i n v e r s i o n of the f i r s t p a t t e r n o f the f i r s t followed eighth)  four notes  f o u r . The rhythm  s e t of p i t c h e s (two q u i n t u p l e t  by a s i n g l e t r i p l e t  Segment B  eighths  e i g h t h and a s i n g l e q u i n t u p l e t  i s i d e n t i c a l to that of the second s e t . Although the  p i t c h s t r u c t u r e s w i t h i n measures 1-7 of VM I are not  -  o r g a n i c a l l y connected to s e c t i o n s ABA',  they  147  nevertheless  foreshadow t h i s formal p l a n . Furthermore, the  outer  p a l i n d r o m i c segments a n t i c i p a t e the s t r u c t u r e of s e c t i o n B.  2E  1 /I  A•1  B  I  II—'  '  *  J  i—t  1 1 1 1  111 if M -UJ & ' r*  i i—i  *  r  J"  *  *  *  —I  A.  — H  I  i t  - 148  -  BIBLIOGRAPHY Ashley, Robert. "Morton Feldman. An I n t e r v i e w with Robert Ashley, August 1964." In Contemporary Composers on Contemporary Music, 362-366. E d i t e d by E l l i o t t Schwartz and Barney C h i l d s . New York: H o l t , R i n e h a r t and Winston (1967). Behrman, David. "What Indeterminate N o t a t i o n Determines." P e r s p e c t i v e s of New Music 3/2 (1965): 58-73. Berry, Wallace. S t r u c t u r a l F u n c t i o n s i n Music. New Dover P u b l i c a t i o n s Inc., 1987.  York:  B o t t i n g e r , P e t e r . "Das exakt Ungefahre." In Morton Feldman. 105-114. E d i t e d by Heinz-Klaus Metzer and Rainer Riehm. Muzik-Konzepte S e r i e s 48/49. Munich: Text und K r i t i k , 1986. Bregman, A l b e r t S. A u d i t o r y Scene A n a l y s i s . Cambridge, Massachusetts: The MIT P r e s s , 1990. Cardew, C o r n e l i u s . " N o t a t i o n - I n t e r p r e t a t i o n , E t c . " Tempo 58 (1961): 21-33. Cooper, Grosvenor W., and Leonard B. Meyer. The Rhythmic S t r u c t u r e of Music. Chicago: The U n i v e r s i t y of Chicago P r e s s , 1960. DeLio, Thomas. "Toward an A r t of Imminence, Morton Feldman's Durations 3. I I I . " I n t e r f a c e 12 (1983): 465-480. D i c k i n s o n , P e t e r . "Feldman E x p l a i n s H i m s e l f . " Music Musicians 14/11 (1966): 22-23. Dominick, L i s a R. "Darmstadt 23/2 (1985): 274-279.  and  1984." P e r s p e c t i v e s of New  Music  E p s t e i n , David. Shaping Time: M u s i c The B r a i n , and Performance. New York: Schirmer Books, 1995. f  Feldman, Morton. "Einfuhrung zu For P h i l i p Guston." In Morton Feldman, 64-66. E d i t e d by Heinz-Klaus Metzer and Rainer Riehm. Muzik-Konzepte S e r i e s 48/49. Munich: Text und K r i t i k , 1986. . " T r i a d i c Memories." T r a n s c r i b e d by L i n d a C a t l i n Smith. L e c t u r e d e l i v e r e d at Mercer Union G a l l e r y , Toronto, Canada, A p r i l 17, 1982.  - 149 -  Hitchcock, H. Wiley. "Current C h r o n i c l e , United S t a t e s . " M u s i c a l Q u a r t e r l y 50 (1964): 91-98. Johnson, Steven. "Organic C o n s t r u c t i o n i n Music of Morton Feldman." Paper presented at the annual meeting of the S o c i e t y f o r Music Theory, Montreal, Canada, November 1993. . "Rothko Chapel and Rothko's Chapel." P e r s p e c t i v e s of New Music 32/2 (1994): 6-53. Kramer, Jonathan D. The Time of Music. New Books, 1988.  York: Schirmer  L e r d a h l , F r e d , and Ray J a c k e n d o f f . A G e n e r a t i v e Theory of Tonal Music. Cambridge, Massachusetts: The MIT P r e s s , 1983. L e s t e r , J o e l . The Rhythms of Tonal Music. Carbondale and E d w a r d s v i l l e : Southern I l l i n o i s U n i v e r s i t y P r e s s , 1986. Roeder, John. " I n t e r a c t i n g P u l s e Streams i n Schoenberg's Atonal Polyphony." Music Theory Spectrum 16/2 (1994): 231-249. R o t h s t e i n , W i l l i a m . Phrase Rhythm i n Tonal Music. New Schirmer Books, 1989.  York:  Wolpe, S t e f a n . "On New (and Not So New) Music i n America." T r a n s l a t e d by A u s t i n C l a r k s o n . J o u r n a l of Music Theory 28/1 (1984): 1-45. Zimmerman, Walter, ed. Morton Feldman Essays. K e r p i n : Beginner P r e s s , 1985.  - 150 APPENDIX MEASURES/BEATS*  VIOLIN MODULES  Violin VM I VM II VM I I I  VM VM VM VM  II ' II•• II' ' • II ' • ' '  1/1 29/1 77/1 49/1 58/1 67/1 74/1 82/1 141/1 219/1 330/1 369/1  -  23/4 48/3 81/3 52/2 63/3 72/2 76/3 90/1 146/4 228/1 339/4 380/1  Piano  76/3 - 83/3  PIANO MODULES PM I PM II PM IV  23/5 - 28/3 64/1 - 66/3 72/3 - 73/3  PM XIV  1/1 33/1 59/5 84/1 330/2  -  32/3 52/2 76/2 90/1 339/4  52/2 90/1 146/5 156/5 163/1 158/3 165/1 192/1 174/1 201/1 210/1 228/1 237/2 247/1 264/5 282/1 291/1 339/5 348/2 380/2  -  59/4 146/4 156/4 158/2 164/3 162/5 173/9 200/7 192/1 209/7 228/1 237/1 246/3 264/4 281/7 290/3 330/1 348/1 380/1 388/7  OTHER MODULES III V VI/1 VII VIII/1 IX/1 X/l XI X/2 IX/2 VIII/2 VI/2 XII XIII XV XVI CODA  52/2 90/1 146/5 156/5 163/1 158/3 165/1 192/1 174/1 201/1 210/1 228/1 237/2 247/1 264/5 282/1 291/1 339/5 348/2 380/2  -  57/3 140/2 156/4 158/2 164/3 162/5 173/9 200/7 192/1 209/7 219/1 237/1 246/3 264/4 281/7 290/3 330/1 348/1 368/3 388/7  *The beats shown here are those w i t h i n which the modules begin and end.  

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