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

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ASPECTS OF MUSICAL LANGUAGE IN GYORGY LIGETI'S TEN PIECES  FOR WIND QUINTET  (1968)  by CHARLES DOUGLAS MORRISON B.Mus., The U n i v e r s i t y of M a n i t o b a , 1981 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES (Department o f M u s i c )  We a c c e p t t h i s t h e s i s as c o n f o r m i n g to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA September  1983  © C h a r l e s Douglas M o r r i s o n , 1983  )E-6  In p r e s e n t i n g  this  thesis  in partial  f u l f i l m e n t of the  r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y of B r i t i s h Columbia, I agree that  the Library  shall  it  and study.  I further  freely  available  agree that for  f o r reference  permission  f o rextensive copying o f t h i s  understood that financial  copying or p u b l i c a t i o n  gain  shall  Department o f  MU^Kl  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3  (3/81)  OCTOBER  S, 1 ^ 8 3  of this  It is thesis  n o t be a l l o w e d w i t h o u t my  permission.  Date  thesis  s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e h e a d o f my  d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . for  make  Columbia  written  ABSTRACT Gyorgy L i g e t i ' s r e p r e s e n t a t i v e of compositional o f many o f earlier traces  pieces the  with  stylistic  are  the  pieces ation.  as  The  and  on  and  isolates  discusses  compositional the  style  aspects  suggested,  i n the  work,  specific  pitch  of  of  each other,  i n excerpts  defining  from  subgroupings of  pieces pieces  identifies  two  each type  and  treats linear  the  f o r m e r , v a r i o u s means o f  unfolding  are  exposed,  i n the  (e.g.,  next,  and  harmonic  connection  harmonic  rhythm,  details  2 to  9  within  such  and  of the  individual segment-  outlines  modes o f  and  illustrated.  linear  latter, i i  and  prevalent  "soloistic,"  discussed  defined  in  own  texture,  texture  are  evolve  delineating factors within  of  period  given,  Ligeti's  effecting  Regarding  while  early  parameters  principles  organization  from h i s  excerpts  o f t e n by  i . e . , " e n s e m b l e " and  groupings are  chapter  which began to  cited,  that  from  first  the  t e x t u r a l aspects  Rhythmic  rhythmic  form,  while  light  section dealing with i n the  of  them  The  style of  than  techniques  parameters—form,  independently  illustrating  of  many  language.  c e r t a i n musical  them  Concerning  discussed  i t illustrates  quintet.  h i s changing musical  a whole a r e  are  other  section  defined  s t r u c t u r e s and  interaction). and  Ligeti's  the  substantiated,  arrangements general  of  throughout  features  quintet.  quintet  Moreover, refinements  Major works a r e  II  work  i n a medium c o n s i d e r a b l y m o r e " c o m p a c t "  apparent  of  (1968) i s a  sixties;  h i s move t o V i e n n a .  pitch—and their  Wind Quintet  to h i s more m a t u r e p e r i o d ,  Chapter  of  for  i n the middle  works.  development  characterizations  and  Pieces  style  procedures  h i s other  i n Hungary 1956  his  Ten  instrument  the  r o l e s of  meter  And  finally,  the  details and  separately.  pitch-class  structures  are  i i i classified  and  related according  dissonance  factors.  above, p r o v i d e s preparation  last  pieces  individually, discussed. specific a  IV  T h e s e and to  structures. to  other the  quintet, In  and  of  resulting  from  latter  last  between the  conclusions  Ligeti's  (the  i n Chapter  music  the a n a l y s i s .  I I I and  with  a l s o approached  pieces'  two  detailed  and  third  on  overall  between parameters  first  first  further  introduced  are  the  the  IV.  are  analyses  pieces  of  the  tenth.  are of  in  studied  II are  being  pieces)  interaction  n i n t h and  devices  parameters are  In a d d i t i o n , these  connection  C h a p t e r V,  musical  and/or  of  and  procedures outlined  extensively with  comprehensive view of  regard.  between the  r e p r e s e n t a t i v e of  a  consonance-  examination  techniques  introduced  first  of  which f o l l o w i n Chapters  Again,  concepts  Instances  in this  include aspects  of  the  system  e x c l u s i v e l y and  many c o n c e p t s  reference  referred  deal  respectively.  larger scale, providing  musical  I I , through  detailed analyses  I I I and  and  derived  basic understanding  f o r the  Chapters and  a  Chapter  to a  given this  which p e r t a i n to  period,  as  the  evidenced  quintet  as  in findings  TABLE OF  CONTENTS  ABSTRACT  i i  L I S T OF EXAMPLES  v i i  ACKNOWLEDGMENTS  x i  E D I T O R I A L NOTES  x i i  Chapter I. INTRODUCTION II.  1  ASPECTS OF MUSICAL LANGUAGE I N GYORGY TEN PIECES FOR WIND QUINTET Introduction Formal Organization Aspects of Textural  LIGETI'S  o f t h e Work a s a W h o l e Structure  T e x t u r a l d e t a i l s i n ensemble p i e c e s Textural d e t a i l s i n s o l o i s t i c pieces Summary P r i n c i p l e s o f Rhythmic and M e t r i c D e s i g n Summary Modes o f P i t c h O r g a n i z a t i o n Linear details Summary Harmonic d e t a i l s Summary Summary III.  ANALYSIS OF P I E C E  NO.  Introduction Delineating Factors Summary Aspects of Textural Textural quality T e x t u r a l space Summary  1  23 23 24 25 26 32 39 40 64 66 66 85 86 103 104 105  of Formal Structure  iv  Segmentation  105 105 106 107 107 110 112  V  P r i n c i p l e s o f Rhythmic and M e t r i c D e s i g n Element-rhythms Rhythm o f i m p u l s e - d e n s i t y f l u c t u a t i o n Rhythm o f d y n a m i c a l l y exposed p i t c h - p a i r groups ... Rhythm o f t e x t u r a l - d e n s i t y f l u c t u a t i o n Rhythm o f t e x t u r a l q u a l i t y f l u c t u a t i o n Rhythm o f h a r m o n i c - d e n s i t y f l u c t u a t i o n Rhythm o f tempo change I n t e r a c t i o n o f element-rhythms Summary Modes o f P i t c h O r g a n i z a t i o n . . . . . Linear d e t a i l s Outer-voice prolongation Linear progressions involving l a t e r a l voice crossing . Timbral connections C o n n e c t i o n t h r o u g h dynamic exposure Connection through a r t i c u l a t i o n a f t e r a r e s t . . . . C o n n e c t i o n s between d y n a m i c a l l y exposed p i t c h - p a i r s . Summary Harmonic d e t a i l s Measures 1-12 Measures 13-15 ( t h e t r a n s i t i o n ) and t h e ' b ' - s e c t i o n . Summary C o n n e c t i v e F a c t o r s Between t h e F i r s t and T h i r d P i e c e s and I n t e r r u p t i v e A s p e c t s o f t h e Second Summary Summary IV.  ANALYSIS OF PIECE NO. 10 Introduction D e l i n e a t i n g F a c t o r s o f Formal Segmentation Summary Aspects of T e x t u r a l S t r u c t u r e Formal s t r u c t u r e as d e f i n e d by t e x t u r a l c o n d i t i o n s . . . T e x t u r a l p r o g r e s s i o n s as m a n i f e s t i n d e n s i t y and spatial fluctuations Textural-density ., T e x t u r a l space Summary P r i n c i p l e s o f Rhythmic and M e t r i c D e s i g n Summary Modes o f P i t c h O r g a n i z a t i o n Linear d e t a i l s Linear r e g i s t r a l connections PC u n f o l d i n g Summary Harmonic d e t a i l s Consonance-dissonance q u a l i t y o f c o l o r a t i o n s S p e c i f i c placement and c o n t e n t o f c o l o r a t i o n s . . . . S p e c i f i c placement o f o c t a v e and u n i s o n d o u b l i n g s . . Summary  112 113 113 116 119 119 120 120 120 123 124 124 124 133 134 134 136 140 144 144 145 151 154 155 158 158 160 160 160 161 162 163 167 167 171 172 173 178 179 179 179 188 193 194 194 198 200 201  C o n n e c t i v e F a c t o r s Between t h e N i n t h and Tenth P i e c e s '. . . Summary Summary V.  CONCLUSION  201 203 204 205  WORKS CITED  209  SELECTED BIBLIOGRAPHY  210  L I S T OF  1.  2.  EXAMPLES  Atmospheres, measures s o u n d mass  1-6, s h o w i n g  Atmospheres,  30-34,  showing  gradually  sonorities  Atmospheres,  4.  Volumina, r e h e a r s a l n o s . 1 t o 2, s h o w i n g c h r o m a t i c sound mass  6.  8.  Apparitions,  10.  showing m i c r o p o l y p h o n y  Concerto,  first  Piece  No. 5, m e a s u r e s  showing 14  10-17,  a rapid  showing  polyphony with  16 succession 18  movement, m e a s u r e s  Instrumentation-density  68-74,  showing  i n d e p e n d e n t components  and s u b g r o u p i n g o f t h e t e n p i e c e s  1-5, s h o w i n g  a single  element  . .  24  8-13, s h o w i n g  12.  P i e c e No. 3, m e a s u r e s 7-10, s h o w i n g a s u b g r o u p i n g o f components i n t h e t r a n s i t i o n a l p a s s a g e P i e c e No. 7, m e a s u r e s 3-8 a n d 4 0 - 4 1 , s h o w i n g d i s p a r a t e c h a r a c t e r i z i n g adjacent  one t e x t u r a l  28  Piece  textures  21  textural  11.  13.  . .  ,  No. 9, m e a s u r e s  10  12  of disparate textures  Aventures, m e a s u r e s 1-11, s h o w i n g of d i s p a r a t e t e x t u r e s Double  . . . . .  static,  67-72,  s e c o n d movement, m e a s u r e s  rapid succession  a more t r a n s p a r e n t 9.  52-53,  Requiem, s e c o n d movement, m e a s u r e s micropolyphony  a 7.  measures  7  3.  5.  chromatic 4  measures  transforming  static,  formal  element  . . .  29  30  sections  31  14.  Piece  No. 2, m e a s u r e s  1-4, s h o w i n g  a two-element  texture  . . .  33  15.  Piece  No. 6, m e a s u r e s  1-4, s h o w i n g  a two-element  texture  . . .  34  16.  P i e c e No. 8, m e a s u r e s 1, 2, 5, 10, a n d 12, s h o w i n g a n " e n s e m b l e - l i k e " t e x t u r e as an accompanimental element . . . P i e c e No. 2, m e a s u r e s 12-15, s h o w i n g o n e t e x t u r a l e l e m e n t w i t h one p r i m a r y and f o u r s e c o n d a r y components  17.  vii  36 37  viii 18.  P i e c e No. 4, measures 1-4, showing one t e x t u r a l element w i t h one p r i m a r y and two secondary components  38  19.  P i e c e No. 8, measures 1-16, i m p u l s e - d e n s i t y graph  43  20.  P i e c e No. 8, measures 12-16 (horn p a r t o n l y ) , showing low-level metric units P i e c e No. 8, measures 1 ( b e a t s 1-2) and 10 ( b e a t s 3-4),  45  21.  showing p o t e n t i a l p u l s e d e f i n i t i o n  47  22.  P i e c e No. 8, measure 5, showing r h y t h m i c and l i n e a r p a t t e r n s .  48  23.  P i e c e No. 4, i m p u l s e - d e n s i t y g r a p h  50  24.  P i e c e No. 4, l a r g e - s c a l e i m p u l s e - d e n s i t y u n i t s  52  25.  P i e c e No. 3, i m p u l s e - d e n s i t y g r a p h  53  26.  P i e c e No. 3, m e t r i c u n i t s  55  27.  P i e c e No. 3, measures 10-12, r h y t h m i c and m e t r i c d e s i g n  28.  P i e c e No. 5, i m p u l s e - d e n s i t y g r a p h  58  29.  P i e c e No. 7, measures 38-44, i m p u l s e - d e n s i t y graph  60  30.  P i e c e No. 2, l o c a l a r r i v a l p o i n t s (measures 9-12 and 23-24)  31.  P i e c e No. 6, l o c a l a r r i v a l / d e p a r t u r e p o i n t s (measures 8-9 and 10-11) P i e c e No. 8, measures 26-32, showing c o n s e c u t i v e d i s p a r a t e  32.  ...  57  .  62  63  musical ideas  65  33.  P i e c e No. 2, measures 12-15, two s i m u l t a n e o u s l i n e a r i z a t i o n s .  34.  P i e c e No. 2, measures 21-22 and 29, two s i m u l t a n e o u s linearizations  68  68  35.  P i e c e No. 4, measures 1-8, s i m u l t a n e o u s l i n e a r c o n n e c t i o n s . .  71  36.  P i e c e No. 7, measures 38-44, l i n e a r p r o g r e s s i o n of t r i t o n e s  73  37.  P i e c e No. 5, PC o r d e r i n g s , showing PC p a i r and IC o r d e r i n g  .  relationships  74  38.  P i e c e s 5 and 6, PC p a i r and IC o r d e r i n g r e l a t i o n s h i p s  ....  75  39.  P i e c e s 9, 5, and 6, p a t t e r n s o f PC u n f o l d i n g  77  40.  PC c o n n e c t i o n between t h e f i f t h and s i x t h p i e c e s  79  41.  P i e c e No. 8, measures 1-12, wedge-patterned l i n e a r i z a t i o n s  .  80  ix 42.  43.  P i e c e No. 8, m e a s u r e s 1-12, patterned as compared t o r h y t h m i c a c t i v i t y Piece  No.  unison  3, m e a s u r e s  1-8,  t r a n s f e r and  pitch  unfolding 80  components  through  interchange  P i e c e No.  45.  P i e c e No. 3, m e a s u r e s 1-8, c o n s o n a n c e - d i s s o n a n c e and h a r m o n i c q u a l i t y f l u c t u a t i o n  46.  P i e c e No. 5, m e a s u r e s l i n e a r and h a r m o n i c  1-8, l i n e - g r a p h r e p r e s e n t a t i o n expansion  Piece  No.  linear 48.  Piece  9,  measures  8-15,  and  harmonic  expansion  No.  2, m e a s u r e s  harmonic 49.  measures'1-8, harmonic  83  44.  47.  3,  linear  pitch  P i e c e No.  interval 4,  12-13; a n d  fluctuation  7-9  P i e c e No.  2,  51.  P i e c e No.  7, m e a s u r e s  52.  L i n e - r e p r e s e n t a t i o n of textural  and  through v o i c e  50.  harmonic  88 criteria 89 of  line-graph representation  fluctuation  measures  complexes  92 of 94  4,  measure  through v o i c e  p i e c e No.  leading  23-26, h a r m o n i c  1, . . . .  interval  leading  98  organization 1-38,  harmonic  textural  101 organization  components,  101  showing  quality  109  53.  T e x t u r a l spaces of  54.  Two  55.  Units of  56.  I n t e r a c t i o n of  57.  Outer-voice  58.  L i n e a r s t r u c t u r e o f t h e ' b ' - s e c t i o n and i t s r e l a t i o n s h i p to the ' a ' - s e c t i o n Two i n s t a n c e s o f t i m b r a l c o n n e c t i o n i n l a t e r a l v o i c e -  59.  levels  of  formal  segments  impulse-density  dynamically  crossing  exposed  I l l  fluctuation pitch-pair  115  groups  prolongation  i n measures  122 1-16  126  132  events  135  One  i n s t a n c e of  connection  t h r o u g h dynamic  61.  One  i n s t a n c e of  connection  through a r t i c u l a t i o n  52-67  118  s i x element-rhythms  60.  Examples  97  (incl.)  p e r t a i n t o p i e c e No.  1.  exposure after  135 a rest  .  136  X  62.  63.  Linear progressions i n m e a s u r e s 1-12 Connections  lateral  voice  crossing 139  through dynamically  i n measures  exposed  pitch-pairs  1-14  142  structure  147  64.  Harmonic  65.  Consonance-dissonance c r i t e r i a  66.  Recurring  sets  dynamically  c  involving  a n d C-D  of equal harmonic exposed  quality  149  i n units of  pitch-pairs  153  67.  P i t c h r e l a t i o n s h i p s between t h e f i r s t  68.  Line-graph representaion  69.  F o u r modes  70.  Impulse-number  proportions  and t h i r d  pieces  . . . .  157 165  of textural-density  impulse-density  factors  fluctuation  170  o f p h r a s e f r a g m e n t s and  graph  176  71.  Motivic  72.  First  and second  l e v e l s of l i n e a r p i t c h  structure  183  73.  Third  and f o u r t h  l e v e l s of l i n e a r p i t c h  structure  187  74.  Motivic  and i i i  188  75.  PC c o n t e n t  76.  Consonance-dissonance f a c t o r s  77.  L i n e a r p r o g r e s s i o n r e l a t i o n s h i p between t h e n i n t h and t e n t h p i e c e s ..' .' Twelve-note aggregate completion from the n i n t h to the t e n t h piece  78.  Examples  d e f i n i t i o n of r e g i s t e r s  organization  68-78  of formal  (incl.)  i and i i  in registers  i , ii,  180  segments  pertain  191 of c o l o r a t i o n v e r t i c a l i t i e s  to piece  No.  10.  . .  197  202 203  ACKNOWLEDGMENTS For are  permission  gratefully  Canadian agent and  Universal  I would his this  to use copyrighted  the following  acknowledged: European American Music f o r B. S c h o t t ' s  Soehne;  C. F . P e t e r s  publishers  Distributors, sole Corporation,  New Y o r k ;  E d i t i o n A.G., W i e n .  like  t o e x p r e s s my u t m o s t  c a r e f u l s u p e r v i s i o n and i n v a l u a b l e project.  materials,  Also,  his  reading  for  h i sguidance  the  thesis, 1 offer  I wish  gratitude  suggestions  t o e x t e n d my t h a n k s  o f t h e p a p e r a n d h e l p f u l comments. i n t h e e a r l y stages my  of this  appreciation.  xi  t o Dr. Wallace Berry throughout  for  the course of  to Dr. Gregory B u t l e r f o r To D r . W i l l i a m  project  Benjamin,  and f o r h i s r e a d i n g o f  EDITORIAL NOTES Subheadings of t h e s e c t i o n s w i t h i n c h a p t e r s of t h i s paper a r e r a n k - o r d e r e d i n t h e f o l l o w i n g manner: F i r s t - L e v e l Subheading Second-Level Subheading Third-level Fourth-level  subheading subheading  R e g i s t r a l l y s p e c i f i c pitches are designated according  to the  f o l l o w i n g octave c l a s s i f i c a t i o n s :  c  ^Y. -/  1  c  2  c  c  3  4  ) ° — (V •)  J.  i  c  5  c  6  c  7  z -e-  Upper-case l e t t e r s w i t h s u p e r s c r i p t numbers thus denote r e g i s t r a l l y s p e c i f i c 4  3  p i t c h e s , e.g., E , D , e t c . P i t c h - c l a s s e s ( i . e . , r e g i s t r a l l y  non-specific  p i t c h e s ) a r e i n d i c a t e d by upper-case l e t t e r s , e.g., D, F//, e t c . PC s t a n d s f o r p i t c h - c l a s s , IC f o r i n t e r v a l - c l a s s , and C-D f a c t o r f o r consonance-dissonance f a c t o r ( e x p l a i n e d  xii  at the appropriate  point i n the text).  CHAPTER I INTRODUCTION The year 1956 may  be c o n s i d e r e d a major t u r n i n g p o i n t i n Gyorgy  L i g e t i ' s l i f e , f o r i t was the move from Hungary ( h i s p l a c e of b i r t h i n 1923) t o V i e n n a i n t h a t y e a r w h i c h put him i n c o n t a c t w i t h s e v e r a l l e a d i n g European a v a n t - g a r d e composers such as E i m e r t , K o e n i g , and Stockhausen. ^" The r e s u l t of t h i s exposure was a marked change i n L i g e t i ' s c o m p o s i t i o n a l style. L i g e t i ' s works p r i o r t o 1956 may groups.  be d i v i d e d i n t o t h r e e s m a l l e r  H i s e a r l i e s t works, composed between 1938 and 1942, c o n s i s t m a i n l y 2  of u n p u b l i s h e d p i a n o p i e c e s , chamber works, and songs.  From the m i d d l e t o  l a t e f o r t i e s , however, the p o l i t i c a l s i t u a t i o n l a r g e l y r e s t r i c t e d the 3 c o m p o s i t i o n of new music t o mere f o l k s o n g arrangements.  And f i n a l l y , i n  t h e e a r l y f i f t i e s , when the r e s t r i c t i o n s were somewhat r e l a x e d , L i g e t i began t o d e v e l o p a new s t y l e : About 1950 I r e a l i z e d t h a t f u r t h e r development i n t h e p o s t - B a r t o k s t y l e i n w h i c h I had been composing was not t h e way f o r w a r d f o r me. . . . I n 1951 I s t a r t e d t o experiment w i t h s i m p l e s t r u c t u r e s of rhythm and sound i n o r d e r , i n a manner of s p e a k i n g , t o b u i l d up a new music from n o t h i n g . . . . I asked m y s e l f : what can I do w i t h a s i n g l e note? what can I do w i t h i t s o c t a v e ? what w i t h one i n t e r v a l ? what w i t h two i n t e r v a l s ? what w i t h d e f i n i t e r h y t h m i c r e l a t i o n s h i p s which c o u l d form t h e f o u n d a t i o n s of a whole based on rhythm and i n t e r v a l ? I n t h i s way s e v e r a l s m a l l *0ve N o r d w a l l , " L i g e t i , Gyorgy," The New Grove Dictionary and Musicians, e d i t e d by S t a n l e y S a d i e , v o l . 10, p.854. 2  Ibid.  ^Ibid.  1  of Music  ,  2  p i e c e s were composed, c h i e f l y f o r t h e p i a n o . His the of  Musica  ricercata  (11 P i e c e s f o r P i a n o , 1951-53) was composed i n  wake of t h e s e questions."' W h i l e t h i s work c o n t a i n s some of t h e seeds L i g e t i ' s new  s t y l e , a f r e e l y t o n a l language remains prominent i n t h e  B a r t o k - i n f l u e n c e d S t r i n g Q u a r t e t No. and Ejszaka, In  Reggel  1 - Metamorphoses  nocturnes  (1953-54),  (1955) f o r c h o r u s .  1956, w i t h t h e move to V i e n n a , L i g e t i developed t h e s t y l e which  brought him i n t e r n a t i o n a l a c c l a i m — a s t y l e w h i c h he m a i n t a i n e d f o r about a decade. are  Apparitions  (1958-59) and Atmospheres  (1961), b o t h f o r o r c h e s t r a ,  t h e works which were l a r g e l y r e s p o n s i b l e f o r t h i s immediate  recognition.  Atmospheres  widespread  i s c h a r a c t e r i z e d by t h e use of s t a t i c , c h r o m a t i c  sound masses, g r a d u a l l y t r a n s f o r m i n g s o n o r i t i e s , and m i c r o p o l y p h o n y .  The  f i r s t of t h e s e t h r e e t e x t u r e s , as i l l u s t r a t e d i n Example 1, i s d e f i n e d as a sustained chromatic c l u s t e r .  I n t h i s p a r t i c u l a r e x c e r p t , t h e sound b l o c k  i n c l u d e s e v e r y p i t c h from ^ 6 "ametrically"  t o  as though suspended T  jyfr*  except CJ.  ^  , sustained  7 i n space.  4 Gyorgy L i g e t i , quoted i n Ove N o r d w a l l , l i n e r n o t e s f o r Musica ricercata  ( 1 9 5 1 - 5 3 ) , on Duo  Pohjola  (Grammofonfirma  BIS  18,  recorded i n  W. Germany, 1974). G i v e n t h e u n a v a i l a b i l i t y of p u b l i s h e d s o u r c e s by L i g e t i , of s o u r c e s w h i c h quote L i g e t i , i n f o r m a t i o n g l e a n e d from l i n e r n o t e s such as t h i s has proved i n v a l u a b l e i n a s c e r t a i n i n g L i g e t i ' s own c h a r a c t e r i z a t i o n s of t h e t e c h n i q u e s of h i s m u s i c a l language. Ibid.  5  6 T h i s s u s t a i n e d sound mass may be c o n s i d e r e d " a m e t r i c " because of the absence of p e r c e i v a b l e , a c c e n t - d e l i n e a t e d m e t r i c u n i t s ; t h e 4 t i m e s i g n a t u r e and n o t a t e d b a r l i n e s a r e e s s e n t i a l l y n o t a t i o n a l c o n v e n i e n c e s . My c h a r a c t e r i z a t i o n of t h e s e measures i s c o r r o b o r a t e d by Thomas C l i f t o n i n h i s r e c e n t book, Music as Heard (New Haven: Y a l e U n i v e r s i t y P r e s s , 1983), pp. 155-56. C l i f t o n s t a t e s : "The most e l e m e n t a l k i n d s of s u r f a c e o c c u r under t h r e e c o n d i t i o n s : the f i r s t r e q u i r e s t h e absence of movement; t h e second, t h e absence of any c o n t r a s t i n dynamics; and the t h i r d , an absence of t i m b r a l c o m p l e x i t y . The opening measures of L i g e t i ' s Atmospheres r e v e a l the 7  3  Example  1.  Atmospheres, sound  mass.  measures  1-6, s h o w i n g  static,  chromatic  unmerklich einsetzen / imperceptible ottack die Tremoli so dicht wie moglich / the tremolos as thick as possible 1) without the hair of the bow 2) scarcely audible 0 1 9 6 3 by Universal Edition A . G . Reprint with permission of Universal Edition Wien  5  Example 2, a l s o from Atmospheres,  i l l u s t r a t e s a t e x t u r e which  c o n s i s t s o f g r a d u a l l y changing s o n o r i t i e s . g of an e s t a b l i s h e d v e r t i c a l s o n o r i t y a new v e r t i c a l i t y has e v o l v e d .  I n t h i s p r o c e s s , each member  moves i n d e p e n d e n t l y  of others  until  This p a r t i c u l a r excerpt f e a t u r e s the  i n t e r a c t i o n o f s e v e r a l sound b l o c k s , each o f w h i c h goes through t h e metamorphic p r o c e s s d e s c r i b e d above. F o r i n s t a n c e , i n measure 30, t h e -)  second v i o l i n s a r e s u s t a i n i n g ^ by one u n t i l  -s  1  —  0 »  9  >  t  n  e  p i t c h e s o f w h i c h move one  i s formed i n b a r 32 and s u b s e q u e n t l y : s u s t a i n e d .  O c c u r r i n g r h y t h m i c a l l y independent o f , but n e v e r t h e l e s s c o n c u r r e n t the second v i o l i n s ' t r a n s f o r m a t i o n i s a p r o g r e s s i o n from i n t h e v i o l a s , e f f e c t e d through oboes, c l a r i n e t s , trumpets,  t h e same p r o c e s s .  f  with, to  The p i c c o l o s ,  f i r s t v i o l i n s , and c e l l o s a r e a l s o engaged i n  independent s o n o r i t y t r a n s f o r m a t i o n s throughout t h e s e measures. "Micropolyphony,"  as i l l u s t r a t e d i n Example 3, i s d e f i n e d by L i g e t i a s :  . . . a t e c h n i q u e by w h i c h i n s t r u m e n t a l p a r t s a r e i n t e r w o v e n and crowded t o g e t h e r i n t o a dense c o n t r a p u n t a l t e x t u r e . There a r e so many p a r t s , and t h e i r p o l y p h o n i c i n t e r w e a v i n g i s so complex, t h a t t h e i n d i v i d u a l p a r t s a r e c o m p l e t e l y submerged i n t o a m i c r o p o l y p h o n i c web, and t h e o v e r a l l m u s i c a l p a t t e r n which emerges from t h i s t e c h n i q u e imposes a f o r m a l shape on t h e w o r k . ^ u  f i r s t two o f t h e s e c o n d i t i o n s . W i t h i n t h e s e m e a s u r e s — I t h i n k p a r t i c u l a r l y of the f i r s t s i x — o n e experiences very l i t t l e sensation of change. W i t h o u t change, w h i c h i s c o n s t i t u t i v e o f rhythm, time i t s e l f i s suspended. . . . A c c o r d i n g l y , t h e t e x t u r e o f t h e opening measures o f Atmospheres can be d e s c r i b e d a s s y n t h e t i c , i n t h e sense t h a t i n d i v i d u a l elements a r e absorbed i n t o t h i s amorphous mass o f sound." g An " e s t a b l i s h e d v e r t i c a l s o n o r i t y " i s one w h i c h has sounded l o n g enough, w i t h o u t i n t e r n a l p i t c h change, t o be r e c o g n i z e d as a s t a t i c verticality. 9  The b l a c k v e r t i c a l b a r i n d i c a t e s a c h r o m a t i c p i t c h e s between and i n c l u d i n g t h e two i n d i c a t e d . ^ G y o r g y L i g e t i , l i n e r n o t e s f o r Ligeti: (Decca H e a d l i n e , Head 12, 1976).  cluster, i.e., a l l  Melodien  for  Orchestra  6  E x a m p l e 2.  Atmospheres, transforming  m e a s u r e s 30-34, sonorities.  showing g r a d u a l l y  8 The denseness of t h e p o l y p h o n i c i n t e r w e a v i n g i n Example 3 i s the :ne r re e ss uu ll tt of or the complex composite rhythm o f , and r e l a t i v e l y narrow ambitus, over which t h e f o r t y - e i g h t independent l i n e a r events o p e r a t e .  The  overall  e f f e c t u n d o u b t e d l y outweighs t h a t of any one of i t s components. S t a t i c sound b l o c k s , g r a d u a l s o n o r i t y t r a n s f o r m a t i o n s , and m i c r o p o l y p h o n y a r e t h e main t e x t u r a l c h a r a c t e r i s t i c s of o t h e r works i n the e a r l y t o m i d d l e s i x t i e s , as e v i d e n c e d i n Volumina  (1961-62) f o r organ,  movements one and two of t h e Requiem (1963-65) f o r two c h o r u s e s and o r c h e s t r a , t h e f i r s t movement of t h e Cello (1966) f o r c h o r u s , and Lontano (Volumina,  Cello  Concerto,  Concerto  ( 1 9 6 6 ) , Lux  aeterna  (1967) f o r l a r g e o r c h e s t r a , t h r e e of w h i c h  and Requiem) a r e d i s c u s s e d i n more d e t a i l below-.-  Example 4 c o n s i s t s of t h e opening of Volumina, i l l u s t r a t e s t h e concept of s t a t i c sound mass.  which g r a p h i c a l l y  Notice i n t h i s excerpt that,  a l t h o u g h t h e dynamics f l u c t u a t e as a r e s u l t of r e g i s t r a t i o n changes, c o n t e n t remains s t a t i c t h r o u g h o u t . Concerto  The opening movement of the  pitch  Cello  t y p i f i e s a s l i g h t l y d i f f e r e n t a p p l i c a t i o n of s l o w l y changing  s o n o r i t i e s from t h a t of t h e b l o c k - l i k e c l u s t e r s of Atmospheres. mode of l i n e a r e x p a n s i o n may  be d i s c e r n e d .  Here, a  S p e c i f i c a l l y , t h e u n i s o n E^ of  measure 11 g r a d u a l l y expands t o more complex v e r t i c a l i t i e s , p i t c h e s b e i n g added i n the f o l l o w i n g o r d e r : Km. f  1  11 '  m.  17  m.  26  m.  28  &  The second movement of the Requiem c o n t a i n s p o r t i o n s e x h i b i t i n g m i c r o p o l y p h o n i c t e x t u r e s such as t h e e x c e r p t g i v e n as Example 5. i n t h e e x c e r p t from Atmospheres,  .  faW  complex Here, as  t h e complex i n t e r w e a v i n g of l i n e a r  components o c c u r s w i t h i n a narrow r a n g e , s p e c i f i c a l l y from O l  to  ~) ^  #  .  L i n e a r independence i s c o n s e q u e n t l y r e n d e r e d s u b o r d i n a t e t o  9  Example  3.  Atmospheres,  m e a s u r e s 52-53,  showing m i c r o p o l y p h o n y .  1) scorcely audible 2) scraps 3) stop suddenly @1963 by Universal Edition A.G. Reprint with permission of Universal Edition Wien  11  Example  4.  Volumina, r e h e a r s a l n o s . sound mass.  1 t o 2,  showing  static,  chromatic  r  (dCt ?if{ti-« btzCeHcn ttch imf die- btc^t-  ti)  le-jttn Anm trie u.n.g  „ //// W  A.  Unker  Remitter - e L i t n i n i t e n <to (wJe Fuij  Cm M<LMU«.0.  13 the  effect  o f t h e whole.  Apparitions, in  the late  Rather  than  features  the other  fifties,  i s somewhat  a continuous  a succession This  of L i g e t i ' s  pieces  Nouvelles third  movement  Example of  Aventures  In occurs  and to  on a l m o s t  The  t h i s more d i s j u n c t  excerpt  contrasting  of these  every  beat,  register,  articulation.  (from each  rhythmic  Notice  transforming  juxtaposition)  solo voices  that  and seven  Concerto.  a change o f m u s i c a l  element  being  defined  by  design,  length, melodic  both  16 t h e i n d e p e n d e n t  "patch-work" t e x t u r e  superimposition reveals  dynamics,  elements  (i.e.,  s u c c e s s i v e and  h i s musical  begin  one o f  of disparate musical  involving non-traditional vocal began t o a l t e r  element  different shape,  elements  1965 L i g e t i  the  7, f r o m Aventures,  also  Around  (1964) and  instruments,  o f t h e Cello  f r o m Aventures often  i n several  style.  by measure  t o one o f c o m p l e x  textures, i t  s u c h a s Aventures  and Example  Apparitions)  the former  above.  (one o f w h i c h i s  i s also discernible  sixties  f r o m Apparitions,  illustrated  transforming  textures  o f t h e Requiem, a n d s e c o n d movement  the f i r s t  overlap,  the middle  immediate r e c o g n i t i o n  from t h e p i e c e s  quality  (1964) f o r t h r e e  illustrate  orchestration,  from  Ligeti's  structure of slowly  "fragmented"  6 i s an e x c e r p t  which  sound  different  o f a b r u p t l y changing  micropolyphony). other  work u n d e r l y i n g  ideas.  superimposed,  style  techniques. once more:  S i n c e about t h e m i d d l e s i x t i e s I have g r a d u a l l y been t r a n s f o r m i n g t h e t e c h n i q u e o f m i c r o p o l y p h o n y , a i m i n g t o make t h e s e p a r a t e l i n e s c l e a r e r and m o r e i n d i v i d u a l l y d i s t i n g u i s h a b l e . T h e p o l y p h o n i c p a t t e r n i s s t i l l complex, but t h e p o l y p h o n y i t s e l f i s l e s s " m i c r o " i n t h a t t h e p o s s i b i l i t y now e x i s t s o f d e s i g n i n g a u t o n o m o u s , d i v e r g e n t , m u t u a l l y c o n t r a s t e d  ''''''Two o b s e r v a t i o n s r e g a r d i n g t h i s e x a m p l e a r e n o t e w o r t h y , t h e f i r s t of which i s t h e f a c t that the v o i c e p a r t s a r e doubled i n the s t r i n g s ; three c h o r a l s e c t i o n s — s o p r a n o , mezzo, and a l t o — a r e i n o p e r a t i o n . The second d e t a i l concerns the texture i t s e l f . W i t h i n each s e c t i o n , micropolyphony i s e f f e c t e d through a f o u r - v o i c e canon. Although these canons a r e not rhythmically s t r i c t , the succession (i.e., unfolding) of pitches i s the same i n e a c h c a s e .  14 Example  5.  Requiem, s e c o n d movement, m e a s u r e s micro polyphony.  © 1966 by Henry L i t o l f f ' s Verlag Reprint with permission of C.F.Peters Music Publishers Frankfurt  67-72,  showing  15  Example  6.  Apparitions, s e c o n d movement, m e a s u r e s 10-17, a rapid succession of disparate textures.  showing  * Sie»*« Efklo'ufg "* Sa-ta 14 / Sea eoienct on ** o" peg* 14 II (harsh/ oudbia) 2) from rhe b'-dgedownwa'di over m«fince*fceo'dT-a nointr of tt'o>ei J 3oc3«^ata. 3l conpVely sont.cello  * Fc'i  «*'ne VK'ccpe vo'handen ;it, sp.ele H no'Sfy oudb'e 2 1 on *fe edge of m a ikin d-umit'CK  **" Siehe FMI6rung $*,<« 14 / See e«Dlonoior *" on poge I* *" "nge'nagei del G'rtf-nge'i ouf die So.ta dtuc*en./• - Pill.; Presi noil ol the (e-t-hond-finoer on rhe (tring. 1) fno' flvtter-tonguel 21 bowed 3] S'fott dekoielv end continually ove> the Hio witn b'uiH, 4) g'oduollyJul totto 51 iul tgsto, grodoofiy.-* to porvictllo 61 groduoNyul toito 7) bowed  men d.,'  ti no  8*ey  i avovabfe. play 0.  3l w n ti 4| bo*«d 5i g'odajiiy completely iul pom calto 6 1 JU! fci'O, grodi<3:!v-*ord. 7) T ha lymbt* ot l"0*a» :»t oppronmo'e. Wl^out •'O'f.  © 1 9 6 4 by Universal Edition A.G. Reprint with permission of Universal Edition Wien  17  E x a m p l e 7.  Aventures, m e a s u r e s 1-11, of disparate textures.  showing a r a p i d  succession  01964  by Henry L i t o l f f ' s Verlag Reprint with permission of C.F.Peters Music Publishers Frankfurt  19 melodic  p r o c e s s e s , which  overriding T h i s newly of  established,  Melodien  an independent  more t r a n s p a r e n t  texture  for Wind Quintet  (1971) f o r o r c h e s t r a ,  oboe, and o r c h e s t r a ,  a n d San Fransisco  Double  Polyphony  e x a m p l e o f t h e more p e r s p i c u o u s t e x t u r e ,  with  lines  first  exhibiting  existence within the  network.^  s u c h w o r k s a s t h e Ten Pieces  (1968-70),  An  lead  contrapuntal  increased  movement o f t h e Double  independence  Concerto,  i sa distinguishing ( 1 9 6 8 ) , Chamber Concerto  feature  Concerto  (1972) f o r  flute,  (1973-74) f o r o r c h e s t r a .  still  rhythmically  and d i r e c t i o n ,  complex b u t  i s found  an e x c e r p t from which  i n the  i s given i n  E x a m p l e 8. It  s h o u l d be c l e a r  structure  i sstill  from t h i s  complex  (e.g.,  each o f t h e l i n e a r  components  direction  o f motion.  to bar  and g o a l  by measure 68 t o  resulting individual  3 | [  reveals  |  although the rhythmic . . . . 5 | | | | against || | | J),  independence  viola  72, a n d so o n .  i n terms  the f i r s t travels  of melodic  viola  from  moves f r o m A^  its initial  Although the " t o t a l i t y "  B -  1  in  of the  p o l y p h o n i c web i s a n i m p o r t a n t a s p e c t , so t o o a r e t h e  components which  comprise  theoverall  Other aspects of m u s i c a l language mature p e r i o d  that,  against  For instance,  70, w h i l e t h e t h i r d  by measure complex  example  are disclosed  of this  i n the following  texture. second  phase  of Ligeti's  quotation:  The m u s i c a l l a n g u a g e o f t h i s w o r k [chamber Concerto], as i n t h e case i n a l l my c o m p o s i t i o n s s i n c e t h e m i d d l e s i x t i e s , i s n e i t h e r t o n a l n o r atonal. T h e r e a r e no t o n a l c e n t r e s , n o r a r e t h e r e a n y h a r m o n i c c o m b i n a t i o n s o r p r o g r e s s i o n s which c a n be f u n c t i o n a l l y a n a l y z e d ; on the o t h e r hand t h e t w e l v e n o t e s o f t h e c h r o m a t i c s c a l e a r e n o t t r e a t e d as n o t e s o f e q u a l importance, a s i n a t o n a l and s e r i a l m u s i c . There are s p e c i f i c predominant arrangements o f i n t e r v a l s , which determine the c o u r s e o f t h e music and t h e development o f t h e form. The complex p o l y p h o n y o f t h e i n d i v i d u a l p a r t s i s embodied i n a h a r m o n i c - m u s i c a l flow, i n which t h e harmonies ( i . e . , t h e v e r t i c a l combinations of i n t e r v a l s ) do n o t c h a n g e s u d d e n l y , b u t m e r g e i n t o o n e a n o t h e r ; o n e c l e a r l y d i s c e r n i b l e i n t e r v a l c o m b i n a t i o n i s g r a d u a l l y b l u r r e d , and  12  Ligeti,  liner  notes f o r  Melodien.  20  Example  8.  Double Concerto, f i r s t movement, m e a s u r e s 68-74, s h o w i n g a more t r a n s p a r e n t p o l y p h o n y w i t h i n d e p e n d e n t components.  21  J = 80  (Piu mosso)  SOLO  OBOE  „  P®  Accelerando  poco  a  poco  al  <to  Oar..  spiel  Cel.  Arpa  . "Ftpr . 1  - err, fif- con fuoco . , -73T--  Vcl.  0 1974 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of B. Schott's Soehne Mainz  - t~  Iw  i/rn rirt Roaenmetturf c o r l l r v * to ? w n a f >wi  22 from t h i s  cloudiness  i t i s p o s s i b l e t o d i s c e r n a new 1  combination  gradually taking  interval  o  shape.  14 Ligeti's adheres to degree  from  found  to  to  in earlier  Chapter  last of  rhythm,  have been a  and  two  detailed  as w i l l  Chapter details  extended  summary o f  "the  the  of  some o f the  fact,  this  the  made  wind  techniques  being  quintet, being  with  quintet  representative of  the  paper,  considerable  q u o t a t i o n was  In  techniques  offers  Ligeti's  type  works  refinements  a chamber w o r k ,  l a r g e r o r c h e s t r a l works f o r the  t a s k too to  great be  textural  are  be  found  language  examined  of  is  of a n a l y s i s  individually,  paper;  in detail  i n Chapters I I I  because  Pieces  for  1)  pieces  inter-  a l l ten the  pieces first  and  each r e p r e s e n t s  one  work.  These  and  (No.  parameters  introduced  f o l l o w i n Chapter  Wind Quintet  i n the  ( p i e c e No.  particular  a p p l i c a t i o n s of concepts will  with  consequently,  c o n f i g u r a t i o n s found  p e r t a i n i n g to these  quintet-§form,  D e t a i l e d s t u d i e s of  for this  analyzed  i n the  I I , approach the v a r i o u s musical  conclusions  The Ten quintet."  of m u s i c a l  where a p p l i c a b l e .  prevalent  analyses  like  Specific  although  Also,  pitch—will  p i e c e s were c h o s e n  the  and,  works.  I I , aspects  r e l a t i o n s h i p s noted would  of  subject  s t a t e d above to a  Chamber Concerto.  sixties,  the  the  here.  In texture,  the  late  more a c c e s s i b l e t h a n presented  Wind Quintet,  procedures  diverse selection  the middle  those  for  become a p p a r e n t ) ,  reference  extremely  Pieces  compositional  (as w i l l  specific an  the  Ten  will  IV  10)  individually.  be d i s c l o s e d ,  i n Chapter  II.  A  V.  i s , henceforth,  referred to  as  CHAPTER I I c  A S P E C T S OF MUSICAL LANGUAGE  I N GYORGY L I G E T I ' S  TEN PIECES FOR WIND QUINTET Introduction The aspects the  intent of this  of musical  language  d e t a i l e d analyses  chapter  chapter  i s to define  i n the ten pieces,  i n Chapters  I I I and IV.  and e x e m p l i f y  certain  thus providing The main  a basis f o r  sections  of this  a r e as f o l l o w s : Formal Organization Aspects  o f t h e Work a s a Whole  of T e x t u r a l  Principles  Structure  o f Rhythmic and M e t r i c  Design  Modes o f P i t c h O r g a n i z a t i o n Linear Details Harmonic D e t a i l s Summary. Many o f t h e c o n c e p t s d i s c u s s e d in  t h e work, p e r t a i n i n g t o s e v e r a l  others and  in this  expose techniques  last  pieces  respectively,  pieces  o f more l i m i t e d  of the quintet  present  chapter  or sections within application.  are the subjects  references  a r e of general  23  pieces,  while  Because t h e f i r s t  of Chapters  t o them a r e m i n i m a l .  significance  ITT and IV,  24 Formal  Organization  P e r h a p s t h e most is  the  the  even-numbered  ones are  in No.  significant  r e g u l a r a l t e r n a t i o n between  Specifically,  the  soloistic  odd-numbered  i s as  8 - horn,  instrumentation-density piece  to  p i e c e , as  t h e Work a s  formal  are  The  (i.e.,  No.  of  order  f o l l o w s : No.  and  aspect  a Whole of  "ensemble" and  pieces  soloistic.  pieces  6 - o b o e , No.  of  10  of  work as  "soloistic"  the  featured  - bassoon.  No.  whole  while  the  instruments 4 -  flute,  Fluctuations in  instruments  in actual  a  pieces.''  ensemble t y p e ,  2 - clarinet,  t h e number o f  w e l l as v a r i a n c e s  the  the  sounding)  instrumentation,  from  suggest  2 subgroupings w i t h i n density below)  of  each  i s given  E x a m p l e 9.  the  piece with  quintet.  (and the  each  I n Example  Instrumentat i o n density: Subgroupings:  Concerning  the  instrumentation-  section within a p i e c e — t o  suggested  subgroupings  Instrumentation-density  P i e c e No.:  9,  and  be  i n d i c a t e d by  subgrouping  of  the  2  3  4  5  6  7  8  5  5  5  3  4  5  5-4  3-4-53  I  I  I I  I  9  1  I  fluctuations in instrumentation-density  several  details  are noteworthy.  pieces,  r e s e r v i n g the  flute  The  alto  flute  for i t s soloistic  i s used  treatment  brackets.  ten  1  I I  explained  I  and  pieces. 10  4-5 I I  instrumentation,  i n the  first  i n the  fourth  three piece.  A l t h o u g h t h e s e two c l a s s i f i c a t i o n s a r e d e f i n e d i n d e t a i l i n t h e n e x t s e c t i o n , they r e f e r e s s e n t i a l l y to pieces i n which a l l of the scored i n s t r u m e n t s p a r t i c i p a t e e q u a l l y ( e n s e m b l e ) and t h o s e i n w h i c h one p a r t i c u l a r instrument i s featured ( s o l o i s t i c ) . 2 O t h e r s u b g r o u p i n g s o f p i e c e s may b e i n t e r p r e t e d a c c o r d i n g t o f a c t o r s o t h e r t h a n i n s t r u m e n t a t i o n - d e n s i t y and i n s t r u m e n t a t i o n . These, however, a r e d i s c l o s e d i n t h e l i g h t of the s p e c i f i c parameters e f f e c t i n g such c o n n e c t i o n s .  25 The  e n g l i s h horn  third, where  and  appears  neither  i t i s the  i n the  i n the  featured  first  f o u r t h and  two  pieces,  fifth;  instrument.  indicated in pieces  similar  above.  piece,  those  f o r example,  featured. horn;  listed  A  does not  horn  along  f o r the  with  soloistic  treatment .(in the  is  for five  piece  do  they  point  of  the main  defined  III  and  IV.  examined etc.)  that  a c t u a l l y sound body o f  D e t a i l s of  i n the  light  which e f f e c t  stated  alternating role of  oboe l a t e r  the  pieces,  and  pieces.  texture others,  T h e s e two  one  i n bar  equal  types  of  occurs  The  parameters  as  the  (e.g.,  bassoon  last  piece  entire  culmination  w e l l as  individual  the  for i t s  large-scale  chapter,  it is  is  i n the  the  seventh  without  9.  sixteenth-note at  the  piece,  although  f a c t o r s of  this  of  Textural  grouping in  Chapters  pieces  texture,  are  rhythm,  Structure  s e c t i o n , the pieces.  Although  unique  importance, pieces  and  quintet  Texture  each p i e c e  which have w i d e s p r e a d of  Finally,  conditions  delineations.  soloistic  types.  the 6  8 where  in preparation  structuring within  textural characterization (i.e., of  on  s e c t i o n s of  previous  e n s e m b l e and  again  on  f o r No.  i n d i c a t e d i n Example  piece).  the v a r i o u s  based  i n the  15).  formal  i n the  i n d e f i n i n g these  aspects  the  piece  Aspects As  of  (specifically,  the  in  f o r No.  section of  however,  together  formal  of  formal  piece,  only  are  in preparation  o f o r g a n i z a t i o n and  i n subsequent  10  eighth  final  amore  oboe i s saved  7 to  second  ninth piece,  instruments,  Other aspects are  the  "stepped" density  p a r t i c i p a t e i n the  scored  the  is silent  good p o r t i o n o f  i t s entry,  responsible  the  In  oboe d'  Internal fluctuations in  instrumentation-density to  the  the  i s organized  plays  a most  explores  in detail),  there  s i g n i f i c a n c e i n the which  are  corresponding  specific  in  decisive  a u n i q u e mode exist  several  ensemble to the  soloistic  textural details  will  26 now  be  discussed  in  detail.  Textural Essentially  two  D e t a i l s i n Ensemble  textural configurations  Pieces  are  found  i n the  ensemble  3 pieces:  one  one  which  are  two  to  be  which c o n s i s t s of  features  disparate  discussed  e n s e m b l e and delineation  elements,  shortly).  in  the  well  number The  textural  of  fifth  element  Texture,  pieces,  form w i t h i n  in fact,  as  t e x t u r a l element elements.  t e x t u r a l elements sounded  case they u s u a l l y scored,  one  several consecutive  soloistic of  only  most  is also  to  O n l y on  often  an  important  factor  transitional  to main formal  departure  differentiates  in  the  Successive t e x t u r a l 4 sections,  instruments f o r which the  p a s s a g e s , w h i c h may  and  occasion  (this  parameter which best  correspond the  one  simultaneously  i n d i v i d u a l ensemble p i e c e s .  i n v o l v e a l l of  as  the  throughout,  feature  i n which  piece a  is  reduction  components.^ and  ninth  which  pieces  involves  are  a l l of  each comprised the  scored  of  one,  continuous  instruments  throughout.  "A t e x t u r a l e l e m e n t i s a h o m o g e n e o u s mode o f i n t e r a c t i o n b e t w e e n i n s t r u m e n t s , as i n a p o l y p h o n i c or homophonic t e x t u r e . The i n d i v i d u a l p a r t s i n s u c h a t e x t u r a l element a r e r e f e r r e d t o as " s o u n d i n g components" o r simply, "components." A t e x t u r a l e l e m e n t may a l s o be c o m p r i s e d o f o n l y one component a s i n a s i n g l e - l i n e m e l o d y . The t e x t u r e o f a p i e c e a t a n y g i v e n t i m e may c o n s i s t o f one o r m o r e t e x t u r a l e l e m e n t s , e a c h h a v i n g one o r more c o m p o n e n t s £e.g., v e r t i c a l t h r e e - n o t e c h o r d s ( o n e e l e m e n t , t h r e e c o m p o n e n t s ) , w i t h a s i n g l e - l i n e m e l o d y (one e l e m e n t , one c o m p o n e n t ) } . T h i s mode o f t e x t u r a l c h a r a c t e r i z a t i o n i s i n f l u e n c e d i n p a r t by W a l l a c e Berry's views. See i n t h i s r e g a r d h i s Structural Functions in Music ( E n g l e w o o d C l i f f s : P r e n t i c e - H a l l , I n c . , 1 9 7 6 ) , Ch. 2. 4 The c o n t r a r y , however, i s n o t a l w a y s t r u e . In o t h e r words, a p i e c e w h i c h f e a t u r e s one c o n t i n u o u s t e x t u r a l e l e m e n t may h a v e s e v e r a l f o r m a l s e c t i o n s d e l i n e a t e d by v a r i a n c e s i n o t h e r p a r a m e t e r s . ^Where s u c h a r e d u c t i o n o c c u r s , h o w e v e r , t h e s o u n d i n g c o n t r i b u t e t o o n l y one t e x t u r a l e l e m e n t .  components  left  27 The t e x t u r e of t h e f i f t h p i e c e i s one o f polyphony, n i n t h i s a three-part canon.  7  w h i l e t h a t of t h e  In the l a t t e r , the t e x t u r a l c o n t i n u i t y  c o r r e s p o n d s t o t h e u n i s e c t i o n a l form, w h i l e i n t h e f o r m e r , d e s p i t e i t s continuous  t e x t u r e , f o r m a l segmentation o c c u r s t h r o u g h v a r i a n c e s i n o t h e r  parameters such a s t e x t u r a l space and r h y t h m i c discussed l a t e r ) . No.  i n t e n s i t y (each o f which i s  Examples 10 and 11 c o n s i s t o f e x c e r p t s from No. 5 and  9 , r e s p e c t i v e l y , each r e v e a l i n g a s i n g l e t e x t u r a l element. Of t h e r e m a i n i n g  ensemble p i e c e s , each of which c o n t a i n s s e v e r a l  s u c c e s s i v e t e x t u r a l elements, t h e f i r s t p i e c e i s d e t a i l e d i n t h e next chapter.  Measures 1-7 o f p i e c e No. 3, however, p r o v i d e a n o t h e r example  of a t e x t u r a l element w h i c h f e a t u r e s equal and t o t a l involvement o f t h e g  instruments one  f o r which i t i s s c o r e d .  i n s t a n c e o f simultaneous  The t h i r d p i e c e a l s o p r o v i d e s t h e  t e x t u r a l elements i n an ensemble p i e c e .  measures 10-12, t h e octave-doubled  In  theme r e p r e s e n t s one t e x t u r a l element, 9  while the t r i l l  ( c l a r i n e t ) and s u s t a i n e d n o t e (horn) r e p r e s e n t  the other.  "The components o f t h i s p a r t i c u l a r p o l y p h o n i c t e x t u r e a r e e x t r e m e l y " a r t i c u l a t e " i n t h e i r use o f r e p e a t e d staccatissimo notes. The i m p l i c a t i o n s of t h i s s u r f a c e d e t a i l w i t h r e s p e c t t o r h y t h m i c d e s i g n a r e d e a l t w i t h i n t h e next s e c t i o n . A l s o , t h e s p e c i f i c mode o f p i t c h o r g a n i z a t i o n o p e r a t i v e i n t h i s p a r t i c u l a r p o l y p h o n i c element i s e x p l a i n e d i n t h e f i n a l s e c t i o n o f t h i s chapter. The c a n o n i c treatment employed here i s a prime example o f l i n e a r independence w i t h i n a p o l y p h o n i c t e x t u r e . That i s , a p a r t from c o n t r i b u t i n g to t h e e f f e c t o f t h e whole, t h e i n d i v i d u a l components e x h i b i t a c o n s i d e r a b l e degree o f independence and d i r e c t i o n . As n o t e d i n t h e p r e v i o u s c h a p t e r , t h i s i n c r e a s e d independence i s c h a r a c t e r i s t i c o f many o f t h e p o l y p h o n i c t e x t u r e s i n L i g e t i ' s music o f t h e l a t e s i x t i e s . g The d e t a i l s o f t h e l i n e a r s t r u c t u r e i n t h i s p a r t i c u l a r t e x t u r a l element w i l l be examined i n t h e s e c t i o n on p i t c h o r g a n i z a t i o n . A l s o , i t might be n o t e d t h a t t h i s t e x t u r a l element comprises a l m o s t h a l f t h e p i e c e . I t i s , i n f a c t , c h a r a c t e r i s t i c o f t h e ensemble p i e c e s t h a t a t e x t u r a l element, once e s t a b l i s h e d , c o n t i n u e s t o o p e r a t e over a s u b s t a n t i a l p o r t i o n of t h e p i e c e . 7  9  The d o u b l i n g o f t h e "theme" i n o c t a v e s soloistic implication.  i n t h i s s e c t i o n n e g a t e s any  28 E x a m p l e 10.  P i e c e No. textural  •) 5  (1,  t  Staccatissimo  £  £  e,c.) bedeutet:  (JjJJJmm  5, m e a s u r e s 1-5,  showing a  single  element.  Tonrepetition  e:c.) so schncll wie m o g l i c h .  *;  /5  =fe i £  \o,  o,  m,  0.  tones staccatissimo  Die n o i i e r t e n Dauerwerte werden mit solchen staccal i s s i m o - T o n f o l g e n ausgeftillt, w o b e i jedes I n s t r u m e n t , von den anderen I n s i r u m e n i e n unabhangig u n d ohne RLicksicht auf die T a k l e i n t e i l u n g , so schnell stacca tiert, wie das seine technische Eigenart u n d die Lage, in der es spielt, zulaUt. E i n f a c h e r b z w . d o p p e l t e r , bei der Klote ad l i b . dreifacher Zungenstofi. K c i n e F l a t terzungel Steis d i s t i n k t e . gesonderte A t t a e k e n . Z u m R h y t h m i s c h e n : Wahrend die Einsatze u n d A b satze exakt angegeben s i n d , ist die innere D i c h t e der staccato-Folgen rhythmisch frei. *) D y n a m i s c h e Balance = s/jp a n n a h e r n d gleich in alien Instrumenten.  ^  \ ere.) means: repeated  (JjJJJjJ etc.)  as fast as possible.  The given note-values are filled with these staccatissimo repeated tones; each instrument plays as fast a staccato as its technique and register permit, independently of the other instruments and with no regard for subdivision of bars Single tonguing, double tonguing. Flute triple tonguing ad lib. So fluttertongue! Distinct, separated attacks throughout. Rhythm: Entries and cut- offs are indicated precisely; the density of the staccato sequences, however, is rhythmically free. **y  Balance of dynamics: sjp approximately equal in all instruments.  @1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne.  29  © 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne.  The  two  texturally  1-7  and  10-12) a r e b r i d g e d  which  diminishes  register, textural featuring  defined  s e c t i o n s o u t l i n e d above  by a r h y t h m i c a l l y i n t e n s i f i e d  i n d e n s i t y from  culminating elements  formal  four to three  on t h e t r i l l  of the second  a r e d u c t i o n or  i n bar  section).  (i.e.,  polyphonic  components, and  9 ( o n e o f t h e two This  transitional  s u b g r o u p i n g o f components  measures  i s given  element  descends  in  simultaneous element, as  Example  12.  30 Example 12.  P i e c e No. 3, measures 7-10, showing a subgrouping o f components i n t h e t r a n s i t i o n a l passage.  end of first  section-\  transition8  Ft.Sol  +J  c CJ s OJ  —  •H q OJ OJ  c 0  /  & E 0  3  ' +J 0 OJ SH +J 3 O OJ Ms 0  © 1969 B. S c h o t t ' s Soehne, Mainz A l l r i g h t s reserved Used by p e r m i s s i o n of European American 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 Canadian agent f o r B. S c h o t t ' s Soehne.  The s e v e n t h p i e c e i s perhaps t h e most e x p l i c i t example of c o n s e c u t i v e , d i s p a r a t e t e x t u r a l elements c h a r a c t e r i z i n g  adjacent formal s e c t i o n s . ^  The  ^ T h e s p e c i f i c t e x t u r a l elements a r e e x t r e m e l y c o n s i s t e n t throughout each s e c t i o n , a g a i n r e v e a l i n g t h e a t t r i b u t e o f t e x t u r a l c o n t i n u i t y .  vertical equal  homorhythmic  involvement  n o t e out  of  followed  suit  'b'-section features  textural  a l l the  vertical  by  the  c l o s e of  of  being  the  five  silent  configurations  13.  Piece  to  No.  the  i n bar  the  the  end),  7,  6,  (cf. bars  f o r the  m e a s u r e s 3-8  i n the  12,  without  and  formal  eighth two  40-41,  1-37)  clarinet  feature  sustains  instruments w i l l  in a contrasting  illustrated  adjacent  a l l the  initiated  in preparation  characterizing  (measures  Although the  section  instruments  are  'a'-section  instruments.  complex  ( m e a s u r e s 38  four  (the horn  Example  the  of  s o n o r i t i e s of  15, a  and  have  34).  The  transition,  polyphonic  piece).  excerpts  a  texture  These  diverse  i n Example  showing d i s p a r a t e  sections.  Clarinctto  in Si t  Corno in l a  Fagotto  ri. Ob.  Cl.$i\> Cor. Fa  Fag.  © 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne.  13.  textures  32 Textural Although soloistic way,  two  all  of  i t i s somewhat more d i f f i c u l t  pieces,.because modes o f  involves  the  the  In  instrument  some c a s e s  the  accompanimental  and  20-21).  partially second  seventh piece,  filled  are  the  a  the  ensemble p i e c e i s the  instructions  Note,  (bars  only).  a texture 1-8)  regarding  the  the  by  the  opening  the  borrowed  two  sixth  piece  some o f w h i c h being  those  the  given  as  piece  ( f e a t u r i n g the piece.  whole o f  p i e c e , and  same.''''''  The  the  In  second  14. oboe)  this  oboe  case  preceding  instruments, the  are  the  the  Example  15,  vertical  of  f o u r measures of  to  1-11,  accompanimental  i n the  the  particular  contribute  (these  over  textural  rests,  same f o u r  are  second  measures  from another  previous  (or  (e.g.,  i t involves the  articulation  which  second  q u a l i t y ) to  texture are of  the  One comprising  resembles a  clarinet  that  harmonic  of  instruments  i s comparable to the  i n s e v e r a l ways:  average of  of  The  element  In  different  element  out  element  the  discerned.  in a distinct,  separated  (and  one),  quintet.  however,  two-element  accompanimental example o f  are  be  textural  sonorities  linearizations  ('a'-section  accompaniment  itself  i n the  i n a much  nevertheless  accompanimental  in effect  g e n e r a l i z e about  i s featured  f o r example, a l l f i v e  element).  illustrating  second  tempo  the  to  featured  five-note vertical  similar  piece  The is  by  the  asserts  These v e r t i c a l i t i e s  textural  complexes  the  Pieces  accompanimental  elsewhere  clarinet),  the  of an  (or a l l but  ensemble t e x t u r e found (featuring  instrument  s t r u c t u r e may  establishment  featured  character.  each  textural  instruments  which) the  Details in Soloistic  the  performance is  isolated  ''"'''Regarding p e r f o r m a n c e i n s t r u c t i o n s s e e G y o r g y L i g e t i , Ten Pieces for Wind Quintet ( M a i n z : B. S c h o t t ' s S o e h n e , 1 9 6 9 ) , pp. 18 a n d 20. Also, i t was n o t e d i n t h e s e c t i o n on f o r m a l a s p e c t s t h a t s u b g r o u p i n g s o f p i e c e s occur through a v a r i e t y of parametric v a r i a n c e s ( i n a d d i t i o n to those i n v o l v i n g i n s t r u m e n t a t i o n - d e n s i t y and a c t u a l i n s t r u m e n t a t i o n ) . The fifth a n d s i x t h p i e c e s may b e c o n s i d e r e d one s u c h s u b g r o u p , w i t h t h e t h r e e  33 Example  14.  P i e c e No.  2, m e a s u r e s 1-4,  showing  a two-element  texture.  Prestissimo minaccioso e burlesco**  •)  A u l i e r d e n sff u n d - A k z e n t e n stels gleichmaftig s p i e l e n , so daft e i n e T a k t e i n t c i l u n g n i c h t w a h r n e h m b a r w i r d . D i e T a k l e u n d T a k t e i n t e i l u n g e n d i e n e n als O r i e n -  *) Play very evenly, except for the sff and sfaccen. ruations, so that the subdivision into bars is not perceptible. Bar lines serve as a means of orienta -  l i e r u n g , e i n e m e t r i s c h e P u l s a t i o n g i b t es n i c h t .  tton; there is no metrical pulsation.  © 1969 B. S c h o t t ' s Soehne, Mainz A l l r i g h t s reserved Used by p e r m i s s i o n of European American 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 Canadian agent f o r B. S c h o t t ' s Soehne.  from  the accompanimental  differentiation,  and  texture  timbral  t h r o u g h dynamic  quality,  as  shown  exposure,  i n Example  articulative 15.  c r i t e r i a a l r e a d y s t a t e d a s c o n n e c t i v e f a c t o r s ( i . e . , i n s t r u m e n t a t i o n , tempo, and a r t i c u l a t i o n ) . S e v e r a l a d d i t i o n a l f a c t o r s may be a d d e d t o t h e l i s t , one o f w h i c h i s t h e attacca i n d i c a t i o n a t t h e end o f t h e f i f t h p i e c e . Other c o n n e c t i v e f a c t o r s , w h i c h i n v o l v e l i n e a r p i t c h - c l a s s c o n n e c t i o n s , w i l l be disclosed i n d e t a i l later i n this chapter.  34 Example  15.  P i e c e No. 6, m e a s u r e s element t e x t u r e .  1-4, s h o w i n g a t w o -  Presto staccatissimo e leggiero  ffpp *)  £ = T o n r e p e t i t i o n staccatissimo, wie in Satz S  *) ~£ = staccatissimo repeated tones as in Movement 5  •) T o n r e p e t i t i o n bei der O b o e : staccatissimo, sehr d i s t i n k t , so schnell wie m o g l i c h . Die Spielart ist identisch m i t der 3. notierten Spielart der Ubrigen Instru-  **) Repeated tones in the Oboe staccatissimo. very distinct, as fast as possible. The manner of playing is identical to the manner of playing notated £ in the  mente (  etc. ). Die andersgeartete  bezieht sich lediglich a u f die K h y t h m i k : tation eP ist die Dauer der T o n f o l g e  Notation bei der N o -  gegeben, die  A n z a h l der Schlage j e d o c h f r e i , bei der N o t a t i o n ist die A n z a h l der Schlage festgelegt, die Dauer der T o n f o l g e j e d o c h frei (so k u r z wie m o g l i c h , da T o n r e p e t i t i o n so raseh wie m b g l i c h ) . Bei der N u tation ist der Kinsatz des ersten Tones metrisch festgelegt (fixierter l J latz tm T a k t d u r c h vorangehende Pausen), darauf folgt d i e T o n r e p e t i t i o n unabhangig v o m M e t r u m . Die 1'ausen in K l a m m e r n sind eine imaginare met rise he Krganzung der N o t a t i o n , s i e werden z u m 'I'eil v o n der T o n r e p e t i t i o n verschlungen; z. B. bedeulet 7 7 1*2 [i\ : einselzen im dritten T r i o l e n a c h l e l , die Pause [7] ist eine virtuelle E r g a n z u n g .  other instruments ( , e^, etc. ). The different notation refers only to the rhythm: in the notation £ the duration of the sequence is fixed, but the numbei of the attacks is free; in the notation fJjJJ the number of the attacks is fixed but the duration of tht sequence is free (as short as possible, since the tones are repeated as fast as possible). In the notation i^J ^1 J fl the entrance of the first tone is metrically fixed by the rests preceding it, whereupon the tones are repeated independently of the metre. The rests in brackets are the imaginary completion of the metre, and will be absorbed in part by the repeated tones. For  example, y 1  [7]  means: attack the third  quaver of the triplet; the rest [V] is the virtual com pletion of the triplet.  © 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne.  The  accompaniment  although  not  suggestive  features  the  flute,  ensemble t e x t u r e , That  i s to  say,  polyphonic  being  in  12  bar  soloistic  discerned one  i n the  the  from  featured  with  one  with  interact  that  two  pieces.  modes o f  accompanying with  featured  instrument  p r i m a r y and  the  dynamically  components,  enough  component.  of  numerous p o l y p h o n i c  featured exposed  taken  suggest  pieces.  the  horn  texture Example  and  enters  eventual  one  a l l the  components.  Two  only  generally components  fail  to be  components overall  be  i n which  c o n t i n u i t y to the  a  16.  instrument of  main  i m p l i c a t i o n of  separately,  Rather,  several secondary  12-15  when t h e  the  an  continuous  predominates,  only  as  be  t e x t u r a l s t r u c t u r e may  i n d e p e n d e n c e and  i n ways w h i c h  t h i s mode o f  a  piece,  ensemble  T'tue s e c o n d mode i s one  i s in operation, and  instrument  "ensemble-like"  well  i n the  within  given  eighth  nevertheless  could very  q u a l i t y that  excerpt  the  quintet,  outlined  i s , in fact,  The  i n the  earlier  continuous  Measures  It  i n the  i n what  criteria  particular  whole.  soloistic  the  illustrate  bassoon  the  is realized.  t e x t u r a l element  separate  to  texture  contrasting sustained  noted  The  and  s i x t e e n measures of  instruments  illustrated  t h e most  involved.  to  was  the  first other  i n w h i c h no  t e x t u r a l element  being  a  are  three  of  texture  horn entry It  a  any  clarinet,  the  that  with  of  the  according  texture  effect  of  define considered  interact  textural  with  element  examples w i l l  serve  textural structure.  the  second  fragments  piece  reveal a  contributed  by  continuous the  clarinet  remaining  line  four  12 instruments. textural  element  Again, of  these  their  own,  fragmented but  are,  " o v e r l a y s " do rather,  not  integral  comprise to  the  a  single  12 T h i s type of e l e m e n t i s one o f two "textural quality."  component i n t e r a c t i o n w i t h i n a s i n g l e t e x t u r a l t o be d i s c u s s e d i n C h a p t e r s I I I a n d I V a s f a c t o r s o f  Example  16.  P i e c e No. 8, m e a s u r e s accompanimental  Allegro (J 1  COn  delicatezza  72) *) fliefiend, alle  x  1, 2, 5, 10, a n d 12, s h o w i n g a n " e n s e m b l e - l i k e "  element.  (sehr gleichmafiig, ohne jede Betonung der Takte bzw. Taktunterteilungen.)  (very evenly, without any accentuation of the bars or their subdivisions.) neuen Einsfitze sehr weich / fluently, every new entry very SOJI s s 5 ~l2 e_ 1  ') fliefiend, alle neuen Einsfitze sehr weich /  fluently, every new entry very soft £  Clarinetto in Sit  S  r  I  sivtUU  PP *) fliefiend, alle neuen Einsatze sehr weich / fluently, every new entry very soft  Fagotto PP Dynamische Balance: pp gleich in F16te, Klarinette, Fagott. Klarinette verhalthismafcig etwas starker blasen.  *J Balance of dynamics: pp equal in Flute, Clarinet Bassoon. Play the clarinet somewhat louder in relation.  Fagott, con sordino: Ein Tuch, in die Schalltiffnung gestopft.  * * ; Bassoon,con sordino: a cloth stuffed into the upper joint. _  3  )  **)  Fl. Fl.  Cl.Siv Cl.$i\>  Cor.Fa Fag. Fag.  © 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne.  texture  as an  37 overall in  texture  i n which  the clarinet  i s primary.  13  This  i s illustrated  E x a m p l e 17.  Example  17.  P i e c e No. 2, m e a s u r e s 12-15, s h o w i n g o n e t e x t u r a l element w i t h one p r i m a r y and f o u r secondary components.  Foco meno mosso , 12 CJ = 144) Fl.Sol  C.Ing.  Cl.Siv  Cor.Fa  Fag;  Fl.Sol C.Ing.  Ct.$i\>  Cor.Fa  Fag.  PPrpossibile  © 1 9 6 9 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne.  T h i s i s a p a r t i c u l a r l y c l e a r example o f f o r m a l d e l i n e a t i o n t h r o u g h textural diversity. T h e o p e n i n g o f t h e s e c o n d p i e c e was shown e a r l i e r t o c o n s i s t o f two s i m u l t a n e o u s , d i s p a r a t e t e x t u r a l e l e m e n t s w h i l e i n t h e passage j u s t d i s c u s s e d and i l l u s t r a t e d a b o v e — a second f o r m a l s e c t i o n - — o n l y one e l e m e n t o p e r a t e s . T h e s e f o r m a l s e g m e n t s a r e f u r t h e r d e f i n e d ". t h r o u g h v a r i a n c e s i n tempo a n d d y n a m i c s .  38 The f o u r t h p i e c e f e a t u r e s a s i n g l e p o l y p h o n i c t e x t u r e i n w h i c h t h e f l u t e i s d y n a m i c a l l y , r e g i s t r a l l y , and r h y t h m i c a l l y exposed r e l a t i v e t o t h e o t h e r two components.  The c l a r i n e t and bassoon ( t h e l a t t e r b e i n g  c o n s i d e r a b l y more fragmented than t h e o t h e r two i n s t r u m e n t a l p a r t s ) c o n t r i b u t e more t o t h e o v e r a l l polyphony than t o a d i s p a r a t e t e x t u r a l element.  An e x c e r p t from No. 4 i s g i v e n as Example 18 .  Example 18.  P i e c e No. 4, measures 1-4, showing one t e x t u r a l element w i t h one p r i m a r y and two secondary components.  © 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne.  In pieces), element  both  outlined  (but multi-component)  be d e a l t  with  i n the f i n a l  textural  earlier  works  drawn.  The ensemble p i e c e s  sonorities.  w h i c h Atmospheres  differentiated that  they  sixth,  i s representative.  frequent  and t e n t h  changes, o f t e n  suggestive  and, o f t e n ,  pieces,  accompanied  pieces,  pieces  to possess a c e r t a i n  the parallel  often  degree  consisting of of e a r l i e r  slowly pieces  also  with the l a t t e r i n  contrast texture each  from  i n tempo, n o t a t e d  "mood."  In this  a n d Aventures. than  changes.  contain  that  texturally  The second, four  to s i x  meter,  sense they a r e  Although the scale  of the aforementioned  mode o f d i f f e r e n t i a t i o n  characterization of textures  may b e  pieces,  by changes  i s much s m a l l e r  Ligeti's  The s o l o i s t i c  abrupt  and g e n e r a l  which  of t h e quintet  are suggestive  f o r example,  o f t h e s t y l e o f Apparitions  the quintet  related  they  harmonic  chapter.  I ) and t h e p i e c e s  regard  of a single-  detail  a p a r a l l e l i s m between  were s a i d e a r l i e r  In this  and s u g g e s t i o n  components—a  section of this  structure,  dynamics, r e g i s t e r , d e n s i t y ,  the  and s e c o n d a r y  i n Chapter  and f o u r t h  a r e r e i n f o r c e d by s t r o n g  from t h e ensemble p i e c e s ,  feature  eighth,  texture  of  t h e second  textural continuity, the individual textures  changing of  (mentioned  (i.e.,  instrument  texture  between t h e p r i m a r y  Concerning  of  above  the primacy of the featured  affiliation will  instances  i s of significance i n  i n the quintet.  Summary Texture of  h a s been  cited  "ensemble" and " s o l o i s t i c "  involve  h e r e asa'^major f a c t o r , i n t h e c h a r a c t e r i z a t i o n pieces.  While  e s s e n t i a l l y one t e x t u r a l e l e m e n t  complete disparate  piece  or at l e a s t a formal  ensemble p i e c e s  at a time  i n the third  shown t o  ( e i t h e r throughput  s e c t i o n ) , one i n s t a n c e  t e x t u r a l e l e m e n t s was n o t e d  were  piece.  a  of simultaneous, Two  configurations  40 were  said  to c h a r a c t e r i z e the s o l o i s t i c  simultaneous, providing with  contrasting textural  registral  exposure,  emerging  Atmospheres  and  While  the rhythmic  of Rhythmic  the pieces  of structure.  i s apparent,  dynamic  and/or  Finally, the  earlier  works  of which  p i e c e s t o a group  typified  and M e t r i c  here  Design  t o attempt  to explicate  structures of a l l t e n pieces, several aspects of  design are accessible,  even a moderate u n d e r s t a n d i n g most u n i v e r s a l  through  t o a group o f L i g e t i ' s  i t i s not the intention  and m e t r i c  element  instrument  Aventures.  Principles  completely  as primary  i s r e p r e s e n t a t i v e , and t h e s o l o i s t i c  b y Apparitions  the featured  only a single  as-well as continuity  ensemble p i e c e s were l i k e n e d  rhythmic  elements occur,  o n e o f them; a n d o n e i n w h i c h  t h e featured instrument  p i e c e s : o n e i n w h i c h two  and, perhaps,  i s the rarity  noteworthy,  of the musical most  significant  and n e c e s s a r y f o r  l a n g u a g e o f t h e work. aspect  o f rhythm  o f o p e r a t i v e meter a t t h e l e v e l  The  i n a l l of  of t h e notated  measure. Meter  i n the present  context  refers  t o one p a r t i c u l a r  mode o f  14 rhythm  —specifically,  one i n which  impulse  of a c c e n t e d ^  and u n a c c e n t e d  beats.  patterns called  measures,  represent  d e p e n d s on a c c e n t ; saying,  groupings  a r e d e f i n e d by  These p a t t e r n e d  the lowest-level metric unit.  metric units  t h e r e f o r e , t h a t meter  Meter,  a r e d e l i n e a t e d by a c c e n t e d  i s h a r d l y ever  groupings, then,  impulses.  In  operative at the l e v e l of  14 specific  Other " e l e m e n t - r h y t h m s " w i l l be d e f i n e d reference to the f i r s t piece.  i n Chapter  I I I with  ^ A p a r t i c u l a r a r t i c u l a t i o n o r i m p u l s e may b e a c c e n t e d through r e g i s t r a l and/or dynamic exposure, a r t i c u l a t i v e a c c e n t s ( e . g . , - - , >, , e t c . ) , a n d / o r e x t e n d e d d u r a t i o n r e l a t i v e t o s u r r o u n d i n g impulses. In s h o r t , a c c e n t here r e f e r s t o emphasis i n h e r e n t i n t h e music, n o t imposed by t h e p e r f o r m e r . A  t h e n o t a t e d measure i n t h e p i e c e s , t h e s u g g e s t i o n i s t h a t p a t t e r n e d u n i t s of  s t r o n g and weak b e a t s a r e r a r e l y e s t a b l i s h e d i n a way  n o t a t e d , apparent m e t r i c u n i t s p e r c e i v a b l e as such.  t h a t makes  The i m p l i c a t i o n s of  t h i s phenomenon a r e c o n s i d e r a b l y d i f f e r e n t i n p i e c e s or s e c t i o n s i n which t h e n o t a t e d meter i s c o n s t a n t , as compared to t h o s e i n which i t i s fluctuant.  I n t h e former, b a r l i n e s appear p r i m a r i l y f o r ease o f r e a d i n g ;  t h e s e p i e c e s (or s e c t i o n s ) may  be c o n s i d e r e d " a m e t r i c " a t t h e l e v e l of t h e  n o t a t e d measure (because of t h e l a c k o f a c c e n t - d e l i n e a t e d m e t r i c u n i t s o f that s i z e ) .  H i g h e r - l e v e l impulse g r o u p i n g s (not n e c e s s a r i l y  large-scale  m e t r i c u n i t s i n t h e sense o f a c c e n t - a r t i c u l a t e d g r o u p i n g s ) may, be d i s c e r n e d .  For i n s t a n c e , l a r g e r phrases w i t h o u t i n t e r n a l m e t r i c  s u b d i v i s i o n s ( a t t h e l e v e l o f t h e measure) may  be f e l t as c o n t i n u o u s  g e s t u r e s which d i s p l a y p a r t i c u l a r r h y t h m i c s t r u c t u r e s ( t o be below).  however,  specified  The l o w e s t - l e v e l impulse u n i t , t h e n , becomes t h e phrase  itself,  not t h e n o t a t e d b a r . Most o f t e n t h e s e c o n t i n u o u s g e s t u r e s or phrases a r e not m e l o d i e s , but r a t h e r t e x t u r a l elements c o n s i s t i n g of s e v e r a l components.  We may,  single-line  sounding  f o r example, speak of a "homophonic p h r a s e , " i n which  a l l of t h e components move i n s t r i c t v e r t i c a l a l i g n m e n t , o r a " p o l y p h o n i c p h r a s e , " i n w h i c h t h e components a r e engaged i n a complex i n t e r w e a v i n g c o n s i d e r e d t o g e t h e r as a s i n g l e g e s t u r e of f l u c t u a t i n g r h y t h m i c In t h e case o f t h e more common p o l y p h o n i c phrase, one fundamental  interaction. a s p e c t of  r h y t h m i c d e s i g n concerns t h e p r o p e r t i e s of " p r o g r e s s i o n " and " r e c e s s i o n " ' ^ i n the l e v e l of r h y t h m i c a c t i v i t y of t h e t e x t u r a l element as a whole. A l t h o u g h such c o n t i n u o u s p o l y p h o n i c phrases a r e found most f r e q u e n t l y 16 " P r o g r e s s i o n " and " r e c e s s i o n " a r e terms and c o n c e p t s used e x t e n s i v e l y by W a l l a c e B e r r y . See h i s Structural Functions, Chapters 2 and 3..  42 i n ensemble p i e c e s (because, as n o t e d e a r l i e r , t h e y c h a r a c t e r i s t i c a l l y f e a t u r e o n l y one  t e x t u r a l element at a t i m e ) , s e v e r a l s o l o i s t i c  o f f e r examples.  The accompanimental element ( i . e . , f l u t e , c l a r i n e t ,  bassoon) of t h e f i r s t s i x t e e n measures of p i e c e No.  pieces and  8, f o r i n s t a n c e ,  o f f e r s an e x c e l l e n t example of r h y t h m i c p r o g r e s s i o n and r e c e s s i o n w i t h i n a s i n g l e , continuous polyphonic  phrase.  Example 19 c o n s i s t s of a  graphic  r e p r e s e n t a t i o n of t h e a c t i v i t y l e v e l i n t h i s s e c t i o n (accompanimental element o n l y ) as t o the number of impulses per q u a r t e r - n o t e composite rhythm ( h e n c e f o r t h termed  i n the  "impulse-density").^  I g n o r i n g t h e horn p a r t f o r now,  the g r a p h r e v e a l s a l a r g e - s c a l e  p r o g r e s s i o n and r e c e s s i o n of r h y t h m i c a c t i v i t y which peaks i n bar  11  (22 i m p u l s e s/ J ) f o l l o w e d by an abrupt d e c l i n e i n a c t i v i t y commencing i n bar 14.  These, t h e n , r e p r e s e n t  consider " q u a n t i t a t i v e " aspects  two  l a r g e - s c a l e impulse u n i t s which  of r h y t h m i c d e s i g n  (i.e., activity levels  e x h i b i t i n g growth and d e c l i n e ) , r a t h e r than s p e c i f i c p a t t e r n s of a c c e n t and unaccent ( i . e . , " q u a l i t a t i v e " a s p e c t s metric u n i t s ) .  i n connection  specific  W h i l e the "downbeat" d e l i n e a t e s m e t r i c u n i t s , we might  speak of a " t u r n - a r o u n d p o i n t " as b e i n g a d e l i n e a t o r of units.  with  Such a j u n c t u r e may  impulse-density  be c h a r a c t e r i z e d as the p o i n t at w h i c h t h e  r h y t h m i c p r o g r e s s i o n ceases and the r e c e s s i o n b e g i n s (as i n t h i s p a r t i c u l a r case) o r v i c e v e r s a .  In t h i s piece the turn-around point  on the t h i r d beat of measure 14 as i n d i c a t e d i n Example The  19.  accompanimental element, t h e r e f o r e , r e v e a l s i t s own  l a r g e - s c a l e rhythmic s t r u c t u r e — o n e  which may  occurs  mode of  a l s o be seen t o i n t e r a c t  w i t h t h e horn p a r t ( t h e second d i s t i n c t t e x t u r a l e l e m e n t ) .  This i n t e r a c t i o n  ^ I f more than one instrument sounds i n s t r i c t v e r t i c a l a l i g n m e n t , i t counts as one impulse o n l y f o r the purposes of t h e i m p u l s e - d e n s i t y graph.  43 Example  19.  P i e c e No. 8, m e a s u r e s  1-16, i m p u l s e - d e n s i t y  graph.  \  measure no.  results is a to  from  several conditions.  a t i t s maximum sense  level  the opening  of activity  rhythmic  function anacrustically  occur  in a registrally  First,  the latter  ( i . e . , 22 i m p u l s e s / J,  t o t h e horn  or dynamically  entry  peak a c t i v i t y  lasts  i n t h e accompaniment the opening  Second,  f o r twelve  12). In  may b e  (although the l a t t e r  exposed manner), w h i l e  element.  with  measure  p r o g r e s s i o n i n t h e accompaniment  c o n t i n u i t y w i t h i n i t s own t e x t u r a l  coincident  e n t e r s when t h e f o r m e r  heard  does n o t  retaining the  t h e maintenance o f quarter-notes,  s u s t a i n e d and d y n a m i c a l l y  intensifying  roughly pitch  44 in  t h e horn.  poco  The f i r s t  in relievo  t h e accompaniment  as  t h e graph  begins  reveals,  small-scale version  the a c t i v i t y  of that  from  these  own l o w e r - l e v e l m e t r i c score,  at which t h e d e c l i n e  t h e turn-around  point).  curve of t h e horn  o f t h e accompaniment,  interactive features, units, defined  d i v i s i o n s i n operation  Example 2 0 c o n s i s t s o f t h e horn configuration version,  found  suggested  levels  part  i n the score  p e r h a p s more  t h e horn  i s itself  part  n o t by t h e n o t a t e d  a  just  (measures  (bottom  staff  exhibits i t s  measures o f t h e  common d e n o m i n a t o r o f  (i.e., | | I* | I ! I 12-16)  x  FI 1 I I =  accent  structure a r e represented  6 0 / J ) . " ^  i n the metric  o f example),  indicative of the perceived  of metric  And t h i r d ,  both c o i n c i d i n g  but a f l u c t u a t i n g meter based on t h e lowest  rhythmic  part  in activity  i n bar 16.  to the zero-activity level Apart  the  (i.e.,  (measure 1 4 ) , marked  i n t h e horn  i s , curiously, the point  in  prior  p i t c h change  and a r e - m e t e r e d  pattern.  Three  by t h e a r r o w s  depicting  u p b e a t s and downbeats. The  criteria  aspects  of duration  a  downbeat  local  its  entry,  and  there  dynamic  as noted  characterizations at level  and r e g i s t e r p r i m a r i l y .  simply  because  earlier,  a r e no o t h e r  culmination  downbeat  f o r t h e downbeat  The f i r s t  i t i s the f i r s t  impulses  t o suggest  on t h e change o f p i t c h t o B ^  characterization, while  line)  and l i n e a r  approach  gives  t h e E^-* a l o c a l  (i.e.,  downbeat  may b e  otherwise.  contributes  The  to i t s  the highest  a f t e r the delay  of progression  The l e a p  (although  by t h e accompaniment),  register (i.e.,  quality.  considered  p i t c h of the l i n e  i s somewhat o v e r p o w e r e d  patterned  A ^  (a) i n c l u d e  pitch i n the t o D^5)  f r o m B^, s t e p w i s e  approach  18  i By c o n s i d e r i n g t h e p u l s e u n i t t o b e 6 0 / 4, a n y i m p u l s e w i t h i n t h e metric configurations involving I I I, I I I I , and I l l I I , t h e t h r e e o p e r a t i v e i n t h e p i e c e , may q u a l i f y a s a d o w n b e a t , o n c o n d i t i o n t h a t i t i s a c c e n t - d e f i n e d through r e g i s t e r , dynamics, d u r a t i o n , e t c . 3  5  :  Example 20.  P i e c e No. 8, m e a s u r e s  12-16 ( h o r n  p a r t o n l y ) , showing l o w - l e v e l m e t r i c  t  (t)  t I  (») W  1 1 11%  remetered  (no. of 6 0  mm.  12  ths  )  (50)  f  r  'MM'  (42) (24)  (39) (15)(15X39)  units.  1  (!) I 1 1 IMJ  IJ-  from  over  which the  emphasize  G^,  feel  the the  having  of  an  delay  of p r o g r e s s i o n ) ,  —also  a downbeat a t  been a p p r o a c h e d  arrival  point  linearly  aided,  and  longer  this  from  i n p a r t , by  duration  particular  the  the  are  factors  level.  sustained  G^,  termination  of  Finally,  has  the  activity  in  19 the  other At  above  three the  approaching final  a  the  arrival  point  subdivision  other of  the  and  the  horn  undifferentiated (beats  1-2)  and  any  by 10  which  activity  the  of  (beats  as  of  downbeats  continue  to  with  to  of  a  phrase  the  clear  the  is  G^. example  (e.g.,  of  in  rhythmic  accompanimental  i n d i c a t e d i n Example piece,  (c).  final  quintet to d e f i n i n g a r e g u l a r  As  in  the  low-level metric  a d d i t i o n a l aspect the  and,  components  the  provides  instances  the  in level  accompanying  continuous  as  i t s articulation.  structural value suggested  specified  emerge  such because of  attributed  Specifically,  pulse. 3-4)  few  one  section i n the 20  accent)  any  i n the  in a  the  part),  as  eighth piece  recession one  local  culminates  significance  s e c t i o n i s noteworthy.  comes c l o s e r t h a n  is felt  whole l i n e  section of  w e l l as  (e.g.,  B^  the  impulses  downbeat o f  accentual  first  as  The  rhythmic  progression  accompaniment),  1  only  i n the  the  E x a m p l e 2u] , two  intensification  cessation of  rhythmic  this  on  points.  i s the  While  in  t h e u n i t s d e l i n e a t e d by  (b)  dynamic  prime f a c t o r  of  of  arrival  G^  fact, i s the Again  level  [i.'.e'. , l e v e l  downbeats o r  The  components.  three  21,  design  element Cif  measures  instrumental  parts  c o i n c i d e o n e a c h q u a r t e r - n o t e , w h i l e i n t e r a c t i n g i n a c o m p l e x way during 19 The h a r m o n i c s t r u c t u r e w h i c h o c c u r s a c r o s s b a r s 15-16 i s a B major c h o r d w i t h an a d d e d s e c o n d ; t h e r e l a t i v e c o n s o n a n c e o f t h i s s o n o r i t y p l a y s an i m p o r t a n t r o l e i n t h e a r r i v a l - p o i n t q u a l i t y o f t h e s u s t a i n e d p i t c h e s ( i n both t e x t u r a l elements). 20 any  L i g e t i does, however, s p e c i f y i n t h e s c o r e : " v e r y e v e n l y , without a c c e n t u a t i o n o f t h e b a r s o r t h e i r s u b d i v i s i o n s . " See L i g e t i , Ten  Pieces,  p. 27.  47 t h e b a l a n c e o f each beat. q u a r t e r s a r e marked t h r o u g h Example 21.  Even w i t h o u t any performer-imposed s t r e s s , t h e t h e concurrence  of a r t i c u l a t i o n .  P i e c e No. 8, measures 1 ( b e a t s 1-2) and 10 ( b e a t s 3 - 4 ) , showing p o t e n t i a l p u l s e d e f i n i t i o n .  BSN  As t h e i n t e r a c t i o n between r h y t h m i c p a t t e r n s becomes more complex and, e s p e c i a l l y i n t h e l i g h t of t h e l i n e a r p i t c h p a t t e r n s w h i c h occur o u t of-phase w i t h t h e rhythmic p a t t e r n s , t h e quarter-note pulse i s e f f e c t i v e l y 21 obscured  i n f a v o r o f t h r e e r h y t h m i c a l l y independent l i n e a r  Example 22(a) c o n s i s t s of measure 5 o f t h e s c o r e w i t h t h e l i n e a r p a t t e r n s marked w i t h s l u r s .  events. aforementioned  T h i s c l e a r l y r e v e a l s t h e l a c k of  s y n c h r o n i z a t i o n between r h y t h m i c and l i n e a r p a t t e r n s . I n (b) o f Example 22, t h e f i r s t n o t e s of t h e l i n e a r p a t t e r n s i n each i n s t r u m e n t  a r e i n d i c a t e d by noteheads w i t h t h i c k stems, a l l of which  a r e connected by a t h i c k beam.  The stems between t h e beamed n o t e s  21 These t h r e e e v e n t s , however, a r e s t i l l t e x t u r a l element i n o p e r a t i o n a t t h i s p o i n t .  components of t h e one  48 represent  the  rhythmic  distances  between p a t t e r n  synchronization (a),  rhythm  in operation  recurrences.  b e t w e e n r h y t h m i c and  further illustrated,  revealed—the are  c o n f i g u r a t i o n s of  of  (one  an  linear  i n each  obscures the  quarter-note  rhythmically  progressive  E x a m p l e 22.  Piece  No.  but  8,  Not  only  linear  thereby  i s the  patterns,  element-rhythm other  pattern  recurrence.  instrument),  pulse, and  each p a r t ,  as  the  m e a s u r e 5,  of  and  the  rhythmic  in  than meter  Three  i s , here, rhythms  which  reinforces  texture  and  system  distinct of  the  of  apparent  indicated earlier,  showing  lack  interaction  recessive qualities  showing  linear  as  a  the whole.  patterns.  P i e c e No. 4, f e a t u r i n g  the flute,  i s notated  completely  i n ^ (the  22 meter b e i n g texturally phrases  essentially structured  polyphony clarinet  for  The r e s u l t i n g  effected  That  are.  i s engaged  i n two  instruments providing single  textural  element  i s , t h e accompanying the flute,  The p h a s i n g  fragmented)  i s one o f p s e u d o with the  a p p e a r i n g more  independent  i n part r e s p o n s i b l e  tendencies i n the piece,  of which r e v e a l  state.  E x a m p l e 23 c o n s i s t s o f a g r a p h i c r e p r e s e n t a t i o n o f t h e r h y t h m i c (i.e.,  move f r o m  an a c t i v e  impulse-density o f t h e composite  t o an  both  phrases  activity  an o v e r a l l  continuous  i n s t r u m e n t s move i n a n d  i s , however,  p r o g r e s s i v e and r e c e s s i v e  ) , and i s  the (often  "phasing" of the f l u t e  synchronization with 23  they a c t u a l l y the l o c a l  the flute  by t h e rhythmic  and bassoon.  of rhythmic  than  so t h a t  w i t h t h e accompanying  counterpoint.  out  non-functional as to perceived effect  inactive  rhythm) o f t h e f o u r t h  piece. The is  obvious  general rhythmic  recession  from  The second  more complex the o v e r a l l bar  18).  abrupt  as i t c o n t a i n s s e v e r a l flow of rhythmic  The f l u t e  changes  measures the f l u t e  t h e graph.  11-12, part  i s silent  in register  in the f i r s t phrase,  during the other  and dynamics  i s affected.  over  alters  the rest i n which f e a t u r e  and b a s s o o n  only the rhythmic  resumes  1-9)  i sconsiderably  interruptions,  i n the clarinet  The f l u t e  (measures  one o f which  (e.g., the fermata  16, a n d 1 7 ) ; i t i s , t h e r e f o r e , which  however,  interruptions,  activity  phrase  i t s level  (e.g.,.  flow of  of a c t i v i t y  i m m e d i a t e l y upon r e - e n t e r i n g . 22 L i g e t i u n d e r s c o r e s t h i s by t h e p e r f o r m a n c e n o t e s i n t h e s c o r e ; "Apart from t h e i n d i c a t e d a c c e n t s , always p l a y v e r y e v e n l y and without a c c e n t u a t i o n , so t h a t t h e s u b d i v i s i o n s i n t o b a r s d o e s n o t become perceptible." S e e L i g e t i , Ten Pieces, p . 15. 23 T h e i r r e l a t i o n s h i p t o t h e f l u t e l i n e w i l l become more a p p a r e n t in the next s e c t i o n .  E x a m p l e 23.  P i e c e No.  4,  measure  impulse-density  graph.  51 Rhythmic "frustrated" the in  final  structure of the flute  as a r e s u l t  of recurring  r e c e s s i o n o f rhythmic  the flute  alone,  part  i n t h e second  i n t e r r u p t i o n s noted  activity  i n measures  as w e l l as i n t h e t r i o ) ,  the p r e v i o u s measures because of t h e abrupt line,  concurrent  parts.  with  Although  close,  one g e t s  t h e extreme r e g i s t e r  the overall  rhythmic  the impression  that  phrase i s Even  19 t o t h e e n d ( b o t h  seems somewhat d i v o r c e d "breaking  shift  i s brought  the flute  from  o f f " of the flute  and dynamic  drive  above.  i s left  i n the other  convincingly to a i n a state of  24 unfulfillment  back  Although a metric unit, in  connection  first  phrase,  i n the fourth piece the notated large-scale units  with  7.  maximum (e.g.,  in  with  The c r i t e r i a  7.  (i.e.,  and  r"T~| f^f\  i s completely  phrase,  p o i n t o c c u r r i n g on t h e f i r s t  interpretation occurs  the flute  Ij I I I J )»  a n t  t h e absence o f t h e f l u t e  The r e c e s s i v e u n i t  tension first  the turn-around forthis  spans measures  relaxed with  are threefold: on t h e l a s t  In t h e  itself  offers  *  third,  of bar 6  a local  the f i r s t  the a c t i v i t y  commencing  beat o f  f i r s t , the  beat  rhythmic quintuplet level  on t h e f i r s t  drops  beat o f  7-9, w h e r e u p o n t h e r h y t h m i c  the sustained v e r t i c a l  a s two l a r g e - s c a l e u n i t s  one r e c e s s i v e ) might  as w e l l .  noted  s i x b a r s may be d e f i n e d a s a  towards that p o i n t , c u l m i n a t i n g w i t h  considerably with bar  the first  a d e n s i t y o f 6 ) ; second,  the piece  i s not .operative as  of impulse-density, not u n l i k e those  impulse-density o f t h e phrase  intensification  measure  t h e e i g h t h p i e c e , may b e d i s c e r n e d h e r e  f o r example,  progressive unit bar  i n b a r 19.  of impulse-density  dyad  C^-D^.  The  (one p r o g r e s s i v e  b e d e p i c t e d a s i n E x a m p l e 24.  24 I f o n e c o m p a r e s t h e " r e c e s s i o n " i n t h e two p h r a s e s , o n e n o t i c e s t h a t , i n t h e f i r s t , t h e f l u t e changes r e g i s t e r smoothly and without interr u p t i o n ( e . g . , b a r 2 ) . I n t h e second p h r a s e , t h e f l u t e s t o p s s u d d e n l y and r e s t s b e f o r e r e - e n t e r i n g a t t h e lower r e g i s t e r and dynamic l e v e l ( e . g . , bar 19).  52 Example 24.  P i e c e No. 4, l a r g e - s c a l e units.  large-scale progressive unit  The  and r e c e s s i o n .  flow i s e s s e n t i a l l y unaffected bar  large-scale recessive unit  second p h r a s e i s more d i f f i c u l t  rhythmic progression  impulse-density  t o c h a r a c t e r i z e as t o u n i t s o f  However, because t h e o v e r a l l r h y t h m i c  by t h e i n t e r r u p t i o n s ( a p a r t from t h e r e s t i n  18), the l a r g e - s c a l e progressive  u n i t might a l s o be c o n s i d e r e d  unaffected.  Even t h e r e s t i n b a r 18 might be f e l t t o h e i g h t e n t h e t e n s i o n because i t i s not approached by an a p p r e c i a b l e lies  d e c l i n e i n rhythmic a c t i v i t y .  i n f i n d i n g t h e turn-around point.  The problem  I n c o n s i d e r a t i o n of t h e impulse-  d e n s i t y curve (Example 2 3 ) , one i n t e r p r e t a t i o n f o r such a p o i n t 21—the beginning of the f i n a l rhythmic recession. one  i s measure  I f , on t h e o t h e r  hand,  t a k e s i n t o account t e n s i o n t h r o u g h r e g i s t r a l and dynamic exposure, t h e  second beat o f b a r 19 might be more p e r s u a s i v e .  After a l l , the f i r s t  of b a r 19 i s u n q u e s t i o n a b l y t h e r e g i s t r a l and dynamic c l i m a x  beat  point of the  p i e c e , w h i l e t h e second beat i n i t i a t e s a r e l a x i n g t r e n d w i t h i n t h o s e same parameters ( b u t n o t w i t h i n t h e parameter o f rhythm).  I n any c a s e , t h e f o u r t h  p i e c e does e x h i b i t t h e p o t e n t i a l f o r c h a r a c t e r i z a t i o n as t o l a r g e - s c a l e u n i t s of impulse-density  w i t h i n a rhythmic s t r u c t u r e of p r o g r e s s i v e  and r e c e s s i v e  qualities.  The  t h i r d piece  (an ensemble type) p r o v i d e s  an example o f l a r g e - s c a l e  53 r h y t h m i c p r o g r e s s i o n and r e c e s s i o n w i t h i n an extended p o l y p h o n i c p h r a s e which spans t h e e n t i r e p i e c e .  Example 25 c o n s i s t s o f t h e i m p u l s e - d e n s i t y  c u r v e o f t h e p i e c e and, a l t h o u g h i t s shape i s g e n e r a l l y s i m i l a r t o t h a t o f t h e e x c e r p t from t h e e i g h t h p i e c e c i t e d e a r l i e r  (even t h e emergence o f a  s i m u l t a n e o u s second t e x t u r a l element o c c u r s i n b o t h ) , No. 3 i s d i f f e r e n t i a t e d by one i m p o r t a n t s t r u c t u r a l f a c t o r . c o n t i n u o u s t e x t u r a l element,  S p e c i f i c a l l y , the single,  i n d i c a t e d on t h e graph, i s composed o f f o u r  c o n s e c u t i v e t e x t u r a l elements.  Three of t h e s e c o n t r i b u t e t o t h e l a r g e -  s c a l e p r o g r e s s i o n (measures 1-8, 8-9, and 9-13), and one c o m p r i s e s t h e r e c e s s i o n (measures 14 t o t h e end).  (The r h y t h m i c i m p l i c a t i o n s o f t h e  o c t a v e - d o u b l e d theme i n b a r s 1 0 - 1 2 — i . e . , t h e s i m u l t a n e o u s second  textural  e l e m e n t — w i l l be d e a l t w i t h s h o r t l y . )  Example 25. • P i e c e No. 3, i m p u l s e - d e n s i t y graph.  turn-around point tr.H  15 measure  no.  1  54 The d i f f e r e n c e i n t h e l e v e l s of o v e r a l l a c t i v i t y i n the t h r e e s t a g e s of p r o g r e s s i o n a r e l a r g e l y the r e s u l t of r h y t h m i c and  textural  p a r t i c u l a r s ( i . e . , s u r f a c e d e t a i l s ) o f the i n d i v i d u a l components of each c o n s e c u t i v e p o l y p h o n i c element.  For example, i n measures 1-8,  the 25  components move r e l a t i v e l y s l o w l y and  i n a fragmented f a s h i o n ;  the  i n c r e a s i n g c o m p l e x i t y of i n t e r a c t i o n between components p r o v i d e s o v e r a l l rhythmic progression. moves more c o n t i n u o u s l y and  I n t h e second s t a g e , b a r s 8-9,  i n smaller note values.  components, each of w h i c h undergoes a r h y t h m i c  The  the  each p a r t  i n t e r a c t i o n of  intensification,  yields  t h e sharp i n c r e a s e i n t o t a l r h y t h m i c a c t i v i t y r e p r e s e n t e d on t h e graph 26 by the almost v e r t i c a l l i n e . by t h e c l a r i n e t t r i l l  The t h i r d s t a g e of p r o g r e s s i o n i s e f f e c t e d  ( e . g . , an i n d e f i n i t e number of impulses per q u a r t e r -  note) . The b e g i n n i n g of each of the t h r e e s t a g e s o f r h y t h m i c  progression  ( d e f i n e d above) as w e l l as t h a t of t h e r e c e s s i v e g e s t u r e i s marked by a concurrence  of a r t i c u l a t i o n .  I n c o n s i d e r a t i o n of t h i s d e t a i l , one may  to a t t r i b u t e m e t r i c accentual s i g n i f i c a n c e to these p a r t i c u l a r  wish  impulses,  t h e r e b y q u a l i f y i n g t h e f o u r c o n s e c u t i v e elements as m e t r i c u n i t s — u n i t s which a r e l a r g e r than the n o t a t e d measure but s m a l l e r than t h e u n i t s of i m p u l s e - d e n s i t y t o be exposed l a t e r .  These a r e i n d i c a t e d i n Example 26  once a g a i n , i n o r d e r t h a t i m p u l s e s — n o t a t e d  " o f f - t h e - b e a t " i n the  and,  score—be  c o n s i d e r e d l o c a l downbeats, t h e m e t r i c i n d i c a t i o n s must be based on a p u l s e 25 The c o n t i n u i t y i n h e r e n t i n the l i n e a r components of t h i s p a r t i c u l a r t e x t u r a l element, d e s p i t e t h e apparent f r a g m e n t a t i o n of the i n s t r u m e n t a l p a r t s , i s d i s c u s s e d i n t h e next s e c t i o n on l i n e a r d e t a i l s of p i t c h o r g a n i z a t i o n . 26 T h i s sharp i n c r e a s e i n r h y t h m i c a c t i v i t y , c o n c u r r e n t w i t h t h e i n s t r u m e n t a t i o n - d e n s i t y r e d u c t i o n , was r e f e r r e d t o e a r l i e r as a t r a n s i t i o n a l s e c t i o n between t h e two main f o r m a l s e c t i o n s of t h e p i e c e .  55 r a t e which w i l l  accommodate  such  E x a m p l e 26.  1  mm.  Taken as  7  one  the octave-doubled progression occurring  theme) may  excerpt  from  No.  of rhythmic  particular  8 cited  activity.  t e x t u r e may  be v i e w e d  be  felt  earlier.  simultaneous, The as  14  the  piece  second  rhythmically anacrustic  16  (not yet  considering  as a l a r g e - s c a l e u n i t recession,  the  (as i n d i c a t e d  i s not Also  units.  14  mode o f r h y t h m i c  at the h i g h e s t l e v e l )  t h e emergence of a rhythmic  one  statement,  the b e g i n n i n g o f measure  (i.e.,  3, m e t r i c  9  continuous  With r e s p e c t to t h i s design  P i e c e No.  8  f o l l o w e d by  at  characterizations.  textural  rhythmic  turn-around i n Example  structure,  the  completely unlike  similar  of  t o t h e No.  point 25).  overall  that  of  the  8 excerpt i s  element  at the  peak o f  progressive portion  of the  continuous  to the octave-doubled  theme,  while  56 retaining  the c o n t i n u i t y  Apart  from  the  the octave-doubled  within  i t s own  interaction  theme may  be  large-scale  b e t w e e n t h e two  heard  to r e v e a l  structure.  27  simultaneous  i t s own  elements,  low-level  metric  28 structure  (again, not  definition, defined linear  metric units  here,  as  approach,  accented,  (refer  view  of  one to  s i g n a t u r e , one  local  downbeat  11,  may  The  also  i n d u r a t i o n and  comes t o o  soon  after  which a r t i c u l a t e s that  8,  next  be  of the  by  F  i n No.  registral  and/or  8).  By  impulses  dynamic  which  might  pitch as  conceive the E of  i t s d u r a t i o n and  a local 29  arrival  Although  point,  emphasis through  registral  10  approach  exposure,  especially  C of bars  as  of bar  linear  the  heard  Ignoring  end  of comparable d u r a t i o n a l  i t .  added  at the  are  exposure,  notated a r t i c u l a t i v e markings.  t h e F t o be  11-12  in  is  exposure,  a metric downbeat—that i s ,  t h e b e g i n n i n g of a m e t r i c u n i t  previous unit.  t h e p r e v i o u s E and  line  accent-differentiated  heard  has  the horn  because  the l e a p which approaches  comparable it  require  of  d u r a t i o n , and/or  to Example 27).  the F of bar  that  i n p i e c e No.  the n o t a t e d meter a s an  unlike  at a  level  comparable  I t i s t h e r e f o r e considered subordinate to  i n terms of m e t r i c  strength.  Finally,  the A  i n bar  12  "'It i s i n t e r e s t i n g t o n o t e t h a t t h e c o n t i n u o u s s t a t e m e n t w o u l d seem to d r i f t i n and o u t o f t e x t u r a l " p r i m a c y . " I n o t h e r words, t h e t h r e e s t a g e s of r h y t h m i c p r o g r e s s i o n a r e t h e p r i m a r y t e x t u r e s i n t h e o p e n i n g s e c t i o n (they are the only ones). As t h e r h y t h m i c a c t i v i t y r e a c h e s i t s p e a k ( i . e . , t h e t r i l l ) , however, t h e i n s t r u m e n t a t i o n - d e n s i t y d e c r e a s e s and t h e r e g i s t e r a n d d y n a m i c s become l e s s i n t e n s e , r e d u c i n g t h e s t a t u s o f t h a t p a r t i c u l a r t e x t u r a l element ( i . e . , the t r i l l ) . T h e o c t a v e - d o u b l e d theme w h i c h e m e r g e s o v e r t h e l a t t e r i s c o n s i d e r e d p r i m a r y u n t i l i t d i s s o l v e s i n b a r 12, w h e r e upon t h e r e c e s s i v e g e s t u r e ( w i t h i n t h e l a r g e c o n t i n u o u s s t a t e m e n t ) emerges as primary. 28 An a d d i t i o n a l g e n e r a l s i m i l a r i t y b e t w e e n p i e c e No. 3 a n d t h e e x c e r p t f r o m No. 8 may be d i s c e r n e d : t h e r h y t h m i c a c t i v i t y c u r v e o f t h e e m e r g i n g theme, i n e a c h c a s e , m i r r o r s on a s m a l l e r s c a l e t h a t o f t h e l a r g e r c o n t i n u o u s element. Note a l s o  the h i g h e r - l e v e l  stepwise approach  from  the E of bar  11.  57 may  be heard as t h e u l t i m a t e a r r i v a l p o i n t of t h e theme ( i t i s the  p i t c h t o be doubled  i n o c t a v e s ) and  a c c e n t u a l and m e t r i c  last  i s , t h e r e f o r e , c o n s i d e r e d t o be of  significance.  Because o f t h e l a c k of e x p l i c i t l y a r t i c u l a t e d p u l s e — e s p e c i a l l y one which concurs w i t h t h e t h r e e downbeats d e f i n e d a b o v e — a p u l s e f a c t o r d e r i v e d from t h e r h y t h m i c  d i v i s i o n s of t h e theme i t s e l f may  be assumed f o r  & the purpose of d e t e r m i n i n g t h e m e t r i c i n d i c a t i o n s . i s used, f o r example, two  111111  e q u a l m e t r i c u n i t s of 1 7 ^ a r e d e l i n e a t e d by  E, F, and A, w i t h the accented "syncopation" of s o r t s ) .  I f a pulse of  the  C f a l l i n g w i t h i n t h e second u n i t ( e . g . , a  This rhythmic/metric  configuration i s illustrated  i n Example 27. Example 27.  mm.  BSN.II')-  P i e c e No.  3, measures 10-12, r h y t h m i c and m e t r i c d e s i g n .  10  11  12  ~  T  |  17x^ 17x1  6 |  17x|  I  remetered  A g a i n , l o w e r - l e v e l m e t r i c o r g a n i z a t i o n i s r e v e a l e d w i t h i n a l a r g e r , more continuous  rhythmic  statement,  t h e l a t t e r e x h i b i t i n g impulse  groupings  c o n s i d e r a b l y l a r g e r than the a s s e r t e d m e t r i c u n i t s o f the theme i t s e l f .  58 W h i l e the f i f t h ,  seventh, and n i n t h p i e c e s ( a l l b e i n g of t h e  ensemble type) a l s o r e v e a l c o n t i n u o u s  rhythmic  p r o g r e s s i o n and r e c e s s i o n , t h e statements turn-around thus f a r .  some i n v o l v i n g  l a c k the presence of  explicit  p o i n t s comparable t o t h o s e exposed i n t h e p i e c e s d i s c u s s e d In the f i f t h piece, f o r instance, four s e c t i o n s are d e l i n e a t e d  by a l t e r n a t i n g t e m p i and dynamics ( e . g . , J=  120 sfz  4 4 The  statements,  J=  132 ff  J=  120  J=  sfz  i m p u l s e - d e n s i t y curve o f t h i s p i e c e i s g i v e n in; Example 28.  ff  3 4  In t h i s  p a r t i c u l a r p i e c e , because the mode of a r t i c u l a t i o n throughout i s one repeated  staccatissimo  132).  of  n o t e s , the i m p u l s e - d e n s i t y i s a c t u a l l y r e p r e s e n t a t i v e  o f t h e rhythm.'.of p i t c h change.  The  i m p l i c a t i o n s of t h i s d e t a i l w i l l  become c l e a r .  Example 28.  P i e c e No.  5, i m p u l s e - d e n s i t y graph.  soon  59  W i t h i n the f i r s t  s e c t i o n ( J = 120,  l e v e l of t h e h i g h l y a r t i c u l a t e  measures 1-8),  the a c t i v i t y  polyphonic texture i s r e l a t i v e l y  s u g g e s t i n g n e i t h e r p r o g r e s s i o n nor r e c e s s i o n .  The  constant,  second s e c t i o n i s  i n t e n s i f i e d t h r o u g h t h e abrupt tempo change ( i . e . , to J = 132)  and  m a r g i n a l i n c r e a s e i n i m p u l s e - d e n s i t y , w h i l e t h e t h i r d s e c t i o n (back t o J = 120)  i n v o l v e s a rhythmic r e c e s s i o n to the o r i g i n a l l e v e l of a c t i v i t y  and beyond t o 0 i m p u l s e s / J f o r s e v e r a l c o n s e c u t i v e beats  i n bar 11.  t h e j u n c t u r e s a t w h i c h r h y t h m i c a c t i v i t y changes d i r e c t i o n o f p r o g r e s s i o n to one o f r e c e s s i o n ( e . g . , measure 9), measure 12)J  might be viewed as t u r n - a r o u n d  While  £i.e., from  one  o r v i c e v e r s a (.e.g.,  p o i n t s , the d i f f e r e n c e i n  magnitude of i m p u l s e - d e n s i t y i s h a r d l y enough to warrant  such a  30  characterization. 4/J  The  effect  o f an i n c r e a s e i n i m p u l s e - d e n s i t y from 2 t o  , f o r example, i s s i g n i f i c a n t l y overpowered by t h e mode of  ( i . e . , the continuous, arhythmic note r e p e t i t i o n s ) . reiterations,  The  articulation  staccatissimo  i n f a c t , prevent a f e e l i n g of r h y t h m i c r e p o s e even when t h e  p i t c h e s a r e kept c o n s t a n t The r h y t h m i c  ( e . g . , i n measure  intensification  piece (bars 3 8 - 4 4 ) — e s s e n t i a l l y  11).  i n t h e second s e c t i o n o f t h e  seventh  a s i n g l e s e c t i o n which i s " t o r n o f f " a t  peak of i t s r h y t h m i c a c t i v i t y — r e s u l t s from g r a d u a l independence o f f o u r sounding  components.  component branches o f f on i t s own  clarinet  i n measure 39,  interaction  the  Each time a component e n t e r s , i t does so i n  rhythmic unison w i t h a part already i n progress. t h e new  the  Soon a f t e r  rhythmic  and bassoon i n bar 40),  course  e n t r y , however,  ( e . g . , oboe and  thus i n t e n s i f y i n g  the  between p a r t s and u l t i m a t e l y the l e v e l of t h e composite  30  In t h i s p i e c e t h e d i f f e r e n c e between t h e most a c t i v e and i n a c t i v e s t a t e s i s o n l y 4 i m p u l s e s / J ; compare t h i s w i t h 22 i n No. 8, 8 i n No. 4, and a t l e a s t 15 i n No. 3 ("at l e a s t " because o f t h e i n d e f i n i t e number p r o v i d e d by t h e t r i l l ) .  60 rhythmic  activity.  activity  as  to  E x a m p l e 29  offers a  graphic  representation  of  rhythmic  impulse-density.  E x a m p l e 29.  Piece  38  No.  39  7,  m e a s u r e s 38-44,  40  41  impulse-density  42  graph.  43  44  measure no.  Although throughout  (i.e.,  representation rather  fact,  piece  c o n s i s t s of  the  three-part  the  impulse-density  the  most  significant  pitch unfolding  progression  i n the  however, p l a y Each of  of  ninth  uninteresting oscillation  c l e a r l y not In  the  the  piece  a vital  three  and than  continuous  canon mentioned of  between aspect  registral rhythmic  r o l e i n the  one,  earlier),  t e x t u r a l element a  graphic  i t s composite rhythm would 0 and of  2  impulses  rhythmic  ascent  are  structure  more  p a r t s moves i n m u l t i p l e s  of  a  the  i n the  Rhythm  canonic  different  a  quarter-note—  important  intensification.  independence of  per  reveal  piece.  factors  of  does,  components.  durational  unit:  61  5  rhythmic  design  At noted  3  - | | | | , oboe - | I | I I  piccolo  prevents  the beginning  , and c l a r i n e t  the imitation  of the present  those  measure a r e d i f f e r e n t  with  fluctuating  (specifically, exist  t h e downbeat  departure  points),  would  quality  soloistic appear  a l r e a d y exposed  i n c r e a s e d dynamics,  offers  two i n s t a n c e s o f e x p l i c i t l y  p l a c e on t h e downbeat p r e v i o u s measure. respectively.  downbeats o c c u r ,  significance. the  would  formal  section  appear  connecting  would  o n e may b e h e a r d  continuation i n the clarinet  next  from  a number o f e x a m p l e s  etc.).  bar 9 , while from  the last  environment  and/or  The second  t h e second beat  takes  of the  i n which  (bar 1 1 ) serving as a connection  (i.e.,  piece  points.  t o c l o s e o f f t h e opening  ( J = 1 4 4 , poco meno mosso).  t o t h e coda  arrival  these  seem t o b e o f s t r u c t u r a l  The downbeat  t o end t h e m a i n body o f t h e p i e c e , w h i l e  link  placed to  i n E x a m p l e 30 ( a ) a n d ( b )  t h e r h y t h m i c a l l y complex  The f i r s t  from  type  d e f i n e d downbeats a s a r r i v a l  placement  of the  n o t a t e d meter  (be they  a r t i c u l a t i v e markings,  excerpts are given  their  i t was  o t h e r means o f a c c e n t u a t i o n  of bar 2 4 , approached  These  Given  points  (or s t r i c t ) .  aspects,  at the level  constant  pieces)  through  i n bar 1 1 , approached  occurs  on r h y t h m i c  meter  This d e t a i l i n  too regular  t o be s t r a t e g i c a l l y  of certain  (e.g.,  first  I .  In consideration of the l a t t e r  four of the f i v e  where t h e b a r l i n e s  heighten  two  section  i n pieces with  meter.  1  becoming  that t h e consequences of non-operative  notated  The  from  - |  measures  eliding  2 8 to the end).  section, to the  of bar2 4 with the  62 Example  (a) m e a s u r e s  30.  Piece  No.  2,  local  arrival  points.  9-11  (b) m e a s u r e s  23-24  © 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributor; Corporation, sole Canadian agent for B. Schott's Soehne.  63 Two  instances of local  significance. (the  featured  elided  Each  downbeats  i s approached  instrument),  downbeat—that  E x a m p l e 31 i l l u s t r a t e s  Example  i n the sixth  by a cadenza-like  marked  senza  31.  (a) m e a s u r e s  i n t h e oboe  arrival  and d e p a r t u r e  point.  i n question.  P i e c e No. 6, l o c a l  arrival/departure points,  8-9  ^ Tempo: Poco sostenuto.legato dolcissimo  8 senza tempo (Presto)  Fl.  passage  tempo, a n d e a c h f u n c t i o n s a s a n  i s , a simultaneous t h e two p o i n t s  piece are of  9 v-JSL  J A  Ob.  Cl.SH,  Cor.Fa  Fag.  (b) m e a s u r e s 10-11 j  Poco sostenuto  senza tempo: Prestiss., staccatiss.  0  Fl. prestissimo  Ob.  possibile  —LL. — j — =  ==  —f- —f- — — T T r«|*TT"rtl*"rtf tartyluil'gkjr'  -  crescenao  Cl.Si\>  tr s  i  u  ;  *  motto -  -  A-^V  ±^L±J senza  sord.\aa  Cor. Fa.  •1'  Jig  pp moito rT\  Fag.  © 1 9 6 9 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne.  calmo  64 A second f u n c t i o n o f t h e b a r l i n e s and m e t r i c i n d i c a t i o n s may of r h y t h m i c g r o u p i n g w i t h o u t a c c e n t - d e l i n e a t i o n . i d e a may  be  one  I n o t h e r words, a m u s i c a l  r e q u i r e t h e time-span of f i v e q u a r t e r - n o t e s a t a g i v e n tempo so i t  would be l a b e l l e d as 4 w i t h o u t any m e t r i c ( i . e . , accent) i m p l i c a t i o n such > > > > or ' ^would appear t o be the s i t u a t i o n i n  f f |* |* f  as^r*p|*|*  Tn  S  p a r t s of t h e e i g h t h p i e c e .  I n measures 26-32, f o r i n s t a n c e , f i v e d i s p a r a t e  m u s i c a l ideas are presented  i n s u c c e s s i o n , each r e q u i r i n g a d i f f e r e n t  span (not n e c e s s a r i l y a d i f f e r e n t p a t t e r n of accented  time-  and unaccented p u l s e s ) .  Example 32 c o n s i s t s of t h e s e seven measures from t h e s c o r e .  Notation i n  s t r a i g h t ^ would be next t o i m p o s s i b l e and would, almost c e r t a i n l y , undermine the d r a m a t i c  impact of the d i s p a r a t e m u s i c a l i d e a s p r e s e n t e d  31 i n the excerpt.  Summary Concerning  r h y t h m i c and m e t r i c d e s i g n , t h r e e main p r i n c i p l e s were  found to be of s i g n i f i c a n c e i n t h e q u i n t e t .  The  f i r s t involves the  f l u c t u a t i o n i n composite r h y t h m i c a c t i v i t y , termed " i m p u l s e - d e n s i t y , " i t s v i t a l i n f l u e n c e on p r o g r e s s i v e and r e c e s s i v e t e n d e n c i e s p i e c e s c o n s i s t i n g p r i m a r i l y of p o l y p h o n i c t e x t u r e s .  The  and  i n s e c t i o n s and  second p r i n c i p l e  concerns t h e f a c t t h a t n o t a t e d meter i s l a r g e l y i n o p e r a t i v e i n the p i e c e s and,  i n f a c t , a c c e n t - a r t i c u l a t e d u n i t s a t t h e l e v e l of t h e n o t a t e d measure  were judged t o be e s s e n t i a l l y i r r e l e v a n t .  However, l o w - l e v e l m e t r i c u n i t s  ( d e l i n e a t e d by f a c t o r s o t h e r than n o t a t e d b a r l i n e s ) were s a i d t o o p e r a t e i n the horn p a r t o f p i e c e No.  8 and the octave-doubled  theme o f No.  3.  The  t h i r d p r i n c i p l e s t a t e d t h a t , i n p i e c e s w i t h a c o n s t a n t n o t a t e d meter, b a r l i n e s were found t o be n o t a t i o n a l conveniences.  In pieces e x h i b i t i n g  31 The e a r l i e r p a r a l l e l drawn between t h e s o l o i s t i c p i e c e s o f the q u i n t e t and t h e l a r g e r p i e c e s c h a r a c t e r i z e d by t h e s t y l e of Apparitions and Aventures i s e x e m p l i f i e d i n t h i s p a r t i c u l a r e x c e r p t .  Example  32.  P i e c e No.  8, m e a s u r e s  26-32,  showing  consecutive  disparate musical  ideas.  Agitato capriccioso "  as  @ 1969 B. Schott's Soehne, Mainz A l l rights reserved Used by permission of European American Music Distributors Corporation, sole Canadian agent for B. Schott's Soehne.  66 fluctuating, and  time-span  relevant  found  from  other  to operate  i s hoped  o f downbeat  c o n s i d e r a t i o n s of d i s p a r a t e m u s i c a l  in addition  While  it  n o t a t e d m e t e r , however, f a c t o r s  to  that of n o t a t i o n a l  details,  and  principles  within the rhythmic  that  the  and  of  i d e a s were f o u n d  to  be  convenience. o f g r e a t e r c o n s e q u e n c e , may  metric design  issues discussed in this  which a g r e a t e r understanding  characterization  section  this musical  of  will  these  be  pieces,  serve as  l a n g u a g e may  a  point  be  developed.  Modes o f P i t c h Linear The study,  linear  refer  to  details  of  pitch  (predominantly)  Organization  Details  o r g a n i z a t i o n , f o r the  stepwise  purposes  p a t t e r n s of r e g i s t r a l l y  of  this  specific  32 p i t c h e s and/or such  linear  linear  which tend  p o i n t s i n the  (PC's). of  this  As  one  might  language,  t o move t o w a r d  pieces, thereby  our  and/or  suggesting  expect  to f i n d  concern  will  away f r o m  many  focus  on  specific  elements of  progression  recession. Two  PC  p a t t e r n s i n music  connections  structural and  pitch-classes  aspects  structuring  of  linear  connection  t o be  w i t h i n t h e v a r i o u s p i e c e s , and  s t u d i e d a r e modes o f large-scale  pitch/  connections  33 between one  pieces.  In the  former,  the  connections  may  be  found  to occur  in  p a r t i c u l a r i n s t r u m e n t ( i . e . , one component w i t h i n a l a r g e r t e x t u r a l 32 A c c o r d i n g t o E d w a r d Cone, s t e p w i s e c o n n e c t i o n s a r e v i t a l t o t h e p e r c e p t i o n of l i n e a r s t r u c t u r e as "the ear w i l l n a t u r a l l y connect each tone with those nearest i t i n p i t c h . The a d j a c e n t p i t c h e s may be d i a t o n i c o r t h e y may be c h r o m a t i c ; t h e y may be a c t u a l l y a d j a c e n t o r d i s p l a c e d b y one o r m o r e o c t a v e s ; t h e y may be p r e s e n t b y i m p l i c a t i o n o n l y . " See " A n a l y s i s T o d a y , " The Musical Quarterly ( A p r i l 1 9 6 0 ) : 177-78. 33 R e g a r d i n g t h e l a t t e r , s u c h i n s t a n c e s may be c o n s i d e r e d a d d i t i o n a l modes o f l a r g e - s c a l e c o n n e c t i o n o r p i e c e s u b g r o u p i n g , s e v e r a l o f w h i c h were o u t l i n e d e a r l i e r i n t h i s c h a p t e r .  67 element),  or  t h e y may  be  the r e s u l t  of  the  interaction  linearizations,  themselves,  being a d d i t i o n a l  Although  significant  linear  pieces,  the  different two  structural  from  the  In the  effected  'b'-section,  by  The  c o n n e c t i o n s may  second  components  components of  or p a r t i c u l a r s  piece to piece.  linearizations  part.  details  of  be  sorts).  found  i n a l l of  of l i n e a r i z a t i o n  piece,  12-15, t h e u p p e r  successive arpeggios create simultaneous,  are  f o r example,  the a r p e g g i a t i o n design of the  measures  and  the  often  reveals clarinet  lower  different  (the  pitches  of  linear  34 continuities. by  In both  ascending  the leap of a t h i r d which  events,  i s further  displaced  connective p a t t e r n s , which provide l i n e a r at  hand, a r e A  i l l u s t r a t e d i n Example  second  linear  event  of  the  c o n s e c u t i v e two  arpeggios) is  c r e a t e an  continued  from  simultaneously line  from  A^  and  t o D^-\  direction  from  to A ^  line  an  i n bar  to the four  measures  similar i n bar  arpeggio  29.  The  design  upper  oscillations  t o G^-* ( b a r s 21-22)  29.  The  lower  t o B-> a n d  an  portrays these  of t h e lower  final  measure, t h e resumption  of  f o r the d i r e c t e d  These  D^->  l i n e from  E x a m p l e 34  octave.  from  continued l i n e a r i z a t i o n  piece  a  continued  While  responsible  by  three-note patterns ( i . e . ,  ascending  ascending  and  p i t c h e s a r e marked  33.  resulting  be d i s c e r n e d i n m e a s u r e s 21-22  the f i n a l  tendency  overlapping  does not  line  i n the upper  towards the h i g h e s t p i t c h  and  to  a  descending  linear  occur  notes  which  contribute  interacting  notes  the ascending  notes  may  events.  i n the part of  is  the  (A * ). 1  6  34 While relationships,  operative  the the  tempo,J =  " i n n e r " p a r t s o f t h e a r p e g g i o s may a l s o r e v e a l l i n e a r " o u t e r " v o i c e s a r e most r e a d i l y p e r c e i v e d a t t h e  144.  Example  mm.  3 3 . P i e c e No.  12  2, m e a s u r e s  12-15,  two  simultaneous  13  linearizations.  14  15  41 CL (inC),  % y  5  5  6  ^ E J LLLU Uill 11 Bf  M  f=±=z  111 I IIiff 51? 6 6 ^L^L3Z^^L^L^0 iX^Li^EJ  ON oo  Example  mm. 21  34.  P i e c e No.  2, measuresv2I-22 a n d 29, two  22  simultaneous  29  linearizations.  69 Much o f t h e f l u t e successive, be  heard  second  bar  the  to d e f i n e independent  piece.  Although  2 to bar  8.  s c o r e ) and  suggested  i n the c l a r i n e t  Although noteworthy.  the  First,  point  of o r i g i n  point  of  35  i t s lower  linearizations  clarinet  progressive  part,  flute's  top  line  Second,  suggested  and  a r e brought bassoon,  and  those of  opens  in a  from  clarinet  i n the f l u t e  space,  the  middle  parts  (above  may  relatively  the  linear  to a  event,  from  the  The  t o F#6  structure  end  may  6,  the arrow from i n the f l u t e  and  p o i n t s on  that  i s the  heard  bars  6-7.  the  arrival connects  through  of  be  clarinet  i n measures and  are  dotted l i n e  the b i - l i n e a r of bar  details  (bar 1),  of E^  convincing close  the a r r i v a l  two  i t is significant  ( i n measure 2 ) .  by  tendencies, i n i t i a t e d  the piece,  clarinet  as  4)  self-explanatory,  regarding r e g i s t r a l  C^.  unlike  of which  (below).  ascending  of the  notes  structure  shows t h e f l u t e  which terminates a b r u p t l y at the  of  ( i n No.  suggesting a conjoined l i n e a r i z a t i o n  prolongation  the  part  lower  not  a bi-linear  connections are  of the  and  linearizations,  exhibits  Example  piece i s constructed of  the upper  the c l a r i n e t  i t also  score with the  t h e two,  i n the fourth  two-note o s c i l l a t i o n s ,  stepwise fashion, of  part  the f l u t e  part,  to continue i n The  linear-  at the  onset  7-8  the  by  coinciding  with  the  35 aforementioned In a  linear  and  the event  registral  rhythmic  repose.  'b'-section may  be  of  the  seventh  p i e c e (measures  discerned which r e s u l t s  exposure,  as w e l l  recurring  dynamic  "swells" are  which has  been a p p r o a c h e d  by  an  from  dynamic,  as m o t i v i c r e c u r r e n c e . often  concurrent with a  ascending  arpeggio  38  and,  The  to the  end),  durational, peaks of  sustained more  pitch  immediately,  35 from  The s e n s e o f c a d e n c e a t t h i s p o i n t i n t h e p i e c e a l s o a p a r t i c u l a r h a r m o n i c d e t a i l t o be e x p l a i n e d l a t e r .  the  results  70  E x a m p l e 35.  P i e c e No.  4, m e a s u r e s  1-8,  simultaneous  linear  connections..  71  by  a  tritone  involves  (ascending  the  or  progression  descending).  of  the  The  linear  recurring tritones  pattern  in  (although,  question in  this  3 6 particular  e x a m p l e , movement by  step  E x a m p l e 36  r e v e a l s the  exposed  tritones  i s exceeded).  The  top  staff  of  t h r o u g h t h e means d e s c r i b e d  above.  37 System ships  (b)  illustrates  inherent  derived  linear  tritones  of  inversion  succession  progression.  the  representing  progression  a descent,  relationship  linearization formal  i n the  the v a r i o u s  are  and  of  while  interlocking system  (c)  between  system  "+"  an  t r a n s p o s i t i o n and  on  The  o p e n i n g and  systems a linear  of which c o n t r i b u t e s to a  (d)  ( c ) , the  closing  and  event,  (e). the  "-" near-  t r i t o n e s of Once a g a i n  stepwise  " d i r e c t e d " tendency  the  contiguous  i n d i c a t e d below ascent.  relation-  shows  are  between t h e  summarized  tritones,  and  I n t e r v a l - c l a s s e s (IC's)  s e c t i o n i s t r a v e r s e d by  structure  "inversion"  the  a  complete  ascending  towards i t s  conclusion. The for  opening  reasons  of  connections. content; the  the  PC  example o f  ordering as  an  content  twelve-note  'b'-section  (of the  organization other  PC's  o r g a n i z a t i o n which  different  to  i s an  twelve  twelve-note  The  the  pitch/PC It  inversionally, PC  of  are  seventh  than  a carefully  those  linear  u n f o l d i n g of  are  repeated.  further treated transpositionally  a c t u a l twelve-tone  "row,"  i s operative  in other  of  5,  p i e c e No.  orderings,  any  i s noteworthy  involving  controlled  sounded once b e f o r e  i s not  piece)  i t does  pieces  of  represent the  f o r example, u n f o l d s  concurrent,  f o r t h e most  3 6 B o t h t h e r e c u r r i n g l i n e a r t r i t o n e s and g e n e r a l s u s t a i n e d p i t c h e s may be c o n s i d e r e d m o t i v i c .  PC  Although of  one  mode o f  quintet. according part, with  arpeggio  to  four  the  approaches  37 Inversion relationship members ( e v e n t h o u g h a t r i t o n e , actual IC).  r e f e r s to the v e r t i c a l order of as such, i s not i n v e r t i b l e w i t h  the t r i t o n e respect to  73 Example  36.  P i e c e No.  7, m e a s u r e s 38-44,  linear  progression  of  tritones.  74 f o u r s e c t i o n s o f t h e p i e c e ( a s d e l i n e a t e d t h r o u g h o t h e r parameters alreadymentioned) .  I n t h e f i r s t and t h i r d s e c t i o n s some PC's a r e r e p e a t e d  before  a l l t w e l v e have sounded, t h e t w e l f t h PC s i g n i f y i n g t h e end o f t h e f i r s t 38 s e c t i o n and, i n t h e l a t t e r case, t h e b e g i n n i n g  of the fourth.  The second  and f o u r t h s e c t i o n s c o n t a i n no such r e p e t i t i o n s ; once t h e t w e l v e PC's have sounded i n each c a s e , t h e s e c t i o n i s o v e r .  A l t h o u g h " t h e f o u r PC o r d e r i n g s  a r e not t r a n s p o s i t i o n a l l y o r i n v e r s i o n a l l y r e l a t e d , many i n t e r n a l PC p a i r s are r e t a i n e d ( b r a c k e t e d  i n Example 3 7 ) , as i s one p a r t i c u l a r I C o r d e r i n g  ("boxed" i n Example 3 7 ) . Example 37.  I  (mm.l-8.8fp1  P i e c e No. 5, PC o r d e r i n g s , showing PC p a i r and IC o r d e r i n g r e l a t i o n s h i p s .  DE^CD^EFBB*  II (mm.8-9.ff)  E  III (mm.9-12.sfp)  C  D  B* B  BE (mm.12-14,ff)  The c o m p l e t i o n o f t h e t h i r d PC o r d e r i n g ( i . e . , t h e E ^ ) c o i n c i d e s w i t h t h e f i r s t n o t e o f t h e f i n a l s e c t i o n ( a s d e f i n e d by tempo and d y n a m i c s ) . The f i n a l s e c t i o n , t h e r e f o r e , c o n t a i n s t h i r t e e n n o t e s : The E ^ from t h e end of t h e t h i r d o r d e r i n g and t h e t w e l v e n o t e s o f i t s own o r d e r i n g , w h i c h a l s o ends on E K  75  The b e g i n n i n g of t h e t w e l v e - n o t e  o f t h e s i x t h p i e c e c o n t i n u e s t h e o r g a n i z a t i o n a l concept  o r d e r i n g but, u n l i k e i n t h e f i f t h p i e c e , o n l y one ordered  u n f o l d i n g o c c u r s , a f t e r which t h e PC's do n o t appear t o be arranged i n specific patterns.  The i n i t i a l o r d e r i n g i s , however, o f i n t e r e s t as i t  r e t a i n s some o f t h e PC p a i r s and t h e r e c u r r e n t I C o r d e r i n g from t h e PC p a t t e r n s used i n t h e p r e v i o u s p i e c e .  Example 38 r e v e a l s t h e PC p a i r  r e l a t i o n s h i p s between t h e f i r s t o r d e r i n g o f t h e s i x t h - p i e c e and t h e f i r s t and  l a s t of t h e f i f t h piece (bracketed  i n t h e example), as w e l l as t h e  r e c u r r i n g IC o r d e r i n g (boxed i n t h e example). Example 38.  No. 5,  P i e c e s 5 and 6, PC p a i r and IC o r d e r i n g relat ionships.  I  No. 6  No. 5,  C  O  3 E  ^  C  Br*D E ^ | A * A » G G ^ E  B  ^  B  A  G  ^  F  E  E  F  ^  F i n a l l y , w i t h r e g a r d t o o r d e r e d PC u n f o l d i n g , t h e n i n t h p i e c e d e s e r v e s mention.  The whole p i e c e c o n s i s t s o f one, n i n e - n o t e  ordering  w h i c h u n f o l d s c a n o n i c a l l y i n t h e p i c c o l o , oboe, and c l a r i n e t . t h e u n i s o n E^ i s r e p e a t e d  i n the opening, the remaining  Although  PC's o f t h e  o r d e r i n g a r e a r t i c u l a t e d o n l y once ( i . e . , once p e r i n s t r u m e n t ) .  • 76 An may  be  Apart  important  the  from c o n t r o l l i n g  the  i n t r o d u c t i o n o f PC's,  reveal linear  simultaneously orderings  their  of  illustrate  c o n f i g u r a t i o n of  linear  pieces just the  sixth  pieces  the  linear  connection  examined.  actual patterns the  of  latter consisting  linearizations.  and  Chapter  IV.  In the  case  In Example  are notated  as  39  PC's,  a n d / o r wedge p a t t e r n s  i n E x a m p l e 39  piece,  apart  cases,  the  from those  black notes  p i t c h e s of  dispersed  over  E x a m p l e 39 Apart piece  "spatial"  the  the  are,  i n d i c a t e d by to A ^ ,  and  inherent  the  octaves;  the  registrally  linear  directive  opening  " p o i n t " towards  C^  black note  in  in the  be  The  5,  the  PC  the latter  notes.)  illustrated events. of  the  wedge-like  f o r the  s e c t i o n , and  energy generated  with  the  orderings  The  linear  registrally  "stepwise"  tendencies.  second  dealt  the  patterns  patterns,  the  (In the of  section i s preparatory  dispersed  i t .  as  which  p i t c h e s of  registers  linear  of  p i e c e No.  below.  fact,  linear  light  specific  above or  is, in  the  f o u r t h s e c t i o n s , however, a r e  one-half  the  from  asserted  s e c t i o n s of  a c t u a l sounding  interrelated of  the  registrally  a black note  the  the  39)  f e a t u r e which w i l l  third  revealing internal  expansion  sense tends to  and  Example  theme, a p a r t  t h e r e f o r e , more p r o b l e m a t i c  exhibit  wide coverage of  are  of  significance  also the  with  second  f o u r and  from  are  (as  connective  first  staff  canonic  added  piece—a  of  (top  f o u r t h E^6  p i e c e , has  final  the  higher  ascending  i n the the  patterns  octave  The  of  fifth  to  three  continuities,  descending  i n the n i n t h piece  sounds an  progression  in  and  the n i n t h , f i f t h ,  pattern  parentheses).  The  wedge-like  ascending  arranged  registral  details  and  the  directed)  orderings.  actually  in  (i.e.,  orderings of  The the  progressive  the  registrally in  of  associated with  unfolding of  aspect  ;  i n the  in  extremely this  latter  is  77 E x a m p l e 39.  Pieces  9,  5,  and  6,  patterns  of  PC  unfolding.  78 somewhat  d i s s i p a t e d by  section—a repose,  linear  fourth  w h i c h may  be  The is and  PC  fourth  to  most  and  the  section,  third the  i n d i c a t i v e of  at  the  end  of  consistent  as  a  the  would 39  final  the  fourth  (as  the  of  point  linear  pitches  third of  earlier.  of  the  such a  The  descent, piece.  continuation  f o u r members o f  linear  point:  significance. piece  Although  does not  of  conclude  first,  the  third  the  the  octave  tempo a n d the  the  earlier  as  dynamics).  intended  r e g i s t e r of  is  occur  l o w e r and  early  the  first  This  connection  the  fourth  to,  of  notion  opens w i t h section  final  may coming  E^  third,  but  fall  with  is  that an  the  short  D  i n the  u  on  D5  final of,  to  would  4  emphatic  qualify  D^  pitches  D4. functional  of  of  the  the  wedge  "stop  as  39 T h i s i s f u r t h e r r e i n f o r c e d by t h e though t o r n o f f . " See L i g e t i , Ten Pieces,  note i n the p. 19.  score:  PC  and  four  opening  configuration  above,  respect  however, have  pitches  registral  suggested  begins  and  c l o s e may,  unfolding  as  "open" f a s h i o n  piece  seventh;  the  to  ordering  linearization,  i n an  linearly  conform to  third  r e i n f o r c e the  "incomplete"  alluded  pitches.  second, the  point  apparently  by  descent,  three  conditions  section  an  s e c t i o n where t h e  to  in unison);  the  occurs  continuation  Several  fourth This  sixth  final  of  defined  progresses through a descending the  four  a detail  and  final  preceding  appear  arrival  F^,  averted  with the  (reiterated  of  noted  i n t e r r u p t the  suggestion  the  of  recede towards a  activity  final  f o r the  equality,  G^,  section  an  the  Despite  unfolding.  the  final  be  piece  the  e q u a l i t y of  registral  in  the  to  linearity  orderings.  While  of  tends to  appear  responsible  compact  in rhythmic  continue with  noteworthy.  pitch  which a l s o  decline  registral  Concerning  the  registrally  s e c t i o n would  seen  condition the  descent  a s s i s t e d by  explosive  the  p a t t e r n noted on t h e bottom s t a f f o f Example 39, i t i s r e s p o n s i b l e , i n PC 40 terms, f o r an aspect o f c o n n e c t i o n between t h e two p i e c e s .  F o r example,  w h i l e t h e end o f t h e f i f t h p i e c e approaches D from above ( i . e . , G^, F, E, E&), t h e opening o f t h e s i x t h p i e c e approaches i t from below ( i . e . , A#, B, C, C#, t h e a c t u a l o r d e r b e i n g B, C#, C, A#). The D ( f i f t h PC o f t h e o r d e r i n g ) i s t h e f e a t u r e d oboe's f i r s t n o t e . w e l l as a r t i c u l a t i o n D more emphatic.  (as s p e c i f i e d  The d i f f e r e n c e i n t i m b r e as  i n t h e s c o r e ) , render t h e long-awaited  The PC c o n n e c t i o n between t h e f i f t h and s i x t h p i e c e s i s  summarized i n Example 40. Example 40. PC c o n n e c t i o n between t h e f i f t h and s i x t h pieces.  No. 5 mm. 13  No. 6 1  _/oboe \  registrally specific pitches  itchclasses  B e f o r e l e a v i n g t h e concept o f l i n e a r wedge-patterns, t w e l v e measures o f t h e e i g h t h p i e c e s h o u l d be examined.  t h e opening  Although twelve-  note o r d e r i n g s a r e n o t i n o p e r a t i o n h e r e , t h e expansion and c o n t r a c t i o n o f the "outer v o i c e s " c o n t r i b u t e t o t h e d i r e c t i v e  q u a l i t y which p o i n t s t o t h e  horn e n t r y i n b a r 12. "Outer v o i c e s , " h e r e , r e f e r t o t h e h i g h e s t and l o w e s t p i t c h e s o f t h e o v e r a l l r e g i s t r a l space c r e a t e d by t h e i n t e r a c t i o n  of the  40 Other a s p e c t s c i t e d e a r l i e r i n c l u d e tempo, a r t i c u l a t i o n , i n s t r u m e n t a t i o n , and t h e attacca i n d i c a t i o n a t t h e end of t h e f i f t h p i e c e .  80 three instruments.  Example 41 summarizes t h e s e p i t c h e x t r e m i t i e s and  r e v e a l s t h e aforementioned w e d g e - l i k e p a t t e r n of l i n e a r i z a t i o n . Example 41.  mm.  1  P i e c e No. 8, measures 1-12, linearizations.  2  3  4  7  7  8  wedge-patterned  10  11  12  The horn e n t r y i s marked by t h e c o n t r a c t i o n t o t h e minor i n t h e accompanimental element.  second,  The i n t e r a c t i o n between p i t c h  and r h y t h m i c p a t t e r n s i n t h e s e opening t w e l v e measures i s noteworthy. t h e s e c t i o n on rhythm, the horn e n t r y was i n composite r h y t h m i c a c t i v i t y .  s a i d to be marked by t h e maximum  During t h i s steady i n c r e a s e i n impulse-  d e n s i t y , t h e p i t c h s t r u c t u r e has r e v e a l e d a t w o f o l d wedge p a t t e r n . i n t e r a c t i o n of b o t h p a t t e r n s ( i . e . , rhythm and p i t c h ) may  pitch  P i e c e No. 8, measures 1-12, p a t t e r n e d p i t c h u n f o l d i n g as compared to r h y t h m i c a c t i v i t y .  unfolding:  rhythmic a c t i v i t y : (impulse-density)  The  be r e p r e s e n t e d  as i n Example 42.  Example 42.  In  81 A unique eight to  mode o f  measures of  the  the polyphonic  present  distinct  to four from  illustrated The of  third  textural  i n the f i r s t  increases  linear  and,  the often  overlapping second C# , 5  measure  indicated  the p i t c h ,  (refer  the f l u t e  transferred Example  from  a l l five  In bars The  5-7  opening  instruments  linear  i n s t r u m e n t a l p a r t s of  the  contribute  actually  t h e number o f  continuous  i n the  components  components, score,  example a r e c r e a t e d t h r o u g h  "unison transfer." of a  i n t h e two  concurrent with  discerned i n the  as  are  43.  fragments  unison  be  o n l y t h r e e components a r e  five.  fragmented  a d e v i c e I have termed two  Although  element,  finally,  i n Example  of  piece.  f o u r measures.  components  connection  c o n n e c t i o n may  single  the horn drops  The  component  involved  f o r example,  entry, also  out.  the f l u t e  linear  instruments  to the s c o r e ) ,  Essentially  on  linear  the  use  to  the  i t refers through  an  i n the t r a n s f e r . the a l t o  C#5.  flute  Once t h e h o r n  component  has,  here,  to the horn v i a the u n i s o n o v e r l a p  In  the  sounds has  a  assumed  been  (refer  to  43). As  i n the  immediately  incident  b e f o r e and  cited  after  above,  i n s t r u m e n t s a r e most o f t e n  presenting a portion  of a p a r t i c u l a r  silent linear  41 component. a  transfer  clarinet  has  o c c a s i o n , however, b o t h  occurred.  has  i n s t r u m e n t s c o n t i n u e t o sound  This i s the case  c o n t i n u e s t o sound  the l a t t e r said  On  been assumed  i t s E^ by  t o h a v e spawned a f o u r t h  (and  the r e s t  the f l u t e . component,  i n bar  Here,  5, of  after  f o r example, where i t s component)  after  the unison t r a n s f e r  thereby a f f e c t i n g  the  the  may  textural-  41 One p a r t i c u l a r d e p a r t u r e f r o m t h i s s t a n d a r d p r o c e d u r e o c c u r s i n b a r 5. The oboe d' amore c o n t i n u e s i t s a f t e r t h a t p i t c h i s a s s u m e d by t h e b a s s o o n , a n d o n l y when i t r e a c h e s D^5, s e v e r a l b e a t s l a t e r , d o e s i t r e s t , a f t e r the i i t u r n , p i c k e d up by t h e h o r n . This exception may be s e e n a s a n " e x t e n d e d " o v e r l a p . S  )  n  be  82  Example  43.  P i e c e No. 3, m e a s u r e s 1-8, l i n e a r c o m p o n e n t s u n i s o n t r a n s f e r and p i t c h i n t e r c h a n g e .  through  83  *These brackets indicate the span over which a particular instrument sounds; the dotted portion at the end of each indicates the point of "unison transfer" and the other instrument involved. 'These diagonal  lines  indicate  instances  of "pitch  interchange.  "  84 density. Unison t r a n s f e r i s a l s o r e s p o n s i b l e f o r t h i n n i n g t h e t e x t u r e . bar 7, t h e horn 's G#  4  i s assumed by t h e bassoon ( a l r e a d y sounding  In  a linear  component), a f t e r which t h e horn drops o u t , t h e r e b y ending one component. An example o f an i n c o m p l e t e u n i s o n t r a n s f e r accounts f o r t h e b r i e f fragment B -A 4  4  i n t h e f l u t e , measures 4-5.  from an e x i s t i n g B i n another  The i n i t i a l B i n t h e f l u t e does n o t come  i n s t r u m e n t , as i n t h e normal t r a n s f e r s .  t h i s respect the t r a n s f e r i s incomplete.  In  The c l o s i n g A, however, i s assumed  by t h e bassoon w i t h t h e c h a r a c t e r i s t i c u n i s o n o v e r l a p . " P i t c h i n t e r c h a n g e " i s a second v o i c e - l e a d i n g d e v i c e employed i n t h i s p a r t i c u l a r s e c t i o n of the piece.  W h i l e components u s u a l l y move i n d e p e n d e n t l y  of one a n o t h e r , t h e r h y t h m i c d i v i s i o n s o f two components engaged i n a p i t c h interchange a r e i d e n t i c a l .  This p a r t i c u l a r device u s u a l l y involves the  exchange o f p i t c h e s between two d i s p a r a t e components (and n o t an exchange o f the a c t u a l components t h e m s e l v e s ) , and i s o c c a s i o n a l l y r e s p o n s i b l e f o r t h e g e n e r a t i o n and t e r m i n a t i o n o f l i n e a r components (not u n l i k e u n i s o n thereby a s s i s t i n g i n the c o n t r o l of t e x t u r a l - d e n s i t y .  transfer),  Referring again to  Example 43, p i t c h i n t e r c h a n g e i s used i n measure 7 t o spawn a new component. The F 4 flute.  a n  d $k  Q  f ^ t  e  bassoon a r e i n t e r c h a n g e d w i t h t h e A ^  4  and F  4  of the  J u s t as t h e i n i t i a l t h r e e components o f t h e p i e c e were engaged i n  p i t c h i n t e r c h a n g e s a t t h e i r o n s e t , so t h e t e c h n i q u e i s employed here t o introduce a f i f t h  component.  O c c u r r i n g s i m u l t a n e o u s l y t o t h e emergence o f  the l i n e j u s t mentioned, i s t h e t e r m i n a t i o n o f an a l r e a d y e x i s t i n g one, e f f e c t e d through p i t c h i n t e r c h a n g e .  I n measure 7, t h e components i n t h e  c l a r i n e t and oboe d' amore a r e i n v o l v e d i n a p i t c h i n t e r c h a n g e a f t e r w h i c h t h e oboe c o n t i n u e s b u t t h e c l a r i n e t d r o p s o u t . W h i l e t h e t e c h n i q u e s o f u n i s o n t r a n s f e r and p i t c h i n t e r c h a n g e may be  85 important opening climax  factors  in linear  pitch  measures,  t h e sense  o f p r o g r e s s i o n towards b a r 6 and t h e f e e l i n g o f  i n that  organization  measure a r e l a r g e l y  the result  i n t h e components  o f t h e expanding  of these  registral  42 boundaries  dictated  and  descending  are  indicated  by t h e l i n e a r  linearizations on system  components t h e m s e l v e s .  which  outline  The a s c e n d i n g  the progressive  wedge-pattern  ( b ) o f E x a m p l e 43.  Summary S e v e r a l modes o f l i n e a r  pitch  a n d PC c o n n e c t i o n h a v e b e e n f o u n d t o 43  operate for  i n the pieces of the quintet.  example,  t h e f e a t u r e d i n s t r u m e n t s were n o t e d  linearizations arpeggios. orderings  involving  t h e upper  In the f i f t h , (most o f t e n  introduction  sixth,  PC c o n t e n t ,  linearizations, Finally, that  transfer  events noted sense  some i n t h e f o r m  and p i t c h  pitches  was a l s o  related. were seen  of wedge-like found  specific  to control the  from  One a t t r i b u t e ,  and c o n t i n u i t y  Apart  from  to reveal  expansions  i n the third  pattern result  interchange.  activity  pieces,  IC ordering, although the successions the control directed  and c o n t r a c t i o n s .  piece;  i t was  suggested  the techniques of unison common :to a l l o f t h e l i n e a r  above, r e g a r d l e s s o f v a r y i n g d e t a i l s  of directed  of successive  Many o f t h e o r d e r i n g s w e r e shown t o c o n t a i n  or inversionally  t h e components o f t h i s  pieces,  as consisting of  and n i n t h  t h e p a t t e r n s o f PC u n f o l d i n g  a wedge-pattern  and f o u r t h  s u c c e s s i o n s ) were f o u n d  and one p a r t i c u l a r  are not t r a n s p o s i t i o n a l l y  and lower  seventh,  twelve-note  o f PC c o n t e n t .  common PC p a i r s  of  I n t h e second  of structure,  which they  i s the  effect.  42  r T h e c l i m a x i s f o r m e d b y t h e h i g h e s t p i t c h i n t h e s e c t i o n , G- , a s w e l l as t h e widest r e g i s t r a l space which accompanies i t , F -G^. 43 Others c e r t a i n l y e x i s t , s e v e r a l o f which w i l l be e x e m p l i f i e d i n t h e n e x t two c h a p t e r s . 5  4  86 Harmonic Two  central  consonance and between  sonorities. largely  a  prevalent  Such  textural  element  particular  situation,  (often  dissonance The light (a)  organization  characterizations  on t h e t e x t u r a l  polyphonic  changing  of harmonic  dissonance in v e r t i c a l i t i e s ,  depend most  issues  Details  environment  condition  consisting  was  and  functional  and  relationships,  i n which  to f i v e  sonorities  one n o t e a t a t i m e ) ,  as t h e  resulting  however, For  example,  single,  components.  are slowly,  are  relationships  they occur.  noted e a r l i e r  of from three  the v e r t i c a l  i n the quintet  but  In  this  continuously,  i n a continuum of  consonance-  fluctuation. opening seven measures  of linear  o f Example  organization, 44  consists  of the t h i r d  exemplify  of the l i n e a r  while  system  (b) i n d i c a t e s  the harmonic  lines  through both systems.  piece,  such harmonic components, changes,  V e r t i c a l i t i e s may  be  just  examined  i n the  fluctuation. as  stated  delineated classified  System  earlier,  by t h e as  vertical  consonant 44  or  dissonant  indicated on (The  according  on t h e l e f t  the graph  (Example  numbers f r o m  1-25  to t h e i r o f Example 45) on  s e m i t o n e and 45  revealing  ( s e e page  whole-tone 8 9).  the f l u c t u a t i o n  content  as  These a r e then i n harmonic  t h e graph c o r r e s p o n d to t h e complexes  plotted  quality. o f Ex.  44.)  " T h e c r i t e r i o n of semitone content i s a suggested " f i r s t step" towards t h e c h a r a c t e r i z a t i o n o f consonance and d i s s o n a n c e i n v e r t i c a l i t i e s . In t h e a n a l y s i s o f t h e f i r s t p i e c e ( C h a p t e r I I I ) t h i s i n i t i a l s t e p s e r v e s as a p o i n t o f d e p a r t u r e f o r a m o r e d e t a i l e d s e t o f c r i t e r i a u s e d t o d i f f e r e n t i a t e c o n s o n a n t and d i s s o n a n t s o n o r i t i e s i n t h e o p e n i n g p o l y p h o n i c section. I t i s c l e a r , however, t h a t i n t h i s p a r t i c u l a r m u s i c a l l a n g u a g e the r e f e r e n c e p o i n t s f o r v e r t i c a l c o n s o n a n c e and d i s s o n a n c e a r e r a d i c a l l y d i f f e r e n t from t h o s e of t r i a d i c music. A w h o l e - t o n e may t a k e o n t h e r o l e of a consonance i n r e l a t i o n t o semitone s t r u c t u r e s . P e r h a p s t h e most b l a t a n t e x a m p l e o f t h i s comes a t t h e e n d o f t h e t h i r d p i e c e . The s i m u l t a n e o u s , b u t o u t - o f - p h a s e , o s c i l l a t i o n b e t w e e n A^ a n d B ^ r e s u l t s i n a r e i t e r a t e d minor second. T h e f i n a l m a j o r s e c o n d , A^-B-^, s o u n d s extremely c o n v i n c i n g as a p o i n t of r e s o l u t i o n ; i t s s t a t u s as a consonance can h a r d l y be d i s p u t e d .  87  Example 44.  P i e c e No.  3, m e a s u r e s  1-8,  harmonic  complexes.  88  Example  45.  Piece  No.  3, m e a s u r e s  1-8,  consonance-dissonance c r i t e r i a  and h a r m o n i c  quality  fluctuation.  i  ;  I  diss.  vertical complexes as to Example No. 44.  90 It  must  essentially dissonance  be  remembered, h o w e v e r , t h a t  points  along  a  q u a l i t i e s may  contributions  to  more s i g n i f i c a n t dissonance  the  c o n t i n u u m and,  be  perceived  for  while  here.  The  instance,  vertical  their  in isolation,  large-scale progression  of  suggested  i s analogous  by  the  complexes  individual  harmonic  i n dimension  is  consonance  above the to  their  q u a l i t y which  from  curve  are  consonance-  i t i s , perhaps,  higher-level progression  >• c o n s o n a n c e ,  E x a m p l e 45,  these  the  >•  graph  level  of  on rhythmic  45 and  metric  c h a r a c t e r i z a t i o n noted  The the  harmonic  third,  reveal continuously  fluctuating first  the  represented  by  density  the  fifth  piece  line-graphs, (see  and  quality.  ninth  Rather  and  measures  7-15  as  Examples  46  given  below) of  fifth  pieces,  changing v e r t i c a l i t i e s  consonance-dissonance  s e c t i o n of  spatial  s t r u c t u r e of  earlier.  the  harmonic  and,  than of  and  that  staff  47.  of  hence, notation,  the n i n t h are,  complexes  consonance-dissonance f l u c t u a t i o n ) i s e f f e c t i v e l y  like  The  here,  increase  (representative  portrayed  through  the  in of  this  means. The  expansion  established  in registral  wedge-pattern of  space, which r e s u l t s  pitch unfolding,  is a  from  primary  the  previously  factor in  the  46 perceived  dissonance  of  registral  boundaries  i n these  reduction  in perceived  the  highest,  the  sonority. two  pieces  dissonance—a  most g e n e r a l ,  The  structural  continuously  represent  pattern level  in this  w h i c h may, of  harmonic  expanding sense a  again, quality  be  gradual considered  fluctuation.  45 In the f o r e g o i n g s e c t i o n s of t h i s chapter, these seven measures w e r e c h a r a c t e r i z e d a s one c o n t i n u o u s g e s t u r e w i t h r e s p e c t t o r h y t h m i c i n t e n s i f i c a t i o n , m e t r i c s t r u c t u r e , and l i n e a r o r g a n i z a t i o n . The l a r g e - s c a l e p r o g r e s s i o n of harmonic q u a l i t y i s congruent w i t h the span of f u n c t i o n a l u n i t y s u g g e s t e d by t h e s e p a r a m e t r i c c h a r a c t e r i z a t i o n s . 46 F o r e x a m p l e , v e r t i c a l i t i e s may c o n s i s t o f s e v e r a l o c c u r r e n c e s of I C 1, b u t i n compound f o r m s ( e . g . , m i n o r n i n t h , e t c . ) . In these instances, t h e p e r c e i v e d d i s s o n a n c e o f t h e I C 1 i s p r e s u m a b l y somewhat r e d u c e d .  91  Example  46.  P i e c e No. 5, m e a s u r e s 1-8, l i n e - g r a p h l i n e a r and harmonic expansion.  representation  of  91  EDCA«G«-  F*E— D- • CA«G*-  F* EDCA*  EDC-  i  i  r  measure flute  /  clarinet horn  *  bassoon  —  /  *  /  no.  r  1  T  93  Example 47.  P i e c e No. 9, m e a s u r e s 8-15, l i n e - g r a p h l i n e a r and h a r m o n i c e x p a n s i o n .  representation  9+  (unison toendK^  a  FLUTE  B  OBOE  A  CLARINET  G F - | E  H  1  1  1  h  ' -f=i _J  _ l  unison to this point) 8  10  11  12  measure no.  13  14  15  16  It that  was  a s s e r t e d at the  textural  environment  beginning  of  this  section  on  harmonic  i n f l u e n c e s the approach to harmonic  details  classifications 47  and  functional  second with  textural  secondary  times.  components,  the  The  however,  the  and  measure  are  boxed, numbered, and the  details  primary  and  relative  relationships  consists  beams f o r e a s e o f  i n the  secondary  tenth  of  the  between t h e  the  of  two  the  tempo and  reading.  both  example r e v e a l ,  the  along 12  of  the  the  and  system of  affiliations  components u s u a l l y  being  13  of p i t c h e s w h i c h  second  activity  be  of which are n o t a t e d  groups  on  to  secondary  a more g l o b a l  relationships  interacts  c a p a c i t y at  and  rhythmic  fleeting  e x c e r p t s , measures  The  detailed  too  i s p e r c e i v e d on  fourth,  line  textural  primary  t e x t u r e , once a g a i n ,  which  pieces, a  o c c u r r i n g i n a fragmented  of the d e t a i l e d  1 of  and  of harmonic o r g a n i z a t i o n i n t h i s  quality  and  As  latter  fourth,  i n which a primary  harmonic r e l a t i o n s h i p s  i s the r e s u l t 48  the  linearity  harmonic  Example  second,  three pieces cited,  individual  significance, point.  aspects  In the  In the  is prevalent—one  c e n t r e around  components.  piece,  situation  Revealing  environment  render  relationships.  level, way.  of  the  without  sound  each  second stems  together 48  excerpt.  between n o t e s  involves dissonance  focal  of  the  followed  by  consonance.  Concerning  the aforementioned  affiliation,  a concept  d i s s o n a n c e r e l a t i o n s may b e p o s i t e d . I n m e a s u r e 13 o f 47 The t e n t h p i e c e i s d e a l t w i t h i n C h a p t e r I V .  the  of  consonance-  second  piece,  48 The s c o r e s h o u l d b e c o n s u l t e d f o r u n d e r s t a n d i n g o f t h e r h y t h m i c c o n f i g u r a t i o n s of the v e r t i c a l i t i e s . O f t e n , f o r example, a s u b t l e r h y t h m i c v a r i a t i o n between components w i l l p r o d u c e c o n s e c u t i v e v e r t i c a l i t i e s . In the rhythmic c o n f i g u r a t i o n • — - J ^ f o r i n s t a n c e , two v e r t i c a l i t i e s  n sound,  although very  briefly.  n  96  Example 48.  P i e c e No. 2, m e a s u r e s 12-13, a n d p i e c e No. 4, m e a s u r e harmonic i n t e r v a l f l u c t u a t i o n through v o i c e l e a d i n g .  1,  one textural e l e m e n t  ma 3 ft  < 0) 0)  w </>  (0 (0  ro I co  Wr I  I  co  I  "<g>  98 for as  example,  a relativity principle  a consonance or a dissonance,  follows third  i t , an  piece.  idea already This  which comprise the sufficiently two  to  instances  point  on  concept  the of  concept  whole-tone  are  of  the  the  as  the  interval  the  being  E x a m p l e 49.  P i e c e No. 4, m e a s u r e s 7-9 f l u c t u a t i o n through voice  considered  end  the  activity harmonic The  is  which proceeds the  ends o f  fluctuating  the  with  rhythmic  "dissonant"  relationship  mm.  the  i n E x a m p l e 49.  also raises  considered  the whole-tone  in connection  Here,  shown  (from  r e l a t i v i t y and  on  i s a l s o r e l e v a n t to  perception  in question  that  depending  a l l u d e d to  fourth piece.  allow  allows  of  two  phrases  has  relaxed  quality.  ultimate  arrival  of  this  particular  a r e s o l u t i v e cadential device.  and 23-26, h a r m o n i c leading.  interval  8  finC)  1 - 2 - 1 - 2 - 2  -  1  -  2  1  -  2  BSN.  mm.  FL  23  CL (inC)  24  1 J JJ 1  -  25  [) ill J\ .0  1  IvA J Ik  -  J_e_  2  -  The  semitone) r e i n f o r c e s the  possibility  7  the  1  ^  »•*!  1  26  or  99 P a r t s of t h e second and seventh p i e c e s f e a t u r e v e r t i c a l i t i e s , component p a r t s of w h i c h a r e s i m u l t a n e o u s l y a r t i c u l a t e d in s t r i c t v e r t i c a l alignment).  the  ( i . e . , they occur  I n t h i s t e x t u r a l environment t h e harmonic  a s p e c t i s p r i m a r y , w i t h t h e p o s s i b i l i t y of d e r i v e d l i n e a r r e l a t i o n s h i p s , r a t h e r than t h e o t h e r way around.  I n t h e second p i e c e , the v e r t i c a l .•:  s o n o r i t i e s comprise t h e secondary t e x t u r a l element i n t h e opening s e c t i o n , over which t h e c l a r i n e t i s f e a t u r e d .  F i v e v e r t i c a l complexes a r e sounded  i n t h i s p a r t i c u l a r s e c t i o n (measures 1-11), t h e f i r s t t h r e e c o n s i s t i n g e n t i r e l y o f a d j a c e n t semitones.  The l a s t two f e a t u r e semitone and  whole-  tone c o n t e n t — a s u b t l e , yet i m p l i c a t i v e d e p a r t u r e from t h e opening sonority. The f i v e - n o t e v e r t i c a l i t i e s appear l a t e r i n t h e p i e c e ( e . g . , b a r s 15, 20, and 21) and s e r v e t o r e c a l l t h e opening s e c t i o n .  In these three  r e c u r r e n c e s , the content i s e x a c t l y t h a t of t h e t h i r d complex o f t h e p i e c e ( i . e . , c o n s e c u t i v e semitones from complex i n t h e p i e c e ) . of  t o G//3—a t r a n s p o s i t i o n of t h e f i r s t  I n t h i s sense t h e y r e s o l v e the harmonic d e p a r t u r e  t h e s o n o r i t i e s which end t h e opening s e c t i o n .  F i n a l l y , i n b a r 29, a  v e r t i c a l i t y o c c u r s which r e c a l l s PC's D#, E, and F from t h e opening s o n o r i t y (where t h e y appear as t h e l o w e s t t h r e e p i t c h e s ) , t h e r e b y p r o v i d i n g a degree o f PC c l o s u r e .  These harmonic complexes a r e i n d i c a t e d on t h e  second s t a f f o f Example 50 ( a l l t h e p i t c h e s w i t h i n each box sounding together).  The o u t e r i n t e r v a l of each s i m u l t a n e i t y ( v a r i e d t h r o u g h  i n t e r n a l c o m b i n a t i o n s of semitones and whole-tones) i s g i v e n on t h e t h i r d system. Three a d d i t i o n a l d e t a i l s i n Example 50 a r e worth n o t i n g . the  First,  t h r e e harmonies w h i c h c o n c l u d e the p i e c e e x h i b i t a n o t h e r i n s t a n c e o f  f u n c t i o n a l consonance-dissonance r e l a t i o n , as p o s i t e d i n c o n n e c t i o n w i t h  100  t h e t h i r d and f o u r t h p i e c e s .  The t h r e e s o n o r i t i e s i n q u e s t i o n ,  w i t h t h e I C ' s of t h e consonance  >>• d i s s o n a n c e  along  progressions are also  49  i n c l u d e d on t h e second s t a f f of Example 50.  Second, a l i n e a r p a t t e r n  may be imposed on t h e complexes i n d i c a t e d on t h e second s t a f f  ( i . e . , the  complexes w h i c h c h a r a c t e r i z e t h e ' a ' - s e c t i o n and subsequent a l l u s i o n s t o it).  The p a t t e r n i n v o l v e s t h e c o n n e c t i o n o f PC's w h i c h r e p r e s e n t  e x t r e m i t i e s of each complex, t h e upper a s c e n d i n g  pitch  l i n e c o n t r i b u t i n g to the  o v e r a l l PC p r o g r e s s i o n , and t h e lower l i n e p r o v i d i n g a d e p a r t u r e  from,  and r e t u r n t o , t h e PC r e p r e s e n t i n g t h e l o w e s t p i t c h of t h e opening sonority.  These l i n e a r events a r e i n d i c a t e d on t h e t o p s t a f f o f Example  5 0 . A n d  f i n a l l y , t h e upper a s c e n d i n g  is,  l i n e a r c o n n e c t i o n j u s t mentioned  i n a sense, "summarized" by t h e s o n o r i t i e s which c l o s e t h e p i e c e .  T h i s r e l a t i o n s h i p i s n o t e d on t h e t h i r d s t a f f o f t h e example. The beginning  i n t e r v a l make-up o f t h e r e c u r r i n g v e r t i c a l i t i e s found a t t h e of t h e seventh  of t h e second p i e c e .  p i e c e i s t h e same as t h a t o f t h e o p e n i n g s o n o r i t y  S p e c i f i c a l l y , t h e y a r e comprised o f f i v e  semitones, f i r s t , from G^ t o ( r e g i s t r a l l y dispersed)  adjacent  (measures 1-23), and t h e n from D t o F#  i n b a r s 30 and 34.  Variety i n the reiterated  s o n o r i t i e s based on G^ i s p r o v i d e d by t h e v a r i o u s i n s t r u m e n t a l v o i c i n g s i n which i t occurs.  ( R e f e r t o Example 51.)  W h i l e t h e r e i t e r a t e d harmonies remain based on G^, t h e s u s t a i n e d s o n o r i t i e s w h i c h grow o u t of them a r e v a r i e d and, i n t h e m s e l v e s , e x h i b i t 49  Here i s another i n s t a n c e t o r e i n f o r c e t h e n o t i o n o f t h e semitone t o whole-tone " r e s o l u t i o n " f u n c t i o n i n g as a c a d e n t i a l d e v i c e . ~^As " s t e p w i s e " e v e n t s t h e s e p a r t i c u l a r l i n e a r i z a t i o n s a r e a d m i t t e d l y more p r o b l e m a t i c (than p r e v i o u s examples) because of t h e . r e g i s t r a l d i s p e r s i o n o f t h e i r members. L i n e a r e v e n t s i n v o l v i n g such o c t a v e - d i s p l a c e d " s t e p s , " however, may be viewed as an important aspect of l i n e a r o r g a n i z a t i o n i n t h i s m u s i c a l language.  Example  n —  1  J  mm. 1,2  3  „  rrrr—n j  ic: 4  Piece  —  1  4  J  No. 2, h a r m o n i c  —  —  11  ^*±±-±— 1  50.  —  i  15,20,21  ufsh T-j  organization.  (ic: 2  *.  . xJ.  6  Example  51.  Piece  4  No. 7, m e a s u r e s  *  12-15  1-38, h a r m o n i c  s  15-19  23  \fy -  , y^±J^%:  \t*—JL.  l_!Li  5  sustained sonorities ^  mm. 1-12  1V  '  4  30,34  , 1  29  =—^=f=i  -H-r^—r*  *  J  organization.  V  3 1 - 2 )  ^"*T> \ —a  jil  j  »  102  a  directed fluctuation.  B*  74  (measures  and  finally  four  6 ff.),  For instance,  followed  the four-note  4  the sustained  of  the five-note v e r t i c a l i t i e s  spacing other  on D — a l l  all-semitone  in has  have,  potent  remains  towards  12 f f . ) ,  thickening  t h e emphatic  display  The change o f s o n o r i t y t o t h e by t h e r e g i s t r a l l y  o n G, t h e  t h e harmonic  straightforward, that which  from,  dispersed  based  Although  departures  t o be examined  doubling.  rhythmic  or octaves.  they  both  consists of  and r e v e r s i o n s t o ,  and l a s t  i n other  pieces  pieces  musical  been mentioned  event  concerns  use of h i g h l y -  i s a motive  o r theme  T h e u s e o f t h i s mode o f d o u b l i n g i n a l l but the fourth)  t h e f u n c t i o n and o c c u r r e n c e will  be d e a l t w i t h  a r e noteworthy  and themes  chapter  i n t e r a c t i o n s c r e a t e s an  (and i t occurs While  i n this  The w i d e s p r e a d  expected  effect.  of the motives  ^Notice content  detail  the least  i n unison  instances  i n fact,  The t e x t u r a l  i t i s interesting  exhibit  i s the  15 f f . ) — t h e t o p  a five-note verticality  and complex  i n the f i r s t  Most  piece,  both  of the quintet  an extremely  chapters,  (bars  4  (bars  7 4  s e c t i o n a r e c o n s i d e r a b l y more  and o c t a v e  i n which  i s doubled  doubling  Also,  sonorities  the pieces  4  B e t w e e n t h e two v e r t i c a l i t i e s — o n e  harmonic  the use of unison  which  4  element  complex.  final  environment  direction  i n bar 23."^  reference,"  semitones.  chromatic  provides  o f t h e second  as a "harmonic  The  4  on D i s a l s o marked  particular  to those  adjacent  G -A -B'  PC's f r o m D t o B a r e r e p r e s e n t e d .  i n this  compared  the  built  of the chord.  aspects  use,  sonorities  4  sustained  f i v e - n o t e complex.  of  complex  by t h e t r i c h o r d  s o n o r i t y G// -A -A# -B  pitches of the o r i g i n a l  five-note  the f i r s t  with  o f such  i n t h e next  here.  involving unison  i n connection  thus  other  and/or aspects  octaves of the  i n the successive v e r t i c a l i t i e s  o f bar 23 that  t h e same; o n l y  distribution varies.  the instrumental  pitch  two  103 m u s i c a l language.  The t h r e e - n o t e , o c t a v e - d o u b l e d  m o t i v e i n the second  p i e c e (bar 2 3 ) , f o r example, was i n t r o d u c e d e a r l i e r a s l e a d i n g i n t o one o f the few a u r a l l y p e r c e i v e d downbeats i n t h e p i e c e .  The  octave-doubled  theme i n the m i d d l e o f the t h i r d p i e c e (measures 10-12) was c h a r a c t e r i z e d as one of the two  s i m u l t a n e o u s l y sounding t e x t u r a l elements i n t h e p i e c e —  t h e o n l y o c c u r r e n c e of such a t e x t u r e i n a p a r t i c u l a r ensemble p i e c e . The f i f t h and n i n t h p i e c e s open w i t h a r e i t e r a t e d and  sustained unison,  r e s p e c t i v e l y , each f u n c t i o n i n g as a d e p a r t u r e p o i n t f o r a wedge-patterned u n f o l d i n g of p i t c h content. In  The n i n t h p i e c e a l s o concludes  on a u n i s o n .  the s i x t h p i e c e , a b r i e f theme which opens i n u n i s o n and c o n c l u d e s  octaves  i n t r o d u c e s t h e coda; see measures 11-14  treatment  i n t h i s regard.  The  i n the seventh p i e c e has a l s o been a l l u d e d to e a r l i e r .  ' b ' - s e c t i o n ( b a r s 38 to the end)  unison  In the  each l i n e a r component, upon e n t e r i n g ,  doubles an e x i s t i n g p a r t a t t h e u n i s o n , a f t e r which i t g a i n s b o t h l i n e a r l y and r h y t h m i c a l l y .  in  independence  F i n a l l y , i n the e i g h t h p i e c e t h e s u s t a i n e d  o c t a v e B^ (measures 23-26), t h e b r i e f o c t a v e m o t i v e (measure 2 9 ) , and  the  u n i s o n m o t i v e .(measure 30) r e p r e s e n t t h e d i s p a r a t e m u s i c a l i d e a s noted e a r l i e r a s b e i n g i n d i c a t i v e o f t h e s t y l e of The  Apparitions  i n t e n s e u n i s o n m o t i v e i n bar 30 p r o v i d e s a d r a m a t i c  and  Aventures.  introduction to  t h e s u s t a i n e d s o n o r i t i e s of the calm f i n a l s e c t i o n .  Summary In dissonance  the f o r e g o i n g d i s c u s s i o n of harmonic d e t a i l s , consonance and i n v e r t i c a l i t i e s , and f u n c t i o n a l harmonic r e l a t i o n s h i p s were  s t a t e d as b e i n g t h e two main i s s u e s . i n f l u e n c i n g such c h a r a c t e r i z a t i o n s .  T e x t u r a l environment was a s s e r t e d a s Three t e x t u r e s were examined:  polyphony, pseudo-polyphony ( i n which one component i s p r i m a r y ) , and homophony.  Regarding  t h e f i r s t o f t h e s e , t h e t h i r d , f i f t h , and n i n t h  104 p i e c e s were  seen  to consist  consonance and d i s s o n a n c e . involving with  s u b t l e changes  t h e second  o f a continuum  of fluctuating  Specifically,  i n semitone  t h e s o n o r i t i e s were n o t e d a s  and whole-tone  t e x t u r e , t h e harmonic  affiliations  secondary  components were examined, and a c o n c e p t  relations  posited.  The second  The  homorhythmic v e r t i c a l i t i e s  and  seventh  involving octave  pieces,  semitone  also  and f o u r t h  content. between  of  of thethird  consonance-dissonance i nthis  t e x t u r e , as found  revealed a consonance-dissonance Finally,  t o be o f d r a m a t i c  In connection  p r i m a r y and  p i e c e s were c i t e d  and whole-tone c o n t e n t .  d o u b l i n g was f o u n d  vertical  import  regard.  i n t h e second  fluctuation  t h e u s e o f u n i s o n and  i n a l l but the f o u r t h  piece.  Summary This musical and  chapter aims t o e s t a b l i s h  language  illustration  meter,  of Ligeti's  and harmonic  c o n n e c t i o n w i t h t h e examples  next  Ten Pieces  for  o f g e n e r a l and s p e c i f i c  and l i n e a r  analyses  a basis  of the f i r s t  two c h a p t e r s .  pitch  Wind Quintet  v i a the definition  a s p e c t s o f form,  t e x t u r e , rhythm,  organization.  studied w i l l  and l a s t  for understanding the  Concepts  serve as a b a s i s  pieces of the quintet,  introduced i n  for  detailed  subjects of the  CHAPTER I I I  ANALYSIS  OF  P I E C E NO.  1  Introduction The previous  following  chapter  parameter  on  i s dealt  applicable.  The  a n a l y s i s of aspects  with  main  of  Delineating of  Principles  of  Factors  this of  1 resembles,  musical  with  Textural of  No.  Ligeti's  separately  sections  Aspects  piece  i n format,  language.  That  i s , each  i n t e r r e l a t i o n s h i p s noted chapter  Formal  are  as  the  where  follows:  Segmentation  Structure  R h y t h m i c and  Metric  Design  Modes o f P i t c h O r g a n i z a t i o n Linear Details Harmonic D e t a i l s Connective Factors Interruptive  Between  A s p e c t s of  the the  First  and  Third  Pieces  and  Second  Summary. Some c o n c e p t s in are  the  first  specific  introduced piece. to  i n Chapter  Often,  piece  No.  The measures brief of  the  (i.e.,  first  1-16  piece  t r a n s i t i o n in bars 'a'-section  ( t o be  measures 22-24).  these w i l l  Factors  exhibits a  comprising  be  shown t o  however, d e t a i l s o f  1;  Delineating  II will  the 15-16  of  also  clearly  'a'-section, bridges  explained A brief  parametric  receive  Formal  the  two  two-part  16-22, t h e  105  attention.  formal  the  structure,  'b'-section.  m a i n d i v i s i o n s and  l a t e r ) occurs at  summary o f  close  organization  Segmentation  defined and  have a p p l i c a t i o n  end  of  an  the  d e l i n e a t i n g f a c t o r s of  A "echo"  piece formal  106 segmentation later  i s given  aspects of texture,  polyphony operating  t o mezzoforte. consists  t h e range  portion  e n t r i e s a t fff,  i ngreater  detail  sostenuto  activity  level  less  i n t e r a c t i o n between p a r t s , and  of the piece  section,  and instruments  3  _  (i.e.,  ) f  e.g.,  dolcissimo quality  i s much h i g h e r  i n t h e former u t i l i z e  • .  A  |  1, I I I  |  | I 1 a r e found.  With respect  J = 40 a n d J = 4 8 , r e s p e c t i v e l y . with  f a c t o r s which  t h e quasi  suggest  forza)  definition, the  than  that  df the  t h e rhythmic  'b'-  divisions  3  I, a n d | | | | |, w h i l e  b a r 22, a l o n g  legato  la  S  |  16-22)  accompany t h e  tutta  (marked  pianissimo  from  measures  marking  I n terms o f rhythmic  i nthe 'a'-section  complex  1  e calmo,  the 'b'-section.  features  • - , dynamically  >y  section, while a r e i t e r a t i v e  distinguishes  axe  with  the 'a'-section  r e g i s t e r and t e x t u r a l space,  a n d molto  character opening  over  The l a t t e r  of paired  contrasting  in  dealt  i n the chapter. Concerning  a  below, a l l o f which a r e  i n thel a t t e r ,  t o tempo, The f i n a l  eco  only  |  |  t h e two s e c t i o n s  land  are  marked  tempo c h a n g e b a c k t o J = 4 0  i n d i c a t i o n and r e t u r n  to  pianissimo  an a l l u s i o n to t h e 'a'-section.^  Summary The defined  formal  forward, levels  aforementioned structure  factors of delineation contribute i n thef i r s t  piece.  however, w i l l  activity  be d e a l t  with  a r e more complex,  and t e x t u r a l c h a r a c t e r i s t i c s . i nd e t a i l  clearly  Some d e t a i l s a r e s t r a i g h t -  s u c h a s tempo a n d d y n a m i c s , w h i l e o t h e r s  of rhythmic  to a  i n subsequent  e.g.,  A l l factors,  sections.  The PC c o n t e n t o f t h e f i n a l d y a d , C a n d D, i s a n o t h e r a s p e c t s u g g e s t i n g r e l a t i o n s h i p t o t h e ' a ' - s e c t i o n ; t h i s , however, w i l l r e c e i v e closer attention i n thesection dealing with linear d e t a i l s of pitch organization.  107 Aspects Textural  characteristics  those  defined  first  p i e c e , f o r example,  is  comprised  main f o r m a l reduction  will  i n the previous  of essentially sections.  chapter  as s p e c i f i c  t o ensemble p i e c e s .  two c o n s e c u t i v e  element  t o t h r e e components  the textural  textural  quality  The  a t a time, and  textures corresponding  Also consistent i s the transition  In approaching  be c o n s i d e r e d :  o f p i e c e No. 1 a r e g e n e r a l l y c o n s i s t e n t w i t h  f e a t u r e s o n l y one t e x t u r a l  in textural-density  element).  of Textural Structure  tothe  which f e a t u r e s a  (yielding  one t e x t u r a l  s t r u c t u r e o f t h e p i e c e , two a s p e c t s  and t e x t u r a l  space.  Textural Quality Texture, for  a s a d e l i n e a t o r o f f o r m , must  t h e ways i n w h i c h  p i e c e may t h e n  instruments  be d i f f e r e n t i a t e d  interact from  first  be u n d e r s t o o d  i n music.  each other  t o account  Sections of a given  by t h e i r  specific  2 characteristics interaction parts. for  of instrument  concerns  Instruments  interaction.  t h e rhythmic  structure of the individual  ( o r components) moving  i n s t a n c e , may b e c o n s i d e r e d 3  A fundamental aspect of  in strict  interdependent,  while  alignment,  those moving  alignment  a r e independent.  therefore  s p e a k o f i n d e p e n d e n c e among c o m p o n e n t s a s o n e t e x t u r a l  and  interdependence  parts  occur,  depending  Such c l a s s i f i c a t i o n s  vertical  instrumental  among c o m p o n e n t s a s a n o t h e r .  v a r i o u s degrees  on t h e t e x t u r a l  are "qualitative";  of each  may  we may  quality  Where s u b g r o u p i n g s  of independence/interdependence  quality  i n non-  of  result,  subgroup.  I n E x a m p l e 52 a q u a l i t a t i v e a n a l y s i s i s a p p l i e d t o t h e t e x t u r a l 2 Instrument i n t e r a c t i o n i s t h e primary f a c t o r i n t h e d e t e r m i n a t i o n of t e x t u r a l elements which i n t u r n d e f i n e o v e r a l l t e x t u r e . 3 The t e r m s " i n d e p e n d e n t " a n d " i n t e r d e p e n d e n t , " i n r e f e r e n c e t o t h e i n t e r a c t i o n o f components, a r e a s s o c i a t e d w i t h t h e work o f W a l l a c e B e r r y . See h i s Structural Functions, Ch. 2.  108  Example  52.  Line-representation textural quality.  TE  =  textural  ITC  =  interdependent  IDC  =  independent  of textural  element component  component  components,  showing  109  'a'-section  5  mm. 1 (  i  i  L  _i_  10 J  L  J  'b'-section  transition  l_  J  I  L  15 »  j  i  ;  i  a-sect. (echo)  20 l  L  25 J  L  J  i  i  I  FL — EH.— C L -  I  '•I  HRN.— BSN.—  1 TE  4  1 TE  0  TEXTURAL QUALITY  1 TE  1 TE  0  2ITC-»»2IDC  2ITC  ^  >2ITC  5 IDC >3 IDC  OVERALL QUALITY  V  independent  V3ITC-»6IDC  CI  2ITC  independent/interdependent  . interdependent  110 components of t h e f i r s t p i e c e .  The ' a ' - s e c t i o n and t r a n s i t i o n a r e  c h a r a c t e r i z e d by a t e x t u r a l q u a l i t y of independence  ( i . e . , polyphony),  the t r a n s i t i o n a l s o f e a t u r i n g t h e d e n s i t y r e d u c t i o n noted e a r l i e r .  The  ' b ' - s e c t i o n i s t e x t u r a l l y c o n t r a s t e d i n t h a t i t i s comprised of subgroups, the components of which move i n d e p e n d e n t l y a t t i m e s , and i n t e r d e p e n d e n t l y at  other times.  The subgroups  themselves  ( s p e c i f i c a l l y a t p o i n t s of  i n t e r d e p e n d e n c e of components) e n t e r i n d e p e n d e n t l y of one a n o t h e r . F i n a l l y , components of t h e c l o s i n g dyad e n t e r i n t e r d e p e n d e n t l y . T h i s p a r t i c u l a r i n s t a n c e o f v e r t i c a l a l i g n m e n t i s p r e p a r e d by t h e i n t e r d e p e n d e n c e of  components w i t h i n t h e p r e v i o u s subgroups.  independence  The s h i f t from  total  t o i n t e r d e p e n d e n c e i s noted i n Example 52 below t h e l i n e -  r e p r e s e n t a t i o n of t e x t u r a l components.  T e x t u r a l Space For t h e purposes of t h i s paper, t e x t u r a l space r e f e r s t o t h e i n t e r v a l l i c d i s t a n c e between outermost r e g i s t r a l l y s p e c i f i c p i t c h e s of a p a r t i c u l a r f o r m a l s e c t i o n o r o t h e r s t r u c t u r a l segment.  I n comparing  t e x t u r a l spaces o f two s e c t i o n s (be they c o n s e c u t i v e o r n o t ) , r e g i s t e r i s of  secondary c o n c e r n ; a f t e r a l l , any p e r f e c t f i f t h i s l a r g e r than any  major t h i r d , e t c . , r e g a r d l e s s o f r e g i s t e r .  The r e g i s t r a l placement  of a  s e c t i o n ' s t e x t u r a l space i s , however, of s i g n i f i c a n c e on a more g l o b a l l e v e l , e.g., t h a t of t h e whole p i e c e . In  t h e p i e c e under d i s c u s s i o n , f o u r t e x t u r a l spaces may be d i s c e r n e d ,  as i n d i c a t e d i n Example 53.  Below t h e s p a t i a l r e p r e s e n t a t i o n s a r e  i n t e r v a l l i c r e l a t i o n s h i p s r e v e a l i n g an o v e r a l l p a t t e r n of s p a t i a l f o l l o w e d by c o n t r a c t i o n .  expansion  F o r example, t h e e x p a n s i o n from t h e 'a' t o 'b'-  s e c t i o n £i.e., t h e minor s e v e n t h (D^-C^) t o t h e o c t a v e (B^-B^)] i s r e i n f o r c e d by t h e more l o c a l e x p a n s i o n o f t h e t r a n s i t i o n ' s minor  third  Ill E x a m p l e 53.  Textural  spaces of formal  segments.  mm.  1-14  15-16  17-21  22-24  (inv.)  to  the 'b -section's 1  major  third  (here  B^/B ) .  S i m i l a r l y , the general  without  t h e o c t a v e B)j t o t h e f i n a l  contraction the  explained  second  of t h i s a s s o c i a t i o n  in detail  the successive  ascent, of  from t h e 'a'-section's  becomes t h e m a j o r  implications  of  contraction  two a r e i n v e r s i o n a l l y r e l a t e d ;  inverted,  later  dyad  doubling,  from t h e 'b'-section  seventh.  4  by an o c t a v e ) .  important  Regarding  the large-scale  instance  s e v e n t h D-^-C , when  C-^-D-* ( d i s p l a c e d  are extremely  (with or  by t h e l a r g e - s c a l e  In this latter  e.g., t h e minor  i n t h e chapter.)  spatial fields,  of the octave  i s reinforced  minor  t h e s i g n i f i c a n c e o f which w i l l  t h i s chapter  independent  and w i l l  registral  progression  be e x p l a i n e d  (on r e l a t i o n s h i p s between t h e f i r s t  be  placement  i s one o f  i n the final and t h i r d  (The  section  pieces).  4 A more immediate e x p a n s i o n i s d i s c e r n i b l e w i t h i n t h e ' b ' - s e c t i o n i t s e l f , s p e c i f i c a l l y i n t h e p r o g r e s s i o n f r o m t h e o p e n i n g u n i s o n C//^ t o B and E^5. 4  112 Summary Two a s p e c t s section:  o f t e x t u r a l s t r u c t u r e have been d e a l t w i t h  t e x t u r a l q u a l i t y and t e x t u r a l space.  independent  and/or  interdependent  c o m p o n e n t s , was f o u n d its  role  as a basis  The f o r m e r ,  modes o f i n t e r a c t i o n  to f u n c t i o n as a formal  in this  defined  by  between t e x t u r a l  delineator  i n addition to  f o r i t s own p a r t i c u l a r mode o f p r o g r e s s i o n .  s p a c e was r e f e r r e d t o a s t h e s p a c e d e f i n e d  by p i t c h  formal  o f t e x t u r a l s t r u c t u r e was a l s o  segments o f t h e p i e c e .  shown t o p r o v i d e  small  mode o f d i r e c t i o n followed  and l a r g e - s c a l e p a t t e r n s  within  the piece,  by c o n t r a c t i o n .  scale a s c e n t — a  detail  which w i l l  regard  first  piece  t o meter.  That  patterned  strong  convenience.  accent in  M e t e r was d e f i n e d  progressive Wallace  piece,  earlier  other  this  expansion  reveals a largei n this  chapter.  ensemble p i e c e s  4 i s essentially  undefined  with  by  i t i s solely a notational a s o n e p a r t i c u l a r mode o f r h y t h m i c  type  impulses according t o  o f rhythmic  element-rhythms c o n t r i b u t e  and r e c e s s i v e t e n d e n c i e s  i n an a d d i t i o n a l  Design  the other  one which g r o u p s r h y t h m i c while  piece  and M e t r i c  rather,  i n various  one o f s p a t i a l  significance later  with  i s , the notated  and u n a c c e n t — a n d ,  the f i r s t  the f i r s t  o f Rhythmic  a n d weak b e a t s ;  grouping--specifically,  gain  i s consistent  resulting  specifically,  Registrally,  Principles The  This aspect  extremities  Textural  inherent  unit  i s not operative  significantly  i n t h e music.  To  to the  quote  Berry:  A l l element-processes a r e rhythmic. I n an i m p o r t a n t sense, t h e study of rhythm i s t h e study o f a l l m u s i c a l elements, t h e a c t i o n s , o f those elements producing t h e e f f e c t s of pace, p a t t e r n , and grouping which c o n s t i t u t e rhythm.-*  ^Berry,  Structural  Functions,  p. 301.  113 For of  our  recurrence  pattern of chapter, the of  with  brief  an  respect  e l e m e n t - r h y t h m may t o an  sixteen bars linear  in three  a  particular of  patterns disparate  the  complexity.  specific  points  rhythms. units  The  based  dynamics,  piece.  flute, Any  by  the  f o l l o w i n g examination of  on  six different  with  and  said  first  the to  pattern  of  operate  parameters:  will  in  said to  to  consist  in varying be  a  recurrence  heard  degrees  a t t r i b u t e d to  several  piece  or  previous  the  be  s i g n i f i c a n c e may  the  a  b a s s o o n were  another  concurrence  elements or  In  p i e c e may one  as  element,  Specifically,  given  structural  of  particular  clarinet,  interacting  w h i c h a r e marked  a  thought  e l e m e n t - r h y t h m was  rhythms.  Occasionally,  within  be  a c e r t a i n element.^  eighth  i n the  o f many s u c h e l e m e n t - r h y t h m s of  event  r e c u r r i n g changes w i t h i n  f o r example,  first  result  purposes,  different  expose  rhythmic  impulse-density,  t e x t u r a l - d e n s i t y , t e x t u r a l q u a l i t y , harmonic-density,  and  tempo.  Element-Rhythms Rhythm o f In units  of  point." first  impulse-density the  previous  impulse-density  progression  Units  comparable design  as  of  and  c o n s i s t of  These u n i t s  underlying  each p l a t e a u  being  was  said  recession delineated  i n d i c a t e d above the  "large-scale units").  activity,  chapter,  rhythmic  piece,  seen to  fluctuation  and  dimension are  g r a p h on  system  (particularly  "stepped" delineated  increases by  a  a  define  widespread  "turn-around  also discernible in of  Example  progressive  and  change  by  (a)  the  to  decreases  i n magnitude  54  one) in in  the  (see may  be  rhythmic the  I n t h e f o r m e r , t h e r e c u r r i n g e v e n t i s t h e same. For example, meter i s one s p e c i f i c e l e m e n t - r h y t h m — o n e w h i c h r e l i e s on r e c u r r i n g a c c e n t delineated patterns. A p a t t e r n o f r e c u r r i n g c h a n g e w o u l d be, f o r i n s t a n c e , a fluctuation in instrumentation-density. The r e c u r r e n t e v e n t ( i . e . , a f l u c t u a t i o n ) i s d i f f e r e n t e a c h t i m e ; sometimes i t i s an i n c r e a s e i n d e n s i t y , at o t h e r t i m e s i t i s a d e c r e a s e . I n e i t h e r c a s e , a s w i l l be e x p l a i n e d , a r h y t h m r e l i e s on a r e c u r r e n c e o f some k i n d .  114  E x a m p l e 54.  Two  levels  of  impulse-density  fluctuation.  us  measure no.  116 progressive  d i r e c t i o n and,  direction  £see s y s t e m  perceived  as establishing  earlier),  theindividual plateaus  density  (b)  after  fluctuation.  t h eturn-around  o f E x a m p l e 54^]. a "rhythm"  This  marked  by magnitude changes, (or  consists initial  thef i r s t  This  small-scale  o f measurement,  pitch  pattern  of linear pitch-pairs b e g i n s a t pianissimo  A t or just  p e a k s a t mezzoforte,  units  by t h e turn-around  repeats  itself  with  each  subsequent  close  proximity.  proximity  pulsation—a  The next  constitutes  groups of d y n a m i c a l l y  t h egraph  group,  The f i r s t  to articulate units  groups  indicate  a t t h e same t i m e ,  of a graphic i nthef i r s t  part The  intensifies  pitch, the begins.  Although the  changes  i n the  t h e y n e v e r t h e l e s s do  i s a "group" o f dynamically pitch  a n d so o n . create  mezzoforte  These  pitch  representation  recurring  occurring  slow  change o f each rhythm.  o f the  twelve measures.  o f o v e r a l l dynamic  changes i n  an o v e r a l l ,  of t h i s p a r t i c u l a r  groups o f p i t c h - p a i r s units  pitch  o f mezzoforte  intensified pitch-pairs  E x a m p l e 55 c o n s i s t s pitch-pair  The r e s u l t  occurrence  another  rhythm o f s o r t s .  g r o u p may b e h e a r d  by r e s t s .  pitch-pair.  i nrelatively  pitch-pairs.  instrumental  a diminuendo  a t which point  independently o f each other,  and,  units  b e f o r e a r t i c u l a t i o n o f t h e second  occur  of  may b e v i e w e d a s  and g r a d u a l l y  instruments  exposed  o f impulse-  thelow-level  separated  five  close  units  then,  No. 1 e a c h  i n t e n s i f i c a t i o n and c o r r e s p o n d i n g  exposed  stated  groups  twelve measures o f p i e c e  of each p a i r  increase  pitch-pair  peaks o f dynamic  so  c h a n g e s may b e  to thecriteria  and t h e h i g h e r - l e v e l  exposed  of a succession  dynamically. dynamic  recessive  change i n d i r e c t i o n ) .  Rhythm o f d y n a m i c a l l y In  (according  p a r t i c u l a r element-rhythm,  two l e v e l s a n d two s t a n d a r d s  i n the  Such r e c u r r e n t  representing  having  point  point,  dynamically  The outer  i n close  fluctuation.  systems  proximity Two s y s t e m s  117  E x a m p l e 55.  U n i t s of  dynamically  exposed  pitch-pair  groups.  118  119 have been employed because o f t h e o v e r l a p p i n g o f groups; t h e graph i s t o be r e a d by a l t e r n a t i n g between t h e t o p and bottom systems.  The d i a g o n a l  arrows above and below t h e c e n t r e l i n e i n d i c a t e t h e dynamic i n c r e a s e towards t h e i n i t i a l  mezzoforte  p i t c h change o f each group, t h e d u r a t i o n  of p i t c h changes a t  mezzoforte  ( i . e . , t h e h o r i z o n t a l p o r t i o n ) , and t h e  overall  diminuendo  (after the last  l i n e i t s e l f shows o n l y t h e i n i t i a l  mezzoforte mezzoforte  p i t c h change).  p o i n t o f each group.  These p a r t i c u l a r j u n c t u r e s may be heard t o d e l i n e a t e d y n a m i c a l l y exposed p i t c h - p a i r s — a  The c e n t r e  recurring units of  second element-rhythm d i s c e r n i b l e i n  the p i e c e .  I n c i d e n t a l l y , a p r o g r e s s i v e tendency i s r e v e a l e d i n t h e  diminishing  l e n g t h s o f dynamic u n i t s commencing i n b a r 9 — a tendency  which complements t h e i n c r e a s e i n i m p u l s e - d e n s i t y n o t e d  Rhythm o f t e x t u r a l - d e n s i t y  earlier.^  fluctuation  W h i l e t e x t u r a l independence and i n t e r d e p e n d e n c e , d i s c u s s e d are  q u a l i t a t i v e features,  textural-density  i r r e g u l a r one.  a mode o f g r o u p i n g i s d e f i n e d by t h e a s p e c t o f  fluctuation—a  abrupt changes i n d e n s i t y  quantitative  feature.  Specifically,  a r t i c u l a t e a p a r t i c u l a r rhythm, a l b e i t an  System (c) on Example 56 (p. 122)' c o n s i s t s o f t h e l i n e -  r e p r e s e n t a t i o n o f t e x t u r a l components used i n Example 52. density  earlier,  The rhythm o f  f l u c t u a t i o n i s i n d i c a t e d by t h e v e r t i c a l l i n e s m a r k i n g changes i n  the number o f sounding components. Rhythm o f t e x t u r a l q u a l i t y The section.  fluctuation  concept o f t e x t u r a l q u a l i t y was d i s c u s s e d i n t h e p r e v i o u s As a p a r t i c u l a r mode o f r h y t h m i c g r o u p i n g , however, o v e r a l l  ^Because each mezzoforte marks a p i t c h change, t h e c l o s e p r o x i m i t y of t h e i n d i v i d u a l dynamic peaks r e p r e s e n t s a r h y t h m i c i n t e n s i f i c a t i o n r e f l e c t e d on t h e i m p u l s e - d e n s i t y graph.  120 q u a l i t a t i v e changes f u n c t i o n as r e c u r r i n g events w h i c h d e l i n e a t e s p e c i f i c units.  These u n i t s a r e i n d i c a t e d on system (d) o f Example 56.  Rhythm o f h a r m o n i c - d e n s i t y  fluctuation  I n t h e ' a ' - s e c t i o n and t r a n s i t i o n , h a r m o n i c - d e n s i t y  ( i . e . , the  number o f v e r t i c a l p i t c h e s sounding) i s e s s e n t i a l l y t i e d t o t e x t u r a l g  d e n s i t y ; t h e number o f sounding components e q u a l s t h e number o f p i t c h e s . The  ' b ' - s e c t i o n i s i n t e r e s t i n g i n t h a t t h e t e x t u r a l and harmonic d e n s i t i e s  do n o t c o r r e s p o n d . begins w i t h a unison 21.  D e s p i t e a five-component t e x t u r e , t h e  C#-* and g r a d u a l l y expands t o a t e t r a c h o r d by measure  Each new p i t c h e n t r y marks a growth i n h a r m o n i c - d e n s i t y  s t a t i c t e x t u r a l - d e n s i t y ) , thereby generating grouping.  harmonic-density  {within the  i t s own mode o f r h y t h m i c  (The i n t e r a c t i o n o f t h e s e two d e n s i t i e s i s i l l u s t r a t e d  g r a p h i c a l l y i n Example 56, t o be i n t r o d u c e d  shortly.)  Rhythm o f tempo change Tempo change i s a n o t h e r event which r e c u r s i n t h e p i e c e and, as noted e a r l i e r , tends t o c o i n c i d e w i t h changes i n t h e f o r m a l s t r u c t u r e . I t n e v e r t h e l e s s a r t i c u l a t e s a w i d e s p r e a d r h y t h m i c p a t t e r n , t o be r e v e a l e d i n c o n j u n c t i o n w i t h those a l r e a d y  defined.  I n t e r a c t i o n o f element-rhythms Example 56 i s a r e p r e s e n t a t i o n o f t h e s i x element-rhythms d e f i n e d above.  I n t h e case o f i m p u l s e - d e n s i t y ,  only the l a r g e - s c a l e progressive  and r e c e s s i v e u n i t s a r e noted and a r e i n d i c a t e d h e r e as s t r a i g h t l i n e s g  Two v e r t i c a l i t i e s i n measure 12 r e p r e s e n t b r i e f d e p a r t u r e s from t h i s norm. I n t h e s e i n s t a n c e s , t o be d i s c l o s e d i n a l a t e r s e c t i o n , t h e f i v e i n s t r u m e n t s sound a f o u r - n o t e s o n o r i t y .  121  E x a m p l e 56.  Interaction  of  s i x element-rhythms.  122  mm.1  (a)  rhythm of impulse-density fluctuation  (b) rhythm of dynamically exposed pitch-pair groups  mf mf  mf mf  ~f  mf  1  mf  I  mf  I. I  mf  \  mf  FL. (c)  (d)  rhythm of E.H. textural-density CLfluctuation HRN. BSN. rhythm of textural quality fluctuation  (e)  rhythm of harmonic-density fluctuation  (f)  rhythm of tempo change  independent  ,  independent/interdependent  —  , interdependent .  +  —>H  ^ 4g 3"2 2o I-  y-4o  J.-48  4"a'-section  formal segmentation  mm.  . transition.  10  -415  J . 4 0  *b'-section  —f— 20  'a*- echo  —r-  25  123 omitting  the d e t a i l e d  fluctuations  and  lower-level units  included  in  9 E x a m p l e 54. also  simplified  group line  The  rhythm o f d y n a m i c a l l y exposed  here  i s indicated o f Example Two  measures sections.  harmonic  22.  the unit  pitch  delineators  is  change o f  taken  from  significant  concurrence  each  the  centre  among e l e m e n t - r h y t h m s a r e i n  These j u n c t u r e s , o f c o u r s e , mark t h e main  lesser  a l s o marked by  mezzoforte  initial  groups  55).  and Of  only the  (these being  p o i n t s of  16  as  pitch-pair  formal  import  i s the t r a n s i t i o n  formal  (measures  15-16),  c o i n c i d e n c e of rhythms: the rhythms of t e x t u r a l  and  densities. Summary  It  was  found  that  ensemble p i e c e s i n t h e cally,  the notated  rather,  4  a notational  the  quintet  does not  h o w e v e r , was  progression,  recession,  involve  textural-density, Substantial piece,  the  signify  found  and  textural  metric groupings  The  t o be  concept of  great  formal delineation (elements)  quality,  importance,  other  was  of  noted  such,  significance  but i s ,  The  impulse-density, and  (other  i n the  of the piece.  pacing, rhythms  dynamics,  tempo.  at s t r u c t u r a l points i n the  formal sections. also noted  as  specifi-  of element-rhythms  harmonic-density,  among t h e s e was  the beginnings of  segment o f l e s s e r  with the  with regard to metric structure;  parameters  concurrence  namely,  piece i s consistent  convenience.  than meter),  examined  first  The  transition,  a s b e i n g d e f i n e d by  a  formal  the  9 T h i s i s m e r e l y f o r c l a r i t y ; a s w i l l be shown, s i g n i f i c a n t i n t e r a c t i o n occurs only at the turn-around point, adequately represented by t h i s l e s s - d e t a i l e d v e r s i o n .  124 simultaneous structure  reduction  i n t e x t u r a l and harmonic d e n s i t i e s .  o f p i e c e No. 1, d e s p i t e a l a c k o f m e t r i c  considerable exemplified  complexity,  as manifest  i n t h e examples c i t e d  a n d / o r PC c o n n e c t i o n s .  as The  the  The f i r s t  Three  s e c o n d mode c o n s i d e r s connect  pitches  comprised  o f element-rhythms  pitch  prolonged  Details  piece  specific  modes o f l i n e a r  progressions  extremities  i n the outer  of dynamically  prolongation  t o , and two-voice  linear  accented  chapter,  the linear  involve stepwise  involves outer-voice  w e l l a s t h e PC c o n n e c t i o n  crossing,  i s one o f  Organization  i n the previous  pitch organization i n the f i r s t  examined.  rhythmic  above.  Linear  of  The  definition,  i n the interaction  Modes o f P i t c h  As  10  connection  which,  will  be  the 'b'-section.  through l a t e r a l (the l a t t e r  r e f e r r e d to above).  pitch-pairs define  of p i t c h  i n the 'a'-section,  structure of,  i n the 'a'-section voices  patterns  details  the third  voice  being  Linearizations mode o f l i n e a r  connection.  Outer-voice The yields  prolongation (five-component)  a continuum o f changing On  (above t h e t o p s t a f f ) complex.  system  of the 'a'-section's  five-note vertical (a) o f Example  i n the f i r s t  The p i t c h e s a r e o r g a n i z e d  verticality second  texture  on t h e second  staff,  twelve  s o n o r i t i e s spanning  57 e a c h v e r t i c a l  bars a  stem  t w e l v e m e a s u r e s m a r k s a new h a r m o n i c such  that  (regardless of instrumentation)  highest  first  etc.  the highest  pitch  o f each  appears on t h e t o p s t a f f , t h e  The " h i g h e s t "  pitches are  ^ A l o n g w i t h t h e r e d u c t i o n i n t e x t u r a l and harmonic d e n s i t i e s i n the t r a n s i t i o n i s a decrease i n t e x t u r a l space (e.g., from a minor seventh t o a m i n o r t h i r d ) a n d d y n a m i c s ( t o a c o n s t a n t pianissimo level).  125  Example  57.  Outer-voice  prolongation  i n measures  e.p.  =  embellishing  l.n.  =  lower  u.n.  =  upper neighbour  m.m.u.n.  =  major-minor upper  neighbour  m.m.l.n.  =  major-minor  neighbour  i.m.m.u.n.  =  incomplete  ant.  =  1-16.  pattern  neighbour  lower  major-minor  anticipation  upper  neighbour  126  mf  mf  oo in a> a E CO  X LU  • C O  TJ 0) D C +->  c o o  i.m.mxi.n  127 c o n s i d e r e d l i n e a r l y t o form a " v o i c e " as d i s t i n c t from t h e a c t u a l instrumental parts. and so on.  The same h o l d s t r u e f o r t h e second h i g h e s t p i t c h e s ,  The f i v e " v o i c e s , " t h e n , a r e t h e r e s u l t o f c o n s t a n t p i t c h and  f r e q u e n t p o s i t i o n changes w i t h i n s u c c e s s i v e v e r t i c a l complexes. i n s t r u m e n t a l p a r t moves from one v o i c e t o another of i t s p i t c h i n t h e v e r t i c a l i t y .  Each  depending on t h e p o s i t i o n  P i t c h e s of a given i n s t r u m e n t a l part a r e  connected by h o r i z o n t a l and d i a g o n a l l i n e s and a r r o w s , r e v e a l i n g t h e m o t i o n a c r o s s v o i c e s as d e s c r i b e d above.  F o r example, i f a l i n e connects  p i t c h e s on t h e same s t a f f , i t means they a r e sounded by t h e same  two  instrument  and t h e second p i t c h r e t a i n s i t s v o i c e p o s i t i o n i n t h e v e r t i c a l complex. r e s t s e p a r a t e s t h e two p i t c h e s i f t h e l i n e i s n o t a t e d w i t h a p a r a l l e l e.g.,  " /•  a  —  . Where a d i a g o n a l l i n e connects  A  slash,  two, l i k e p i t c h e s on  s e p a r a t e s t a v e s , i t s v o i c e p o s i t i o n has changed ( b u t n o t i t s i n s t r u m e n t a t i o n ) as a r e s u l t o f a p i t c h change elsewhere i n t h e v e r t i c a l i t y . a d i a g o n a l arrow connects  F i n a l l y , where  two d i f f e r e n t p i t c h e s on s e p a r a t e s t a v e s , i t  i n d i c a t e s a p i t c h and p o s i t i o n change ( w i t h i n t h e same i n s t r u m e n t ) , a g a i n , s e p a r a t e d by a r e s t i f t h e arrow has a p a r a l l e l s l a s h through  i t , e.g.,  2 Our f o c u s on t h e o u t e r v o i c e s i n p a r t i c u l a r as one mode o f l i n e a r connection i s f o r three r e a s o n s . ^ most r e a d i l y p e r c e i v e d .  F i r s t , they a r e c h a r a c t e r i s t i c a l l y t h e  Second, they r e v e a l p r o l o n g a t i o n s o f D3 and C  4  ( t h e p i t c h e x t r e m i t i e s ) and, hence, c o n t r i b u t e t o t h e d e l i n e a t i o n o f form. And  t h i r d , t h e PC's C and D have f u n c t i o n a l import i n t h e l a r g e - s c a l e  l i n e a r s t r u c t u r e of the p i e c e .  Concerning  t h e second c o n d i t i o n , r e f e r t o  ^ M e a s u r e s 13-16 as r e p r e s e n t e d on system (a) o f Example 57 w i l l be d e a l t w i t h l a t e r .  128 system  (b)  o f E x a m p l e 57,  indicated. are  The  extremities,  stemmed, beamed, a n d  pitches  where a l l p i t c h e s  are a l s o  and  slurred  stemmed  but  C^,  are notated as  together.  are  i n the outer v o i c e s are  Neighbour  indicated  by  open n o t e s  notes  to  black notes.  which  these  Embellishing  12 patterns,  of  a  also  n o t a t e d as  "major" and  labelled  "minor"  MMUN o r MMLN  black notes,  second  are  are notated  (major-minor  upper  stemmed  to the  thus:  f  slur  ,  J  *—r-  V  which  1  n Pf or major-minor  neighbour  and  lower  neighbour). Once t h e respectively, on  system  and  they  (b).  are  One  extremities prolonged  particular  in a  detail  are reached  i s noteworthy  between  pitch  extremities.  N o t i c e , f o r example,  7,  9,  11,  in  bars  Given  the  are adjacent to those of the  8,  11  (first  function  of  of t h e  e x t r e m i t i e s would  and  seem t o be  of  C^,  distinction  by  including  of  black note,  be  of  "secondary."  and may  C^  'a'-section,  occurrences  appearing  that  13  C^  7.  occurrences of lower  the outermost  reiterated "primary" System  The  an  concerns  such  pitches  importance,  the  i n bars  e x t r e m i t y , D3,  instances of  while  concurrence.  and,  hence,  form  adjacent  with the  intervening  ( c ) r e p r e s e n t s t h i s mode o f  The  anticipation  initial  indicated  It  only adjacent, corroborating ( i . e . ,  as  7,  instances of  they are without  (as open n o t e s ) .  heard  i n measure  as  13  however.  "secondary"  and  delineators  instances  " p r i m a r y " and  b e a t ) , and  5 and  s t r a i g h t f o r w a r d manner a s  the d i f f e r e n t i a t i o n  5,  i n bars  initial of  primary)  C^,  notated  the f i r s t  primary  "incomplete" major-minor  as  a  upper  12 An e m b e l l i s h i n g p a t t e r n , i n t h i s c o n t e x t , r e f e r s t o s t e p w i s e m o t i o n ( b e y o n d a m a j o r s e c o n d ) away f r o m , and b a c k t o , a p a r t i c u l a r s t r u c t u r a l note. I t may a l s o c o n s i s t o f a l e a p away f r o m t h e m a i n n o t e and s t e p w i s e m o t i o n b a c k , o r v i c e v e r s a .  • neighbour system  13-15),  system  and  preceding Rhythmic  (a)  of  i n that  the  intensification, rather, a  the  nevertheless,  c a r r i e s the  focus  close reiteration of measures  measures  with brackets  of  on  and On  these  (b)  from  J  4  transitional  15-16),  of  are  (the  notes  on  of  the  lower  remaining  however,  i s not  primary r e g i s t r a l In  Example  The  each  with brackets  maintenance,  h i g h e r - l e v e l system  F^  on  system  measures,  the  (b)  (bar  underlying  16-22) i n s c o r e system  different  (c)  as  J  included  (a)  Systems  from Example  This  to  the  i s the  an on  points  not  unlike  above while  (e.g., those  which  are  Incidentally,  suggests  upper v o i c e  57  previously reduction  interim basis. system  for  and  (i.e.,  ( c ) ; D3  the  consists  (b)  i n t e r p r e t a t i o n s f o r the  relationship 13  form.  prolongations  that, prolongs  13  D )  system  14)  is  instruments,  both of  (c).  difficult  part  the  embellishment  the  given.  instrumental  i n t e r a c t i o n of  linear  lower-voice  the  from  individual verticalities  upper-voice prolongation,  reference 58,  are  to  to  on  score  (a), pitches  the  (measures  differently  established outer-voice  and  4  'a'-section  notated  parts  renders  C ,  the  o  detail,  of  in black  system  and C  end  attention.  •5  F  indicated  c o n t i n u i t y of  below e f f e c t the system  the  previously  of  1-12.  linearization  during  here,  13-14) c o n t r i b u t e  indicated  57,  instrumental  linear  as  the  i s also  t r a n s i t i o n (measures  bars  isolate;  that  D3  Example  more a p p a r e n t  by  to  (c). On  to  (IMMUN) a p p r o a c h  129  (c)  and  C  4  lower-level  remain  the  'a'-section. of  the  'b'-section  begin with  measures  1-16),  structure of  prolonged  This  and  the C . 4  (measures  identical but  offer  'b'-section The  i n t e x t u r a l space noted  first earlier.  summaries two and  its  views  the  130 prolonged bar  16 a s  E^->  of  is  as a an  bar  "pitch-class  incomplete  21  being  then viewed  i t s incomplete  c o n v e r s e l y as  C^  lower  neighbour.  i s considered a  16 a n d  B^  of  bar  "PC  20  D-^ f r o m  of  D ,  the  final  respectively, In  with  as  complete  C^),  and  interpretation  this and  neighbour  the f i n a l  In the  one  of  i s the  of t h e  with  C^,  second  C//  (bar  5  lower  16)  and  and  7 5  upper  interpretation C/C#  l a r g e - s c a l e PC D  E*  and  'a'-section.^  C^,  20  D^,  the  here  as  being i t s  {system  with  complete  ( b a r 21)  0  (c)] , f  bar  u p p e r and  a PC r e p r e s e n t a t i v e  functioning,  i n v o l v e s two, D/D^  D^).  The  shift  (d)  simultaneous  to  C, of  end  of the  while C  the  (involving  result  of  either  prolonged  o f E x a m p l e 58  allusion  and  to the  quasi  eco  indication  ' a ' - s e c t i o n suggested  i n the  score,  pitch  summarizes  r e l a t i o n s h i p — o n e which, a l o n g w i t h the r e t u r n to the o r i g i n a l dynamics,  lower  neighbours.  register System  of  5  incomplete  interpretation  t o D and  and  ah  of bar  p r o l o n g a t i o n s , one  (involving  inversion  as  5  as  C#  of t h e ' a ' - s e c t i o n  t h e B^  respectively,  with  to the f i n a l  upper neighbour.  major-minor neighbours,  C^  extremities  C#  first  r e c o g n i z e s two  neighbour  'a'-section i s treated  5  second and  to  lower  functioning  r e p r e s e n t a t i v e " of the f i n a l  the  short, the  incomplete  a PC  functioning,  neighbours.  neighbour,"  major-minor  major-minor upper neighbour incomplete  (PC)  strengthens  tempo  the  earlier.  14 neighbour  "Pitch-class notes.  (PC)  neighbour"  refers  to r e g i s t r a l l y  non-specific  ^ T h e PC's C a n d D, i n f a c t , f i g u r e v e r y p r o m i n e n t l y i n t h e a u d i t o r y e x p e r i e n c e a s a r e s u l t o f t h e a f o r e m e n t i o n e d o u t e r - v o i c e p r o l o n g a t i o n and l i n e a r d i r e c t e d n e s s t o m e a s u r e 22.  131  Example  58.  Linear to the  s t r u c t u r e of t h e 'a'-section.  'b'-section  and  its relationship  132. .  / 9  t—  I  i  * i  ^  I I " •  (E.H.)  (CL.)  —  _  J.  4  ^  _i  T> |  lll|  V  li*  —  (HRN.)  (BSN.) 4 ZZZZZZZZZZZZZZZZZZZZZl  mm.  2 i.l.n.  (b)  (O  7  7-14  15-16  16  17  20  20  2|  22-24  133 Linear  progressions As  this  noted  idiom  is  i n Chapter  a r e those  In measures and,  involving lateral  by s t e p ,  I I , t h e most  instrument  i n the f i r s t  linear  nine  defined  of linear  events  connecting  and  pitch  by measure of lateral  prolongations Three  7).  Voice  voice  rests  the five-voice Two  crossing w i l l  and s u b o r d i n a t e .  conditions  t h e two p i t c h a principal  condition: stepwise  which  be  The  i n measures  connect  D-^ a n d C^  2-5, a n d represent  complements t h e l i n e a r examined.  v o i c e - c r o s s i n g event  as  i t may n o t s p a n t h e e n t i r e r a n g e o f t h e ' a ' - s e c t i o n progression);  e x t r e m i t i e s ; and t h i r d , progression  a t some p o i n t  connections,  already  a principal  underway. progression  progression),  I f the progression  back at t h e s t a r t i n g  which  pitch  second,  i t must  one i n t h e d i r e c t i o n  continuation of the principal direction.  E-^ a n d  characterize a lateral  be a " p r i n c i p a l "  i t would  (i.e.,  e f f e c t e d b y t h e o u t e r - v o i c e movement j u s t  (or  arrives  principal  c r o s s i n g s which  prolongation—one  first,  from  rests  to d i s c e r n  crossing).  involving lateral  extremities  subordinate:  of  In order  movement a c r o s s  lateral voice  in  whole-tones.  m e a s u r e s movement b e t w e e n  stepwise  paper:  connections  i s c h a r a c t e r i z e d by t r a v e r s a l o f t h e e n t i r e r a n g e o f t h e ' a ' - s e c t i o n ,  thereby  type  linear  two p i t c h e s b e t w e e n  i s o f t e n by l e a p .  (i.e.,  f o r the purposes o f t h i s  former  a  of these  connections,  s t r u c t u r e must b e c o n s i d e r e d classifications  perceivable  articulates  movement a c r o s s r e s t s  more e x t e n d e d  crossing  i n v o l v i n g movement b y s e m i t o n e s .arid  1-12 e a c h  although  voice  i t must  arrive  originate—be Concerning  on one  spawned—  the third  may h a v e two a v a i l a b l e  i t started  (i.e., the  and t h e o t h e r  i n the opposite  branches o f f i n t h e opposite  of the o r i g i n a l  principal  direction  progression  134 It  i sconsidered Stepwise  events  t o be a subordinate pitch  connections  linearization.  effecting  or articulative  connection w i l l  Timbral  exposure.  now b e d i s c u s s e d  These t h r e e types  i n greater  qualifies  as a timbral connection.  boxed o n system  summarized  o f "exposed"  i n one p a r t i c u l a r  on system  through  (b).  The f i r s t  dynamic  instrument,  by a d i a g o n a l  5 9 , two s u c h  arrangement  t h e second  arrow,  connections  a s Example  instance of connection  either  57—and  i n E x a m p l e 59  involves voice crossing.  exposure  Movement a t mezzoforte above o r below t h e  I n Example  ( a ) — t h e same " v o i c i n g "  i n t h e same v o i c e , w h i l e  Connection  t o a p i t c h which  preceding  pitch  instrument  and which continues  exposure.  This particular  first  timbral,  detail.  t h e same v o i c e o f a c r o s s v o i c e s , ^ a s i n d i c a t e d  occurs  through  connection S e m i t o n e o f w h o l e - t o n e movement  are  lateral voice-crossing  i n v o l v e p i t c h e s w h i c h emerge a s ( a u d i b l y ) p r o m i n e n t  dynamic,  in  these  16  of t h eprogression  (heard  t o sound) d e f i n e s c o n n e c t i o n  connection  one s u s t a i n i n g i t s p i t c h  i s a semitone o r whole-tone  after  always  i n another through  dynamic  i n v o l v e s two i n s t r u m e n t s , t h e  t h e second  one c o n t i n u e s  the  linear 18  progression  with  i t s dynamically  exposed  pitch;  refer  t o E x a m p l e 60.  16 I f a t some p o i n t a p r i n c i p a l p r o g r e s s i o n h a s two a v a i l a b l e s t e p w i s e c o n n e c t i o n s , e a c h i n t h e same d i r e c t i o n a s i t s t a r t e d ( e . g . , f r o m G to and G t o F ) , both o f which continue i n that d i r e c t i o n and a r r i v e on t h e l o w e r p i t c h e x t r e m i t y ( t h e u p p e r e x t r e m i t y i f t h e l i n e s a r e a s c e n d i n g ) t h e s e a r e c o n s i d e r e d t o b e , a n d n o t a t e d a s , two s e p a r a t e p r i n c i p a l p r o g r e s s i o n s o c c u r r i n g over d i f f e r e n t time spans.  equal  ^ V o i c e s , remember, a r e l i n e a r c o n t i n u i t i e s c o m p r i s e d o f t o n e s o f position i n successive v e r t i c a l i t i e s (regardless of instrumentation). 18  In t h i s p a r t i c u l a r t y p e o f c o n n e c t i o n , dynamic e x p o s u r e i s o f primary importance. Compare t h i s w i t h t h e f i r s t t y p e w h e r e mezzoforte accent i s secondary t o t h easpect o f t i m b r a l consistency.-  Example 59.  mm.  4  2 3  Example  mm.  60.  9  W'  t  Two i n s t a n c e s o f t i m b r a l in l a t e r a l voice-crossing  connection:  connection events.  5  One i n s t a n c e o f c o n n e c t i o n dynamic exposure.  through  10  136 Connection  through  articulation  When a p i t c h  after  i s articulated  a  rest  after  a rest,  whole-tone above o r below t h e p r e c e d i n g p i t c h heard to  i n another  instrument  condition  of linear  Example  61.  across voices.  progression through  or  of the progression (again,  and which c o n t i n u e s t o sound),  continue the l i n e a r i z a t i o n  third  and i s a semitone  Example  i t may b e h e a r d  61 i l l u s t r a t e s  lateral voice  One i n s t a n c e o f c o n n e c t i o n articulation after a rest.  this  crossing.  through  mm.  L  Notice the  connection:  i n t h e second  instrument  dynamic  which  and t h i r d  sounding  instrument  While  (i.e.,  s o u n d s t h e new p i t c h  or articulative  own p r e c e d i n g n o t e .  criteria  exposure)  Rather,  Examples  60 a n d 61) t h a t  o f t h e p r o g r e s s i o n (be i t t h r o u g h  d o e s n o t h a v e t o move b y s t e p f r o m i t s  t h e stepwise connection occurs from  t o t h e one which p r o v i d e s t h e exposed  many b r i e f  c o n n e c t i o n s may be d i s c e r n e d , b a s e d  an a l r e a d y  pitch. on a n y one o f  137 the  three  criteria  principles defined  with  s t a t e d above,  i t i s the joint  the conditions of p r i n c i p a l  earlier,  which r e v e a l s  linear  consideration of  and s u b o r d i n a t e  these  linear  c o n t i n u i t y i n the opening  events,  twelve  19 measures of t h e p i e c e . "voice"  System  (a) o f Example  r e p r e s e n t a t i o n a s E x a m p l e 57 ( u s e d  prolongation), the v a r i o u s  here,  up t o measure  principal  through a p p l i c a t i o n of the c r i t e r i a All  occurrences  progression;  of bars  progressions lateral of  to C .  departure  4  appear adjacent discussion occurred  consistent, lateral  (principal  which f a i l  then,  that  progressions, System  progressions.  of C , 4  connections  to i n i t i a t e  to occurrences  t o a D^,  by a p r i n c i p a l  or subordinate),  lateral  Remember  prolongation,  voice-crossing  pointsff.or l a t e r a l  a l l a r e approached  to D  .  a C  4  that,  As i t t u r n s o u t ,  i n the  was l a b e l l e d  i f i t appeared  a l l a r e s e c o n d a r y by  T h o s e on t h e t o p s t a f f  do n o t  preceding  primary  "alone."  4  62 o f f e r s  by a  but not a l l a r e p o i n t s  of t h e C ' s which a r e not i n i t i a t o r s  ( c ) o f Example  defined  voice-crossing progressions  o f D^.  and s e c o n d a r y  (b) i s c o m p r i s e d o f  above.  7 a n d 10 a r e a l s o d e p a r t u r e  on o u t e r - v o i c e  next  stated  a r e approached  f o r descending  of C  System  outer-voice  v o i c e - c r o s s i n g events  Of t h e o c c u r r e n c e s  4  progression  instances  of  to i l l u s t r a t e  12 o n l y .  and s u b o r d i n a t e  62 c o n s i s t s o f t h e same  i f  i t  Itis of descending  definition.  a summary o f t h e i n t e r a c t i n g progress  toward  a n d away  lateral  from  19 A l t h o u g h b a r s 13-15 a r e p a r t o f t h e ' a ' - s e c t i o n , i n c r e a s e d rhythmic a c t i v i t y , slow dynamic f l u c t u a t i o n r e l a t i v e t o p i t c h changes, and a b s e n c e o f r e s t s p r e c l u d e l i n e a r c o n n e c t i o n s a s d e f i n e d by t h e a s s e r t e d c r i t e r i a of lateral voice crossing. I t i s i n t e r e s t i n g t h a t , w h i l e b a r s 1516 h a v e b e e n d e f i n e d a s t r a n s i t i o n a l , a d i s s o l u t i o n o f p a r a m e t r i c c o n t i n u i t y i s a l r e a d y e m e r g i n g i n b a r s 13-15 a s s u g g e s t e d b y t h e c h a n g e s n o t e d a b o v e ( i . e . , r h y t h m i c , dynamic, and a r t i c u l a t i v e ) , and by t h e c o n d i t i o n a l changes regarding outer-voice prolongation described e a r l i e r .  138  Example  62.  Linear progressions in.measures 1-12.  involving lateral  voice- crossing  13?  mm.  2  3  8  140 prolongational extended  p o i n t s noted  and o v e r l a p the  Connections The  earlier,  former  the derivation instrument Pitch  this  pitch-pairs  i t was n o t e d  their  not  give r i s e  dyads  the  to surrounding  to stepwise  three details  actual  pairs.  continuities  e x t r e m i t i e s , as i nthe  more  1-12 e a c h  by r e s t s .  peak o f dynamic  exposed  pitch  pitch-pairs.  content  Although  o f such  contiguous  which t r a v e r s e o r prolong  two modes o f l i n e a r  of this  the  aspect  earlier  To r e c a p i t u l a t e  separated  dynamically  with  was d e f i n e d  i n measures  a t mezzoforte—hence,  relationship  described,  that  a t o r v e r y near  concerned  bottom a r e  grouping.  occur  p o i n t we a r e  and  pitch  exposed  features a succession of linear  changes between r e s t s  on the  pitch-pairs  mode o f r h y t h m i c  of pitch-pairs,  intensification At  exposed  of dynamically  as m a n i f e s t i n g a p a r t i c u l a r  those  progressions.  between d y n a m i c a l l y concept  while  pairs,  p a i r s do outer-  connection previously  of linear  organization are  worth  noting. The  first  involves local  prolongation o f specific  neighbour  motion provided  instances  of l o w - l e v e l prolongation are noted  is  the  system  p r e v i o u s l y employed (b)  each p a i r changing  changing  i sslurred r a t h e r than  (i.e.,  separated  and the  first  by dotted v e r t i c a l pitch  major-minor neighbour  on system  (c).  o f each  63 t h e s e  System (a)  content,  while  pairs.  In the  latter,  i s notated  just  exposed  prior to  p o i n t o f i n c e p t i o n {[since i t i s f i r s t  and i s t h e r e f o r e most  a t mezzoforte)}.  first  pitch  through  I n Example  representation of pitch  dynamically  at i t s actual  a t pianissimo  E x a m p l e 54) t h e or  linear  i s a summary o f t h e  articulated  as  by i n t e r v e n i n g p i t c h - p a i r s .  pitches  I n most lines  as indicated  pitch-pair  and which  i s prolonged  perceptible just  through  on system  groups  correspond either  (i.e.,  groups  t o those o f  a double  (c) o f t h e  prior to  graph.  neighbour  141  Example  63.  Connections i n measures  through 1-14.  d y n a m i c a l l y exposed  pitch-pairs  143 O c c a s i o n a l l y the i n t e r v a l of a t h i r d w i l l approach the f i n a l p i t c h of the p r o l o n g a t i o n as i n measures 11 and  12.  Because the f i r s t p i t c h of  each group i s not always a p i t c h e x t r e m i t y of the s e c t i o n ( e . g . , C ), 4  or  the c o n n e c t i o n of p i t c h e s i n t h i s manner r e s u l t s , a t t i m e s , i n low-  l e v e l " i n n e r - v o i c e " p r o l o n g a t i o n s , e.g.,  measures 4-5,  6, 10, and  Perhaps more s i g n i f i c a n t i s the p r o g r e s s i v e e x p a n s i o n of o c c u r r i n g between ( l i n k i n g ) p i t c h e s of i n d i v i d u a l p a i r s . the d e s i g n a t i o n m/M2  11-12.  intervals  Below system ( c ) ,  suggests t h a t , up to measure 10, movement between the  r e s t s i n each i n s t r u m e n t  i s by s t e p .  I n measure 10 t h i s i s expanded to  i n c l u d e minor t h i r d s and by measure 12, major t h i r d s .  T h i s might be  viewed as a n o t h e r m a n i f e s t a t i o n of t h e e x p a n s i o n concept d i s c u s s e d i n the preceding  chapter.  A t h i r d d e t a i l of i n t e r e s t c o n c e r n s measures 13-15, two b a r s which have a l r e a d y been mentioned i n c o n n e c t i o n w i t h the d i s s o l u t i o n of s e v e r a l patterns.  For example, heightened  rhythmic  a c t i v i t y i n t h e s e measures  was  s a i d t o render v e r t i c a l s o n o r i t i e s and o u t e r - v o i c e p r o l o n g a t i o n s more difficult to  to d i s c e r n .  L a t e r a l v o i c e - c r o s s i n g connections  stop s h o r t of bar 13.  To be added t o t h i s l i s t of d e p a r t u r e s  absence of p i t c h - p a i r s s e p a r a t e d each i n s t r u m e n t  were a l s o found i s the  by r e s t s ; r a t h e r , l i n e a r c o n t i n u i t y i n  i s now more a p p a r e n t .  However, one f i n a l dynamic " s w e l l "  takes p l a c e i n each i n s t r u m e n t , a g a i n , exposing  a p a i r of p i t c h e s .  But  r a t h e r than o c c u r r i n g c o n t i g u o u s l y , the p a i r s o v e r l a p as a r e s u l t of increased rhythmic are bracketed C  4  activity.  The d y n a m i c a l l y exposed p a i r s i n q u e s t i o n  on system (a) of Example 63.  A l o w - l e v e l p r o l o n g a t i o n of  ( t h r o u g h a major-minor lower n e i g h b o u r ) i s perhaps the most s i g n i f i c a n t  outcome of t h i s dynamic f l u c t u a t i o n [see system (c)l;  i t r e i n f o r c e s the  144 outer-voice  prolongation of C  4  illustrated  earlier.  20  Summary T h r e e modes o f l i n e a r been examined  i n the foregoing  voice-crossing In t h e f i r s t  events,  primary.  4  prolonged,  of  linearization,  and to  C .  complement  section.  involving  lateral  exposed  Concerning  I n t h e s e c o n d mode and a r t i c u l a -  which  connect said  extremities of the  pitch-pairs  the latter,  from minor and major thirds  i n bars  controlled  chapter,  'a'-  i n close  through  seconds  11 a n d 12.  movement  between  in the first ten Linear continuity  the-modes o f l i n e a r  connection  organization.  Details  consonance and dissonance  between, v e r t i c a l i t i e s  pitch  were  section.  the previous  harmonic  of each  l o w - l e v e l p r o l o n g a t i o n s o f inner v o i c e s as w e l l as a  mode o f e x p a n s i o n .  relationships  exposure.  v o i c e - c r o s s i n g s were  of dynamically  in this  lateral  dynamic  dynamics,  v o i c e - c r o s s i n g events  Harmonic  of  timbre,  The c o n n e c t i o n  seem t o b e t i g h t l y  In  extremities.  the pitch  was s e e n t o e x p a n d  suggested  pitch  p r o l o n g a t i o n s and l a t e r a l  measures t o minor and major would  articulations  i n maintaining  particular  have  e x t r e m i t i e s of t h e ' a ' - s e c t i o n —  each other  proximity revealed  motion  s t r u c t u r e o f t h e ' b ' - s e c t i o n was shown t o  prolonged  criteria  to establish  Outer-voice  4  rests  three  pitch  and a d j a c e n t  The t w o - v o i c e  a continuation of these  were used  stepwise  section: outer-voice prolongations,  and C — t h e  be  tion  utilizing  and l o w - l e v e l p r o l o n g a t i o n s t h r o u g h  of these,  were s i m u l t a n e o u s l y labelled  connection  were s t a t e d a s b e i n g  Concerning  the f i r s t  i n , and f u n c t i o n a l two c e n t r a l  of these,  issues  semitone and  20 G i v e n t h a t o n l y t h e p r o l o n g a t i o n o f D^ a n d n o t c 4 i s c o n t i n u e d i n the subsequent t r a n s i t i o n (measures 15-16), t h i s f i n a l maintenance o f C t h r o u g h dynamic exposure has added s i g n i f i c a n c e . 4  145 whole-tone for  classifying  first be  content w i l l  will  harmonic  twelve measures  dealt  with f i r s t .  t h e n be  Measures  in  one be  i t was  Measures  earlier,  Because of t e x t u r a l  (already noted), that 13-15  the f i v e - p a r t  i s a continuum  aggregate  affected  system  harmonic  portion  as a main  criterion  consistency i n the  of the  (the t r a n s i t i o n ) ,  'a'-section  and  the  will  'b'-section  sonorities  The  be  pitch  reader  employed  of each v e r t i c a l i t y  relationships  t e x t u r e of measures  changing v e r t i c a l o n l y one  considerably.  quality  independent  of  to the next  (a), the p r e v i o u s l y  higher-level these  quality.  as  1-12  harmonically,  may  here,  examined.  Underlying  from  be u s e d  pitch  must  be  Although  i s changed, harmonic  i s referred  discerned.  are r e l a t i v e l y  sonorities.  1-12,  t o Example  representation established  The  s i m p l e f o r two  criteria  64  where,  i s given.  i n order  for  quality  The  that  classifying  r e a s o n s : a l l but  two  of  them 2  contain  f i v e members, a n d In  of  the l e f t  the f i r s t  combinations semitone  to  2  combinations  are r e g i s t r a l l y 65  entries  (p. 149)  spaced  f o r five-member  sets are given.  each  between  interval-class  having the  i s given a v a l u e of i n the f i r s t  1.  sets  For the purpose of  1 (per v e r t i c a l i t y )  Whole-tone content sets  w i t h i n one  a l l possible  i s considered the primary determinant  a v a l u e o f 4.  interval-class the  interval-vector  quality;  differentiate  sets  column o f Example  f o r four-member  content  dissonance assigned  two  the  i s used  combinations and  two  of t h i s  study,  consonancei s therefore  as a f u r t h e r  same s e m i t o n e  octave.  content;  criterion each  When t h e s e v a l u e s a r e a p p l i e d  column, q u a l i t a t i v e t o t a l s  are  to  determined;  21 S e m i t o n e s and w h o l e - t o n e s w o u l d , p r e s u m a b l y , d i f f e r e n t i n s o n o r i t i e s where t h e y appear r e g i s t r a l l y o r more o c t a v e s ( i . e . , a s compound i n t e r v a l s ) .  h a v e t o be t r e a t e d d i s p l a c e d b y one  Example  64.  Harmonic  structure.  14-7  mm.2 C-D factors: 7  3  10  4  1b 10  9  7  8  7  9  11  11  14 10  9  13 1  9 J  [5  5\ 13 1  1  11  6  9  1  1  1  13 PlO 1  «i  10 1  1ol 9 1J  1  13  6  .  7  ii  i i U l !  IO  J i T i 1 T T 11 t J M [  12  ? tT T ^ V ? T ! [?  r ? Ir  ? v. DP ti&  13  3T T I  ? **  14  15  16  17  20  21  22  148  Example  65.  Consonance-dissonance  criteria  and  C-D  factors.  149  a,b of Interval Vector  C-D Quality IC 1=4, IC 2=1  C-D Factor  4,3  19  (Diss.) 15  3,3  15  14  3,2  14  f  Representative Sets m. 12 0,1,2,3,4  1  13  ******  m. i i 0,1,2,3,5  j  m. 3  0,1,2,4,5 m. 9  3,1  13  12  2,3  11  11  0,2,3,4,6  2,2  10  10  0,2,3,4,7  2,1  9  9  2,0  8  8  7-**-*-  0,1,2,6,7 m. 4  • »T' *  m. 7  m. 8 0,1,4,5,7 m. 9 0,1,4,7,8 m. 4 1,3  7  7  £  0,2,3,5,7  m  s *  m. 6 1,2  6  6  0,2,3,6,8 m. 5  1,1  5  5  0,1,3,6,9  0,4  4  4  0,2,4,6,8  0,3  3  3  0,1  1  2  it**  m. 8  |  m. 12 0,2,4,7,9 m. 12  1 |  0,2,5,8  1 0,0  0  m. 12  1  0,3,6,9  (Cons.) 1  V-  150 t h e s e appear i n t h e second column.  The f a c t o r s 4 and 1 were s e l e c t e d i n  o r d e r t h a t t h e q u a l i t a t i v e t o t a l s r e f l e c t semitone primacy,  particularly  a c r o s s groups where whole-tone content i s r a d i c a l l y d i f f e r e n t .  For example,  a set w i t h t h r e e semitones and one whole-tone i s presumed more d i s s o n a n t t h a n one w i t h o n l y two  semitones and t h r e e whole-tones.  H i g h e r whole-tone ;  c o n t e n t , t h e n , o n l y a f f e c t s harmonic q u a l i t y of s e t s w i t h e q u a l semitone content.  Q u a l i t a t i v e t o t a l s a r e a d j u s t e d t o c o n s e c u t i v e numbers f o r ease  of r e f e r e n c e and l i s t e d i n column t h r e e ; t h e s e a r e h e n c e f o r t h termed consonance-dissonance f a c t o r s ( o r s i m p l y C-D  factors).  column c o n s i s t s of r e p r e s e n t a t i v e s e t s from t h e opening The C-D  The  right-hand  t w e l v e measures.  f a c t o r s e s t a b l i s h e d by t h e p r o c e s s e x p l a i n e d above a r e  i n d i c a t e d above t h e v e r t i c a l i t i e s on system (a) o f Example 64.  With  r e s p e c t to t h e f r e q u e n c y of t h e v a r i o u s f a c t o r s , a t l e a s t t h r e e  statistical  d e t a i l s a r e noteworthy. f a c t o r s 9 and  The most f r e q u e n t l y used s o n o r i t i e s a r e t h o s e of  10; t h e y occur 12 and  number o f s o n o r i t i e s of C-D  16 t i m e s r e s p e c t i v e l y .  A l s o , the  f a c t o r 10 and above i s a p p r o x i m a t e l y t h a t o f  f a c t o r 9 and b e l o w — r e s p e c t i v e l y , 39 and 36.  V e r t i c a l i t i e s of f a c t o r 9  and 10 might be c o n s i d e r e d "average"  r e f e r e n c e p o i n t s based on t h e s e d a t a .  F i n a l l y , o n l y one v e r t i c a l i t y of C-D  f a c t o r 1 i s used and one of f a c t o r  15, and b o t h occur i n r e l a t i v e l y c l o s e p r o x i m i t y ( e . g . , measure 12). Regarding  s p e c i f i c l o c a t i o n s of t h e v a r i o u s s o n o r i t i e s of a g i v e n  harmonic q u a l i t y , two which concern factor.  important r e l a t i o n s h i p s may  be d i s c e r n e d , b o t h o f  i n s t a n c e s of c o n s e c u t i v e v e r t i c a l i t i e s of t h e same  C-D  The f i r s t a l s o i n v o l v e s r e c u r r i n g s e t s of t h e same f a c t o r .  R e f e r r i n g back t o Example 64, system (b) c o n s i s t s o f t h e i n s t a n c e s of and C^ p r o l o n g e d through t h e t e c h n i q u e s o u t l i n e d i n t h e p r e v i o u s Noteworthy i s t h e f a c t t h a t most o c c u r r e n c e s of D^ and  are  D^  section.  articulated—  151 i n a sense " h a r m o n i z e d " — b y v e r t i c a l i t i e s of C-D f a c t o r s 9 or 1 0 — t h e two most w i d e l y used i n t h e p i e c e .  This reinforces the previously asserted  " r e f e r e n t i a l " p r o p e r t y o f t h e s e two harmonic q u a l i t i e s . c o n n e c t i o n s a r e i n d i c a t e d by t h e l i n e , on system  (b).  These p a r t i c u l a r -, above each s t a f f  A l s o o f import i s t h e u s e o f c o n s e c u t i v e v e r t i c a l i t i e s o f  e q u a l harmonic q u a l i t y i n two o f t h e t h r e e i n s t a n c e s o f a d j a c e n t  arrivals  on D^ and C^ ( d e f i n e d e a r l i e r as " p r i m a r y " p o i n t s of p r o l o n g a t i o n ) . I n measures 9-10, f o r i n s t a n c e , b o t h p i t c h e x t r e m i t i e s a r e accompanied by aggregates  o f C-D f a c t o r 3, w h i l e t h o s e i n bar 11 a r e o f t h e f a c t o r 10.  These a s s o c i a t i o n s a r e i n d i c a t e d on system A second  (b) by t h e d i a g o n a l  line"^  v  important r e l a t i o n s h i p i n v o l v e s i n t e r a c t i o n between harmonic  q u a l i t y and dynamic f l u c t u a t i o n .  A d j a c e n t C-D f a c t o r s o f t h e same magnitude  which r e p r e s e n t v e r t i c a l i t i e s i n v o l v e d i n t h i s i n t e r a c t i o n a r e b r a c k e t e d above system  (a) on Example 64.  These f a c t o r s a r e a l s o i n d i c a t e d on  Example 66, a r e p r i n t o f an e a r l i e r example used t o i l l u s t r a t e t h e rhythm of d y n a m i c a l l y exposed p i t c h - p a i r groups.  As t h e graph r e v e a l s , a t l e a s t  some c o n t i g u o u s m e z z o f o r t e p a i r s w i t h i n a g i v e n group o c c u r i n v e r t i c a l s o n o r i t i e s of e q u a l harmonic q u a l i t y .  The ebb and f l o w o f t h e a s s e r t e d  r h y t h m i c p a t t e r n would seem t o be s t r e n g t h e n e d by t h i s aspect o f harmonic structure.  Measures 13-15 ( t h e t r a n s i t i o n ) , and t h e ' b ' - s e c t i o n As noted throughout  t h i s c h a p t e r , measures 13-15, a l t h o u g h p a r t o f  t h e ' a ' - s e c t i o n , e x h i b i t d e p a r t u r e s from t h e t e x t u r a l and r h y t h m i c d e s i g n of t h e p r e c e d i n g measures.  The s u r f a c e " b u s i n e s s " o f t h e s e b a r s c o n t i n u e s  i n t o t h e subsequent t r a n s i t i o n , t h e l a t t e r f e a t u r i n g f u r t h e r  rhythmic  i n t e n s i f i c a t i o n a s w e l l a s a r e d u c t i o n i n t e x t u r a l - d e n s i t y to. t h r e e components, a l l of which o p e r a t e between D^ and F^.  The c o n t i n u o u s  152  Example  66.  Recurring of  sets of equal  dynamically  exposed  harmonic  quality  pitch-pairs.  in units  I S3  |  I I I | I I I | I  I  t | I  I  I |  II  I | I  1 I | I 7  I I |  I I I |  8 measure no.  9  1 I  1 | I I 10  I | 11  I I  I | I 12  I I | I I 13  I  | 14  1 I  I | 15  154 articulation a  o f D^, D//3, E ^ , a n d  r e i t e r a t e d four-note  components.  i n the t r a n s i t i o n gives  sonority,  despite  The l a c k o f harmonic  the effect of  the presence of only  eventfulness  three  i n the 'b'-section  linear  renders  22 individual expansion is the  s o n o r i t i e s extremely from a u n i s o n  the fact most  that  this  frequent  members). previous  Obvious  C//5 t o t h e f o u r - n o t e  set,  despite  of those  Finally,  perceptible.  set  , C#^-D^-E^;  (most  "resolution" verticality attribute  t h e whole-tone (in a relative  B-C/Z-D-E^ . 7  of which contain  of harmonic o r g a n i z a t i o n  c h a p t e r may h a v e a p p l i c a t i o n i n t h e f i n a l  Specifically,  sonority  introduced  dyad  of this  may be h e a r d  sense) from t h e p e n u l t i m a t e  In this  sense  o f t h e whole-tone noted  interesting  i t s c a r d i n a l i t y , h a s a C-D f a c t o r o f 1 0 —  i n the 'a'-section  a detail  i s the wedge-like  i t i s suggestive  already  i n the third  as a  five  i nthe piece.  consonant  chromatic  of the " c a d e n t i a l " and f o u r t h  pieces.  Summary Consonance and d i s s o n a n c e between, v e r t i c a l establishing  s o n o r i t i e s were  in  t h e i r make-up. used  was r e v e a l e d . consecutive units  were  identified  at through assigning  frequently  stated  p r i n c i p l e s of harmonic  note v e r t i c a l i t i e s arrived  i n , and consequent  organization.  two m a i n c o n c e r n s i n In measures  found  by:successive  five-  o f 4 and 1 t o semitones and w h o l e - t o n e s with  C-D f a c t o r s , 9 a n d 10, a n d t h e p r o l o n g a t i o n Also  1-12,  as to consonance-dissonance " f a c t o r s , "  A c o r r e l a t i o n between v e r t i c a l i t i e s  t h e most o f D-* a n d C^  t o be o f s i g n i f i c a n c e i s t h e a s s o c i a t i o n  sonorities with  defined  values  as being  functional relationships  t h e same h a r m o n i c dynamically  between  f a c t o r , and peaks o f t h e  exposed  pitch-pairs.  I n t h e 'b'-  22 In t h e ' a ' - s e c t i o n , harmonic rhythm i s t i e d t o r h y t h m i c a c t i v i t y i n g e n e r a l b e c a u s e e a c h a r t i c u l a t i o n s o u n d s a new v e r t i c a l i t y . I n t h e 'b's e c t i o n , t h e h a r m o n i c r h y t h m i s most o f t e n s l o w e r t h a n t h e l e v e l o f i m p u l s e d e n s i t y because o f t h e r e i t e r a t i o n o f p i t c h e s .  155 section,  the largest  penultimate  verticality  1 0 — t h e most the  sonority  i n bars  f r e q u e n t l y used  p i e c e was s u g g e s t e d  tone  of  pieces  defined  i n the quintet.  (e.g.,  between,  the f i f t h  interrupted  instruments and  Each  do s o b e t w e e n  common t o b o t h register piece's  opening  register will  piece  i n , and PC  pieces  to a  1 and 3 a r e ensemble  s e c t i o n i n which a l l  i n predominantly  each opens regard,  stepwise  t o mezzoforte. i n one c l e a r l y  the register  a t t h e end o f t h e t h i r d i s that  connections  ( o n l y one o f w h i c h i s  f r o m pianissimo  In t h i s  been  as a l a r g e - s c a l e c o n t i n u i t y ,  polyphonic  that  since  of the third  piece,  piece's  motion, Also defined  of the f i r s t and t h e c l o s i n g  opening.  (This  shortly.)  event" a f t e r  t h e opening  an o c t a v e - d o u b l e d  listed  above,  polyphonic  i t i s i n the form o f a f i v e - p a r t  the third,  have  subgroupings  of f a c t o r s point  instruments  addition to the similarities  "dramatic  piece in  of the f i r s t  be i l l u s t r a t e d In  a  i s restored  pieces  move  range  i s the fact  i n another.  aspects  F o r example,  dolcissimo,  t h e dynamic  pieces  and ends  and t h i r d  for five  f o r apparent  A number  f e a t u r e s an opening  a r e marked  instrumentation-density  similarities  pieces).  piece.  40, and s c o r e d  different).  connective  and T h i r d  o f t h e Second  t o be r e s p o n s i b l e  of the f i r s t  by t h e second  a t J=  the First  chapter,  a n d tempo  and s i x t h  dyad o f  i n Chapter I I .  Between  Other  articulative  characterization  pieces  said  the closing  instance o f t h e semitone-to-whole-  o f t h e second  were  i s the  t o be o f a f a c t o r  Finally,  and I n t e r r u p t i v e Aspects  the beginning  instrumentation  Factors  to cardinality)  I t was f o u n d  i n the piece.  t o be a n o t h e r  Connective  At  respect  21-22.  cadential resolution asserted  Pieces  and  (with  unison  theme p r o v i d e s  each p i e c e  section.  (e.g.,  features  In the f i r s t  C//5 o f b a r 16X, w h i l e  the dramatic  contrast.  The  156 two  p i e c e s may  a l s o be seen as r e l a t e d i n terms of p r o p o r t i o n .  p i e c e the d r a m a t i c lengths.  event b e g i n s at the g o l d e n s e c t i o n of t h e i r r e s p e c t i v e  P i e c e No.  i s 62, and  I n each  1, f o r example, i s 100 b e a t s l o n g .  t h e u n i s o n C# e n t e r s i n beat 63.  The  golden s e c t i o n  I n the second p i e c e , 64 b e a t s  l o n g , the o c t a v e - d o u b l e d theme e n t e r s i n beat 39, the g o l d e n s e c t i o n of  64.  On a l a r g e r s c a l e , p i e c e s 1 and 3, t a k e n as an u n i n t e r r u p t e d c o n t i n u i t y , a r e themselves i n a g o l d e n s e c t i o n r e l a t i o n s h i p . The  t w e n t y - f i v e measure  f i r s t p i e c e i s the g o l d e n s e c t i o n of t h e t o t a l f o r t y - o n e b a r s of b o t h pieces. P i t c h r e l a t i o n s h i p s between t h e opening and c l o s i n g of t h e f i r s t t h i r d p i e c e s may  a l s o be d i s c e r n e d .  and  These a r e i n d i c a t e d on t h e second  system of Example 67, t h e t o p system b e i n g a summary of s t r u c t u r a l p a i n t s i n the p i e c e s . connections.  The The  senza diminuendo  bottom system i l l u s t r a t e s the a f o r e m e n t i o n e d  f i r s t of two  important  d e t a i l s i n Example 67 i s the  marking which appears w i t h the f i n a l dyad of t h e  piece, p o s s i b l y suggesting ( e . g . , t h e opening of No.  a connection 3?).  The  registral  to something w h i c h o c c u r s  attacca  first later  i n d i c a t i o n a t . t h e end of  p i e c e would a l s o seem t o i m p l y a c o n t i n u a t i o n .  The  the  second d e t a i l concerns  the opening i n t e r v a l of a f i f t h i n t h e f i r s t p i e c e , l i n e a r i z e d at t h e of t h e t h i r d p i e c e .  23  I n t h i s sense, t h e B  J  o  end  which i s t h e u l t i m a t e a r r i v a l  p o i n t of t h e t h i r d p i e c e , p r o v i d e s a degree o f l a r g e - s c a l e c l o s u r e from the f i r s t  piece.  W h i l e t h e c o n d i t i o n s o u t l i n e d above suggest c o n n e c t i v e  aspects  between p i e c e s 1 and 3, a number of c o n t r a s t i n g f e a t u r e s support c h a r a c t e r i z i n g of t h e second p i e c e as an i n t e r r u p t i o n .  First, i t is a  23 I n p i e c e No. 1 the f i f t h r e p r e s e n t s the p i t c h e x t r e m i t i e s of i n i t i a l s o n o r i t y . In p i e c e No, 3 t h e l i n e a r i z e d f i f t h o c c u r s i n t h e a s c e n d i n g t r i l l of t h e c l a r i n e t i n b a r s 12-16.  the  158 soloistic and  piece with  a quicker  which frame  an o f t e n f r a g m e n t e d  tempo.  Second,  texture, fluctuating  i t h a s a much w i d e r  i t , and i t f e a t u r e s f r e q u e n t  range than  and a b r u p t  changes  notated  meter,  the pieces i n r e g i s t e r and ..24  dynamics.  The note  suggests  a denial  a t t h e end: " s t o p  of direct  suddenly  continuity  as though t o r n o f f , "  t o t h e opening  of the third  piece.  Summary While to  suggest  notion  i n s t r u m e n t a t i o n - d e n s i t y and i n s t r u m e n t a t i o n were s a i d  subgroupings,  of a connection  a number o f d i f f e r e n t  between  the f i r s t  connective factors are aspects register,  event  features  o f t h e second  said  i s also  to qualify  connection.  common t o b o t h . piece  and t h i r d  add s u p p o r t  pieces.  (e.g.,  dynamics,  The u s e o f a u n i s o n  Finally,  or  octave  several contrasting  t e x t u r e , tempo, a n d d y n a m i c s )  i t a s an i n t e r r u p t i o n  to the  Among t h e  o f t e x t u r e , tempo, a r t i c u l a t i o n ,  p r o p o r t i o n , and p i t c h  dramatic  factors  earlier  of the continuity  between  were  pieces  1 a n d 3.  Summary The  foregoing chapter  the  quintet.  Aspects  and  metric design,  interrelationships be and  i s a detailed  of formal  and p i t c h noted  delineation,  introduced concepts  such  where a p p l i c a b l e .  . . Ligetx,  other  I I , were found  textural  quality,  element-rhythms) a r e s p e c i f i c  24  textural  The f i r s t  with  to the analysis  T  Ten Pieces,  t o have a p p l i c a t i o n space,  p. 11.  rhythmic  i n d i v i d u a l l y and  p i e c e was f o u n d t o  ensemble p i e c e s  textural  piece of  structure,  i n the quintet,  a s i m p u l s e - d e n s i t y and c o n s o n a n c e - d i s s o n a n c e  i n Chapter  (e.g.,  of the f i r s t  o r g a n i z a t i o n were d e a l t  c o n s i s t e n t , i n many ways, w i t h concepts  analysis  here.  criteria, Other  and i n t e r a c t i o n o f  o f p i e c e No. 1.  Finally,  159 the notion  of  piece  was  found  to  be  and  third  pieces.  subgrouping,  also  introduced  r e i n f o r c e d i n elements of  i n the  connection  second  between  chapter,  the  first  CHAPTER IV ANALYSIS OF PIECE NO. 10 Introduction I n t h e a n a l y s i s of p i e c e No. 10 each parameter i s examined i n d i v i d u a l l y as i n t h e p r e v i o u s two c h a p t e r s .  The main f o r m a l s e c t i o n s  a r e as f o l l o w s : D e l i n e a t i n g F a c t o r s of Formal Segmentation A s p e c t s of T e x t u r a l S t r u c t u r e P r i n c i p l e s of Rhythmic and M e t r i c D e s i g n Modes of P i t c h O r g a n i z a t i o n Linear D e t a i l s Harmonic D e t a i l s Connective  F a c t o r s Between t h e N i n t h and Tenth P i e c e s  Summary. As i n t h e a n a l y s i s of t h e f i r s t p i e c e , some c o n c e p t s here a r e extended a p p l i c a t i o n s of those i n t r o d u c e d i n Chapter I I , w h i l e o t h e r s a r e p a r t i c u l a r to t h e t e n t h p i e c e .  D e l i n e a t i n g F a c t o r s o f Formal Segmentation U n l i k e o t h e r s o l o i s t i c p i e c e s i n t h e q u i n t e t ( e . g . , Nos. 2, 6, and 8 ) , where f o r m a l s e c t i o n s and d i s p a r a t e m u s i c a l i d e a s o f t e n c o a l e s c e a continuous  into  stream, t h e t e n t h p i e c e f e a t u r e s f o r m a l s e g m e n t a t i o n w h i c h i s  more d i s t i n c t and pronounced.  Two main s e c t i o n s may be d i s c e r n e d : measures  1-12 and 13-22 and, a l t h o u g h t h e i r s u r f a c e s may appear s i m i l a r , many d e t a i l s u n d e r l i e t h e i n d i v i d u a l i t y of each s e c t i o n . 160  Such d e t a i l s c o n c e r n parameters  161 of  texture  and  organization;  rhythm, as these w i l l  well be  as  aspects of  disclosed  in  l i n e a r and  subsequent  harmonic  sections  of  pitch this  chapter. More o b v i o u s i n measure notes) of of  12,  prior  actual  segmentation;  melodic  structure  portion these  the  p,  the  pochiss.  having  rail,  tempo and  bassoon part  i s another  section,  for  e x a m p l e , may  be  a conjunct  the  i n the of  in a  a wider  participation  the  gets  dynamic range.  i s i n agreement w i t h silent  during  the  cadenza,  thus marking  the the  formal  disjunct end  and  by the  of  i n bar  of  of  a  and  portion  of  each  The  accompanying  the  part  in  each  pp.  the  s e g m e n t a t i o n as  13.  a  disjunct  and  soft  fluctuation  by  delineation.  ff  fff  •pp  point  (accompanied  indications  i s at  replaced  finally,  10-12  quarterthis  i n d i v i d u a l i t y of  expansion:  And  (i.e.,  consist  portion  louder  generalpause  reinforce  factor  to  the  the  indications  Dynamic  to  these are  p a r t i c u l a r mode o f  piccolo,  heard  disjunct  'b'-section  The  abrupto  "cadenza."  'b'-section  the  ex  contribute  'a'-section  beats  in bars  the  by  include  indications also  of  part  resulting  Tempo  a  In  loud  however,  a f t e r which t h i r t y - o n e  i n t e r n a l segments a l s o  while  factors,  and  followed  section. at  and  witness  ritardando),  formal  to,  sound o c c u r .  written  Each  form d e f i n i n g  formal  cadenza In  gets  short, softer,  'b'-section instrumentation  defined  section,  above. enters  in  each main f o r m a l d i v i s i o n .  Summary Many f a c t o r s rhythmic in  structure,  forthcoming  include  the  bassoon  part,  of  formal  as  well  sections.  generalpause dynamics,  segmentation  as  those of  Patent i n bar and  involve  pitch  indicators 12,  of  d e t a i l s of  organization, formal  be  and  examined  delineation,  tempo m a r k i n g s , m e l o d i c  instrumentation.  to  textural  contour  however, of  the  162  Aspects In operate  the  i n the  accompanying which the other  second  c h a p t e r , two  soloistic  instrument, with e i t h e r colorations" difference,  then,  only  i s operative.  structured  while  by  asserts  linear  the remaining  the o v e r a l l The  textural  final  I n one  principles  of  textural  these  event,  effected or  configuration,  The  while  quintet  of the l a t t e r  is  type.  disjunct  i n s t r u m e n t s p r o v i d e u n i s o n and  manner.  The  i n the featured  2  octave  and  essential  simultaneous  continuous,  types,  "sporadic doublings  instruments.'''  t y p e two  to  pattern over  in a contrasting  piece of the  i s featured in a nearly  the remaining  itself  i n the f i r s t  according to the  the bassoon  quintet.  "contrapuntal fragments"  i s that  comprise  c o n f i g u r a t i o n s were s a i d  a particular  continuous  contributed  elements one  establish  featured instrument of a  textural  pieces of the  instruments  i s comprised  of T e x t u r a l S t r u c t u r e  textural i n the  second  texturally Specifically, linear  event  doublings,  and  3 semitone  and  In  whole-tone c o l o r a t i o n s  addition  conditions  to the t e x t u r a l  are noteworthy.  stepwise motion  ( i n contrast  One  throughout. arrangement  is a  "cadenza"  to the f i r s t  d e f i n e d above, figure  type).  two  other  consisting mainly  Instances of t h i s  of  occur  '''The l a t t e r d e s i g n a t i o n r e f e r s t o t h e t e x t u r a l q u a l i t y o f i n t e r a c t i o n between t h e b a s s o o n and o t h e r i n s t r u m e n t s . For example, c o n t r a p u n t a l f r a g m e n t s were n o t e d as b e i n g b r i e f , r h y t h m i c a l l y independent p a s s a g e s w h i c h appear s u p e r i m p o s e d on t h e f e a t u r e d i n s t r u m e n t ' s p a r t . This results in p e r i o d i c fragments of polyphony. D o u b l i n g s a n d c o l o r a t i o n s , on t h e o t h e r hand, a r e c h a r a c t e r i z e d by r h y t h m i c i n t e r d e p e n d e n c e ; t h e i r v e r t i c a l a l i g n m e n t r e s u l t s i n b r i e f i n s t a n c e s o f homophony. 2 The d i s j u n c t d i s p o s i t i o n o f t h e b a s s o o n l i n e , f e a t u r i n g a b r u p t and e x t r e m e r e g i s t e r c h a n g e s , s u g g e s t s an i m p l i e d m u l t i - v o i c e d l i n e a r . s t r u c t u r e — one w h i c h w i l l be i l l u s t r a t e d l a t e r i n t h e c h a p t e r . 3 Semitone c o l o r a t i o n s vertically °note.  That  aligned  w i t h , and  refer a  to a p i t c h  semitone  d e s i g n a t e d as a whole-tone  ( i n an  above or coloration  accompanying  instrument)  below, a p a r t i c u l a r  bassoon  o c c u r s a w h o l e - t o n e away.  163  i n measures 5-6, 8-9 c o n t i n u e d i n 10-11 ( p i c c o l o ) , and 16-18 ( t h e f i r s t bar occurring i n the c l a r i n e t ) .  These f i g u r e s c o n t r a s t t h e d i s j u n c t fragments  i n two o t h e r r e s p e c t s : they occur a t p o r pp ( r a t h e r than ff o r fff), and d o u b l i n g s and c o l o r a t i o n s do n o t occur d u r i n g t h e i r e x e c u t i o n .  The t h i r d  t e x t u r a l c o n d i t i o n i s one of s i l e n c e — a d e v i c e which w i l l be shown t o have a marked e f f e c t on p a c i n g and p r o g r e s s i o n i n t h e p i e c e .  Two a s p e c t s t o be  examined here a r e f o r m a l s t r u c t u r e as d e f i n e d by t h e t h r e e t e x t u r a l c o n d i t i o n s s t a t e d above, and t e x t u r a l p r o g r e s s i o n as m a n i f e s t and s p a t i a l f l u c t u a t i o n s .  i n density  The l a t t e r concept d e a l s w i t h i n s t a n c e s of  d o u b l i n g and c o l o r a t i o n s p e c i f i c a l l y . Formal S t r u c t u r e as D e f i n e d by T e x t u r a l C o n d i t i o n s As suggested  e a r l i e r i n t h e c h a p t e r , t h e piece:, may be heard t o  c o n s i s t of two main f o r m a l s e c t i o n s , each e x h i b i t i n g t h e use of t h e t h r e e t e x t u r a l c o n d i t i o n s d e f i n e d above.  F o r i n s t a n c e , i n Example 68, a l i n e -  graph r e p r e s e n t a t i o n of t h e p i e c e , t h e ' a ' - s e c t i o n i s shown t o be comprised of two p h r a s e s , cadenza.  each of w h i c h c o n s i s t s of t h r e e d i s j u n c t fragments and a  Large u n i t s of s i l e n c e s e p a r a t e d i s j u n c t fragments i n t h e f i r s t 4  phrase w h i l e t h e s e a r e r e p l a c e d by b r i e f r e s t s i n t h e second.  Generally  s p e a k i n g , t h e d i s j u n c t p o r t i o n o f t h e second phrase i s more "condensed" as a result.  Each p h r a s e c o n c l u d e s w i t h a cadenza, approached from t h e f i n a l  d i s j u n c t fragment w i t h o u t i n t e r r u p t i o n . chapter, the rhythmic on  (As w i l l be shown l a t e r i n t h e  s t r u c t u r e s of t h e cadenzas have a s i g n i f i c a n t  effect  pacing.) W h i l e t h e ' b ' - s e c t i o n a l s o f e a t u r e s two p h r a s e s , t h e i r  internal  4  In t h a t t h e use and e f f e c t s o f r e s t s concern r h y t h m i c p r o g r e s s i o n and r e c e s s i o n , they w i l l be examined i n t h e next s e c t i o n , on r h y t h m i c design.  164  Example  68.  Line-graph  [j]  representation  =  octave doubling  f«A  'f  =  semitone or whole-tone coloration  p.d.  =  phrase divider  I  I  of  piece  No.  10.  165  | | i  166 structures are above. and  For  instance,  does not  adheres  somewhat d i f f e r e n t  appear  strictly  the f i r s t  which,  phrases  particularly  d y n a m i c s and previous  5-6 it  "p.d." has  and,  unfolding  f r o m A^,  which  reasons  linear  frame  i t may  integral  or  the f i r s t  one  be  part  of only  (at l e a s t  fragment  (i.e.,  may  directive  i t ^isolate  two  not  be h e a r d  divider" close  colorations  5-6).  Its disjunct quality  i t from  of the phrase which  to previous  specific  In  cadenza  fact, ( c f . bars  however,  of preceding cadenzas,  surrounding phrases.  precedes  to  fragment, i t s  structure,  considered a separate e n t i t y — a  separate  I t s reduced  are factors  of the f i r s t  close  graph)—one  s t e p w i s e : A^-G-G^, E ^ E - F . PC's  which On  relationship  measures  fragments  one  to  on t h e  although i t o c c u r s as a d i s j u n c t is clearly  outlined  of previous cadenzas).  "phrase  these are the opening  the e x p l i c i t  of the phrases  i s comprised  a considerably  where A b e g i n s t h e c a d e n z a ) .  rests  an  disjunct  l a c k o f d o u b l i n g s and  cadenzas  o r d e r o f PC apart  (labelled  i n some r e s p e c t s ,  cadenzas,  phrase  to the c h a r a c t e r i s t i c s  :  two  that  to conclude w i t h a cadenza  i n s p e c t i o n , however, a b r i e f , the  from  For  denies  and  the  these  "divider"—rather  than  i t (as w i t h p r e v i o u s  cadenzas). The but,  second  rather,  phrase of the  i s one  'b'-section  continuous gesture culminating  Factors  of doubling, c o l o r a t i o n ,  design,  and  pitch  c o n t a i n s no  organization  textural-density,  ( a l l of which  such  subdivisions  a t t h e end register,  are discussed  o f bar  15.  rhythmic later)  ^The " r e s t " w h i c h f o l l o w s t h e b r i e f f r a g m e n t i s a c t u a l l y i n t h e f o r m o f a b r e a t h m a r k (') o f w h i c h L i g e t i s t a t e s t h a t i t s d u r a t i o n i s t o be no more t h a n a s i x t e e n t h - r e s t (*f ) . S e e Ten Pieces, p. 34. A s e n s e o f t e x t u r a l p r o g r e s s i o n m i g h t be c o n s i d e r e d t o a r i s e from the i n c r e a s i n g "urgency" of the phrases ( i . e . , the tendency from t e x t u r e o f m u l t i - f r a g m e n t e d p h r a s e s t o one o f c o n t i n u i t y ) .  a  167  c o n t r i b u t e t o t h e c h a r a c t e r i z a t i o n o f t h e D-> i n bar 15 a s a c u l m i n a t i o n point.  The f i n a l cadenza i s t h e r e f o r e n o t c o n s i d e r e d  second phrase b u t , r a t h e r , a s a " p o s t - c a d e n t i a l The  integral to the  extension."  p h r a s e s of t h e ' a ' - s e c t i o n , t h e n , a r e c o n s i s t e n t i n t h e i r  s t r u c t u r e : t h r e e d i s j u n c t fragments p l u s an i n t e g r a t e d cadenza.  Those  of t h e ' b ' - s e c t i o n a r e c o n s i s t e n t n e i t h e r among themselves n o r w i t h t h o s e of t h e o p e n i n g ; r a t h e r , t h e y a r e comprised o f two and f i n a l l y one fragment, each w i t h o u t an i n t e g r a t e d cadenza.  One common d e t a i l of t e x t u r a l d e s i g n ,  however, concerns t h e employment o f d o u b l i n g s  and c o l o r a t i o n s .  In the  f i r s t phrase o f each s e c t i o n semitone and whole-tone c o l o r a t i o n s f i g u r e most f r e q u e n t l y , whereas t h e second phrase of each i s marked by t h e use o f octave doublings.  These two modes o f t e x t u r a l i n t e r a c t i o n a r e r e s p o n s i b l e  for p a r t i c u l a r q u a l i t i e s of progression,  t o be d i s c l o s e d n e x t .  T e x t u r a l P r o g r e s s i o n as M a n i f e s t i n D e n s i t y and S p a t i a l F l u c t u a t i o n s Because i n t e r d e p e n d e n t d o u b l i n g s  and c o l o r a t i o n s a r e t h e o n l y two  modes o f i n t e r a c t i o n between t h e bassoon and o t h e r represent  t h e o n l y means o f t e x t u r a l t h i c k e n i n g .  instruments,  they also  Semitone and whole-tone  c o l o r a t i o n s i n f l u e n c e s m a l l - s c a l e s p a t i a l f l u c t u a t i o n and, w i t h o c t a v e and unison doublings,  a f f e c t t h e f l u c t u a t i o n of i n s t r u m e n t a t i o n - d e n s i t y (or  s i m p l y t h e number o f i n s t r u m e n t s sounding a t any g i v e n t i m e ) . doublings  Octave  t h e m s e l v e s may be heard t o a f f e c t o v e r a l l t e x t u r a l space, a  more g l o b a l c o n s i d e r a t i o n . be d i s c u s s e d  i n greater  T e x t u r a l - d e n s i t y and t e x t u r a l space w i l l now  detail.  Textural-dens i t y R e f e r r i n g a g a i n t o Example 68, i n s t a n c e s of c o l o r a t i o n a r e bracketed  (!) and t h e number o f members i n each v e r t i c a l i t y  circled.  168 Notice  i n phrase I of the 'a'-section that  registrally three that  members. its  highest points of the fragments,  members high  colorations  and t h e m i d d l e ones, o n l y  points  a r e accented  the f i r s t  two.^  c o l o r a t i o n marking  having  Phrase I I i s s i m i l a r i n  e x h i b i t s a mode o f p r o g r e s s i o n i n  exclusive use of colorations.. S p e c i f i c a l l y , contains  and l a s t  b y c o l o r a t i o n s , e a c h o f w h i c h h a s two  Phrase I of the 'b'-section  instances  articulate  two members  (i.e.,  distinct  each o f t h e f i r s t  pitches)  t h e end o f t h e p h r a s e c o n t a i n s  four,  four  while the the largest  g number h e a r d instances greater  i n the piece.  In consideration  of coloration, a large-scale progression  d e n s i t y may be d i s c e r n e d .  representation  System  as defined  depicted  by t h e arrow above t h e graph.  O t h e r modes instruments  above,  the general  i n occurrences  These a r e i n d i c a t e d on systems the  former peaking  illustrates The  ^The pitch  on t h e f o u r - p a r t  point  here  i s also  number o f members  graphic  direction  being  f l u c t u a t i o n s i n t h e number  of unison  and o c t a v e  doubling.  (b) a n d ( c ) , r e s p e c t i v e l y , o n Example 69,  instrumentation-density  culmination  69 i s a  ( o n e mode o f t e x t u r a l -  progressive  of textural-density include  involved  towards p o i n t s o f  (a) o f Example  of f l u c t u a t i n g coloration-density  density)  of  of the aforementioned  unison  o n D~* i n b a r 15.  System (d)  fluctuation, referred to earlier. i n measure 15.  i n a given  coloration includes  t h e bassoon  itself, g  N o t i c e a l s o t h a t t h e end o f p h r a s e I i n t h e ' a ' - s e c t i o n i s a r t i c u l a t e d b y a c o l o r a t i o n o f t h r e e members, t h e l a r g e s t number h e a r d to that p o i n t . T h e h a r m o n i c q u a l i t y o f t h e s e two v e r t i c a l i t i e s i s o f s i g n i f i c a n c e and w i l l be d i s c l o s e d l a t e r i n t h e c h a p t e r .  169  Example  69.  F o u r modes o f  textural-density  fluctuation.  o o — I o 1  (octave) doubling-density  instrumentation-density  M M  M i l l  (unison) doubling-density  coloration-density  M i l l  X)  p. Jo  rt cn  rt- cu n rt  o co D" O (T> o CO 3  1 1 1 1 1  n> cn  o  3  J  /  /  \ J  \  IK.  \  1 <  4m -4  \  S  2.  7  4W  —  <  4U  1  HI  %  <,  »  —  • r a t e  \ 4_  ^  —<  (  t  —4  •!1  /  Ii-  t  x  -f-  i  \  I  \  Z.  5  \  l  •4*  ^ A  \,  w  < •  171 Textural  space  W i t h r e f e r e n c e t o Example of  each formal  featuring the  a  e.g.,  s e c t i o n i s "boxed"  f o u r t h box  temporal  in :textural  cadenzas,  boundary of  octave  doublings  one  extend  etc.  the  first  i n the  semitone,  the upper  two  to  indicated  on  register)  i s one  section itself  of ascent.  in a higher higher,  the  register  e.g.,  cadenza.  This  register,  is itself  phrase,  F#-*  the upper The  4  and  i n an  overall For  direction  example, n o t  than  i n the  traversal,  of  only  sense  but  opening  without  "incompletion"—a  the to  9  lower for  increase  by  however,  provide  Second,  i s the  the  were i t n o t  of r e g i s t r a l  i t s beginning, 4  First,  doublings,  important  fields,"  fluctuations  boundary would  octave  content  formal subdivisions,  i s B ^ l and,  cadenza which f o l l o w s .  extreme s p a t i a l factor  "spatial  i n c o n n e c t i o n . ;with  fields  to A .  pitch  'b'-section  These represent  details  compare B ^ - A ^  a  the  (the  coincident with  spatial  4  preparation f o r the graph,  165),  'a'-section are noteworthy.  registral  the  roughly  f r o m G//  extremity  (p.  t h r e e groups  end).  Two  second  e.g.,  once again  into  the v e r y  space w i t h i n the  pitch  only  at  spans of which are  phrases,  68  as  space end  of  spatial  A -E^  (not the  the  registrally  just 'a'-  field  i n the  4  r e t u r n to  clearly  is  final,  opening  articulated  "half-cadence." Although the  final  and  ascent  in  both  octave  cadenza  i n the  do  not  provide  registral  'b'-section, a  similar  pattern of'spatial  i s n e v e r t h e l e s s apparent.  directions  narrower  doublings  field  as  i n the  second  d e f i n e d by  the  field  Here, and  cadenza—a  the  spatial  i s followed field  preparation for  boundary by  a  which l i e s  expansion  i s expanded  considerably in  the  9 " S p a t i a l f i e l d s " a r e r e g i s t r a l s p a c e s d e f i n e d by p i t c h e x t r e m i t i e s of p a r t i c u l a r formal s e c t i o n s or, i n t h i s case, s u b d i v i s i o n s of such sections.  172 uppermost The  register  overall Two  direction additional  are worth n o t i n g . space  from  the  the middle A//^ of  the opening  field of  box  and  of  the f i n a l  of r e g i s t r a l details  One  space  i s the minimal,  fields  of  each  i n the  abrupt  effected  by  'b'-section).  .  The  the realm of  textural  space  i n the  expansion  ascent  from  is a  subtle  recollection  may  would  registral  in overall  this  f i n a 1 C#  cadenza  'b'-section  connecting  the r e l a t i v e l y  allusion and  ascent.  —  other  the bassoon's  Although  registral  important  'a'-section.^  of  space  exhibits  t e r m i n a t i o n of the f i n a l brief  the  dotted l i n e  section B^)  of  i s a g a i n one  yet  The  boundary remaining register  cadenza  regarding textural  1  "openness," t h i s  within  that  ' a ' t o 'b'" ^ s e c t i o n .  spatial  ( t h e lower  spatial  like  2  (the  to  fourth'  static  be v i e w e d  F#-*  spatial as  seem t o d e n o t e  factors closure  traversal."''"''  Summary Disjunct unison  fragments  d o u b l i n g s , and  i n s t r u m e n t s were Conjunct, extended  semitone  periods of  silence  accompanied  by  sporadic octave  whole-tone c o l o r a t i o n s textural  element  were n o t e d  as being  as w e l l  two  i n the  i n the tenth  ( w i t h o u t d o u b l i n g s and  Coloration-density,  were s a i d  progressive  and  t o d e f i n e one  c a d e n z a - l i k e passages  arrangements. doubling,  said  i n the bassoon  towards  a s ^ t h a t o f u n i s o n and  specific  piece.  p o i n t s i n the  and  textural  to d e f i n e s p e c i f i c i m o d e s of t e x t u r a l - d e n s i t y  intensification  remaining  colorations)  additional  and  octave revealing  piece.  ^ C o n c e r n i n g t h e s e two c a d e n z a s , i t i s i n t e r e s t i n g t h a t t h e p a t t e r n o f s p a t i a l d e f i n i t i o n i n m e a s u r e s 9-11 i s o n e o f t a p e r e d c o n t r a c t i o n , w h i l e t h a t o f b a r s 16-19 i s e x t r e m e l y s t a t i c . A l t h o u g h g e n e r a l l y a p p a r e n t on t h e g r a p h , t h e r h y t h m i c a c t i v i t y o f t h e s e c a d e n z a s w i l l l a t e r b e shown t o complement t h e s e p a t t e r n s . o f s p a t i a l f l u c t u a t i o n . ^ I n terms of l i n e a r p i t c h o r g a n i z a t i o n , a d d i t i o n a l r e i n f o r c e m e n t f o r the a s s e r t i o n of openness i s o f f e r e d ; d e t a i l s appear l a t e r i n the chapter.  173 I n s t r u m e n t a t i o n - d e n s i t y , a f o u r t h mode, was t y p e s of instrument A c l i m a x on  s a i d t o t a k e i n t o account a l l  i n t e r a c t i o n be i t i n t h e form o f d o u b l i n g o r c o l o r a t i o n .  i n measure 15 was noted w i t h r e s p e c t t o t h i s a s p e c t  textural-density. p a r t i c u l a r , was  of  F i n a l l y , t e x t u r a l space, a f f e c t e d by o c t a v e d o u b l i n g s i n  a l s o shown t o r e v e a l p a t t e r n s of d i r e c t i o n and  expansion  throughout t h e p i e c e . P r i n c i p l e s of Rhythmic and M e t r i c Design In v i e w i n g the r h y t h m i c and m e t r i c d e s i g n of p i e c e No.  10 t h r e e  p r i n c i p l e s w i l l be d i s c u s s e d : t h e f u n c t i o n of n o t a t e d b a r l i n e s and  their  r o l e i n a r r i v a l p o i n t d e f i n i t i o n , impulse-number p r o p o r t i o n s of phrase fragments,  and d i r e c t e d p a t t e r n s of i m p u l s e - d e n s i t y f l u c t u a t i o n .  In  c o n s i d e r i n g t h e f i r s t of t h e s e , i t has been a s s e r t e d throughout t h i s paper t h a t n o t a t e d b a r l i n e s a r e l a r g e l y f o r ease of r e a d i n g — a  convenience o f  n o t a t i o n a l o r g a n i z a t i o n r a t h e r than an i n d i c a t o r of a c c e n t - d e f i n e d m e t r i c units.  I t was  a l s o noted  i n Chapter I I t h a t n o t a t e d b a r l i n e s i n s o l o i s t i c  p i e c e s of the q u i n t e t o c c a s i o n a l l y appear t o be p l a c e d i n o r d e r t o mark 12 specific a r r i v a l points.  The  t e n t h p i e c e i s c o n s i s t e n t w i t h the  of t h e s e a s s e r t i o n s ; i t a l s o f e a t u r e s a c l e a r l y f e l t one which i s independent of t h e demarcation  first  a r r i v a l p o i n t , but  of n o t a t e d b a r l i n e s .  The  on t h e f i n a l s i x t e e n t h - n o t e of measure 15 i s t h e j u n c t u r e i n q u e s t i o n i s , as noted  e a r l i e r , t h e c l i m a x p o i n t f o r (unison) d o u b l i n g - d e n s i t y  the f o u r - p a r t u n i s o n ) and sound a t once).  i n s t r u m e n t a t i o n - d e n s i t y (e.g., a l l f i v e  and (e.g.,  instruments  As w i l l be e x p l a i n e d l a t e r , l i n e a r c o n t i n u i t i e s a l s o  c u l m i n a t e a t t h i s p o i n t and here.  D^  i m p l i c a t i o n s o f PC c e n t r i c i t y (on D) a r e r e a l i z e d  I t i s c l e a r l y (and a u d i b l y ) t h e " s t r u c t u r a l " a r r i v a l p o i n t of t h e 12 In t h e s e i n s t a n c e s , "downbeats" were d e f i n e d as t o parameters o t h e r than a c c e n t - d e l i n e a t e d m e t r i c p a t t e r n s .  174 entire  piece  clarinet an  yet,  p o r t i o n of  the  the  this  apparently  such) t h e  situation  barline i s indicated just  cadenza  "afterbeat" relative  Given as  and,  to  the  association,  that  preceding,  treat  downbeat  the  occurs  i s , immediately  after  such a  "incompleteness"  or  "inconclusiveness"  feeling  16  has  which the  on  D  "treatment"  p e r f o r m e r may,  the  arrival  differently the  a  on  D-*.  perceptible from  a  a  precise  feeling  of  t o accompany t h e  in fact,  of  conventional  While  is difficult,  The  effect  i t i s not  barline.  is likely  i t .  the  exposed  i n accordance with  of  D—a  highly  arrival  characterization  on  i n bar  c o n t r a d i c t o r y b a r l i n e (although  performer, may  where t h e  commencing  after  convey to  the  arrival  listener.  13 The  resulting  ensuing  tension  i s dissipated, although  principle  of  interaction rhythmic  with  completely,  in  the  cadenza. Impulse-number  bassoon  not  rhythmic  design  i s i n the  pacing part  proportions  of  form of  the  itself.  impulse-number  piece Example  to  be  phrase fragments  discussed  interdependent  70  progression proportions  phrase  i s the  i n that and  d i c t a t e d by  c o n s i s t s of o£  and,  doubling  is essentially  proportions  g r a p h , a n d two l e v e l s o f R e g a r d i n g impulse-number  of  an  second  a l l  coloration,  that  of  impulse-density  segments  instrument the  the graph  i n d i c a t e d above  the  and r e c e s s i o n d e p i c t e d b e l o w . ( i . e . , t h e t o t a l number o f i m p u l s e s  14 and  " a c t i v e " beats  i n each  segment),  disjunct portions  of  the  'a'-section  13 The r h y t h m i c " s t e a d i n e s s " o f t h e c a d e n z a ( t o be commented o n l a t e r ) and a b r u p t t e r m i n a t i o n of a c t i v i t y ( a l l u d e d t o e a r l i e r ) r e s u l t i n t h e r e t e n t i o n of a c e r t a i n degree of i n t e n s i t y . My own v i e w i s t h a t o n l y a f t e r the piece i s a c t u a l l y f i n i s h e d i s the i n t e n s i t y f u l l y d i s s i p a t e d . 14 The l a r g e u n i t s of s i l e n c e have n o t been i n c l u d e d i n t h e i m p u l s e c a l c u l a t i o n of a c t i v e beats. A l s o , because of the rhythmic interdependence o f t h e d o u b l i n g s and c o l o r a t i o n s , t h e y h a v e n o t been c o u n t e d as separate impulses.  175  Example  70.  Impulse-number p r o p o r t i o n s impulse-density graph.  of phrase  fragments  and  176  177 and  the  first  cadenza  (measures  active  beats  of  actual  time,  the three d i s j u n c t  of  silence.  sense are  A  the f i r s t  s e p a r a t e d by  a  bars  f o r example, a  "hesitant" departure other two  ambiance,  hand,  i n bar exhibits  being  seventeen  s e p a r a t e d by  phrases  of  by  the  (piccolo).^  a steady rhythmic  The  large  final  periods  activity  are In  creates a pitch  ' b ' - s e c t i o n ' s cadenza, that  a  cadenza.  "reluctant"  d r i v e matching  of  fragments  tendencies  section's  seemingly  beats  where d i s j u n c t  i n rhythmic  six  i s r e p l a c e d by  T h e s e two  each  steady d e c l i n e  11  occur over  a t most.  structure  reinforced  balanced.The  r e s u l t s — o n e which  i n subsequent  the rhythmic  to  fragments  sixteenth-rest  by  are r e l a t i v e l y  however,  quality  urgency  reinforced 8-11,  phrase,  "tentative"  of d r i v e and  5-6)  of  the  on  the  preceding  phrases. The  (i.e., 5-6)  extended  "extended"  may  l e n g t h s of  relative  be v i e w e d  as  ' a ' - s e c t i o n ' s second  its  first  the d i s s i p a t i o n second  phrase  and of  but  Concerning rhythmic  activity  f a c t o r s which  phrase  generates  In a d d i t i o n  punctuates the f i n a l i n bar  the  that  end  cadenza  16 a n d  i n m e a s u r e s '7-11 p o r t i o n s and  necessities.  therefore requires  energy.  suggest  cadenzas  to the d i s j u n c t  functional  the  phrase  the  The  and  cadenza  "pressing  16-22 i n bars  forward"  c o n s i d e r a b l y m o r e momentum  a g r e a t e r "wind-down" p e r i o d to t h i s ,  of the of the  i t not  'a'-section piece,  sustained  i t operates within  the  of than for  only concludes as a  the  whole.  c o n t i n u a t i o n of  c o n n e c t i n g bar or at the  15  level  to of  16  are  the  "''"'Regarding t h e c a d e n z a i n b a r s 8-11, t h e b a s s o o n p o r t i o n ( c u r i o u s l y t h a t w h i c h i s r h y t h m i c a l l y i d e n t i c a l t o t h e f i r s t c a d e n z a , i . e . , | | | | F^ | | | | ] | | | | | 3I J ) i s a l s o roughly balanced with the other phrase portions. n  s  16 T h i s p a r t i c u l a r p i t c h d e p a r t u r e m a r k s an i m p o r t a n t p o i n t s t r u c t u r e o f l i n e a r p i t c h o r g a n i z a t i o n , one w h i c h w i l l be e x p o s e d in the chapter.  i n the later  178 'b'-section. and  extended  section) end a  of  the  length  suggest  the  other  as  hand,  (e.g.,  that  piece  (partial)  the  On  longer  the  than  the  i t also operates  a whole.  The  "wind-down" p e r i o d  cadenza,  i t s " p o s t - c a d e n t i a l " q u a l i t y noted  'b'-section,  at  a higher  inactivity  f o r the and  preceding  on  of  still  level,  bars  rhythmic  a  p o r t i o n of  earlier,  the  'b'-  punctuating  19-21  energy of  may  be  the  the  heard  opening  l a r g e r s c a l e , f o r the  as  of  entire  piece. In  consideration of  the  "balanced"  phrase fragments  numbers o f  impulses,  progressive level  (a)  exhibit at a  the  of  rhythmic reveals  intensification be  discerned.  irrespective  graph  rhythmic  beginning  (a)  discussed of  recessive tendencies  below the  brief  definite  level  and  impulse-density  cadenza  recession  little  Level  (b)  to  bar  arrival  illustrates  the  'a'-section revealing a  and  the  the  recession of  'b'-section  already  apparently  balanced  alluded  to.  phrase fragments  growing  11.  in  in intensity  The  The  of  the  and  progression;  on  D at  end  of  bar  'a'-section  then  a  may,  of  rhythmic  unit followed  by  a  implicatively  consistent  however, direction,  recessive  level  in  slight  patterns  exhibiting a relatively  effects  depicted  15  in  culminating  cadenza  rhythmic  overall  reveal suggested  'b'-section as  the  relative  As  of  progressive  which occurs  the  configurations)  i n m e a s u r e s 7-8.  i n t h e way  towards the  (i.e.,  rhythmic  i n E x a m p l e 70,  progressions,  the  above  graph,  of  one,  activity,  through the  inactivity  (like  found  of  bars  19-21.  Summary Although barline-suggested soloistic  pieces)  in  emerges a s  bar  15  density.  An  are  essentially a  apparently  structural  downbeats  non-existent arrival  point  those  i n the  tenth  exposed  c o n t r a d i c t o r y b a r l i n e was  noted  in  other  piece,  the  through  textural-  at  point.  this  In  179 addition  to  this  aspect  f r a g m e n t s were f o u n d configurations, depicted  as  to  exhibited  down" p e r i o d  rhythm,  be  approximately  balanced,  Regarding  latter,  directed.  a rhythmic  'b'-section  of  of  impulse-number  progression  followed  a relatively  which occurs  Pitch  previous  a number o f successive  d i f f e r e n t ways. arpeggiations  while  i n No.  Other  factors  were a l s o  c h a p t e r s we  4,  shown t o  crossing  provided  complete  formal  bassoon part  dynamic  generate  And  organization.  were f o u n d  i n No. support  section  Because of and  in  bassoon  itself.  Linear  part  will  by  the  registral In  the  take  A  oboe,  exhibited (No.  an  clarinet,  the  piece  a  7),  events  the  the  "wind-  measures.  structured  in  pitch extremities  of  comparable s i g n i f i c a n c e .  and  unison  prolongation  aspect  other  will  transfer  of  and  lateral  large-scale  the  on  linear  highly  in  a  pitch  disjunct this  registral  study  of  connections  organization,  whole-tone  3)  voice  pitch extremities of  (No.  relative  instruments,  focus  s e m i t o n e and  and  while  final  connections  s e c o n d mode o f  into account  was  specific linearizations  t e x t u r a l primacy of  tenth  the  example,  maintenance of  subordinate r o l e of i n the  provided  reveal  outer-voice  the  organization  unfolding,  to  thus r e v e a l i n g  linear the  for  exposure  f o r the  of  rhythmic  'a'-section  activity,  linear  2,  stepwise l i n e a r  1,  of  phrase  Details  two-note o s c i l l a t i o n s  such as  significance.  No.  the  their  of  Organization  have o b s e r v e d  In  and  a recession,  inactivity  Linear In  by  steady l e v e l  i n the  Modes o f  the  proportions  PC  colorations  horn.  connections  light  of  the  bassoon's h i g h l y  disjunct  structure,  alluded  to  180 above, i t may r e a d i l y be p e r c e i v e d as " m u l t i - v o i c e d . " ^ p i t c h e s may be heard t o form s t e p w i s e  Specifically,  c o n t i n u i t i e s unfolding i n four  r e g i s t e r s simultaneously: i ,  and  iv,  •^  .  The j u s t i f i c a t i o n f o r t h e s e r e g i s t r a l  involves motivic considerations—an l a t e r i n the chapter.  designations  a s p e c t t o be e x p l a i n e d more f u l l y  I t s r o l e i n r e g i s t r a l d e f i n i t i o n , however, i s  i l l u s t r a t e d i n t h e f i r s t e i g h t n o t e s o f t h e bassoon p a r t as shown i n Example 71.  The t o p s t a f f c o n s i s t s o f t h e p i t c h e s as t h e y o c c u r i n t h e  s c o r e ; each o f t h e lower s t a v e s r e v e a l s a f o u r - n o t e m o t i v e , t h e l o w e s t p i t c h o f each i n i t i a t e s one o f t h e f o u r r e g i s t e r s noted above. Example 71. M o t i v i c d e f i n i t i o n o f r e g i s t e r s i and i i .  The  same f o u r - n o t e m o t i v e i n t h e next o c t a v e ( i . e . , B ^  o c c u r s over a much l o n g e r span, but f a i l s t o c o n t i n u e  to D  4  t o D^ ) 4  a t any p o i n t  ^ I n t h i s sense l i n e a r o r g a n i z a t i o n here i s n o t c o m p l e t e l y t h a t found i n t h e second and f o u r t h p i e c e s .  unlike  181 i n the p i e c e .  18  motive i t s e l f .  R e g i s t e r i i i t h e r e f o r e c o n s i s t s of only the four-note The r e g i s t r a l l y " i s o l a t e d " E ^  then i n i t i a t e s r e g i s t e r i v  19  (T  which c o n t i n u e s up to E  4  by measure 11.  J  The r e a d e r i s now  r e f e r r e d t o Example 72 i n w h i c h a l l of the bassoon  p i t c h e s a r e i n d i c a t e d on the bottom f o u r s t a v e s of system (a) ( c o r r e s p o n d i n g to t h e f o u r r e g i s t e r s d e f i n e d above).  The top two s t a v e s show t h e d o u b l i n g s  and c o l o r a t i o n s p r o v i d e d by the o t h e r i n s t r u m e n t s . down t o t h e a p p r o p r i a t e bassoon n o t e s . )  (The l a t t e r a r e stemmed  System (b) shows t h e r e l a t i v e l y  f o r e g r o u n d l e v e l o f p i t c h o r g a n i z a t i o n i n which t h e f u n c t i o n s of a l l p i t c h e s i n the bassoon p a r t a r e d e s i g n a t e d . the l e f t o f Example  ( N o t a t i o n a l symbols a r e i n d i c a t e d t o  72.)  W h i l e l i n e a r p r o g r e s s i o n s and p r o l o n g a t i o n s on systems (b) and a r e s t r a i g h t f o r w a r d , s e v e r a l f a c t o r s of p i t c h exposure a r e  (c)  noteworthy.  For example, c e r t a i n r h y t h m i c d e t a i l s s e r v e t o h i g h l i g h t s t r u c t u r a l p i t c h e s of l i n e a r p r o g r e s s i o n s , p a r t i c u l a r l y the a s c e n d i n g f o u r t h , E ^  4  3-5); here, each p i t c h of the ascent i s preceded  I n the case of  A^  4  a d e l a y of p r o g r e s s i o n r e p l a c e s the r e s t .  r h y t h m i c a l l y s i m i l a r to t h a t of F#  4  by a r e s t .  I t s approach,  i n bar 3 ( c f . " f j  t o A^  (bars  4  in fact, i s  ^ and  | | | | | ).  3  3  In a d d i t i o n to t h i s r h y t h m i c d e t a i l and t h e more o b v i o u s d i s j u n c t approach and r e g i s t r a l exposure, t h r e e o f t h e f o u r p i t c h e s a r e punctuated  by a  c o l o r a t i o n i n one of t h e r e m a i n i n g i n s t r u m e n t s . (The harmonic i m p l i c a t i o n s ^ I n r e g i s t e r s i and i i t h e f o u r - n o t e motive c o n t i n u e s up t o D and and e v e n t u a l l y up t o A and A^, r e s p e c t i v e l y . The d e n i a l o f D m r e g i s t e r i i i i s the main f a c t o r of s e p a r a t i o n between r e g i s t e r s i i i and iv. The PC D, i n f a c t , w i l l be shown t o have s t r u c t u r a l s i g n i f i c a n c e i n t h i s p i e c e as i t d i d i n Nos. 1, 4, 5, and 6. 2  2  19  4  be:  W h i l e the bassoon extends up to E^- o n l y , the p i c c o l o n o t e s i n bars 10 and 11 a r e c o n s i d e r e d to f u n c t i o n i n t h e l i n e a r c o n n e c t i o n and r e g i s t r a l e x t e n s i o n up t o E^; t h e y a r e t h u s a c o n t i n u a t i o n of the bassoon's cadenza, not s i m p l y d o u b l i n g s o r c o l o r a t i o n s . 5  182  Example  72.  First  and  second  l e v e l s of  linear  pitch  structure.  primary linear progression (see text for criteria of "primary"  =  less  exposed linear  prolongation (neighbours  designation)  progression  of a particular pitch stemmed to beam, embellishing  patterns  pitch in parentheses is "relocated" for interpretation of a linear progression  "secondary" prolongation (see text for criteria of  denotes "reinterpretation" (see text for details)  "secondary"  of the second  designation)  pitch  to  slur)  184 of  these  colorations w i l l  structural  pitches  established  A ^  which begins and in  be c o n s i d e r e d l a t e r . )  in this  register  i n bar 7 (which  the 'b'-section  A^ two b e a t s  later  (this  i s approached  proceeds  almost  of three other  by a r e s t :  immediately  ( p r e c e d e d b y t h e generalpause pitch  initiating  the r e t o A^) ,  A ^  of bar 12),  the ascending  fourth to  measure 15). With  the  r e f e r e n c e to system  initial  ascending  eventual this  from  concerns  i n the f i n a l  cadenza's  N  At t h e second  A ^  ( b a r 7) i s r e i n t e r p r e t e d ^  its  status  ( a s D#)  higher-level  t o suggest  pertains  ^  level  i s counterbalanced  detail  of E \  mentioned  £i.e.,  T h e same  quality  linear  tendency  i n the  The  detail t h e "wave-  ( c ) ] , the re-established  situation  reinterpreted  i t spassing-tone  B^-B-C-D^, f o r e x a m p l e ,  and i n v o l v e s  system  First,  mirrored,  A second  and e n h a r m o n i c a l l y n o t a t e d  21  ( a s G#)  arises  to depict  i n bars  10-11  and e n h a r m o n i c a l l y  t o E^.  Through  this  p r o g r e s s i o n s are connected  event.  of s i g n i f i c a n c e  t o t h e apparent  13-15).  up t o E ^ i s a l s o  pattern of reinterpretat ion brief  third  are noteworthy.  (measures  reiteration  . E -> i s u l t i m a t e l y  a more c o m p r e h e n s i v e The  motive,  to ascent  a s a p a s s i n g - t o n e t o A^.  where t h e r e i t e r a t e d  form  to A ^ ,  t h e c o n t i n u a t i o n up t o E ^ j u s t  ("""~ s«*') .  notated  A ^  continuation of the i n i t i a l  time  slur"  (c), three details  progression, E ^  'b'-section with the descent  to  Each  i n the linear  t o w a r d s t h e PC D.  exhibits  inclination  pitch  structure  The i n i t i a l  four-note  t o D, r e a l i z e d i n  20 That i s , i t i s r e i n t e r p r e t e d f u n c t i o n s as a goal o f motion. 21  from  i t sinitial  o c c u r r e n c e where i t  \lK  The i n i t i a l E - a l s o s t a n d s a s a l o c a l g o a l o f m o t i o n o f t h e a s c e n t f r o m A^ i n b a r 7. 9  3  arrival  point,  i . e . , the  185  r e g i s t e r i i where D I n r e g i s t e r s i and  J  o  i s reached i n bar 3 and prolonged  iii,  22  u n t i l bar 1 5 .  however, t h e m o t i v e c o n t i n u a l l y f a l l s s h o r t o f  i t s r e s p e c t i v e D, hence t h e p a s s i n g - t o n e  d e s i g n a t i o n o f C#  4  and  C#  in  2  measures 1 5 and 2 1 r e s p e c t i v e l y £see system ( c ) ] . (b) o f Example 7 3 r e p r e s e n t t h i r d and f o u r t h l e v e l s  Systems (a) and of l i n e a r s t r u c t u r e .  Each r e v e a l s t h e f i v e e s s e n t i a l l i n e a r  progressions  i n the p i e c e , the h i g h e s t , most encompassing l e v e l o m i t t i n g t h e octave ascent from E ^ In short, E^5  ana  ;  to E^5  4  l  anc  f o u r t h progression, E^  to A'' to  4  ( t o which i t moves i n bar 1 5 ) .  upper n e i g h b o u r t o  ii,  and  4  major-minor  IF  E'  4  and E ,  also  4  an incomplete major-minor upper n e i g h b o u r , do not however.move t o Concerning r e g i s t e r s i ,  E^ .  4  E^-are c o n s i d e r e d j o i n t l y as an incomplete 23  initial  D. 4  i i i — p r e d o m i n a n t l y u n f o l d i n g s of t h e f o u r -  n o t e m o t i v e , B ^ - B - C - D ^ — o n l y i n r e g i s t e r i i i s the m o t i v e c o n t i n u e d the o t h e r s , as n o t e d above, a r e l e f t One  to  D;  "hanging."  f i n a l aspect of l i n e a r p i t c h o r g a n i z a t i o n concerns m o t i v i c  s t r u c t u r e , a l r e a d y d i s c u s s e d t o some e x t e n t . occurrences registers i ,  Example 7 4 i l l u s t r a t e s  of the f o u r - n o t e m o t i v e ( t h e n o t e s of w h i c h a r e beamed) i n ii,  and  iii.  pattern i n register i ,  Apart from o v e r l a p p i n g o c c u r r e n c e s  of  the  i t i s i n t e r e s t i n g t o n o t e t h e i n t e r a c t i o n between  m o t i v i c s t r u c t u r e s as such, and  " a n t i c i p a t e d c l o s u r e " on t h e PC D (a  tendency i n h e r e n t i n t h e m o t i v e i t s e l f ) .  I n r e g i s t e r i i i the second of  22  System (b) r e v e a l s t h e s t r u c t u r a l d e t a i l s of t h e prolongation: upper n e i g h b o u r ( b a r s 3 - 5 ) , e m b e l l i s h i n g p a t t e r n ( b a r s 6 - 7 ) , and f i n a l l y a descending l i n e a r approach from A^ ( b a r s 1 3 - 1 5 ) . 23  As was n o t e d e a r l i e r , t h i s c u l m i n a t i o n p o i n t i s a l s o t h e c l i m a x of i n s t r u m e n t a t i o n - d e n s i t y ( i . e . , i t i s the o n l y p o i n t where a l l f i v e i n s t r u m e n t s sound a t once) and (unison) d o u b l i n g - d e n s i t y ( i . e . , i t i s the o n l y PC doubled i n f o u r p a r t s ) . The C//5 w h i c h accompanies i t w i l l be d e a l t w i t h i n the s e c t i o n on harmonic d e t a i l s .  186  Example  73.  Third  and  fourth  l e v e l s of  linear pitch  structure.  mm.  1  3  7  8  11  13  15  16-18  21  immuri  00  188  two  Example  74.  occurrences  of  Motivic  the motive  contains  no  B^)  continue  to  D).  o n c e and  does extend  therefore the C#  being  the  also  to  PC  3  sense of  in that  whereupon t h e  i s "closed" with of  the  in a motivic  closure  i i i s unique  i n both respects.  f o u r t h PC  i n the  D  i n r e g i s t e r s i , i i , and  i s complete  i n terms of  Register  most a c t i v e ,  (i.e.,  PC  and  complete  organization  latter  Finally,  respect  pattern)  (e.g., the  open  (e.g.,  i t does  i s prolonged;  it  not  motive occurs  only  it is  register i ,motivically  to m o t i v i c  but  sense  iii.  structure  i n terms of  PC  (the  final  closure  a D-centricity).  unfolding Apart  connections,  f r o m modes o f patterns  were a l s o n o t e d applied  i n the  particular  of  PC  i n Chapter tenth  mode o f  PC  piece  linearization  i n v o l v i n g p i t c h and/or  unfolding—specifically, II. as,  While say,  unfolding.  such  the  patterns  fifth,  Example  75  No.  PC  twelve-note are  10  not  as  orderings—  consistently  does e x h i b i t  c o n s i s t s of  three  a  staves  189 representing  coloration  Segments c o r r e s p o n d i n g earlier,  a r e numbered  One  immediate  PC's,  b a s s o o n PC's,  to d i s j u n c t  and  fragments,  total  PC  cadenzas,  content.  24  etc., established  f o r ease of r e f e r e n c e . observation of  importance  concerns  the  chromatic  or  25 near-chromatic of  a whole fragment  fashion, the  i n which  third  staff  colorations 8,  9,  and  chromatic normal 10,  13  of  (i.e.,  the  12.  i n each  ( i n the  segment.  piece)  the  s t a v e s o f Example  two  relationship.  that of  give r i s e  of  or  Others  75).  to  chromatic  content  near-chromatic  content  the bassoon  part  S e g m e n t s 1,  exhibit  w h i c h , when c o n s i d e r e d j o i n t l y  The  t h e PC  "normal form" o r d e r i n g of t o t a l resembles  top  Often  i n a chromatic  E x a m p l e 75)  reveal this 26  i n t h e way  their  content  unfolds  "subsets"  and  PC  case  form, a g a i n  11,  little of  total  (i.e., and 4,  several smaller  and  p a t t e r n s , e.g.,  organized  into  s e g m e n t s 2,  p a t t e r n s o f u n f o l d i n g i n segments 3 and  7 reveal  stepwise  form  respective total  PC  connections,  contents  still  yet  display  5,  the normal  a near-chromatic  6,  ordering PC  linearization. 24 C o n c e r n i n g t h e t h i r d s t a f f , t o t a l PC c o n t e n t o f e a c h segment i s arranged i n "normal form" i n the d i r e c t i o n i n d i c a t i v e of the a c t u a l p i t c h u n f o l d i n g i n the music. T h a t i s , i n a l l s e g m e n t s b u t n o s . 4, 9, 11, and 13 PC's a r e o r d e r e d i n a n a s c e n d i n g p a t t e r n w i t h t h e s m a l l e s t i n t e r v a l s to t h e l e f t . The o t h e r f o u r s e g m e n t s a r e " r e v e r s e d " v e r s i o n s o f t h e normal form o r d e r i n g , i . e . , descending from l e f t to r i g h t w i t h the s m a l l e s t i n t e r v a l s to the r i g h t , again arranged to r e f l e c t the d i r e c t i o n of u n f o l d i n g i n the a c t u a l music. 25 S e g m e n t s w i t h m o r e t h a n s e v e n PC's w i l l n a t u r a l l y r e v e a l s t e p w i s e orderings. S m a l l e r s e t s , however, s t i l l e x h i b i t p r e d o m i n a n t l y chromatic u n f o l d i n g s r a t h e r t h a n c o l l e c t i o n s i n v o l v i n g n u m e r o u s w h o l e - t o n e s and small leaps. 26 A " s u b s e t " i n t h i s context r e f e r s to a group of p i t c h e s ( w i t h i n a segment) w h i c h u n f o l d i n a c h r o m a t i c f a s h i o n i n t h e p i e c e . I n segment No. 2 f o r e x a m p l e , two s u b s e t s may be d i s c e r n e d : D^^ down c h r o m a t i c a l l y to A ^ S and up t o F#3 ( t h e F b e i n g a n o t e o f c o l o r a t i o n ) . (See s t a v e s i and i i . ) When t h e s e two s u b s e t s a r e c o n j o i n e d and a r r a n g e d i n t o n o r m a l f o r m , a l l PC's e x c e p t G a r e p r e s e n t .  190  Example  75.  PC  content  of formal  segments.  \9\  'a'-section  measure: 1 segment:  1  -disjunct  fragments  cadenza  disjunct  fragments  cadenza  1 phrase  I  phrase  II  b'-section  i • coloration  p-c's  ii = b s n . p - c ' s  iii= t o t a l p - c  ^disjunct  phrase  fragments ^ -  I  phrase  divider  disj.  cadenza  fr.  phrase  H  content  192 In  a d d i t i o n t o t h e c h a r a c t e r i s t i c o f c h r o m a t i c o r d e r i n g , PC c o n t e n t  i s i t s e l f an i m p o r t a n t a s p e c t of l i n e a r o r g a n i z a t i o n .  It i s , in fact,  r e s p o n s i b l e f o r s p e c i f i c r e l a t i o n s h i p s between c o n t i g u o u s and  non-contiguous  s e g m e n t s — r e l a t i o n s h i p s such as e x p a n s i o n , i n c l u s i o n , o v e r l a p p i n g , and t w e l v e - n o t e aggregate c o m p l e t i o n .  Segment no. 1, f o r example, i s embedded  i n t o the expanded no. 2, t h e l a t t e r c o n t a i n i n g a l l PC's  except G.  While  t h e normal form o r d e r i n g of t h e t h i r d segment o v e r l a p s t h a t of t h e second (e.g., F and F#), t h e f i r s t a r t i c u l a t e d PC i n no. 3 ( i . e . , i n t h e a c t u a l music) i s G, thus c o m p l e t i n g t h e t w e l v e - n o t e aggregate i n i t i a t e d i n no. (The square b r a c k e t from no. 2 t o no. 3 i n Example 75 i l l u s t r a t e s completion.)  2.  this  Segment no. 3 o m i t s A and A#, A b e i n g t h e f i r s t and h i g h e s t  p i t c h of no. 4, and A//, t h e l o w e s t . except one, t h i s time G#.  Segment no. 4 a l s o c o n t a i n s a l l  PC's  I n t e r e s t i n g l y G# i n no. 3 i s t h e r e g i s t r a l 27  h i g h p o i n t of t h e i n i t i a l a s c e n d i n g f o u r t h p r o g r e s s i o n exposed  earlier.  The second phrase o f t h e ' a ' - s e c t i o n opens w i t h a t r a n s p o s i t i o n o f •T+3  the f i r s t  segment of phrase I : e.g.,  m  *  x  1  Segments 5 and 6 o v e r l a p and j o i n t l y i n c l u d e a l l PC's the f i r s t two a r t i c u l a t e d i n segment no. 7.  j15  "  except A* and  C—  T h i s second o v e r l a p p i n g  c o m p l e t i o n of t h e t o t a l aggregate i s a l s o i n d i c a t e d i n Example 75 by a square b r a c k e t . of  Each phrase of t h e ' a ' - s e c t i o n e x h i b i t s a n e a r - c o m p l e t i o n  t h e t w e l v e - n o t e aggregate i n i t s opening two segments.  The m i s s i n g  p i t c h ( e s ) i s (are) f u r n i s h e d by t h e " a r t i c u l a t e d " opening o f t h e t h i r d segment i n each case ( i . e . , nos. 3 and 7 r e s p e c t i v e l y ) . Phrase I of t h e ' b ' - s e c t i o n opens i n a s i m i l a r f a s h i o n t o t h a t of The s t r u c t u r a l v a l u e of A^ i n segment no. 3 w a r r a n t s i t s o m i s s i o n i n no. 4 and j u s t i f i e s n e g a t i o n of A i n no. 3. (The r e g i s t r a l c o n n e c t i o n to A, remember, o c c u r s i n bar 7, not w i t h t h e A of segment no. 4.) '  193 the  'a'-section.  That i s , i t s f i r s t  the l a t t e r c o n s i s t i n g of a l l PC's  segment i s embedded i n t o i t s second,  except one.  not the f i r s t a r t i c u l a t e d PC of segment no.  The m i s s i n g D#,  11, i s the lowest  although i n the  2 8  normal form o r d e r i n g .  An o v e r l a p p i n g t w e l v e - n o t e c o m p l e t i o n  a g a i n be n o t e d , as i n d i c a t e d i n Example 75. ' b ' - s e c t i o n was  second p h r a s e of  s t a t e d e a r l i e r to be u n i q u e l y c o n s t r u c t e d of  c o n t i n u o u s d i s j u n c t fragment. PC content  The  may  once the  one  I t i s a l s o u n p a r a l l e l e d i n terms of i t s  as i t i s the o n l y s i n g l e segment which c o n t a i n s a l l t w e l v e .  T h i s sense of c o m p l e t i o n  i s complemented by t h e c u l m i n a t i o n of t e x t u r a l  and l i n e a r p r o g r e s s i o n s ,  s p e c i f i c a l l y on t h e f i n a l  noted e a r l i e r ) .  One  f i n a l r e l a t i o n s h i p i s noteworthy.. I t concerns t h e  bassoon p a r t i n segments 11 and  13 and,  towards t h e PC D i n each case.  Segment no.  stops s h o r t on the upper n e i g h b o u r E^, the same PC's  specifically i t s inclination 11  ( t h e phrase d i v i d e r )  w h i l e no.  13 sounds e s s e n t i a l l y  but s u b s t i t u t e s t h e lower n e i g h b o u r C# f o r E^.  segments a l s o d i f f e r i n t h a t no. n o t e , " D, p r o v i d e d content,  of t h e segment (as  The  two  13 c o n t a i n s the u l t i m a t e " r e s o l u t i o n -  by the p i c c o l o .  I n t h i s s e n s e — o n e p u r e l y of  i r r e s p e c t i v e of t h e a c t u a l o r d e r of a r t i c u l a t i o n — s e g m e n t  might be viewed as " c l o s e d " r e l a t i v e t o no.  PC no.  13  11.  Summary Because of t h e d i s j u n c t d i s p o s i t i o n of the bassoon p a r t , r e g i s t r a l l i n e a r connections p i t c h content  were found to be of s i g n i f i c a n c e i n the o r g a n i z a t i o n of  i n t h i s piece.  through m o t i v i c consistency  Four r e g i s t e r s were e s t a b l i s h e d , e s s e n t i a l l y ( i . e . , t h e f o u r - n o t e m o t i v e B^-B-C-D^), i n  28  The s i g n i f i c a n c e of t h i s c o m p l e t i o n l i e s i n t h e f a c t t h a t the composed o r d e r i n g c l o s e l y resembles t h a t of t h e "normal form," and the D# i n i t i a t e s the second " s u b s e t " of the segment.  194 which f i v e D,  primary  inherent  progressions  i n the four-note  progressions  thus  motive  reiterating  actually but  B^3 t o C/P, occurs;  falling  B^  short  2  to D  suggesting  (including  were f o u n d ships  i n previous  and B ^  a  pieces  a r e E^-VE->, a s an  s  a  incomplete  n  occurring which,  4  primary  t o C//  2  but rather  again, tending  never towards,  of, D . 2  that  earlier  were  of c o l o r a t i o n s a l s o ) ,  segments, w i t h  were a l s o f o u n d  never  towards D  t o C//^ a n d u p t o D^;  to r e v e a l chromatic  between  E^4/g4^  t o w a r d s t h e PC i n the  progressions  t o D^;  motion  Segments o f p h r a s e s d e f i n e d content  witnessed  (the latter  4  A tendency  was r e v e a l e d  These primary  major-minor upper neighbour  major-minor upper neighbour implied);  itself,  a D-centricity  ( e . g . , N o s . 1, 4, 5, a n d 6 ) . incomplete  were e x p o s e d .  studied here  and p a t t e r n s  and n e a r - c h r o m a t i c  respect  for their  of unfolding  collections.  Relation-  to twelve-note aggregate  t o be o f s i g n i f i c a n c e  PC  completion,  i n the piece.  Harmonic D e t a i l s In  that  interaction  c o l o r a t i o n and d o u b l i n g  i n the piece,  they  also represent  harmonic u n i t s — i . e . ,  verticalities  Consonance-dissonance  quality  a  specific  of  discussion of their the various  doublings  Consonance-dissonance The consonant [o,l,2],  five  placement  dissonant  and [ o , l , 2 , 4 ] .  number o f members  specific  placement  i n s t a n c e s of  interval  content.  be examined  and c o n t e n t will  instrument  first,  to follow.  conclude  A  with study  the section.  of c o l o r a t i o n s  s i m u l t a n e i t i e s used  t o most  with  forms of  the only  of colorations w i l l  and t h e i r  quality  are the only  i n the piece  (explained  below) a r e  Semitone and whole-tone  i n each v e r t i c a l i t y  i n order [ 0 , 2 ] ,  content,  o f t h e most  [o,l],  [ 0 , 1 , 3 ] ,  as w e l l as t h e  are f a c t o r s i n the c l a s s i f i c a t i o n of  195 harmonic q u a l i t y . has a C-D  For example, [ 0 , 2 ] i s t h e most consonant (and t h e r e f o r e  f a c t o r of 1) because i t i s t h e o n l y v e r t i c a l i t y w i t h o u t a  semitone.  The most d i s s o n a n t harmony i s [ o , 1 , 2 , 4 ] ( w i t h a f a c t o r o f 5)  because i t has t h e g r e a t e s t number o f members and two semitones.  The  v e r t i c a l i t y [ o , l ] i s t h e second most consonant because i t i s t h e o n l y o t h e r set w i t h two elements; i t has a C-D [ 0 , 1 , 2 ] ,  f a c t o r of  t h e former i s more consonant  2 .  Between  ( w i t h a f a c t o r of  3 )  [o,l,3]|  and  as i t c o n t a i n s  o n l y one semitone compared t o t h e l a t t e r ' s two ( t h e r e f o r e h a v i n g a f a c t o r of 4 ) .  Example 76 i l l u s t r a t e s a l l  they d o u b l i n g s o r c o l o r a t i o n s . c o r r e s p o n d i n g C-D  i n s t a n c e s o f i n s t r u m e n t i n t e r a c t i o n be  The a f o r e m e n t i o n e d " s e t - t y p e s " w i t h t h e i r  f a c t o r s a r e i n d i c a t e d below t h e v a r i o u s i n s t a n c e s of  coloration. R e f e r r i n g t o Example 76, one p a r t i c u l a r o b s e r v a t i o n c o n c e r n i n g consonance-dissonance f l u c t u a t i o n i s noteworthy.  P h r a s e I of t h e 'a'-  s e c t i o n e x h i b i t s a s h i f t from r e l a t i v e consonance  (i.e., factors 3 ,  2)  to dissonance ( i . e . , f a c t o r 4 ) .  1, and  The t h r e e - n o t e s o n o r i t y i n measure 5,  i n f a c t , o c c u r s o n l y once and i s t h e most d i s s o n a n t found i n t h e 'a'section.  P h r a s e I I l e a n s towards t h e consonant s i d e w i t h harmonies of  f a c t o r s 1 and 2 .  The ' b ' - s e c t i o n r e v e a l s a s i m i l a r p a t t e r n : phrase I  p i c k s up where t h e ' a ' - s e c t i o n l e f t o f f — i . e . , w i t h r e l a t i v e  consonance—  and moves t o t h e most d i s s o n a n t v e r t i c a l i t y i n t h e p i e c e i n bar 14.  Phrase  I I d i s p l a y s s e t s o f f a c t o r s 1 and 2 not u n l i k e t h e second phrase of t h e 'a'section.  I n b o t h s e c t i o n s , t h e n , a consonance  dissonance  consonance p a t t e r n emerges, w i t h t h e peak o f d i s s o n a n c e o c c u r r i n g a t or near t h e end o f t h e f i r s t phrase o f each.  The r e t u r n t o r e l a t i v e l y  consonant s o n o r i t i e s i n t h e second phrase o f each s e c t i o n may resolutive.  I n a sense t h i s a s p e c t of "consequence"  be heard as  contradicts other  196  Example  76.  Consonance-dissonance  factors  of c o l o r a t i o n  verticalities.  197  'a'-section phrase I I  phrase I  ir  measure n o s . :  coloration pitches: bassoon pitches: set-types:  [0,1,3] [0,2][0,l] [0,1,2] 3  C-D f a c t o r s :  1 2  4  doublings:  [0,2]  [0,1]  [0,1]  1  2  2  two-threepart o c t . and u n i s • / t h r e e cons, notes  two-part unison/ three cons. notes  oct./ one note  three-part octaves/ two cons. notes  2  unis./ one note  three-part unison/ f o u r cons, notes  b -section phrase I I  phrase I  coloration pitches:  a—1 j  C-D f a c t o r s : doublings:  1  1  bassoon pitches: set-types:  ir  14  13  measure nos.:  m [0,1] 2 unis./ one note  ^  M  rHH  -/•—  15  1  *  n. ,  / w  •a 1  [0,1][0,1] [0,2] 2  two-part unis./ one n o t e  2  ft-  ^  s  [0,l][0,2]  [0,1,2,4]  1  u n i s . and oct./two cons, n o t e s  2  5 two-threepart o c t . / t h r e e cons, notes  1  [0,l] 2 two-part f o u r - p a r t unis./ unis./one two cons. n o t e notes  198 factors as  o f " o p e n n e s s " a t t h e end o f t h e ' a ' - s e c t i o n  registral  ascent  and " h e s i t a n t " - p i t c h d e p a r t u r e  reinforcing  the feeling  culmination  of instrumentation-density  well  o f " c l o s u r e " on t h e  as twelve-note aggregate  Specific  placement  Many c o l o r a t i o n s w o u l d punctuate  structural points  illustrated (e.g.,  earlier,  phrases  while  others  or fragments).  i . e . , the four-note  Curiously,  of the motive  later  motive,  The  E  placed;  progressions  some  defined  and  segments  coloration i n the piece, f o r  , illustrated  i s D^, the asserted  disjunct earlier. "arrivalIn this  colorations i n the f i r s t  i n the i n i t i a l  ascending  fourth-  29 earlier).  p i t c h of the f i r s t  p h r a s e I , i s marked  connection].  t h e ends o f f o r m a l  B -B-C-D  Li  to A 4 (as noted  final  linear  The r e m a i n i n g  structural pitches  L7  progression,  pitch  i n r e g i s t e r i i ( m e a s u r e 3, b a s s o o n ) .  i n t h e bassoon.  phrase harmonize  and l i n e a r  as  i s an " a n t i c i p a t i o n " o f t h e s t r u c t u r a l D3  sense the c o l o r a t i o n appearing  doubling-density,  p i t c h of the bassoon's opening  one o f t h e c o l o r a t i o n p i t c h e s  point-pitch"  i n b a r 15 [ e f f e c t e d b y t h e  articulate  The f i r s t  fragment,  to E5), while  t o be s t r a t e g i c a l l y  in registral  harmonizes t h e f i n a l  such  of colorations appear  instance,  factors  from  and ( u n i s o n )  completion  and content  (e.g.,  fragment  by a c o l o r a t i o n ( a l t h o u g h  i n phrase  II, like  t h e harmonic  that  of  quality i s  30 different).  The l a s t  two c o l o r a t i o n s  i n the 'a'-section  harmonize the  bA  29 It  i s the arrival  has  t h e C-D  Its  articulation  "disguised"  point  of this  factor 4 harmonization, i s highly accented  by t h e d i s s o n a n t  progression,  t h e most  A  dissonant  on t h e one hand,  i n b a r 5, w h i c h of t h e 'a'-section.  b u t somewhat  harmony on t h e o t h e r .  30 T h e s e two f r a g m e n t s , e a c h t e r m i n a t e d w i t h a c o l o r a t i o n , a r e t r a n s p o s i t i o n a l l y r e l a t e d as explained e a r l i e r . The p a r a l l e l i s m o f t h e two p h r a s e s i n t h e ' a ' - s e c t i o n , a l s o n o t e d e a r l i e r , i s h e i g h t e n e d b y this relationship.  199 re-established iv  and  the A  w h i l e each step, half  A  4  A^  ( m e a s u r e 7)  4  (measure  o f t h e s e two  i s harmonized  and  whole-step  The  of  the  motive  Notice  pitches  a lower  i s colored  by  from measure 5  4  to E ^ , 4  here  of the A^ 3,  F#4  4  (where  that, half-  i t s lower  are noteworthy  earlier.  the opening  just  mentioned, The  4  points  next  as  fourth,  A^  A^  two  4  to  E  4  F#  importance the  i n phrase  i n the  second 14  tone  i s , however,  4  verticalities  of bar  A is  i t s coloration  i . e . , G.  initiates  i i i , while the colored  Although  ascent,  of l e s s e r  f o r example,  of the bassoon's  13  the "counterbalancing" descending  with F .  13,  i n measure  illustrated  from  articulate  of bar  and  4  of the remaining v e r t i c a l i t i e s  coloration  register  i t u l t i m a t e l y moves.  here  initiate  i n the descending Two  the  B^  in register  pitches  A^  i n bar  'b'-section  structure.  of A^  differently  as  progression in  sound).  fourth-progression,  harmonized  to which  structural  pitches  concurs with that  the ascending  differently  colorations  these p a r t i c u l a r  harmonized  7)  of  I  linear  four-note  i s another  of  the  E^^. a r e worthy  i n measure  of mention:  14 p u n c t u a t e s  first,  t h e end  of  31 phrase  I w i t h t h e most  involves PC the  dissonant sonority  t h e D^/C#^ v e r t i c a l  D and,  more s p e c i f i c a l l y ,  d i s s o n a n t C// i n t e n s i f i e s  dyad the  of the piece.  i n measure pitch  the a r r i v a l  15.  The  The  second  centricity  of  have a l r e a d y been n o t e d . on D,  i t also  tends  to  the While  slightly  32 "blur"  the  latter.  The  four-part  unison doubling of  and  subsequent  31 T h i s p o i n t , as i n d i c a t e d e a r l i e r , i s analogous to t h e c l o s e of p h r a s e I i n t h e ' a ' - s e c t i o n w h e r e C-D f a c t o r 4 ( t h e m o s t d i s s o n a n t t o that p o i n t ) i s found. 32 I t i s i n t e r e s t i n g t o compare t h e d i s p o s i t i o n o f p i t c h e s i n t h i s f i n a l c o l o r a t i o n t o t h o s e o f t h e f i r s t one i n b a r .1. In the e a r l i e r instance the ( c o l o r a t i o n ) was n o t e d a s a n a n t i c i p a t i o n o f t h e b a s s o o n ' s s t r u c t u r a l two b a r s l a t e r . In the f i n a l c o l o r a t i o n , i s t h e m a i n n o t e a n d C//^ i s the c o l o r a t i o n p i t c h ; t h e two PC's h a v e e s s e n t i a l l y t r a d e d f u n c t i o n s .  200  s u s t a i n i n g of  i n the p i c c o l o , however, c o n f i r m i t s r o l e as a.point of 33  pitch closure. S p e c i f i c placement of o c t a v e and u n i s o n  doublings  Octave and u n i s o n d o u b l i n g s were d i s c u s s e d e a r l i e r i n the l i g h t of t h e i r c o n t r i b u t i o n to the f l u c t u a t i o n of t e x t u r a l - d e n s i t y . i n s t a n c e s of c o l o r a t i o n , however, t h e s e d o u b l i n g s may c e r t a i n cases as f a c t o r s of i n t e n s i f i c a t i o n . the 'a'-section.  The f i r s t  As i n many  a l s o be viewed i n  Three such p o i n t s e x i s t i n  i s i n measure 5 where t h e l a s t t h r e e n o t e s  t h e d i s j u n c t p o r t i o n of phrase I ( l e a d i n g i n t o the cadenza) a r e  of  doubled  34 in unison. phrase I I .  The  second i n s t a n c e accompanies the opening t h r e e n o t e s  of  These i n t u r n l e a d i n t o t h e f o u r t h and f i n a l n o t e of t h e  fragment w h i c h , as s t a t e d e a r l i e r , i s c o l o r e d by a semitone.  Perhaps t h e  most emphatic i n s t a n c e , however, i s t h a t which o c c u r s i n measure 7.  The  f o u r n o t e s c u l m i n a t i n g on the s t r u c t u r a l A  the  oboe and c l a r i n e t .  (This p a r t i c u l a r A  4  immediate g o a l of the i n i t i a l a s c e n d i n g  4  a r e doubled  i s s t r u c t u r a l as i t i s the fourth-progression, E^  and on a l a r g e r s c a l e , the t r i t o n e d i v i d e r of t h e  b4 E^  i n u n i s o n by  4  to  A^ , 4  octave-progression,  b to E*5.)  The u n i s o n d o u b l i n g ( f o u r - p a r t ) of  i n bar 15 i s the most  s t r a t e g i c d o u b l i n g i n the ' b ' - s e c t i o n ; as noted e a r l i e r , i t s r e a l s i g n i f i c a n c e l i e s i n i t s placement as a peak w i t h i n t h e p r o g r e s s i o n of (unison)33 d o u b l i n g - d e n s i t y . 9 The bassoon's f i n a l C# , however, may be heard as a s u b t l e "reminder " o f C// which accompanies i n bar 15. 5  The f i r s t n o t e o f the t h r e e i s t h e A g o a l o f the i n i t i a l ascending f o u r t h - p r o g r e s s i o n , a l s o c o l o r e d as noted e a r l i e r . And t h e f i n a l n o t e i s D3, the p r o l o n g e d a r r i v a l p o i n t of t h e f o u r - n o t e m o t i v e i n r e g i s t e r i i , a l s o d i s c u s s e d i n the p r e v i o u s s e c t i o n . 4  201 Summary I n d e a l i n g w i t h t h e harmonic s t r u c t u r e of t h i s p i e c e consonanced i s s o n a n c e f a c t o r s (based on semitone and whole-tone c o n t e n t , and c a r d i n a l i t y of the v a r i o u s v e r t i c a l i t i e s ) were e s t a b l i s h e d f o r t h e o f c o l o r a t i o n used t h r o u g h o u t .  the instances  Each s e c t i o n e x h i b i t e d p r o g r e s s i v e l y more  d i s s o n a n t s t r u c t u r e s towards the end  of i t s f i r s t p h r a s e , f o l l o w e d by more  consonant s o n o r i t i e s i n i t s second.  The most d i s s o n a n t s o n o r i t y of t h e  was  found i n the  ' b ' - s e c t i o n , t h e r e b y r e v e a l i n g one  harmonic d i r e c t i o n from the  'a' t o  piece  element of o v e r a l l  'b'-section.  I n s t a n c e s of c o l o r a t i o n were f r e q u e n t l y found t o h i g h l i g h t s t r u c t u r a l pitches i n r e g i s t r a l l i n e a r progressions  ( p a r t i c u l a r l y t h o s e i n t h e upper-  most r e g i s t e r ) , and o t h e r i m p o r t a n t j u n c t u r e s endings.  such as p h r a s e b e g i n n i n g s  and  Octave and u n i s o n d o u b l i n g s were a l s o found t o i n t e n s i f y s t r a t e g i c  p o i n t s i n the p i e c e , the  of bar 15 b e i n g the most s i g n i f i c a n t of such  points.  C o n n e c t i v e F a c t o r s Between the N i n t h and Tenth P i e c e s Four f a c t o r s p o i n t t o a p o s s i b l e r e l a t i o n s h i p between t h e n i n t h tenth pieces.  The  and  f i r s t of t h e s e concerns i n d i c a t i o n s i n t h e s c o r e a t  the  35 end of the n i n t h p i e c e .  Such i n d i c a t i o n s i n c l u d e "break o f f s u d d e n l y "  (as though a c o n t i n u a t i o n were f o r t h c o m i n g ) , an "expectant" q u a l i t y ) , senza diminuendo c l o s u r e ) , and  attacca  silenzio  assoluto  (suggesting  ( t h u s d e f e r r i n g a f e e l i n g of  ( d i r e c t i n g an immediate c o n t i n u a t i o n ) . 36  The  second f a c t o r i n v o l v e s t h e f i r s t t h r e e PC's  of p i e c e No.  9.  35 L i g e t i , Ten  Pieces,  p.  33.  36 The whole p i e c e , remember, c o n s i s t s of o n l y n i n e PC's unfolding.  i n an o r d e r e d  202 Specifically, and  D are  piece  the  opening  sustained  of  primary  importance  PC's  ( E ^ and  E  being  upper neighbour The  to  linear  s t r u c t u r e of  progression  the  f a c t o r of  ninth  piece  unfolding (this  i n the  i s comprised  essentially  register  involved). ascending  being  PC's  E^  of  the  A^  point  an  fourth-progression  s t r u c t u r e of  the  E tenth  major-minor  D).  appear two.  to As  unfolding.  ascending  be  and  stated As  the  particular  earlier,  i t turns  the  also the  i v of  one  related, this  progression  interestingly  in register  subsequent  incomplete  extreme upper range of are  and  entire ninth piece  a nine-note  i n the  linear  as  between t h e  o u t l i n e s an  and  i n the  t e n t h would  connection  reiterated  jointly  the main a r r i v a l  registral third  considered  and  being the  out,  from  to  this A^6  instruments e x t r e m i t i e s of  tenth  piece  the  (measures  37 3-5).  This  r e l a t i o n s h i p i s summarized  Example  Finally, No.  9  (discussed  completion  noted  77.  i n the  i n Example  77.  L i n e a r p r o g r e s s i o n r e l a t i o n s h i p between n i n t h and t e n t h p i e c e s .  light  of  the  pattern  i n Chapter II)  and  the  between  of  PC  unfolding  concept  of  twelve-note  certainvcontiguous  s e g m e n t s o f No.  in  10,  the  piece aggregate a  37 The i n t e n s i t y o f No. 9, r e s u l t i n g i n s t r u m e n t s , i s matched i n the t e n t h p i e c e i s at the top of the bassoon's range.  from the upper range of the as the p r o g r e s s i o n i n question  203 particularly As n o t e d  s t r o n g c o n n e c t i o n may  i n Example  78,  it  generates  at  t h e b e g i n n i n g o f No.  aggregate in  addition,  10.  absent  from  PC  line  important  the use  of  t h e two  i n No.  9 is  the p i e c e — c u r i o u s l y ,  This large-scale  p r o v i d e s an  i t anticipates  the tenth piece  d i s c e r n e d between  i f the descending  t h e t h r e e PC's  completion  be  instance of  bond  pieces. extended  those  twelve-note  b e t w e e n t h e two  inter-segment  found  completion  pieces; within  itself.  Example  78.  Twelve-note aggregate completion the n i n t h to the tenth piece.  from  Summary A number o f  factors  connection or r e l a t i o n s h i p the  score at  t h e end  a need  to continue  (e.g.,  E^-E-D a n d  an  association  c o n n e c t i o n was  o f No.  have been  between also  9 were s a i d  p r o g r e s s i o n from t h e two  No.  9.  to  and  pointing  pieces.  E^  7  imply a  t o A^)  And  lack  the f i r s t  an  o f PC  Notes  in  to  and  unfolding provide  important  aggregate  n i n e PC's  a  of c o m p l e t i o n  were f o u n d  finally,  revealed i n the twelve-note  to  tenth pieces.  while underlying details  the beginning of the tenth piece, in  above as  between t h e n i n t h  immediately, the  cited  completion  having  unfolded  at  204 Summary The  foregoing  analysis of the tenth  piece  has i n c l u d e d  independent  e x a m i n a t i o n s o f form d e l i n e a t i n g f a c t o r s , t e x t u r a l s t r u c t u r e , r h y t h m i c and metric  design,  have been linear  chapters  progressive  to  (albeit  tendencies  under  the l i s t  While  considerably  pieces  o f those  concepts  such as r e g i s t r a l  q u a l i t y were different  parameters  introduced i n  circumstances),  i n t e x t u r a l s p a c e a n d modes o f t e x t u r a l - d e n s i t y , proportions  to the a n a l y s i s of the tenth  n i n t h and t e n t h  A s s o c i a t i o n s between  and consonance-dissonance  w e l l a s impulse-number  specific  organization.  i n d i c a t e d where a p p l i c a b l e .  connections  previous  as  and p i t c h  of phrase piece.  were a l s o d i s c u s s e d ,  previously  defined.  segments a r e a s p e c t s  Relationships thereby  adding  between t h e another  subgroup  CHAPTER  V  CONCLUSION In Ligeti's  seeking Ten  individual and  in  pitch.  for  the  10  dealing  with  a more g l o b a l illustrated, structure  the  two  them  I I I and  in this  such as  a l l musical allows  before  form,  basis  IV).  texture,  for  In  the  presented  ( o r any)  an  II focussed  the  the  on  complete  treated  entities—i.e.,  musical  to n i n t h of  pieces pieces  musical  separately, looking  at  i n t e r a c t i o n between parameters  a more c o m p r e h e n s i v e v i e w of  their  certain  various  second  the  them  understanding  d e t a i l e d analyses  were a l s o  music  d e t a i l s of  these p a r t i c u l a r studies,  etc.)  rhythm  parameters, viewing  attempting  from  Gyorgy  texture,  this  specific  Chapter  i n excerpts a  as  s t u d y has  more s p e c i f i c ) w i t h i n  but  them  in on  were  overall  musical  case. was  suggested  the  middle  i n Chapter sixties,  i n a medium c o n s i d e r a b l y The  of  language of  e x p e r i e n c e of  interaction.  provided  thus p r o v i d i n g  foregoing  assertained  others  pieces  the  analysis  l e v e l — i n s t a n c e s of  quintet  works.  language  be  their  form,  works s i n c e  procedures other  of  This  i n each  The Ligeti's  to  musical  auditory  purposes of  exemplified  (e.g.,  the  the  parameters  consideration  ( i n Chapters  parameters  of m u s i c a l  (some g e n e r a l ,  quintet.  of  Wind Quintet,  While  structures  p a r a m e t e r s and  1 and  the  intricacies  principles  in  for  examinations  isolation  the  understanding  simultaneous  individual of  Pieces  m e t e r , and  involves  an  fact period  i s that  I to  be  illustrating  more "compact"  Ligeti's  i s accurately  own  many  than  that  i n the  of  compositional of most  c h a r a c t e r i z a t i o n of  represented  205  representative  his  quintet.  of  his  musical He  speaks  206 of  h i s music  one  sixties)  as having  hand, but n o t t r e a t i n g a l l t w e l v e n o t e s  tonal and to  (since the middle  " e q u a l l y " on t h e o t h e r . *  While  n o t be i n o p e r a t i o n  especially  10, r e v e a l e d  a strong  durational  Linear  centricity  inclination  directedness,  appeared  o f , that  particular  towards  of the 'a'-section, maintained  and  voice  lateral to  crossing.  a n d C^, Ligeti  also  that  The  the f i n a l comments  doubling,  such an  In the f i r s t  t o i n v o l v e b o t h D a n d C, t h e s e  pieces  being  5,  6,  t h e PC D, r e f e r r e d  instrumental  PC.  extremities  sixties)  i n the quintet,  e x p o s u r e a r e some o f t h e f a c t o r s s u g g e s t i n g  and r e i n f o r c e m e n t  ness  on t h e  a s s u c h , may  as a " D - c e n t r i c i t y . "  to,  tonal centres"  centres,  "no  and  inclination  piece,  PC  the pitch  through outer-voice  'b'-section also revealed  prolongation  linear  directed-  pitches of the piece. ( i n connection  with  h i s works from  c e r t a i n "arrangements" of i n t e r v a l s  "determine  the middle  the course  of  2 the music  and t h e development  numerous  instances  vertical  c o m p l e x e s w e r e shown  to a  the asserted trend  towards  Also, v e r t i c a l segmentation were n o t e d  was  criteria increased  as being  piece,  piece;  discerned. were  of the four  restricted  disposition),  t o be r e g i s t r a l l y  as to the f l u c t u a t i o n  shown  Ibid.  2  liner  notes  where  in overall while  dispersed.  i n harmonic  for  Melodien.  the climax,  (according  after  which  ( S e e E x a m p l e s 44 a n d 45.) t o be a f a c t o r o f  sections, the f i r s t  formal  and  third  t e x t u r a l space (and,  the second  and  fourth  And f i n a l l y ,  piece  q u a l i t y through a  system of consonance-dissonance c l a s s i f i c a t i o n ; ''"Ligeti,  furnishes  f o r example,  q u a l i t y ) toward  c o n s o n a n c e was  relatively  The q u i n t e t  t o grow p r o g r e s s i v e l y more d i s s o n a n t  of harmonic  intervallic  w e r e shown  defined  as i n the t h i r d  arrangements of i n t e r v a l s  i n the f i f t h  hence, v e r t i c a l sections  of this  of the form."  verticalities  No.  1  derived  with  specific  207 C-D  ( c o n s o n a n c e - d i s s o n a n c e ) f a c t o r s w e r e shown t o p l a y  maintenance of p i t c h e x t r e m i t i e s The  harmonic  i n the 'a'-section.  structure of the f i r s t  piece's  a vital  r o l e i nthe  ( S e e E x a m p l e 64.)  'a'-section also  illustrates  3  Ligeti's  concept  merge s l o w l y  of "harmonic-musical  i n t o one another r a t h e r  Ligeti  further defines  micropolyphonic  textures  flow," than  h i s music  change  from  i n which l i n e s  i n which  interval  combinations  abruptly.  the middle  sixties  as u t i l i z i n g  a r e more d i r e c t e d and r e t a i n a 4  certain Again,  degree of independence w i t h i n pieces  1 a n d 3 come t o m i n d .  techniques—unison within  first  piece,  outer-voice  noted  earlier,  an o v e r a l l  texture  of instrumental  works t y p i f i e d  music  of the middle  rapid  successions  the  quintet, The  style  illustration, (as  i n Chapter  and  IV)—aims 3  Ibid. Ibid.  then,  voice-crossing  structures underlying  o f Apparitions ideas—was  i n t h e s i x t h and e i g h t h c a n be v i e w e d  of e a r l i e r  linear  Regarding the  ( i n addition to representing  the style  i n the middle  said to create  events, t h e web-  o u t l i n e d above a r e r e p r e s e n t a t i v e of  of disparate musical  quintet,  expose r e f i n e m e n t s  4  sixties),  suggested  polyphony.  and l a t e r a l  linear  b y Atmospheres  particularly  compositional  two  network."  parts.  W h i l e many o f t h e t e c h n i q u e s earlier  o f complex  prolongations  emerge a s i n d e p e n d e n t  interweaving  In the l a t t e r ,  t r a n s f e r and p i t c h i n t e r c h a n g e — w e r e  continuities  like  the "overriding contrapuntal  also  pieces.  i n addition,  and d e v i c e s .  I I ) , and i n more e x t e n d e d a p p l i c a t i o n s  of L i g e t i ' s  i t may b e s e e n t o The e x p l i c a t i o n ,  and d e t a i l e d a n a l y s i s o f t h e s e c o n c e p t s ^ - i n  t o e s t a b l i s h a fundamental working  Aventures—i.e.,  seen t o s u r f a c e i n  as representative  sixties;  techniques  and  Ligeti':s  relative  isolation  (as i n Chapters I I I  knowledge o f L i g e t i ' s  208  musical  l a n g u a g e i n t h e Ten Pieces  for  Wind  Quintet.  WORKS  CITED  Books and P e r i o d i c a l s Berry, Wallace. Structural Functions P r e n t i c e - H a l l , I n c . , 1976. Clifton,  Thomas.  Cone, E d w a r d . Ligeti,  Music  as Heard.  " A n a l y s i s Today."  in Music.  Englewood  New H a v e n : Y a l e The Musical  Cliffs:  U n i v e r s i t y P r e s s , 1983.  Quarterly  (April  1960):  172-188.  Gyorgy. Q u o t e d i n Ove N o r d w a l l , l i n e r n o t e s f o r Musica ricercata ( 1 9 5 1 - 5 3 ) , o n Duo Pohjola. Grammofonfirma B I S 18, r e c o r d e d i n W. Germany, 1 9 7 4 . . Head  Nordwall,  L i n e r notes 12, 1 9 7 6 .  Ove.  "Ligeti,  f o r Ligeti:  Gyorgy."  Melodien  for Orchestra.  The New Grove  Musicians. E d i t e d by S t a n l e y S a d i e . L i m i t e d , 1 9 8 0 . V o l . 10, p p . 853-856.'  Dictionary  Decca  Headline,  of Music  London:' M a c m i l l a n  and  Publishers  Music Ligeti,  Gyorgy.  Apparitions.  Atmospheres. Aventures. Double  Wien:. " U n i v e r s a l , , E d i t i o n , F r a n k f u r t : C.'F.  Concerto.  Requiem. Ten  Wien: U n i v e r s a l E d i t i o n ,  Pieces  Volumina.  cl963 .  Peters Music  M a i n z : B. S c h o t t ' s  cl964 .  Publishers,  Soehne,  M a i n z : B. S c h o t t ' s  F r a n k f u r t : C. F . P e t e r s M u s i c  209  cl964.  el974.  F r a n k f u r t : C. F . P e t e r s M u s i c P u b l i s h e r s , for Wind Quintet.  .  cl966  Soehne,ccl969.  Publishers, cl967.  SELECTED BIBLIOGRAPHY Beyer, W. H. " C o m p o s i t i o n a l P r i n c i p l e s i n Three Works o f Gyorgy D.M.A. D i s s e r t a t i o n , U n i v e r s i t y o f Washington, 1975. G r i f f i t h s , Paul.  Modern Music:  George B r a z i l l e r ,  The avant  garde since  1945.  Ligeti."  New Y o r k :  I n c . , 1981.  L i c h t e n f e l d , Monika. "Gyorgy L i g e t i oder das Ende der s e r i e l l e n Melos 39 (1972): 74-80. .  L i n e r n o t e s f o r Ligeti:  Zehn Stucke  fur  Musik."  Blaserquintett.  Wergo 60059, 1.97.0. "Zehn'Stucke f u r B l a s e r q u i n t e t t von Gyorgy L i g e t i . " (1972): 326-333. L i g e t i , Gyorgy. N o r d w a l l , Ove.  "Metamorphosis o f M u s i c a l Form." "Two Hungarians Abroad."  P l a i s t o w , Stephen. 379-81.  Die Reihe  Tempo 88 ( S p r i n g  " L i g e t i ' s Recent M u s i c . "  Musical  Melos 39  1 (1965): 5-19.  1969):  22-25.  Times 115 (May 1974):  R o l l i n , R. L. "The G e n e s i s o f t h e Technique o f Canonic Sound Mass i n L i g e t i ' s Lontano."  Indiana  Theory Review 2 (1979):  22-33.  The P r o c e s s o f T e x t u r a l Change and the O r g a n i z a t i o n o f P i t c h i n L i g e t i ' s Lontano." D.M.A. D i s s e r t a t i o n , C o r n e l l U n i v e r s i t y , 1973. Salmenhaara, E. Das musikalische Material und seine Behandlung in den Werken "Apparitions," "Atmospheres," "Aventures," und "Requiem"  von Gyorgy Ligeti.  Regensburg:  Gustav Bosse V e r l a g ,  1969.  Yannay, Y. "Towards an Open-Ended Method o f A n a l y s i s o f Contemporary M u s i c : A Study o f S e l e c t e d Works by Edgard V a r e s e and Gyorgy L i g e t i . " D.M.A. D i s s e r t a t i o n , U n i v e r s i t y o f I l l i n o i s , 1974.  210  

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