Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

comparative study of selected Twentieth-century piano works involving the elements of chance and indeterminacy. Silvester , Trudy Helen 1971

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

Item Metadata

Download

Media
831-UBC_1971_A6_5 S54.pdf [ 3.4MB ]
Metadata
JSON: 831-1.0101738.json
JSON-LD: 831-1.0101738-ld.json
RDF/XML (Pretty): 831-1.0101738-rdf.xml
RDF/JSON: 831-1.0101738-rdf.json
Turtle: 831-1.0101738-turtle.txt
N-Triples: 831-1.0101738-rdf-ntriples.txt
Original Record: 831-1.0101738-source.json
Full Text
831-1.0101738-fulltext.txt
Citation
831-1.0101738.ris

Full Text

A COMPARATIVE STUDY OF SELECTED TWENTIETH-CENTURY PIANO WORKS INVOLVING THE ELEMENTS OF CHANCE AND INDETERMINACY by TRUDY HELEN SILVESTER B. Mus., U n i v e r s i t y o f B r i t i s h Columbia, 1968  A THESIS SUBMITTED. IN. PARTIAL. FULFILMENT OF THE  REQUIREMENTS. FOR THE DEGREE OF MASTER. OF MUSIC  i n the Department of MUSIC  We accept t h i s t h e s i s as conforming  t o the  r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1971  In p r e s e n t i n g t h i s  thesis  in p a r t i a l  f u l f i l m e n t o f the requirements f o r  an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, the L i b r a r y s h a l l I  make i t f r e e l y a v a i l a b l e  f u r t h e r agree t h a t p e r m i s s i o n  for  I agree  r e f e r e n c e and  f o r e x t e n s i v e copying o f t h i s  that  study. thesis  f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s of  representatives.  this  thesis  It  i s understood that copying o r p u b l i c a t i o n  f o r f i n a n c i a l gain shall  written permission.  Department of  l YU^u^C_, r  The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada  Date  (Xf^J-  7  ,  1^7/  Columbia  not be allowed without my  A study o f s e l e c t e d chance and indeterminate was made with a t w o - f o l d purpose: stage between the composition  piano  pieces  (1) t o provide an i n t e r m e d i a t e  and performance o f the s e l e c t e d  works and (2) t o i l l u s t r a t e the d i v e r s e ways s p o n t a n e i t y may be invoked.  The i n v e s t i g a t i o n centered on t h r e e p o i n t s : (1) t h e  problems t h e performer  might encounter i n examining the p i e c e s ,  (2) i m p l i c a t i o n s o f t h e i n s t r u c t i o n s and (3) p o s s i b l e r e a l i z a t i o n s of the score. While each score examined showed a s l i g h t l y approach t o chance o r indeterminacy,  t h e p i e c e s w i t h i n the two  c a t e g o r i e s were seen to e x h i b i t common f e a t u r e s . were made i n t h r e e broad scores,  areas:  different  Generalizations  (1) the i n s t r u c t i o n s i n the  (2) the n o t a t i o n and (3) p o s s i b l e s o l u t i o n s .  The i n s t r u c t i o n s i n the indeterminate be r e l a t i v e l y s t r a i g h t f o r w a r d ; t h e performer  scores were found t o i s made aware of h i s  c h o i c e s o r a l t e r n a t i v e s and manner o f performance i s d i s c u s s e d . I n s t r u c t i o n s i n chance works a r e l e s s e x p l i c i t ; the performer i s not d i r e c t e d t o any one s o l u t i o n . t i o n i s given and t h e performer  Some e x p l a n a t i o n o f the nota-  i s l e d t o d i s c o v e r how e x t e n s i v e  h i s freedoms a r e . Indeterminate notation.  works on the whole are.found  t o use t r a d i t i o n a l  The n o t a t i o n may be a l t e r e d i n some way, but r e t a i n s a  resemblance t o i t s t r a d i t i o n a l source.  Chance n o t a t i o n i s very  d i v e r s e , but t h r e e g e n e r a l c a t e g o r i e s e x i s t :  (1) works u s i n g  t r a d i t i o n a l notation, traditional  (2) works u s i n g t r a d i t i o n a l and non-  (graphic) n o t a t i o n and (.3) works u s i n g only  graphic  notation. The p o s s i b l e s o l u t i o n s of indeterminate works are concerned w i t h e i t h e r the j u x t a p o s i t i o n o r the m e t r i c r e l a t i o n s h i p o f material.  The degree t o which the c h o i c e s are guided v a r i e s i n  the works d i s c u s s e d .  P o s s i b l e s o l u t i o n s o f the chance works  i n v o l v e i n t e r p r e t a t i o n o f n o t a t i o n and v a r i o u s ideas i n the i n s t r u c t i o n s .  The performer  presented  must respond i n an i n d i v i d u a l  way, drawing on h i s own i d e a s . In g e n e r a l , analyses of the works i l l u s t r a t e d some f e a t u r e s t h a t might be expected  i n other chance and indeterminate works.  INTRODUCTION  1  CHAPTER I. II.  DEFINITION OF THE TERMS  2  THE MUSICAL PHILOSOPHY: the ideas u n d e r l y i n g  chance  and indeterminacy  7  Assumptions o f Chance  8  Assumptions o f Indeterminacy III.  THE CHANCE PIECES  15  November 1952 (Earle Brown) . . . . . .  16  Octet  18  1953  '61 (Cornelius Cardew) ( E a r l e Brown)  Cassiopeia  19  (George Cacioppo)  Music f o r Piano #7  (Toshi I c h i y a n a g i )  Music f o r Piano #2  (Toshi I c h i y a n a g i )  21 . . . . . . .  25 28  December 1952 ( E a r l e Brown) . . . . . . . . . . . .  31  Four Systems  35  Timepiece IV.  . 12  (Earle Brown)  (Udo Kasemets)  . 36  THE INDETERMINATE PIECES Two Books o f Study  41  ( C o r n e l i u s Cardew)  42  Pour C l a v i e r (Sylvano B u s s o t t i )  44  Caracteres  46  (Henri Pousseur)  Nr. 7 K l a v i e r s t u c k XI ( K a r l h e i n z Stockhausen)  . . .  48  Duo f o r P i a n i s t s I I ( C h r i s t i a n W o l f f )  49  Pianopiece  53  I I (George Cacioppo) . . .  V.  March 1953 (Earle Brown)  57  Dance  58  (Earle Brown)  V a r i a t i o n s I (John Cage)  58  V a r i a t i o n s I I (John Cage) . . .  61  CONCLUSIONS  BIBLIOGRAPHY  64 •  71  The main purpose o f t h i s study i s a d i d a c t i c one, p r o v i d i n g an i n t e r m e d i a t e stage between the composition  and the performance  of s e l e c t e d chance and indeterminate piano p i e c e s . of the works centers on three p o i n t s : might encounter  Investigation  (1) problems the performer  i n examining the p i e c e s , (2) i m p l i c a t i o n s o f the  i n s t r u c t i o n s and (3) p o s s i b l e r e a l i z a t i o n s o f the s c o r e .  While  c e r t a i n a m b i g u i t i e s i n the works may be c l a r i f i e d and t h i s may be u s e f u l t o the performer,  the attempt has been n o t so much t o  make the scores and t h e i r i n s t r u c t i o n s e n t i r e l y e x p l i c i t as to h e l p the performer  o r i e n t h i s t h i n k i n g i n terms o f the m u s i c a l  p h i l o s o p h y u n d e r l y i n g the works and to s t i m u l a t e h i s i n t e r e s t and i m a g i n a t i o n along the l i n e s o f p o s s i b l e s o l u t i o n s . A secondary  purpose i s the i l l u s t r a t i o n o f the d i v e r s e  means used to invoke spontaneous c h o i c e .  Each score examined  e x h i b i t s a d i f f e r e n t approach t o chance and indeterminacy, and f o r t h i s reason  two chapters have been devoted  of the scores i n d i v i d u a l l y .  to a d i s c u s s i o n  W i t h i n the chapter on indeterminate  works, p i e c e s are grouped a c c o r d i n g t o the type o f indeterminacy present.  In the f o l l o w i n g chapter the chance works are categor-  ized according to n o t a t i o n a l s i m i l a r i t i e s .  In a f u r t h e r chapter  the r e s u l t s o f the analyses w i l l be d i s c u s s e d and g e n e r a l i z a t i o n s concerning the p i e c e s made.  Preceding the a n a l y s e s , a background  to the study i s p r o v i d e d by a d i s c u s s i o n o f the terminology and the musical p h i l o s o p h y  a s s o c i a t e d with the works.  DEFINITION OF THE TERMS In  t h i s chapter e x i s t i n g d e f i n i t i o n s and a p p l i c a t i o n s o f  the terms chance,  indeterminacy and a l e a t o r i c i s m w i l l be  p r e s e n t e d , n o t i n g the p r e s e n t c o n f u s i o n i n t h e i r usage.  Following  t h i s , the terms w i l l be d e f i n e d as they are t o be used i n t h i s study. The term chance by g e n e r a l d e f i n i t i o n i m p l i e s t h a t an event "happens u n p r e d i c t a b l y , without any d i s c e r n i b l e human i n t e n t i o n or  d i r e c t i o n and i n d i s s o c i a t i o n from any observable p a t t e r n ,  causal r e l a t i o n , natural necessity,  A chance event  happens "unaccountably, without p r e m e d i t a t i o n , pre-arrangement or  any s i g n o f m o t i v a t i o n and without observable c a u s a l r e l a t i o n 2 to attendant circumstances." Indeterminacy suggests a vagueness  or  l a c k o f p r e c o n c e i v e d end r e s u l t .  A l e a t o r y means "depending on 3  an u n c e r t a i n event o r contingency."  By d e f i n i t i o n , chance and  indeterminacy are c l o s e i n meaning; u n l i k e chance, does not n e c e s s a r i l y connote  indeterminacy  contingency, the undefined aspect  may not be s o l v e d i n an unexpected  manner.  Confusion has a r i s e n i n the a p p l i c a t i o n o f these terms t o Webster's T h i r d New I n t e r n a t i o n a l D i c t i o n a r y , Mass., G. & C. Merriam Co., 1969, p. 373. 2  I b i d . , p. 373. I b i d . , p. 51.  Springfield,  music. the  Heinz-Klaus Metzger, n o t i n g t h i s c o n f u s i o n , c l a i m s t h a t  m u s i c a l a p p l i c a t i o n of the term a l e a t o r i c e v o l v e s from two 4  i n d i v i d u a l s , Werner Meyer-Eppler and P i e r r e Boulez.  The  first  volume o f Die Reihe c o n t a i n s an a r t i c l e by Meyer-Eppler i n which he g i v e s the f o l l o w i n g d e f i n i t i o n : aleatoric  "A process i s s a i d t o be  (from the L a t i n A l e a = d i c e ) i f i t s course i s determined 5  i n g e n e r a l but depends on chance i n d e t a i l . " of  In the f i r s t  the Darmstadter B e i t r a g e a t r a n s l a t i o n o f the a r t i c l e  by Boulez appears.  issue  "Alea"  In the a r t i c l e Boulez d e a l s w i t h chance as a  c o m p o s i t i o n a l t e c h n i q u e , r e f e r r i n g a t one p o i n t to " a l e a t o r i c happenings."  No r e f e r e n c e i s made to a l e a t o r i c form.  Elsewhere,  Boulez w r i t e s t h a t the "notion of shunting does not belong t o t h a t o f pure chance, but t h a t o f non-determinate c h o i c e , and t h i s 7 d i f f e r e n c e i s fundamental  . . . ."  Metzger i n f e r s from these  sources t h a t chance and a l e a t o r i c i s m are synonymous, both r e f e r r i n g t o works i n which the d e t a i l i s u n s p e c i f i e d , b e i n g f i n a l i z e d i n the performance.  I f the d e t a i l i s determined but  t h e r e i s c h o i c e i n i t s o r d e r i n g , the work may  be c o n s i d e r e d  indeterminate. Heinz-Klaus Metzger, "Abortive Concepts i n the Theory and C r i t i c i s m of Music," Die Reihe, 5 ( 1 9 6 1 ) , p. 2 6 . 5 Werner Meyer-Eppler, " S t a t i s t i c and P s y c h o l o g i c Problems of Sound," Die Reihe, 1 ( 1 9 5 8 ) , p. 5 5 . P i e r r e Boulez, " A l e a , " Darmstadter B e i t r a g e , 1 p.  (1958),  53. 7  Boulez, "Sonate, Que Me Veux-tu?" Music, 1 (Spring 1 9 6 3 ) , p. 3 5 .  Perspectives of  New  A l e a t o r i c music i s d e f i n e d i n the Harvard D i c t i o n a r y "music i n which the composer i n t r o d u c e s elements  as  of chance or  u n p r e d i c t a b i l i t y w i t h regard t o . e i t h e r the composition or i t s performance."  T h i s g e n e r a l statement  and a l e a t o r i c i s m .  The c o n t r i b u t o r s noted the terms  i n d e t e r m i n a t e and a l e a t o r i c c r e a t e d s i n c e 1945  a l i g n s the terms chance chance,  "have been a p p l i e d t o many works  by composers who  d i f f e r w i d e l y as to concepts,  methods and r i g o r w i t h which they employ procedures of random 9 selection.'.  1  The a r t i c l e g i v e s the r e a d e r no b a s i s f o r d i s -  t i n g u i s h i n g indeterminacy from-chance and a l e a t o r i c ; the three terms are not c l e a r l y d e f i n e d . Howard R i l e y s t a t e s t h a t a l e a t o r i c procedures are which are dependent on u n c e r t a i n contingencies."'''^  "those  Riley  uses  a l e a t o r i c i n a g e n e r i c sense, t o embrace compositions i n which d e t a i l s are s p e c i f i e d but which l a c k formal d e f i n i t i o n , as w e l l as compositions i n which the performer must supply the  details,  being g i v e n a g e n e r a l course to f o l l o w . . In o t h e r words, R i l e y departs from the meaning of a l e a t o r i c s e t up by Metzger and Meyer E p p l e r by implying, t h a t i n d e t e r m i n a t e and a l e a t o r i c are synonymou A c c o r d i n g to Roger Reynolds,  "indeterminacy and chance are  J.R. White and A. B o u c o u r e c h l i e v , " A l e a t o r i c Music," Harvard D i c t i o n a r y , Harvard U n i v e r s i t y P r e s s , Cambridge, Mass., 1 9 6 9 , p. 2 6 . 9 Ibxd., pp. 2 6 - 2 7 . "^°Howard R i l e y , " A l e a t o r i c Procedures i n Contemporary Piano Music," M u s i c a l Times, 107 ( A p r i l 1 9 6 6 ) , p. 3 1 1 .  p r o g r e s s i v e degrees o f ' a tendency t o leave d e t a i l e d . . . .  unspecified  I f . . . a composer wants an indetermined s i t u a t i o n ,  there can be no p r e f e r r e d s o l u t i o n s —  and, u l t i m a t e l y , i n the  case o f chance, v i r t u a l l y no ' r u l e s ' . " " ^  He f u r t h e r submits t h a t  i n indeterminacy " c a t e g o r i e s o f events" a r e determined, t h e i r o r d e r i n g b e i n g the undetermined a s p e c t .  In chance, any event  w i t h i n c e r t a i n l i m i t s may o c c u r . John Cage w r i t e s o f works conceived by chance and works which are "indeterminate of performance."  operations When the  d e t a i l s o f p a r t s a r e . e s t a b l i s h e d but t h e form o r sequence o f the whole i s not, Cage would c l a s s i f y the work as "indeterminate o f performance," t h a t i s , f a l l i n g i n t h e c a t e g o r y o f indeterminacy. The sources above have been used as the b a s i s f o r d e r i v i n g the f o l l o w i n g c a t e g o r i e s t o be used i n t h i s study: a.  works i n which the d e t a i l s o f s e c t i o n s o r groups are determined, the o r d e r i n g o f these p a r t s b e i n g undetermined; and works i n which s p e c i f i e d sounds a r e i n a g i v e n sequence, but t h e i r m e t r i c r e l a t i o n s h i p t o one another i s undetermined.  b.  works i n which the score e x i s t s as a stimulus t o the performer, who must supply t h e d e t a i l s .  A form may be  g i v e n t o some degree, o r t h e form may evolve d u r i n g performance.  Roger Reynolds, "Indeterminacy: Some C o n s i d e r a t i o n s , " P e r s p e c t i v e s o f New Music, 4 ( F a l l - W i n t e r 1965), p. 136.  The former category w i l l be r e f e r r e d t o as i n d e t e r m i n a t e , the 12 l a t t e r as chance or a l e a t o r i c . s p o n t a n e i t y i s assumed. the  In both c a t e g o r i e s a degree o f  The terms w i l l be f u r t h e r c l a r i f i e d i n  d i s c u s s i o n o f the works.  .Having d e f i n e d chance and a l e a t o r i c as synonymous m u s i c a l terms, the term chance r a t h e r than a l e a t o r i c w i l l be used hereafter.  THE  MUSICAL PHILOSOPHY:  u n d e r l y i n g chance and The  chance and  indeterminate  the  ideas  indeterminacy  works are u n i f i e d i n concept  by the d e n i a l of p r e v a i l i n g b e l i e f s or assumptions. t o n a l i t y had  Historically  assumed an o r g a n i z a t i o n s t r u c t u r e d on a key  system.  P r e d i c t a b l e r e l a t i o n s h i p s were a p a r t o f t o n a l i t y ; so was icity.  Not  o n l y were there r o o t p r o g r e s s i o n s  a p i e c e , but a p i e c e was i s , the whole was  an i n t e g r a t i o n . o r c a u s a l i n t e r r e l a t i o n o f p a r t s .  p r e d i c t a b i l i t y was  p i t c h and  non-periodic  structure,  no l o n g e r a f e a t u r e , although coherence or  still  a concern.  Timbre came to be  demands upon the performer.  of a k i n d arose;  Con-  exactness of n o t a t i o n exerted  almost  By c r e a t i n g a s i t u a t i o n  where the performer c o u l d not respond a c c u r a t e l y ,  it  emphasized;  o f t e n other parameters were h i g h l y o r g a n i z e d .  s i d e r a b l e s p e c i f i c a t i o n and impossible  r e l a t e d throughout  d i v i d e d i n t o r e l a t e d components; t h a t  With the advent o f a t o n a l i t y and  c o n t i n u i t y was  period-  indeterminacy  the more numerous the demands, the more probable  i s t h a t unplanned a c t i o n s w i l l occur.  This sort of indeter-  minacy, however, i s not d e s i r e d . The extent  —  philosophy focused  circumventing chance and  of chance —  on new  and  assumptions, s e a r c h i n g  the t r a d i t i o n a l ones.  indeterminacy  indeterminacy  to a l e s s e r  f o r ways of  Since the assumptions o f  do not e n t i r e l y c o i n c i d e , the  c a t e g o r i e s w i l l be d i s c u s s e d  separately.  two  Composers a d v o c a t i n g the chance p h i l o s o p h y f e e l  that  p u r p o s e f u l s t r u c t u r i n g or o r g a n i z a t i o n prevents, the p e r c e p t i o n of sounds as s e n s a t i o n .  H a b i t s of l i s t e n i n g , bound by t h e o r i e s about  the o r g a n i z a t i o n o f sound, are a h i n d r a n c e .  Sounds as d i s c r e t e  e n t i t i e s and t h e i r s i t u a t i o n i n time are major concerns o f the new  assumptions.  The p o s s i b i l i t y of i s o l a t i n g any p a r t i c u l a r  event as the cause of another event i s denied.  Cage b e l i e v e s  t h a t "there are an i n c a l c u l a b l e i n f i n i t y o f causes and  effects  . . . . i n f a c t , each and every t h i n g i n a l l o f time and space 13 i s r e l a t e d t o each and every t h i n g i n a l l of time and space." There are no separable causes and e f f e c t s .  E a r l e Brown r e f e r s to  "the impenetrable i n f i n i t e c o m p l e x i t i e s and c o n n e c t i o n s of a l l II  14  things-  Thus, events should be allowed to happen without  d i r e c t i o n , t h e i r c o n n e c t i o n being too . i n t r i c a t e t o s i n g l e out a one-to-one r e l a t i o n s h i p .  J u x t a p o s i t i o n o f sounds no longer  indicates a direct relationship.  . I t i s sounds as s e n s a t i o n ,  complete i n themselves and independent of s t r u c t u r i n g , t h a t i s important, not t h e i r r e l a t i o n s h i p or t h e i r placement i n a progression.  Cage s t a t e s , "a sound does not view i t s e l f  as  thought, as ought, as needing another sound f o r i t s e l u c i d a John Cage, S i l e n c e , Middletown, Conn., Wesleyan U n i v e r s i t y P r e s s , 1939, p.- 47. ^ E a r l e Brown, "Form," Darmstadter B e i t r a g e , 10 4  p. 66.  (1966),  tion." own  15  Each sound should be u n i q u e l y p e r c e i v e d , heard  . for i t s  s i m p l i c i t y o f , f o r example, being g i v e n A and  from t h a t  sake. The  e x p e c t i n g c e r t a i n a l t e r n a t i v e s i n B, does not e x i s t . b i l i t y of the performer  e n v i s i o n i n g the r e s u l t s of  The p o s s i -  alternative  courses of a c t i o n and of making a r a t i o n a l c h o i c e on t h i s b a s i s i s no longer a c c e p t a b l e .  The composer may  g e n e r a l response to what he has w r i t t e n .  no longer p r e d i c t a P r e d i c t i o n depends to  a c o n s i d e r a b l e degree upon the use o f an e s t a b l i s h e d "grammar," a common ground, a "language" which when understood it  c a r r i e s with  c e r t a i n meanings or i m p l i c a t i o n s ; i n chance music t h i s  language i s absent. The m u s i c a l experience  becomes a " t o t a l i t y of  possibilities"  where "no knowing a c t i o n i s commensurate, s i n c e the c h a r a c t e r of 16 the knowledge acted u p o n . p r o h i b i t s  a l l but some e v e n t u a l i t i e s . "  I f t h e r e i s s e l e c t i v i t y , the s i n g l i n g out of some p o s s i b i l i t i e s , t h e r e i s ' n o longer a t o t a l f i e l d of p o s s i b l e r e s u l t s .  The meaning  of " t o t a l f i e l d " v a r i e s from score to score; the l e s s t h e r e i s s p e c i f i e d i n a score, the more m a n i f o l d the r e s u l t s are to be.  W i t h i n the l i m i t a t i o n s imposed by a " t o t a l f i e l d "  experience  must be an experimental  one, with no  John Cage, "Experimental 65. "^Ibid. ,  66.  the  preconceptions  about the m u s i c a l r e s u l t ; any outcome w i l l be acceptable  p.  likely  Music," Score, 12  since .  (June 1955),  there are no e s t a b l i s h e d r e s u l t s . can be no e r r o r s or approximations.  With t h i s assumption, t h e r e Mistakes suggest a  measuring up to e x p e c t a t i o n s ; f o r a mistake to occur t h e r e must be some knowledge beforehand o f what should o c c u r , . a r e s t r i c t i o n of what may  occur.  In chance music communication  becomes involvement.  The  composer no l o n g e r ..determines e x a c t l y what w i l l be heard but r a t h e r i n s t i g a t e s . a p r o c e s s , making the l i s t e n e r i n v o l v e h i s senses i n response t o a.unique.experience. The performer responds to a score which, e x i s t s to e l i c i t t h i s response.  E a r l e Brown s t r e s s e s the i d e a o f a  momentary, spontaneous.response q u a l i t y ; the environment  primarily  t o a s c o r e , an  immediate  and circumstances are an i n f l u e n c e on  17 t h i s response.  A work i s not r e - c r e a t e d complete  in details  and form but c r e a t e d from g i v e n i d e a s , t h e . s c o r e s e r v i n g as a p l a c e t o s t a r t , an o c c a s i o n f o r i n c i d e n t , with.the degree type of chance v a r y i n g w i d e l y from score to s c o r e .  The  and  performer  i s g i v e n . c l u e s or suggested d i r e c t i o n s . b u t much i s l e f t  free,  a l l o w i n g the performer to c o n t r i b u t e r e s p o n s i v e l y .  end  The  r e s u l t goes beyond the s u g g e s t e d . d i r e c t i v e s , beyond what 'the composer had  imagined.  A p u r p o s e f u l . a m b i g u i t y impels the performer t o become i n v o l v e d , t o respond.to the i d e a s presented-by. the composer and The reader i s r e f e r r e d t o Brown's a r t i c l e Darmstadter Beitrage,.10 (1966), pp. 57-69.  "Form,"  directions.  The  should be one  s o l u t i o n a r r i v e d at by the i n d i v i d u a l  performer  out of many p o s s i b l e responses to the m a t e r i a l s at  one moment i n time. Some works c o n t a i n a h i g h degree of ambiguity;  no  specific  d i r e c t i o n s are i n d i c a t e d , the c l u e s b e i n g vague t o the p o i n t of i m p l y i n g almost anything.  However, a c e r t a i n amount of pre-  t h i n k i n g i s needed to grasp the freedoms and  limitations  given  i n the s c o r e , and to p o s s i b l y narrow down the a l t e r n a t i v e s from the t o t a l f i e l d .  The  d i f f i c u l t y , of performing  score i s conceded; the performer impressions  o f a s c o r e , keeping  use d u r i n g a performance. out or planned  may  directly  decide to respond to  t o the p o i n t of d e t e r m i n a t i o n ;  d u r i n g the performance.  C o r n e l i u s Cardew f e e l s t h a t the "only c r i t e r i o n  a mistake,  thought  room must be  left  I t i s the  a l l o w i n g f o r and a c c e p t i n g of c o n t i n g e n c i e s t h a t i s  the p l a y e r e x p e c t i n g  first  i n mind a l t e r n a t i v e s f o r p o s s i b l e  The work, however, must not be  f o r s p o n t a n e i t y to operate  was  from the  important.  f o r a sound i s :  (intending) to make i t ?  I f not, i t was  and makes a d i f f e r e n t s o r t o f c l a i m to beauty.  mistake i t comes under c r i t e r i a  As  a  f o r a c t i o n : mistakes are the 18  only t r u l y spontaneous a c t i o n s we  are capable  With the l a c k of determination o r d e r i n g , form as i t i s t r a d i t i o n a l l y  of."  of sounds and  their  c o n s i d e r e d does not  apply  C o r n e l i u s Cardew, " N o t a t i o n , I n t e r p r e t a t i o n , E t c . , " Tempo, 58 (Summer 1961), p. 26.  to chance.  Form, has t r a d i t i o n a l l y been a r e l a t i o n a l concept.  Beginning-middle-end, antecedent-consequent elements o f t h i s form; i t was about by what preceded i t .  and p e r i o d i c i t y were  i m p l i c i t t h a t . t h e end was  brought  A c c o r d i n g t o Brown, form i s "not a 19  r e c e p t a c l e but a f x e l d of a c t i v i t y . "  Brown c l a i m s t h a t i t i s  i m p o s s i b l e f o r music t o be f o r m l e s s , f o r i f . i t were, we would be unable t o p e r c e i v e i t s existence.. u s u a l l y are d i r e c t e d toward  A c c u s a t i o n s o f formlessness  sounds having an unexpected  form.  Brown notes t h a t the."form which the work takes each time i s a form o f c o l l e c t i v e consciousness as i t moves through a l a b y r i n t h 20 of environmental i n f l u e n c e s . " not  Thus, the form o f a p i e c e i s  a c o n f i g u r a t i o n determined by composer or performer; i t i s  a p r o c e s s i n a c o n s t a n t s t a t e o f f l u x , a l t e r i n g i n each  new  situation. The Assumptions-of Tradition.is it  i s i n chance.  Indeterminacy  not as completely denied i n indeterminacy as By d e f i n i t i o n , indeterminacy admits the  e x i s t e n c e of d e f i n i t i v e , s t r u c t u r e d s e c t i o n s . w i t h i n t h e s e - s e c t i o n s may  The m a t e r i a l  be s u b j e c t to t r a d i t i o n a l  The work i s not t o t a l l y determined, however.  assumptions. Choices must  e x i s t f o r the.performer, perhaps of the o r d e r i n g o f the s e c t i o n s  E a r l e Brown, op. c i t . , p. I b i d . , pp. 60-61.  68.  or of the placement of sounds w i t h i n a m e t r i c a l l y unordered sequence.  Choices may  be guided  j u x t a p o s i t i o n or c o n t i n u i t y may  to a c e r t a i n extent, or  any  be allowed, but s p o n t a n e i t y i n  making the c h o i c e s i s u s u a l l y assumed. P r e d i c t i o n o f the r e a l i z a t i o n f o r any.one performance of a score i s not p o s s i b l e .  The p o s s i b i l i t i e s are o f t e n more c l e a r l y  e s t a b l i s h e d i n an indeterminate work than i n a chance work. A l s o , the performer,  as a r e s u l t of h i s p r e p a r a t i o n of the work,  might be aware t h a t c e r t a i n a l t e r n a t i v e s may the performance.  or may  not occur i n  P r e d i c t i o n might occur i n t h i s sense  the r e a l i z a t i o n w i l l be the r e s u l t of The composer may  although  spontaneity.  not p r e d i c t the a l t e r n a t i v e s the  performer  w i l l choose, but depending upon the degree of c h o i c e g i v e n , may  p r e d i c t p o s s i b l e , general s o l u t i o n s .  given are l i m i t e d , the composer may choices.  He may  The  he  In p i e c e s where c h o i c e s  be aware of a l l p o s s i b l e  form the p i e c e to a l l o w o n l y c e r t a i n c o n t i n u i t i e s .  " t o t a l i t y of p o s s i b i l i t i e s " w i l l be r e s t r i c t e d  c e r t a i n . p o s s i b i l i t i e s , even though these may  to  be numerous.  Within  21 these boundaries  s e l e c t i v i t y i s denied.  should not predetermine any  I d e a l l y the  aspect of the c o n t i n u i t y , "the 22  step of d e f i n i t i v e arrangement" should be  See p.  performer  9.  E a r l e Brown, op. c i t . , p.  60.  " l e f t out."  final  • As i n  chance works, the response to a score w i l l be i n f l u e n c e d by the circumstances o f the performance.  The form a work assumes i n  each performance w i l l be the r e s u l t o f the performer's spontaneous, momentary s e l e c t i o n s from the " t o t a l f i e l d " of possibilities. The assumptions of chance and indeterminacy w i l l  receive  f u r t h e r e x p l i c a t i o n i n the f o l l o w i n g d i s c u s s i o n o f the works.  I t i s suggested because o f the r e f e r e n c e s made to the scores and t h e i r i n s t r u c t i o n s t h a t the r e a d e r o f the f o l l o w i n g analyses c o n s u l t the works.  23  THE Although formed with any  CHANCE PIECES  c e r t a i n of the chance works d i s c u s s e d may  be  per-  i n s t r u m e n t a t i o n , i n c l u d i n g two or more p i a n o s ,  the problems c o n s i d e r e d are mainly  those t h a t would be encountered  i f the works were performed by one  pianist.  In t h i s chapter the p i e c e s are grouped a c c o r d i n g to notational s i m i l a r i t i e s .  There i s d i v e r s i t y i n . n o t a t i o n , but  t h r e e c l a s s i f i c a t i o n s may  be made:  (1) works i n which only  t r a d i t i o n a l symbols are used, p i t c h e s being m e t r i c a l l y on a s t a f f ;  notated  (2) works i n which t r a d i t i o n a l and n o n - t r a d i t i o n a l  symbols are used, one  or two  other than t r a d i t i o n a l . m e a n s ;  parameters being represented (3) works i n which  "graphic"  n o t a t i o n i s employed, -signs of v a r y i n g shapes having meaning, the performer  by  ambiguous  a s s i g n i n g meanings to l i n e s , squares or  shapes. Since each, p i e c e d i f f e r s i n i t s means of o c c a s i o n i n g chance, the p i e c e s w i l l be d i s c u s s e d i n d i v i d u a l l y .  Basically,  each p i e c e has been examined to d i s c o v e r what i s s p e c i f i e d  and  by i m p l i c a t i o n , what i s not s p e c i f i e d , with p o s s i b l e " i n t e r p r e t a t i o n s " of the score being given and the degree chance being noted.  G e n e r a l i z a t i o n s concerning  the chance p i e c e s have been  i n c l u d e d in. the f i n a l chapter of the  study.  The  " d e f i n e d space" of November 1952 c o n s i s t s of f i f t y -  l i n e s c o n t a i n i n g notes w i t h m e t r i c v a l u e s and dynamic s i g n s . C l e f s are.not s i g n i f i e d ; they are " f l o a t i n g . "  While a note has  a p o s i t i o n on one o f the l i n e s or spaces and i s preceded by an a c c i d e n t a l , i t s p i t c h i s not e s t a b l i s h e d u n t i l a c l e f i s a s s i g n e d . While a t f i r s t glance the p i t c h e s appear determined, i n f a c t , c l e f may for  any  be m e n t a l l y a s s i g n e d t o any note being e f f e c t i v e only  t h a t note; a c l e f i s not a s s i g n e d c o n s i s t e n t l y t o any  line.  I f d u r i n g . a performance each note i s . used once and the curved connecting l i n e  (  p i t c h e s are p o s s i b l e .  ) signifies a tie,  pitch.  different  The composer does not s p e c i f y , however,  t h a t each note i s t o be used only once. whether,  thirty-four  The q u e s t i o n then a r i s e s  i n . r e t u r n i n g t o a note, the note must m a i n t a i n the same T h e o r e t i c a l l y , one extreme p o s s i b i l i t y o f c l e f  assignment  c o u l d r e s u l t , i n a l l the notes being the same p i t c h . There are many p o s s i b l e i n t e r p r e t a t i o n s of the d e f i n e d space and f l o a t i n g c l e f s , however. d i v i s i o n o f the f i f t y  make any  l i n e s , expanding o r c o n t r a c t i n g the d i s t a n c e  between them.or t h e i r l e n g t h . the  The performer may  He might a l t e r the space between  l i n e s depending upon h i s i n t e r p r e t a t i o n o f the c l e f s . The l a y o u t o f the page does, not n e c e s s a r i l y imply an  o r d e r i n g o f the p i t c h e s .  The piece, may  be "performed i n any  d i r e c t i o n . " . No tempo i s s p e c i f i e d f o r any p a r t o f the p i e c e . The suggested tempo i s "as f a s t as p o s s i b l e t o as slow as possible, inclusive."  The statement may  imply t h a t tempo v a r i a -  t i o n s e x i s t , the p r o p o r t i o n s of v a r i a n c e being a t the discretion.  The performer  a s s i g n to "as f a s t as  ...  performer's  must then decide what meanings to ." and  "as slow, as  . . . ."  The meaning  may  be v a r i a b l e a c c o r d i n g to the d i f f i c u l t i e s the performer  for  h i m s e l f , or v a r i a b l e a c c o r d i n g t o the context, the " s t y l e " or  concept  o f the p i e c e .  while m a i n t a i n i n g w i t h i n a widely  The meaning may  "accuracy."  "as f a s t as p o s s i b l e "  The notes are given d u r a t i o n s , but  f l u c t u a t i n g tempo i t i s debatable  would have .any a c t u a l meaning. for  be  sets  whether they  O n l y . i f the tempo remained  constant  several, p i t c h e s would t h e i r m e t r i c . v a l u e be p e r c e p t i b l e . N e i t h e r the manner nor the exact placement of a t t a c k s i s  given.  An a t t a c k may  time d e f i n e d by the  occur at any p o i n t d u r i n g the l e n g t h of  "performance."  Since i t i s p o s s i b l e t h a t  two  or more symbols w i l l be i d e n t i c a l i n p i t c h , dynamics and d u r a t i o n , and c o u l d occur  simultaneously,  taken care of with.one a t t a c k . might occur simultaneously;  two  or more symbols might be  In an extreme case a l l p i t c h e s  the performance would c o n s i s t of  one  attack. Since the a t t a c k of any p i t c h may  occur at any p o i n t i n  the performance and w i t h i n any o r d e r , combination,.range  and  tempo, a l l t h a t has been determined i s the o c c a s i o n f o r a performance.  I t i s presumed the composer wishes o n l y to  s t i m u l a t e a response to the s c o r e . u n l e s s the performer The  performer  No mistakes are p o s s i b l e  has e s t a b l i s h e d c r i t e r i a  needs to understand  f o r the performance.  the i n s t r u c t i o n s accompanying  the score to be aware of h i s freedom, and he might conceive of p o s s i b l e r e a l i z a t i o n s , but the more spontaneous the performance of the s c o r e , t h e . t r u e r i t . w o u l d seem to be to Brown's i n t e n t .  C o r n e l i u s Cardew: Octet In Octet  '61,  sixty different  comprise the s c o r e . the performer  may  '61 "events" or composite symbols  They are numbered, suggesting t h a t although  begin and.end anywhere, once the performance  b e g i n s , the symbols are to be i n t e r p r e t e d i n sequence.  Most of  the symbols c o n t a i n a s i n g l e s t a f f i n c o r p o r a t i n g notes and/or dynamic s i g n s and numbers as w e l l as v a r i o u s o t h e r s i g n s . p a r t of any performer  symbol, however, may  be i g n o r e d .  For example, a  c o u l d heed dynamic i n d i c a t i o n s of an event but  them.to a p i t c h o t h e r than the suggested  Any  one.  apply  Black notes i n a  symbol, when used, must be p l a y e d i n the notated r e g i s t e r ; white notes are f r e e of t h i s r e s t r i c t i o n . the "event" be  and the t o t a l performance are f r e e .  " f r e e l y " c o p i e d by hand.  choose any notes may  Since the performer  The  score  may  i n the  f o r an event, an exact r e p r o d u c t i o n . o f the  be c o n s i d e r e d The  Durations of notated p i t c h e s , may end score  unnecessary.  score e x i s t s as a s t i m u l a t i o n to b r i n g ideas i n t o  existence.  I t may  b e . i n t e r p r e t e d by f o l l o w i n g what appears to  be obvious;  i t may  be used only as a s t a r t i n g p o i n t f o r a more  spontaneous i n t e r p r e t a t i o n .  The p i t c h e s or v a r i o u s s i g n s having  t r a d i t i o n a l c o n n o t a t i o n s might suggest former,  and the performance may  some sound to the per-  evolve from t h a t p o i n t on.  To  f u r t h e r spur on the performer,  Cardew has w r i t t e n out i n the  "notes" accompanying the score some p o s s i b l e r e a l i z a t i o n s . Cardew a l s o recommends the performer providing a "bloc of m a t e r i a l . " versions, of a s i g n , spontaneously  work out the s i g n s  thus  He may i n c l u d e a l t e r n a t i v e choosing.one d u r i n g performance  or he may a l t e r o r add t o w r i t t e n - o u t m a t e r i a l a t the l a s t moment.  Some pre-composed material.might, ensure.a  continuity. not necessary  An i d e a may be conceived t o leave i t u n r e f i n e d .  p r e t e r w i l l , draw may.be w e l l thought  reasonable  spontaneously,  but i t i s  Ideas from which the i n t e r through.  One p o s s i b l e "formal" suggestion i s g i v e n .  The performer  may i n c l u d e a s i g n which may be used as "punctuation." d i v i d e the p i e c e i n t o s e c t i o n s .  I f Octet  I t would  '61 were being performed  by an ensemble, one p l a y e r might be assigned t o p l a y i n g o n l y one sign. There are many p o s s i b i l i t i e s f o r v a r i a t i o n o f an event i n the O c t e t , even when u s i n g the g r a p h i c suggestions; t h i n g c o u l d happen.  almost any-  To r e a l i z e t h a t nothing g i v e n i s necessary  and t h a t any notes, may.be f r e e l y added opens the s i t u a t i o n completely.  In essence,  any i n t e r p r e t a t i o n would meet the  requirements  o f the s c o r e .  E a r l e Brown: 1953 In 1953 there i s a gradual narrowing down, o f p o s s i b i l i t i e s by a s e r i e s o f c h o i c e s .  The f i r s t c h o i c e c o n s i s t s o f a s s i g n i n g  e i t h e r a bass o r t r e b l e c l e f t o each s t a f f of the four t w o - l i n e  systems.  Once chosen, the c l e f presumably does not change d u r i n g  a performance of t h a t l i n e .  Each.notated  event, t h e r e f o r e , has  two p o s s i b l e p i t c h e s v i a one p o s i t i o n of the s c o r e ; p i t c h becomes p r e c i s e once the c l e f i s . d e t e r m i n e d . up, double  Since e i t h e r s i d e may  s e t s of a c c i d e n t a l s and a t t a c k s , which may  confusing at f i r s t  s i g h t , are g i v e n .  be  appear  The dynamic s i g n s are  w r i t t e n i n such a f ashion . as.to be l e g i b l e e i t h e r s i d e up: or £lF  9  dp  .  D u r a t i o n of p i t c h e s i s i n d i c a t e d by the l e n g t h of the  "bars"  denoting p i t c h e s . D e c i s i o n s concerning time are made i n three stages. the t o t a l l e n g t h of the p i e c e must be chosen. are a v a i l a b l e .  The composer suggests  from twenty seconds to two.minutes.  Two  basic choices  the d u r a t i o n may The performer  may  time l e n g t h , not n e c e s s a r i l y one between these l i m i t s . choosing the t o t a l t i m e . l e n g t h the performer  First,  be anywhere choose In  might keep i n mind  t h a t h i s second stage o f . d e t e r m i n a t i o n w i l l be to decide the i n seconds.of  each t w o - l i n e system.  any  time  Here three c h o i c e s e x i s t :  "times p r e - s e t by the composer, times obtained from the composer" 24 or times d e r i v e d . s p o n t a n e o u s l y . performer  W i t h i n t h i s framework the  p r e s c r i b e s , d u r a t i o n s f o r the i n d i v i d u a l notes, con-  s i d e r i n g t h e i r g r a p h i c l e n g t h i n r e l a t i o n . t o the l e n g t h s o f the systems and to each o t h e r .  No notated r e s t s appear.  The  gaps  between "bars" presumably i n d i c a t e time between events, t h a t i s , Brown i s . u n s p e c i f i c concerning the meaning of "times p r e s e t by the composer" and "times o b t a i n e d from the composer." T h i s i s j u s t one more p u z z l e f o r the performer.  "rests" or s i l e n c e s .  In t h i s case the performer must a s s i g n a  r e l a t i v e value t o the spaces. In making d e c i s i o n s concerning d u r a t i o n , many c o n s i d e r a t i o n s arise.  F o r example, a.choice made i n the f i r s t category w i l l t o  some e x t e n t l i m i t the c h o i c e p o s s i b l e i n the second Durations chosen,  category.  the "tempo" w i l l i n p a r t determine  c i t y o r complexity o f the p i e c e .  the s i m p l i -  The f a s t e r the tempo, the more  p e r c e p t u a l l y complicated the o v e r l a p p i n g o f sounds and time r e l a t i o n s become. V a r i a b l e elements i n order o f settlement a r e page and c l e f d i s p o s i t i o n , and time.  The performer  begins with an o u t l i n e f o r  a performance and by steps s u p p l i e s the d e t a i l s , a l l o w i n g f o r s p o n t a n e i t y i f d e s i r e d d u r i n g the performance  situation.  George C a c i o p p o : . C a s s i o p e i a On the one-page score there a r e f o u r networks w i t h an e l l i p s e p a r t i a l l y superimposed on two o f the networks and " i s l a n d s " i n t e r s p e r s e d i n o r around a l l . networks. and i s l a n d symbols are c o n s i d e r e d f a n t a s y forms.  The e l l i p s e The networks  c o n s i s t o f "paths" c o n n e c t i n g p i t c h e s which are r e p r e s e n t e d by black, and white noteheads.  F o r the most, p a r t t h e p i t c h e s a r e  s p e c i f i c a l l y d e s i g n a t e d ; a few a r e not.  The s p a t i a l d i s t a n c e  between the s p e c i f i e d and the u n s p e c i f i e d p i t c h e s may be used as a gauge f o r determining the u n s p e c i f i e d p i t c h e s . notehead.is pitch.  The s i z e of the  an i n d i c a t i o n of the r e l a t i v e dynamic l e v e l o f the  Two ways o f choosing time v a l u e s are suggested.  The  l i n e a r space between the pitches.may suggest a time v a l u e , o r the v a l u e s may e v o l v e spontaneously, w i t h no s e t c r i t e r i o n , d u r i n g the performance. The performance may b e g i n i n any one o f . t h e f o u r and may.or may not i n c l u d e f a n t a s y elements. networks -- o r as l i t t l e  as a p a r t o f one —  networks  From one t o four may be used.  While  the performance may i n c l u d e f a n t a s y forms, a t l e a s t p a r t o f one network must be played as w e l l . notehead t o notehead.moving  The performer proceeds from  i n any d i r e c t i o n .  When paths i n t e r -  s e c t between noteheads the performer may change d i r e c t i o n .  Not  a l l notes on a path must n e c e s s a r i l y be played b e f o r e branching o f f or reversing d i r e c t i o n .  The performer may choose t o f o l l o w  a c e r t a i n p a t t e r n , forming a " c l o s e d c i r c u i t . "  To form a c i r c u i t  the performer would have t o make use o f i n t e r s e c t i o n s and "superimposed" paths.  The c i r c u i t may be repeated any number of  times and may be a l t e r e d a t w i l l .  To " e x i t " from a c i r c u i t  e i t h e r an i n t e r s e c t i o n o r " o r b i t a l jump" t o any o t h e r p a r t o f the p i e c e i s made.  The p i e c e may end. anywhere, spontaneously o r  at the end o f a chosen t i m e - l e n g t h . While elements are e i t h e r determined.or suggested i n t h e graphic s c o r e , there i s c o n s i d e r a b l e room f o r s p o n t a n e i t y .  The  performer might be aware o f c e r t a i n a s p e c t s such as. the g e n e r a l p i t c h l a y o u t , dynamics, harmonics, f a n t a s y elements, a time v a l u e system and how t o get from p i t c h t o p i t c h o r network t o network; however, innumerable sound combinations e x i s t . .  The performer  must become r e s p o n s i b l y i n v o l v e d i n d e v e l o p i n g the m a t e r i a l  into  a performance.  In d e a l i n g with t h e networks the performer's  c h o i c e s c e n t e r on o r d e r i n g m a t e r i a l , choosing r o u t e s and possiblyforming. p a t t e r n s o r " c o n f i g u r a t i o n s . '  The forming o f f i g u r e s ,  1  which .may be repeated, or permutated. suggests c h o i c e i s o p e r a t i n g w i t h some t r a d i t i o n a l i m p l i c a t i o n s . suggests a r e c o g n i z a b l e s t r u c t u r e . essence t h a t an "elementary  Recurrence o f p a t t e r n s The composer i s proposing i n  form" may be s e t up; t h e p i e c e i s  not j u s t a s e r i e s o f random sounds,  complete  i n themselves.  The  performer,.however,. may choose not t o repeat m a t e r i a l , not t o thus.form . " f i g u r e s . " The performer must be f a m i l i a r with the m a t e r i a l o f t h e piece.  In o r d e r t o r e a d i l y l o c a t e a p i t c h he must become  accustomed t o t h i n k i n g o f p i t c h e s and t h e keyboard.in terms o f r e g i s t e r s r a t h e r than notes on a s t a f f .  I t would h e l p t o n o t i c e  the -general s t r u c t u r i n g o f octave r e g i s t e r s i n the. s c o r e . r e g i s t e r s are not mixed i n a random.fashion  The  w i t h i n the networks  but a r e "layered".; octave seven i s h i g h e r than s i x , s i x h i g h e r than f i v e , and so on down the page.  The performer might  then  g a i n some knowledge, of the p o s s i b i l i t i e s , perhaps d e c i d i n g what w i l l be p l a y e d spontaneously and what w i l l be c o n s i d e r e d or planned. Whatever d e c i s i o n s , g e n e r a l o r s p e c i f i c , are made concerning, treatment o f t h e networks,  the area w i t h i n the semi-  enclosed d o t t e d l i n e s need not be governed  by them.  may be c o n s i d e r e d anew, even played, by a d i f f e r e n t from t h a t used f o r the r e s t o f the performance.  T h i s area instrument  Most s u b j e c t t o s p o n t a n e i t y are the f a n t a s y forms. performer  The  r e a c t s t o a v i s u a l s t i m u l a t i o n , t r a n s l a t i n g the  r e a c t i o n s i n t o a performance.  A r e a c t i o n may o r may not l e a d t o  an a u r a l . e x p e r i e n c e ; the r e s u l t may be an a c t i o n , some v i s u a l event o r t h e a t r i c a l e f f e c t , not n e c e s s a r i l y producing a sound. The r e a c t i o n may produce a sound event but from a sound source other than the piano.  There a r e no r e s t r i c t i o n s on.what the  performer may d e r i v e from the f a n t a s y forms. merely  The e l l i p s e may  serve .as a "cover"; any l i n e s going i n t o i t may be  imagined  t o pass behind i t ,  emerging i n t o a new network.  Two o f  the networks may be j o i n e d i n t h i s manner. Although  some d e t e r m i n a t i o n s are made by Cacioppo, the  c o n s i d e r a b l e freedom t h a t e x i s t s i s a t times o f the indeterminate category, a t o t h e r times chance. c o n f i g u r a t i o n , permutation meanings.  Use of terms such as network,  and i n t e r s e c t i o n suggest d e f i n e d  P i t c h i s mostly determined,  dynamics a r e g i v e n i n a  g e n e r a l way, suggestions concerning.time these elements,  Ordering of  although s u b j e c t t o r a t h e r f r e e r u l e s o f p l a y , are  open t o s p o n t a n e i t y . pre-thought,  are made.  The i n s t r u c t i o n s a r e s u g g e s t i v e o f p o s s i b l e  p l a n n i n g , an awareness o f p o s s i b i l i t i e s , the  o r d e r i n g o f the m a t e r i a l s being i n d e t e r m i n a t e . on the o t h e r hand, are t o t a l l y undetermined. or sound i s p o s s i b l e .  The f a n t a s y  forms,  Any meaning, a c t i o n  D e t a i l s need.not.be p r e - e s t a b l i s h e d but  may evolve completely spontaneously,  any r e s u l t being a c c e p t a b l e .  The g r e a t e r u n p r e d i c t a b i l i t y r e s u l t i n g .from t h e l a c k of d e t e r mination p l a c e s the f a n t a s y elements i n the chance c a t e g o r y .  The  p i e c e must i n c l u d e a t l e a s t p a r t i a l networks, the aspect, but may  indeterminate  a l s o i n v o l v e f a n t a s y forms, or the i n c l u s i o n of  chance.  T o s h i I c h i y a n a g i : Music f o r Piano  #7  The n o t a t i o n of Music f o r Piano  #7  i s entirely  graphic.  P a t t e r n s i n the c e n t r e of the score, c o n t a i n very g e n e r a l  indica-  tions : 0  s h o r t sound, non-keyboard, but  O  long sound,.non-keyboard, but  •  s h o r t sound, non-piano  piano piano  Q . long sound, non-piano "t^  arpeggios  Other symbols on e i t h e r . s i d e of the c e n t r e p a t t e r n r e p r e s e n t a type of sound: 0  white and b l a c k keyboard used,  tones  chosen i n random o r d e r 0  o n l y white keyboard used  £  b l a c k keyboard only  C e r t a i n t r a d i t i o n a l a s s o c i a t i o n s may usage of b l a c k and white symbols.  be made from the composer's  A white shape i n d i c a t e s a  longer d u r a t i o n as a "white note" t r a d i t i o n a l l y r e c e i v e s more time than, a "black note ." !  A l s o , .the b l a c k and white c e n t r e  p a t t e r n s i l l u s t r a t e the b l a c k and white keys. l i n e s a l s o found  Thin h o r i z o n t a l  on e i t h e r s i d e of the p a t t e r n s i n d i c a t e an  approximate range.  L i n e s to the r i g h t of the p a t t e r n  designate  h i g h e r sounds, from the upper keyboard; l i n e s t o the l e f t nate lower sounds.  desig-  The n o t a t i o n has a f a m i l i a r c o n n o t a t i o n ,  s u g g e s t i v e . o f the keyboard  arrangement.  Since t h e i n d i c a t i o n s given.by the n o t a t i o n are g e n e r a l , d e c i s i o n s w i l l have to.be made a t some p o i n t .  The performer w i l l  have t o g i v e the h o r i z o n t a l range l i n e s a more s p e c i f i c meaning. An approximate breakdown i n t o areas covered by c e r t a i n mightbe  made.  lines  The placement o f the p a t t e r n s down the c e n t r e o f  the score might suggest a t r a d i t i o n a l d i v i s i o n . p a t t e r n might d i v i d e the keyboard i n " h a l f . "  That i s , the  When.the p a t t e r n  shows a mixture o f b l a c k and white keyboard, d e c i s i o n s w i l l have to be made c o n c e r n i n g how much o f each and in.what o r d e r the black and white keys w i l l be p l a y e d .  The performer c o u l d thus  set l i m i t s , on v a r i o u s aspects o f the m a t e r i a l and p r e s c r i b e s p o n t a n e i t y w i t h i n . t h e s e . l i m i t s , so t h a t a symbol r e p r e s e n t s the same g e n e r a l i d e a .  consistently  On the o t h e r hand, the meaning  of a symbol could.change from c o n t e x t t o c o n t e x t . The b a s i c elements of ..Music f o r . Piano. #7 are. not .determined. While t h e r e may be r e l a t i v e meanings, as one sound i s "higher" or "longer" than another, t h e r e i s ambiguity as t o t h e i r exact meaning.  For i n s t a n c e , a l o n g e r l i n e may, but does not  n e c e s s a r i l y i n d i c a t e a g r e a t e r d e n s i t y o f sound.  A performer  could.choose one o r two notes from a s h o r t e r l i n e but s i m i l a r l y c o u l d choose one o r two notes from a. l o n g e r l i n e .  The exact  p i t c h and even ..the number o f p i t c h e s t o be chosen i s not specified.  I t i s determined, however, t h a t when two o r more  notes from a l i n e are chosen they-must be played as a chord or c l u s t e r . . A l s o . u n s p e c i f i e d are a t t a c k s , dynamics and p e d a l l i n g ; o v e r l a p p i n g o f sounds i s f r e e .  The only i n d i c a t i o n f o r some  sounds i s t h a t they are not t o be played on the keyboard, or i n some c a s e s , not on the piano.  In these i n s t a n c e s any sounds may  be chosen; a wide range and v a r i e t y o f sounds a r e p o s s i b l e .  It  i s n o t . i n d i c a t e d t h a t non-piano sounds need be l i m i t e d t o e s t a b l i s h e d musical instruments. engaged;  The i m a g i n a t i o n may be f r e e l y  d e c i s i o n s might be a r b i t r a r y o r q u i t e  spontaneous.  The. n i n e pages are.numbered,. perhaps s u g g e s t i n g they be played i n o r d e r .  Each page may be read e i t h e r side, up, o r both  ways, and the.pages may be arranged s o . t h a t they o v e r l a p , the performer p l a y i n g only the p a r t o f the page showing. the arrangement  Choices i n  o f the pages i n . t h e above ways i s another freedom.  Since a l l pages are r e q u i r e d t o take the same time t h e r e w i l l be d i v e r s i t y o f a c t i v i t y among pages.  There a r e c o n s i d e r a b l y  fewer events on some pages than on o t h e r s .  No two pages a r e  e x a c t l y a l i k e i n the type o f c o n t e n t .  Some pages c o n t a i n o n l y  sounds produced a t the keyboard, some .only harmonics. pages c o n t a i n mixtures o f keyboard, non-keyboard  Other  and non-piano  sounds. . Only a g e n e r a l s t r u c t u r e has been d e l i n e a t e d i n t h i s p i e c e . An. imprecise area o f the keyboard.or q u a l i t y o f sound i s d e s i g nated, but the treatment o f the nine pages, t h e i r placement and t h e i r . p o s i t i o n i n g w i l l produce d i f f e r i n g o v e r a l l  structures.  There are c h o i c e s t o be made i n .the-handling o f a l l elements  comprising t h e . s t r u c t u r e .  L i t t l e has been determined  by the  composer. With so few suggestions g i v e n , i t would be hard t o say t h a t any c h o i c e made, p r o v i d i n g i t followed.the g e n e r a l was wrong.  requirements,  How f i x e d the d e t a i l s a r e b e f o r e the performance w i l l  depend upon the performer's  c o n c e p t i o n o f the p i e c e .  He might  p r e d e t e r m i n e . d e t a i l s , p r o v i d i n g a l t e r n a t i v e means o f performance. He might decide upon g e n e r a l meanings f o r the g r a p h i c  indications  or he might allow the meanings to .change spontaneously  d u r i n g the  performance.  In any case, i n d i v i d u a l . r e a l i z a t i o n s of the score  are bound t o e x h i b i t wide v a r i a t i o n .  T o s h i Ichiyanagi.:. Music f o r Piano #2 The  s c o r e . f o r Music for. Piano #2 c o n s i s t s of f o u r small  sheets with g r a p h i c symbols.  Symbols, except.those  found  i n the  four c o r n e r s o f the sheets, i n d i c a t e t h e f o l l o w i n g f e a t u r e s : a.  Register.  T h i s depends.upon the d i r e c t i o n o f a branch  in relation to a c i r c l e .  The d i r e c t i o n r e p r e s e n t s one  of f i v e ranges i n t o which the keyboard i s d i v i d e d . b.  L o c a t i o n o f t h e sound.  The type o f c i r c l e i n d i c a t e s  how the sound i s t o be made. c.  R e l a t i v e d u r a t i o n o f t h e sound. indicates  d.  Length o f the branch  this.  Simultaneity.  Whether sounds a r e t o be played  singly  or together i s i n d i c a t e d by the absence or presence o f a  "slur."  e.  The number o f sounds. of  T h i s i s i n d i c a t e d by the number  branches.  Although the g r a p h i c n o t a t i o n i s d i f f e r e n t , Music f o r Piano #2 i s i n many r e s p e c t s s i m i l a r t o Music f o r Piano #7.  As  i n the l a t t e r , no p i t c h e s are s p e c i f i e d ; o n l y g e n e r a l ranges are given.  In the former, however, the performer, i s d i r e c t e d t o  choose a s p e c i f i c number.of tones, .for example, one from the h i g h e s t r e g i s t e r and one from the middle r e g i s t e r . . Example 1.  (Example 1.)  M u s i c . f o r Piano #2, page 0.  In example 1 the two notes.are t o be p l a y e d s e p a r a t e l y . symbol does.not first.  The  i n d i c a t e which o f the two tones i s t o be played  I t a l s o does not i n d i c a t e whether they are heard  s e p a r a t e l y o r whether.one sounds b e f o r e the o t h e r . i s r e l e a s e d . As i n Music  f o r Piano #7, no dynamic l e v e l o f the sounds i s g i v e n .  The performer, may choose  i n d i v i d u a l dynamics,  attacks, general  dynamic l e v e l s , perhaps choosing d e l i b e r a t e l y , o r spontaneously. P e d a l l i n g e f f e c t s are chosen a t the.performer's d i s c r e t i o n . .The symbols i n the f o u r . c o r n e r s o f . t h e sheets —  o r , on one  sheet, the l a c k o f symbols.in the four c o r n e r s . — are the cues or l i n k s , which j o i n the four pages, p r o v i d i n g c o n t i n u i t y i n the piece.  Although not i n d i c a t e d , presumably  the. performer may  begin.anywhere, w i t h any symbol from any o f the four pages.  As  soon as he performs  the requirements  o f a symbol he moves to the  page whose cue matches .the c i r c l e of the symbol he has played.  For example, i f »• <c  just  has j u s t been p l a y e d , the per-  former would next choose a symbol from a sheet.with the b l a c k c i r c l e cues  ( # ), and so forth..  The  f o u r sheets, thus would  have t o be arranged on the piano making a l l sheets v i s i b l e . of the f o u r s i d e s of each sheet may the symbols o f any one  As soon as a l l of  sheet have, been performed,  r o t a t e d c l o c k w i s e n i n e t y degrees. p l a y i n g as b e f o r e .  be up.  Any  The performer  the sheet i s then  continues  When any sheet has been r o t a t e d f o u r times,  the performance i s over. With r o t a t i o n , symbols a l t e r i n meaning.  Whereas i n one  p o s i t i o n one would be d i r e c t e d to p l a y i n s i d e the piano i n the "low"  r e g i s t e r , w i t h one r o t a t i o n one would be d i r e c t e d to p l a y  i n s i d e the piano i n the "high" r e g i s t e r symbol has f o u r p o s s i b l e , g e n e r a l meanings.  .  Thus, each  With the r o t a t i o n of  o n l y one  sheet at a time, many d i f f e r i n g c o n t i n u i t i e s  result.  With each r o t a t i o n the v a r i a b l e aspects of a symbol  r e c e i v e new  meanings.  notes connected performed  by,the  will  For i n s t a n c e , i f i n the symbol the  may  two  s l u r and hence played together are  b e f o r e the s i n g l e note, i t i s not r e q u i s i t e  m a i n t a i n t h i s order i n any  succeeding  rotation.  Apart from g e n e r a l d u r a t i o n s i n d i c a t e d by.the l e n g t h , t h e r e i s . no i n d i c a t i o n of e i t h e r tempo.or time.of t h e . p i e c e as.a whole.  Nor  the amount of time a performer may  they  i s there any  branch  chronometric  i n d i c a t i o n of  take between sounds comprising  the symbol o r between symbols.  Rests o r s i l e n c e s , thus, have not  been n o t a t e d . In Music  f o r Piano #2 the performer i s accorded  r e s p o n s i b i l i t i e s t o those i n M u s i c . f o r Piano #7.  similar  As i n the  l a t t e r , a g e n e r a l . c o n t i n u i t y i s o u t l i n e d w i t h d e t a i l s t o be completed.  The performer w i l l d o u b t l e s s become q u i t e  familiar  with the symbols and t h e i r g e n e r a l and p o s s i b l e meanings b e f o r e p l a y i n g . t h e . p i e c e , b u t . t h i s should.not prevent spontaneous from being made d u r i n g a.performance.  choices  Again i t w i l l be the p e r -  former's c o n c e p t i o n o f the. piece.and how he handles the v a r i a b l e aspects t h a t w i l l determine t h e f i n a l outcome.  E a r l e Brown: December 1952 In.December 1952 the " d e f i n e d space" Brown r e f e r s t o c o n s i s t s o f h o r i z o n t a l and v e r t i c a l l i n e s o f v a r y i n g l e n g t h s , width and p o s i t i o n s .  The score.has four p o s i t i o n s ; with one  ninety-:degree r o t a t i o n , a h o r i z o n t a l l i n e becomes a v e r t i c a l one, each l i n e having f o u r . p o s s i b l e p o s i t i o n s i n the s c o r e . not s p e c i f i e d t h a t the performer must p l a y a l l ' e v e n t s  It i s (lines)  before r o t a t i n g the score or even t h a t a l l events must be p l a y e d b e f o r e the performance  i s complete.  The performer may b e g i n with.any proceed i n any d i r e c t i o n . o r d e r i n g s e x i s t ; presumably interspersion.  one o f the l i n e s and  W i t h . t h i r t y - o n e events many p o s s i b l e t h e r e i s no p r e - s e l e c t e d o r d e r i n g o r  There appears to.be no r e s t r i c t i o n on r e t u r n i n g  to an event one o r more t i m e s .  Two broad lines.  c h o i c e s a r e g i v e n f o r the i n t e r p r e t a t i o n o f the  The performer  may c o n s i d e r t h r e e o r four "dimensions" as  " a c t i v e . " . When three are a c t i v e , they are v e r t i c a l , h o r i z o n t a l and  "time";  the " t h i c k n e s s " o f an event may be r e p r e s e n t a t i v e o f  r e l a t i v e i n t e n s i t y and/or c l u s t e r s .  When four are a c t i v e  ( h o r i z o n t a l , v e r t i c a l , . d e p t h , and t i m e ) , the t h i c k n e s s  (depth) i s  not g i v e n a s p e c i f i e d meaning. A t r a n s l a t i o n o f the l i n e s i n t o . m u s i c a l t e r m s . w i l l depend b a s i c a l l y upon the performer's "dimension" and " a c t i v e . " ties: and  c o n c e p t i o n o f t h e terms  The l i n e s have three apparent  proper-  (1) h o r i z o n t a l and v e r t i c a l o r i e n t a t i o n , (2) t h i c k n e s s  (3) p o s i t i o n on the page.  m u s i c a l meanings.  These p r o p e r t i e s a r e t o be g i v e n  They a r e t o be a s s o c i a t e d with the c h a r a c t e r -  i s t i c s .assigned t o a sound: p i t c h d u r a t i o n , dynamics  (register, simultaneity . .  ( i n t e n s i t y ) and a t t a c k .  When t h r e e dimensions a r e " a c t i v e , " the only, p r o p e r t y a suggested  meaning i s t h i c k n e s s .  I f the performer  .),  Even here u n c e r t a i n t i e s a r i s e .  chooses t h i c k n e s s t o r e p r e s e n t i n t e n s i t y  may c l u s t e r s be r e p r e s e n t e d  another  with  only,  way, o r i f t h i c k n e s s .  r e p r e s e n t s c l u s t e r s o n l y , how w i l l dynamics be represented? H o r i z o n t a l and v e r t i c a l might by t r a d i t i o n a l i m p l i c a t i o n suggest pitch.  H o r i z o n t a l might r e f e r t o a number o f events i n  succession, v e r t i c a l r e f e r r i n g . t o . s i m u l t a n e i t y , while the length of t h e l i n e might i n d i c a t e an approximate number o f events.  The  q u e s t i o n remains, then, how the dimension o f time i s t o be represented.  A plane such as the score i s two-dimensional.  In  the i n s t r u c t i o n s , time i s c o n c e p t u a l l y represented i n a t h i r d dimension,  p e r p e n d i c u l a r t o the p l a n e .  The t h i r d  dimensional  l i n e might or might not be comparable i n s i z e t o one r e p r e s e n t i n g an aspect o f the  graphically  event.  Time i n t h i s work e x i s t s on v a r i o u s l e v e l s .  There i s the  time or d u r a t i o n o f . a n i n d i v i d u a l event, the time between events and the l e n g t h of the p i e c e . decided beforehand.  The performance l e n g t h i s t o be  Time as the t h i r d dimensions  be the time of an event.  might presumably  The other aspects of time are not  i n d i c a t e d and the composer g i v e s no suggestions concerning tempo. Time between events might p o s s i b l y be taken from the d i s t a n c e between events. i t takes t o go from one c o n s i d e r e d p a r t of the  spatial  S i l e n c e then would not be j u s t the time event t o another, but a momentarily  composition.  I f the number of sounds c o n t a i n e d w i t h i n a s i m u l t a n e i t y or a s u c c e s s i o n i s l e f t undetermined, the time o f the event might be g r a p h i c a l l y r e p r e s e n t e d .  The  l e n g t h of the l i n e might r e p r e -  sent the d u r a t i o n d u r i n g which the s i m u l t a n e i t i e s o r . s u c c e s s i o n s occur. When the performer  chooses to c o n s i d e r f o u r dimensions  " a c t i v e , " h o r i z o n t a l and v e r t i c a l a g a i n may graphically.  The depth  be r e p r e s e n t e d  (thickness) of the event may  r e p r e s e n t c l u s t e r s and/or dynamics. have a c o n c e p t u a l p o s i t i o n .  as  or may  not  Time a g a i n might p o s s i b l y  B a s i c a l l y the same c o n s i d e r a t i o n s  a r i s e whether t h r e e or f o u r dimensions  are " a c t i v e , "  the  d i f f e r e n c e being t h a t t h i c k n e s s i n the l a t t e r c h o i c e has an even  The performer must d e c i d e how  to i n t e r p r e t  "active."  One  p o s s i b i l i t y would be t o c o n s i d e r a dimension which i s not d e t e r mined, or g i v e n a suggested meaning, as a c t i v e .  I t might  further  be c o n s i d e r e d t h a t w h i l e the dimension i s g r a p h i c a l l y r e p r e s e n t e d , the concept of i t s r e p r e s e n t a t i o n i s s u b j e c t to transformation or.modification.  The meaning a s s i g n e d to a  c e r t a i n . l i n e would not n e c e s s a r i l y be c o n s i s t e n t throughout the performance; i t could.be a l t e r e d f r e e l y .  I f a performer d i d  r e t u r n t o an event, he might p o s s i b l y r e - i n t e r p r e t i t . With the b a s i c assumptions so undetermined, i t might be presumed t h a t a p o s i t i o n w i t h i n the d e f i n e d space i s not n e c e s s a r i l y i n d i c a t i v e of a r e l a t i o n s h i p .  One event need not be  h i g h e r , lower than or i d e n t i c a l in., p i t c h w i t h another a c c o r d i n g to i t s p o s i t i o n w i t h i n the d e f i n e d space. The composer suggests performances be made d i r e c t l y  from  the g r a p h i c " i m p l i c a t i o n . " ' I f something.in the score or i n s t r u c t i o n s appears i m p l i c i t t o the performer, however, he choose to i n c o r p o r a t e t h i s i d e a i n t o the performance. v e r t i c a l lines., f o r example,  may  Should  seem to. i n d i c a t e s i m u l t a n e i t y , the  performer, may.decide.that h e . w i l l , do t h i s throughout the p i e c e . While g i v i n g no expressed.meaning, accompanying  the terms used i n the  i n s t r u c t i o n s t o the. g r a p h i c score may  s u b c o n s c i o u s l y , a working-out o f the s c o r e , or may l e a s t to s e t a performance i n motion.  Meanings  terms and s o l u t i o n s chosen w i l l be. m u l t i f a r i o u s .  suggest, even be enough a t  assigned t o the Almost anything  c o u l d r e s u l t , depending upon the performer's seems i m p l i e d to him, spontaneity.  h i s response and  There i s no one  c o n c e p t i o n , what  imagination,  s o l u t i o n ; any  and  alternative i s  acceptable.  E a r l e Brown: Four Systems For help i n understanding  Four Systems the performer  r e f e r r e d to the i n s t r u c t i o n s , of December 1952.  is  In each system  the l i n e s of v a r y i n g l e n g t h s and t h i c k n e s s e s are h o r i z o n t a l and are c o n f i n e d between two  "continuous"  horizontal lines.  such.systems comprise the one-page s c o r e .  The  Four  continuous  lines  bounding each system " d e f i n e the outer l i m i t s of the keyboard." I t i s not s t i p u l a t e d whether the l i n e s from, l e f t to r i g h t are to be t r a n s l a t e d . " b o t t o m  to top" o f the keyboard or whether the  d i s t a n c e between the two Apart  l i n e s r e p r e s e n t s the outer  limits.  from the general d e s i g n a t i o n of. the continuous  f u r t h e r i n d i c a t i o n s . a r e made.  The performer  other, elements are to be r e p r e s e n t e d .  The  lines,  must decide how  l e n g t h of the  c o u l d p o s s i b l y i n d i c a t e . d u r a t i o n , the p i t c h being taken s t a r t i n g p o i n t o f the l i n e .  no the  line from the  Or the l e n g t h c o u l d i n d i c a t e an  approximate.number o f - n o t e s grouped i n s u c c e s s i o n or p o s s i b l y heard.simultaneously.  Dynamics, as in-December 1952,  r e p r e s e n t e d by. the t h i c k n e s s of the  may  be  line.  No o r d e r i n g e i t h e r of the four systems or o f the  lines  within i s specified.  I t i s not i n d i c a t e d i n the score whether  l i n e s are to be heard  s e p a r a t e l y o r whether any  two  o r more  may  be chosen t o be heard s i m u l t a n e o u s l y . Consequently, the performer presumably c o u l d p l a y any sound  (or combination o f  sounds) a t any p o i n t d u r i n g the performance of the p i e c e .  Sounds  might be heard s i n g l y , s i m u l t a n e o u s l y . o r i n d i v e r s e o v e r l a p p i n g arrangements.  The p r o f u s i o n o f l i n e s w i t h i n each system might  suggest a type of s i m u l t a n e i t y .  Although a p o s s i b l e s o l u t i o n , i t  might be assumed, t h a t the system would not be read from e i t h e r l e f t t o r i g h t o r v i c e v e r s a , but t h a t events might be chosen spontaneously from any p o i n t w i t h i n a system. I t i s not determined whether a.performer must p l a y every event w i t h i n a system b e f o r e moving to another system. be presumed s i n c e the e n t i r e performance time may t h a t any event may  I t might  be any l e n g t h ,  be r e t u r n e d t o any number o f t i m e s .  Some  events might not be played a t a l l . As in. December 1952 the g r a p h i c score i s ambiguously d e f i n e d by.the composer.  A f t e r becoming  aware of how  little is  s p e c i f i e d , the performer should respond t o the s c o r e , e v o l v i n g or c r e a t i n g a performance spontaneously. and would.be a c c e p t a b l e .  Anything.might happen  A v e r y g e n e r a l o u t l i n e f o r a.performance  e x i s t s ; a l l d e t a i l s must be s u p p l i e d by the performer and they, i n t u r n , depend upon h i s r e a c t i o n t o the s c o r e .  Udo Kasemets:  Timepiece  The g r a p h i c n o t a t i o n o f Timepiece c o n s i s t s o f .dots and dashes above and below, events.  These dots and dashes  indicate  a r t i c u l a t i o n , d e n o t i n g the d i f f e r e n c e between " s h o r t / l o n g . "  "detached/sustained," the performer  "staccato/legato," "etcetera."  Presumably  g i v e s the dash a meaning, perhaps long o r s u s t a i n e d  or l e g a t o , depending upon the c o n t e x t . dot would have.the o p p o s i t e meaning.  I t might be supposed the I f an event has two d o t s ,  o r two dashes, the " a t t a c k " i s uniform; i f not, both symbols must i n some way be expressed.  When both must be used, the propor-  t i o n i n g o f the notes t o one o r the other s i g n i s not s p e c i f i e d . Dots and dashes appear t o the l e f t and r i g h t o f events, "same" and " d i f f e r e n t , "  indicating  "colour.and/or p l a y i n g technique."  Again  the p l a y e r g i v e s h i s i n t e r p r e t a t i o n o f the dots and dashes. i n t e r p r e t a t i o n s . a r e p o s s i b l e ; the assigned meaning may v a r y  Many from  event t o event, the meaning g i v e n being c o n s i s t e n t o n l y f o r t h a t event. The t h i r t y - s i x events a r e r e p r e s e n t e d i n two ways: t h i r t y c o n s i s t o f b l a c k or white comprised  "noteheads" w h i l e s i x events a r e  of l a r g e r , black i n t e r l o c k i n g c i r c l e s .  head i n d i c a t e s a sound i s "consonant" " c l o s e s t neighbouring sound." dissonance.  A white  note-  w i t h the p r e c e d i n g o r  A b l a c k notehead r e p r e s e n t s  Consonant and d i s s o n a n t "need" not have t r a d i t i o n a l  i m p l i c a t i o n s ; . t h e performer  d e f i n e s the terms.  set up must remain c o n s t a n t o n l y throughout " c y c l e " of the t h i r t y - s i x events.  The d e f i n i t i o n s  one performance o r  The terms may be r e d e f i n e d  from c y c l e t o c y c l e .  Kasemets uses the term " e t c . " ; presumably the performer may g i v e the dots and dashes a meaning other than those suggested.  The  large black c i r c l e s represent  extra-instrumental noises et a l . "  Two  "clusters, glissando, c i r c l e s i s a small  " c l u s t e r , " three a l a r g e " c l u s t e r " and  four a "very l a r g e , a l l -  encompassing c l u s t e r . "  of the c l u s t e r s  The boundaries  are  v a r i a b l e , apart from the g e n e r a l i n d i c a t i o n s " s m a l l , " " l a r g e " or "very l a r g e . "  I t . i s not s p e c i f i e d whether the c l u s t e r i s  comprised.of b l a c k and white keys, a l l b l a c k or.white, p r o p o r t i o n s of each.  Only the type of sound i s g i v e n .  Each notehead.represents, a s i n g l e note. event  (there w i l l be one  i n any way.  or what  t o s i x ) may  Notes w i t h i n an  be combined or  juxtaposed  P i t c h and range of the notes are s u b j e c t o n l y to  general considerations.  A movement from one  event  to a higher  one on the score r e p r e s e n t s an upward movement on the keyboard, and v i c e v e r s a .  With r e s p e c t t o . h o r i z o n t a l movements,  choices e x i s t .  .The  event may  i n any range.  The performer  two  s t a y i n the same range or be must i n some way  d e l i m i t the  S p e c i f i c p i t c h e s w i t h i n the ranges are. not d e s i g n a t e d ;  played ranges.  their  c h o i c e may  be l e f t to s p o n t a n e i t y , a l l o w i n g f o r consonance-  dissonance  limitations.  The p o s i t i o n of the events on the score need not  represent  exact d i s t a n c e s or l o c a t i o n s on the keyboard, r e p r e s e n t i n g instead only a general relationship..  Presumably the  c o n s i d e r s o n l y the r e l a t i o n s h i p s between two When .considering.events of events  three and  the performer  events  performer a t a time.  seven and e i g h t , f o r example, the p o s i t i o n  four i s not n e c e s s a r i l y . r e l e v a n t . Only i f  chooses to i n t e r p r e t the " g e o g r a p h i c a l " p o s i t i o n of  "events" w i l l , t h e i r p o s i t i o n on the page i n d i c a t e t h e i r r e l a t i o n s h i p s t o each.other.  range  P o s i t i o n would then i n d i c a t e a  s p e c i f i c range r a t h e r than j u s t  "higher" or "lower."  The h o r i z o n t a l "movements on the score . . . from one to  attack  the next" are made w i t h i n g i v e n d u r a t i o n s :  Movements t o the r i g h t are "slow": 1 column — 2  "  2 seconds  — 4 -  3  —  6  4  "  —  8  5  "  —  10  "  '  "  Movements t o the l e f t are " f a s t " : 1 column —  1 second  2  "  —  1/2  3  "  ~  1/3  4  "  ~  1/4  5  "  ~  1/5  The t a b l e s may  be a l t e r e d so long as the o r i g i n a l p r o p o r t i o n s  remain c o n s t a n t throughout the c y c l e . the of  that  speed w i t h which the event i s approached i s a l s o the speed the event.  might be f r e e . may  I t might be i m p l i e d  I t i s not specified.; the d u r a t i o n o f the event Two  c h o i c e s e x i s t f o r v e r t i c a l movements: they  "maintain the 'tempo' by which the column was approached" or  they may  be  "free."  Superimposed wedges i n d i c a t e c o n t r a s t between " s o f t e r " and "louder."  The dynamic  c o n t r a s t between events depends upon t h e i r  r e l a t i o n t o the p o i n t of the wedge.  The c l o s e r t o the p o i n t , the  q u i e t e r the event. There appears to be a d i s c r e p a n c y i n the i n s t r u c t i o n s . performer i s f i r s t a d v i s e d t h a t he may  move from event to event  choosing any d i r e c t i o n and d i s t a n c e u n t i l a l l t h i r t y - s i x have been played once.  L a t e r he i s t o l d t h a t  events belong i n one common wedge."  The  events  "any two s u c c e s s i v e  From t h i s i t might be p r e -  sumed t h a t although wedges o v e r l a p , a l l o w i n g the performer to get from one wedge to another, movement i s somewhat r e s t r i c t e d ; c e r t a i n events cannot be performed  successively.  In Timepiece the performer i s g i v e n a g r a p h i c score w i t h some g e n e r a l r e s t r i c t i o n s .  L i m i t a t i o n s are g r a d u a l l y imposed by  the performer as he chooses  from innumerable  possibilities.  might r e a l i z e the score a s . i t s l a y o u t suggests or he might almost any ideas.on c e r t a i n a s p e c t s .  He impose  I f the p i e c e i s being  played by more than. one ..performer, agreement on treatment of the elements must be made between the performers.  Some c h o i c e s w i l l  be e s t a b l i s h e d beforehand; t h e r e w i l l be a degree of u n i f o r m i t y or c o n s i s t e n c y .  The c o n c e p t i o n of the performer w i l l  the degree of chance i n Timepiece.  determine  THE  INDETERMINATE PIECES  In t h i s chapter the p i e c e s a r e grouped a c c o r d i n g type o f indeterminacy.  to their  A l l p i e c e s are comprised o f s p e c i f i e d  m a t e r i a l , the o r g a n i z a t i o n o f which i n some way i s not s p e c i f i e d . Although i t i s assumed t h a t s p o n t a n e i t y . t o a l l works d i s c u s s e d ,  the c h o i c e s  some degree w i l l  shape  are guided i n c e r t a i n works.  Spontaneity i s l i m i t e d . The  works f a l l (1)  i n t o two b a s i c  categories:  works which are c l e a r l y d i v i d e d i n t o s e c t i o n s , the treatment o f these s e c t i o n s i n v o l v i n g c h o i c e s .  (2)  works i n which the given m a t e r i a l i s i n a d e t e r mined sequence, the m e t r i c sounds being  r e l a t i o n s h i p o f the  unspecific.  Works i n the f i r s t category vary;  the o r d e r i n g o f complete  s e c t i o n s may be f r e e l y chosen o r guided, s e c t i o n s may have t o be i n t e g r a t e d , or. c h o i c e s between determined m a t e r i a l w i t h i n  sections  may have to be made. V a r i a t i o n s I and II_ by Cage do not c o i n c i d e w i t h e i t h e r category.. I t i s assumed t h a t most choices w i l l be made w h i l e determining a p a r t t o be used i n performance, but t h a t some aspects w i l l be l e f t f o r l a s t minute d e c i s i o n s .  Cardew g i v e s a s t a t e d purpose f o r the indeterminacy of Two  Books of Study: the work i s "a study f o r the p i a n i s t s  (two)  not o n l y i n the rhythmic p r e s e n t a t i o n . o f sounds i n time, i t i s a l s o a study in. combining  these sounds with, those presented  by  26 the other p i a n i s t . " P i t c h i s . d e t e r m i n e d i n the.Study.  No omissions or r e p e a t s  are allowed and p i t c h e s must be p l a y e d i n t h e i r w r i t t e n o r d e r ; a t t a c k s and c l u s t e r s are a l s o s p e c i f i e d . page i s one minute. "groups,"  The d u r a t i o n of each  The p i e c e i s d i v i d e d i n t o s e c t i o n s or  the beginning and end.points being s t r i c t l y a s s i g n e d  by the minute and/or second  they o c c u r .  p i t c h e s are r h y t h m i c a l l y notated.  W i t h i n the groups  Although there are  gaps between the sounds, no r e s t s are notated. time boundaries to  spatial  Within designated  the d i s t r i b u t i o n of the notated sounds i s f r e e ,  be. decided by. the.performer.  The performer  a l s o chooses a  g e n e r a l dynamic l e v e l . f o r each.group with s p e c i f i c dynamic markings being i n d i c a t e d f o r i n d i v i d u a l sounds. d e c i s i o n s are l e f t to the performer.  Pedalling  When a chord which  o r d i n a r i l y would be j o i n e d t o o t h e r chords on a beam i s given a separate f l a g , the notes of t h a t chord are to be played  singly  in.any o r d e r . Each p i a n i s t ' s p a r t c o n s i s t s of " l a y e r s " or groups. up to t h e . p l a y e r to i n t e g r a t e the groups, Notes., Two  Books of Study.  superimposing  London, H i n r i c h s e n ,  It is  the p a r t s 1966.  in  "counterpoint."  Thus i t might be t h a t two i n d i v i d u a l  sounds  are  heard s i m u l t a n e o u s l y , o r , because the sounds o f a l l groups  may  be f r e e l y d i s t r i b u t e d w i t h i n time l i m i t s , sounds o f one p a r t  may  be i n s e r t e d between sounds of another p a r t . The two p l a y e r s must c o l l a b o r a t e , i n t e g r a t i n g t h e i r p a r t s  i n t o a two-piano work. from the two p a r t s may  Several a l t e r n a t i v e s . a r e given: material be heard s i m u l t a n e o u s l y , there may  o v e r l a p p i n g , o r sounds from one.part may  be  be i n t e r p o l a t e d between  sounds.of.the other p a r t . There are t h r e e ways .Study, may formers may  be approached.  The p e r -  choose the v e r s i o n , which has been.already i n t e g r a t e d  by the composer.  In t h i s case i t i s suggested the p i e c e be  t i t l e d Music f o r Two  Pianos.  Or the two performers may work out  a . v e r s i o n beforehand, c o l l a b o r a t i n g i n the i n t e g r a t i o n , each having ideas about h i s p a r t , but remaining f l e x i b l e . case the p i e c e becomes e s s e n t i a l l y determined. may  be indeterminate i n performance.  performers, may  In t h i s  The p i e c e a l s o  In- t h i s case, the  be q u i t e f a m i l i a r w i t h the score, g i v i n g p r e -  thought to v a r i o u s p o s s i b i l i t i e s and even working out on the bottom  (empty)  score passages which, might be too d i f f i c u l t f o r  a spontaneous approach. While the performer i s faced w i t h d e c i s i o n s p r i o r to and p o s s i b l y during, the.performance, the spontaneous aspect does not appear to be s t r e s s e d i n Study. for  the performer to make —  g e n e r a l dynamic  There, are a s e r i e s of d e c i s i o n s  d i s p o s i t i o n of n o t e s . w i t h i n a.group,  l e v e l , i n t e g r a t i o n o f groups and p a r t s , and  degree o f indeterminacy  -- but the composer i s not concerned  about the degree o f p r e d e t e r m i n a t i o n Although  the performer  c h o i c e s a r e l e f t f o r the performer,.the  over, even.in.cases the performance.  chooses.  score i s worked  where indeterminacy, w i l l be o p e r a t i n g d u r i n g  The exact r e s u l t s may not be foreseen by the  composer, but i t i s p r o b a b l e . t h a t  the performers  w i l l have a t  l e a s t some expectations, r e g a r d i n g the performance.  S y l v a n o . B u s s o t t i : Pour C l a v i e r Apart  from some rhythmic  C l a v i e r are s p e c i f i e d . of  the material..  The i n d e t e r m i n a c i e s occur i n the o r d e r i n g  On some pages o f t h i s p i e c e the performer  e x a c t l y as w r i t t e n . The. performer  f l e x i b i l i t y , t h e . d e t a i l s i n Pour  plays  On other pages there are l i m i t e d c h o i c e s .  may not produce j u s t a n y . j u x t a p o s i t i o n , may not  i n s e r t m a t e r i a l j u s t anywhere, but i s . r e s t r i c t e d t o c e r t a i n alternatives.  There are t o be no i n t e r r u p t i o n s o r pauses  except  those.marked i n the text.. The means o f p r o v i d i n g c h o i c e s v a r i e s from page t o page. The The  f i r s t c h o i c e s i n o r d e r i n g occur on pages 3, 4 and 5.  performer 1.  i s given three  alternatives:  t o p l a y as w r i t t e n , i g n o r i n g d o t t e d l i n e s and arrows accompanying numbers.  2.  t o f o l l o w the d o t t e d l i n e s and numbers, o m i t t i n g groups i n parentheses.  3.  t o p l a y a mixture  o f the f i r s t two c h o i c e s .  Choices again are guided on pages 10 to 13. performance, two  a l t e r n a t i v e s are  For  live  given:  1.  to p l a y as w r i t t e n , i g n o r i n g "boxes," or  2.  to segregate the m a t e r i a l , p l a y i n g the m a t e r i a l i n the boxes before  playing material outside  i n s i d e another box.  The  rectangles.  the boxes or  order of the m a t e r i a l i s  s l i g h t l y d i f f e r e n t from t h a t suggested by the page layout.  Numbers followed  by.brackets r e f e r the  former to page 17 which c o n t a i n s  per-  f o u r t e e n .small groups.  These groups.may be i n s e r t e d a t the i n d i c a t e d p o i n t s . I f the p i e c e i s being s e p a r a t e l y recorded imposition  and  r e c o r d e d , the segregated m a t e r i a l s may  and  l a t e r pieced  together,  j u x t a p o s i t i o n not being  their  be  super-  s u b j e c t to a determined  time scheme. I n s e r t i o n s of groups from page 17 may 14 to 16.  Page 17 i s to be memorized.  not to p l a y any 16,  performer may  p o i n t on pages 13  "normally," group 1 through 14.  c o n s i d e r pages 20 and  p l a c e them s i d e by joining.  When the performer chooses  of the page 17 groups at any  page 17 i s to be played  a l s o occur on pages  21 s e p a r a t e l y , or he  be performed "normally," i g n o r i n g  a n d . s o l i d l i n k s , or by f o l l o w i n g the l i n e s and together.  The  simultaneity  performer i s to aim  "possible."  be done.  The  staves  dotted  grouping the  sounds  f o r the g r e a t e s t degree of  In the recorded  e d i t i n g , as done f o r the recorded  The  may  s i d e so t h a t they become one.page, the  Page 22 may  to  v e r s i o n of page  22,  v e r s i o n of pages 10 to 13,  may  composer p o i n t s out t h a t i t i s p o s s i b l e to reduce  the page t o f i v e groups, played s i m u l t a n e o u s l y . and arrows guide the performer 23.  Dotted  lines  through the a l t e r n a t i v e s o f page  Presumably each group may be i n s e r t e d i n o n l y one o f i t s  possible places. In Pour C l a v i e r c h o i c e s • a r e . o f t e n between u s i n g the d e t e r mined order or a . s l i g h t l y . l e s s determined alternatives.exist.  order where some  Thus, w h i l e some m a t e r i a l i s mobile, i t s  movements are r e s t r i c t e d .  The composer guides the c h o i c e s  a l l o w i n g c e r t a i n j u x t a p o s i t i o n s o f b l o c k s of m a t e r i a l s . o f s i m u l t a n e i t y may be s l i g h t l y l e s s p r e d i c t a b l e . be heard  Matters  The b l o c k s t o  s i m u l t a n e o u s l y . a r e d e s i g n a t e d , but the composer does  not c o n t r o l placement o f i n d i v i d u a l sounds w i t h i n the b l o c k s . The  f a m i l i a r i t y . w i t h the score r e q u i r e d f o r a performance o f  Pour. C l a v i e r suggests  the performer  i s -probably c o g n i z a n t o f the  r e s u l t s . o f .the v a r i o u s a l t e r n a t i v e s . p o s s i b l e , pre-planned  L a s t minute c h o i c e s between  r e s u l t s , could.make..the work  indeterminate  of performance.  Henri Pousseur.: C a r a c t e r e s Most aspects o f C a r a c t e r e s a r e determined undetermined, aspects are guided.  and even the  The composer has l i m i t e d the  c h o i c e s t o a l t e r n a t i v e s m a i n t a i n i n g h i s determined d u r a t i o n a l scheme.  Spontaneity  There are.two p a r t s — two  i s thus  harmonic and  restricted.  l a and l b —  t o the s c o r e .  p o s s i b i l i t i e s f o r shaping the performance e x i s t .  c h o i c e i s w i t h which o f the s i x double  In l a  The f i r s t  pages the performer  i s to  begin.  During the performance  of a double page f u r t h e r c h o i c e s  arise.  The performer chooses between one of the two  groups, then p l a y s a l l the remaining groups without The performer may  upper repetition.  proceed from the f i r s t chosen group t o any  "neighbouring" group below, going from l e f t t o r i g h t or v i a a r i s i n g diagonal. the two  Performance  lower groups.  of the double page ends with one of  Next, the performer chooses.one  of two  l e t t e r s from the. "index ,'' t u r n i n g t o the double page a d j o i n e d by 1  t h a t l e t t e r , performing i t , and so on through the p i e c e .  If i n  the course of p l a y i n g the p i e c e one of the l e t t e r s of a double page has a l r e a d y been chosen, the performer must choose other.  the  I f both have been.chosen, the p i e c e ends. The second p o s s i b l e way  first possibility did.  of performing l a begins as the  Groups, except groups a c t i n g as  t i o n s from double page to double page, may  transi-  be repeated.  It i s  not necessary to p l a y a l l groups, although the page must end w i t h a lower group c h o i c e .  One may  r e t u r n t o a page which has a l r e a d y  been p l a y e d . In  l b the performer makes c h o i c e s , but p r i o r to the  performance.  The work i s i n d e t e r m i n a t e o n l y i n t h i s pre-  performance  stage,. j u x t a p o s i t i o n of m a t e r i a l s being decided at  t h a t time.  The score c o n s i s t s of a double page w r i t t e n on both  s i d e s and f o u r s i n g l e pages w i t h windows.  The performer  chooses e i t h e r s i d e of the double page, which w i l l "envelope" or cover. p l a c e d i n t h i s cover.  first  serve as an  The s i n g l e pages are put i n any order and Ib i s then p l a y e d l i k e a normal  volume.  Whatever shows i n the windows i s performed.  Some m a t e r i a l on the  s i n g l e pages w i l l not a p p e a r . i n the windows and not be played i n t h a t performance.  Not a l l m a t e r i a l can be heard i n each p e r f o r -  mance .  K a r l h e i n z Stockhausen: Nr.. 7 K l a v i e r s t u c k XI The score o f Nr. 7 K l a v i e r s t u c k XI c o n s i s t s of n i n e t e e n "groups" assembled on a l a r g e sheet backed by a wooden frame. T h i s l a y o u t enables the performer to keep a l l groups r e a d i l y w i t h i n view.  Only t h e . o r d e r i n g o f the groups i s i n d e t e r m i n a t e .  B a s i c a l l y the performance i s as f o l l o w s : performer chooses the f i r s t may  To b e g i n , the  group t h a t "catches h i s eye."  then choose a tempo, dynamic  He  l e v e l and a r t i c u l a t i o n f o r t h i s  group.  At the.end o f t h i s group, however, there  dynamic  and a r t i c u l a t i o n i n d i c a t i o n s .  are.tempo,  The performer must apply  these t o the next group t h a t he a t random chooses.  This  procedure c o n t i n u e s . u n t i l a group i s played t h r e e times, whence the  conclusion i s - s i g n i f i e d .  time may  be v a r i e d .  Groups r e t u r n e d t o . f o r the second  For example,  the i n s t r u c t i o n s i n b r a c k e t s  w i l l vary the p a r t of- a group over or under, which they appear. The v a r i a t i o n appears i n the form o f s h i f t i n g o f the m a t e r i a l up or  down an octave, or adding or d e l e t i n g notes. Two  initial  c h o i c e s are.made: (1) a s t a r t i n g group and  (2) i t s tempo, dynamic order i s unspecified.  l e v e l and a r t i c u l a t i o n . .  From then on o n l y  I d e a l l y , the performer should look over the  score w i t h no p r e c o n c e i v e d n o t i o n s about any o f the groups, or  about where to s t a r t . t h a t the performer  To perform  them.so. t h a t once h i s eye caught a group he  i t fluently.  He should have no h e s i t a t i o n or  p r e f e r e n c e with r e s p e c t to any Since the performer  may  group. go from any group to any  group, innumerable r e a l i z a t i o n s e x i s t . performer groups and  requisite  b e . " f a m i l i a r " w i t h the n i n e t e e n groups,  s k i l l e d a t performing c o u l d perform  the work i t would be  . I f i t i s p o s s i b l e f o r the  to get away from any preconceptions from any.tendencies  p o s s i b l e t h a t no two  other  about the v a r i o u s  towards c e r t a i n r o u t e s , then i t i s  performances w i l l be a l i k e .  It i s  suggested  t h a t when p o s s i b l e the p i e c e be performed a t l e a s t twice d u r i n g a program, thus showing a t l e a s t two d i f f e r e n t r e a l i z a t i o n s of pre-formed m a t e r i a l s .  C h r i s t i a n W o l f f : Duo The  for Pianists II  score of Duo  for .Pianists I I , c o n s i s t i n g of a part f o r  each p i a n i s t , i s comprised b l o c k s may block,  of " b l o c k s " and  " p i t c h sources."  The  (1) c o n t a i n r e f e r e n c e t o . a . p i t c h source o u t s i d e the  (2) d e s i g n a t e the number of p i t c h e s to be p l a y e d from the  p i t c h source and  (3) g i v e suggestions  a r t i c u l a t i o n . a n d block timings. a l l these s p e c i f i c a t i o n s made.  f o r dynamics, d u r a t i o n s ,  However, i n no s i n g l e b l o c k are The .pitch source i s i n c o r p o r a t e d  i n some b l o c k s w h i l e i n a few b l o c k s there i s n e i t h e r the i n c l u s i o n of a p i t c h source nor r e f e r e n c e to one. case any p i t c h may  be p l a y e d .  the t r a d i t i o n a l manner.  In the  latter  The p i t c h sources are notated i n  Illustrative  of the g r e a t e s t degree o f s p e c i f i c a t i o n i n Duo  i s the f o l l o w i n g b l o c k :  Following f i f t e e n "a"  seconds o f . s i l e n c e , two tones from p i t c h  a r e p l a y e d i n t h r e e seconds.  and d u r a t i o n s .  source  There i s a c h o i c e of dynamics  The measurement of time i s chronometric; i t i s  i n d i c a t e d i n seconds r a t h e r than i n u n i t beats and measures.  The  n o t e . v a l u e s , a l s o , r e p r e s e n t a s p e c i f i e d number, o f sounds: J  = 1 second, 1=1  also  second  These a r e v a l u e s o f d u r a t i o n s o f . i n d i v i d u a l tones, t h e i r spacing w i t h i n the time l i m i t b e i n g u n s p e c i f i e d . i n d i c a t e s the presence o f d u r a t i o n a l At  i n . t h e p r e c e d i n g example, t h e r e a r e . c h o i c e s t o be  The performer, for.example, may use one i n d i c a t i o n f o r a l l  notes or one i n d i c a t i o n per note,.and are  possibilities.  times dynamics are l e f t u n s p e c i f i e d , a t times, as  illustrated made.  The p l u s s i g n (+)  so on.  When i n d i c a t i o n s  g i v e n a t l e a s t one must be used i n some way.  A t times two,  f o r example fp_, may be a p p l i e d t o one note. Further s p e c i f i c a t i o n s e x i s t .  The performer may be  r e q u i r e d t o s h i f t a note up t o any h i g h e r octave any lower octave octave  (*--).  (* " l  ), down t o  ( x — I ) or he may be asked t o p l a y i t i n any A r t i c u l a t i o n s such as mute, touch, snap and  p i z z i c a t o are i n c l u d e d i n some b l o c k s . a s p e c i f i c means of a t t a c k and 9  Q  2)  The  following pertains to  release:  3  Of nine tones, two  (£2)  are r e l e a s e d s i m u l t a n e o u s l y , t h e i r a t t a c k  not being determined and two tones  (2J )  which are p l a y e d t h r e e  3  times are a t t a c k e d but not n e c e s s a r i l y r e l e a s e d s i m u l t a n e o u s l y . The o r d e r i n g o f . t h e b l o c k s i s by response to cues.  The  cues, which are the same f o r both p i a n i s t ' s p a r t s , c o n s i s t o f "low mute," "high except f f , " and so on.  "low pp,"  "middle f f , "  "high f f , "  They are found a t the beginning of each b l o c k .  The  performer l i s t e n s f o r a.cue as he i s f i n i s h i n g the r e a l i z a t i o n of a block.  A f t e r he has r e c o g n i z e d the cue he moves to a b l o c k  preceded by t h a t cue. player's part. miss a cue.  Each performer must be aware of the other  I t i s . a n t i c i p a t e d by Wolff t h a t a performer  may  In t h i s case the performer moves to "no cue" where  two g e n e r a l p o s s i b i l i t i e s e x i s t : p i t c h source "g," or  (2)  (1) 17 seconds of two  tones from  3 seconds of f o u r - t o n e s from "e."  In  the second.choice, the performer i s faced with.choosing four out of seventeen p i t c h e s and t h e n . p l a y i n g these p i t c h e s i n t h r e e seconds.  I t might.be presumed t h a t the performer would have t o  be q u i t e f a m i l i a r w i t h the p i e c e t o keep the b l o c k s anywhere near t h e i r designated time-lengths.  I t might  a l s o be presumed t h a t by  compressing much a c t i v i t y or many i n s t r u c t i o n s i n t o a s h o r t space of time, indeterminacy o f an unintended type might r e s u l t . cue may  be m i s i n t e r p r e t e d i n some way,  A  and the s t i p u l a t i o n of  "no pause between s e c t i o n s " may r e q u i r i n g the. performer  cause a misjudgement.  Also,  to measure f r a c t i o n a l seconds i s bound  to l e a d t o i n a c c u r a c i e s .  The  requirement  appears to be  an  e x a c t i t u d e , but to c o r r e c t l y measure t h a t amount o f time would be i m p o s s i b l e .  The  g r e a t e r the r e s t r i c t i o n or  the more l i k e l y u n s p e c i f i e d indeterminacy  will  specification, occur.  While t h e r e are aspects of the score which are undetermined or v a r i a b l e , p o s s i b i l i t i e s or a l t e r n a t i v e methods of h a n d l i n g m a t e r i a l can be almost pre-determined.  That i s , the  the  performer  might, approach the p i e c e from a t e l e o l o g i c a l p o i n t of view, f o r example choosing dynamics f o r a purpose.such as emphasizing some p o i n t i n the p i e c e , or a r r a n g i n g . p o s s i b l e s p e c i f i c tones w i t h i n a rhythmic  p a t t e r n . .The  performer  may  c o n s t r u c t from the  m a t e r i a l c e r t a i n pre-formed ideas about i t s usage. contingencies.may s t i l l occur  given  Despite  this,  i n the h a n d l i n g of the c h o i c e s .  There a r e , then, aspects of the score which are prone to i n d e t e r minacy and even with, the most p l a n n e d . s o l u t i o n s of the  score,  the demands c o u l d l e a d to e i t h e r e r r o r s or l a s t - m i n u t e c h o i c e s . The degree to which the p i e c e i s pre-determined upon the performer.  He may  decide how  m a t e r i a l s of each b l o c k , he may  the  work out a l t e r n a t i v e v e r s i o n s to  be chosen a t the l a s t minute, or he may ideas of how  he w i l l perform  w i l l depend  have o n l y . v e r y  to work out the b l o c k s i n performance.  general  George Cacioppo.:  Pianopiece I I  P i a n o p i e c e I I i s comprised different Si  o f f o u r groups, each  slightly  from the o t h e r s and d e s i g n a t e d by t h e Greek l e t t e r s  (Omega), <^ ( P h i ) , y  (Chi) and ^ ( P s i ) .  One o f the four groups  (Phi) c o n s i s t s o f a network s i m i l a r to.those o f C a s s i o p e i a .  The  o t h e r t h r e e groups . ( P s i , Omega, Chi) c o n t a i n networks which are l o c a t e d on a s t a f f .  P i t c h i s determined  i n each o f the four  networks.  S i m u l t a n e i t y at.times i s i n d i c a t e d  suggested,  but when i n d i c a t e d the tones w i t h i n the symbol  may be played  ( P h i ) , a t times  singly.  In P i a n o p i e c e I I c e r t a i n aspects are determined, undetermined.  In groups.Phi,  Omega, however, i s marked f f .  and  The s t r i n g c l u s t e r i n  Dynamics a r e notated  groups.may be f r e e l y d i s t r i b u t e d .  The sounds w i t h i n these  A measure o f guidance  exists,  .In C h i , time may be p r o p o r t i o n a l t o the l i n e a r d i s t a n c e  between sounds and i n Omega t h e sounding w i t h the soft-headed envelope,  traditionally  Suggested time l e n g t h s f o r . t h e four groups ( s t r u c t u r e s )  f o r . t h e time between groups i s g i v e n .  however.  others  C h i and Omega, dynamics are pro-  p o r t i o n a l t o the s i z e o f the notehead.  in Psi.  still  of t h e . s t r i n g  cluster  drum m a l l e t i s represented by a decay  sounds notated below the envelope  p o s s i b l e although not  n e c e s s a r i l y being performed.as.the c l u s t e r , d i e s .  The c u r v a t u r e  of the l i n e s j o i n i n g sounds in.Omega r e p r e s e n t s r i t a r d and accelerando.  In P h i no time suggestions a r e made, but the per-  former might use l i n e a r d i s t a n c e as a guide. suggested  t h a t the small-headed  For P s i i t i s  notes may be f r e e i n tempo, t o  F u r t h e r freedoms concerning time may be taken. performer  The  may d i s r e g a r d the above suggestions, d e v e l o p i n g a l l  values a c c o r d i n g t o . h i s own i d e a s .  Thus, the performer  a l t e r n a t i v e s : he may. choose d u r a t i o n s suggested f r e e l y develop  has two  i n the score o r  all.values.  Omega c o n s i s t s - o f ..five p i t c h groups, separated by a comma (.,) which i n d i c a t e s a b r i e f pause.  W i t h i n the p i t c h groups  f u r t h e r sub-groups may be made; these sub-groups may be p l a y e d i n any o r d e r .  I t might be presumed t h a t the p i t c h e s w i t h i n the  sub-groups f o l l o w an order suggested, by t h e i r l a y o u t and connecting  lines.  Their, v e r t i c a l alignment,  n e c e s s a r i l y i n d i c a t i v e of simultaneity.  however, i s not  I f a sub-group i s  repeated, t h e p r e v i o u s l y . c h o s e n order o f p i t c h e s may be permutated Thus, the performer  f i r s t d e c i d e s on.an o r d e r o f groups and then  c o n s i d e r s p o s s i b l e sub-groups.and t h e i r o r d e r i n g . In P s i , s i x p i t c h e s a r e depressed a chord i s p l a y e d .  s i l e n t l y and h e l d w h i l e  While t h e chord i s s t r u c k s f z , the small  above a r e . p l a y e d a t a dynamic l e v e l r e l a t i v e t o t h e i r s i z e . other h a l f . o f P s i i s a group o f nine small-headed pp,  notes,  notes The  played  i n any time. The P h i network c o n t a i n s open-ended, paths.  The performer  s t a r t s a t any open end and f o l l o w s the networks, choosing d i r e c t i o n s a t the i n t e r s e c t i o n s .  I f h i s c h o i c e leads him to an  open end, he i s faced with f o u r f u r t h e r c h o i c e s : performance o f t h e . s t r u c t u r e may be ended,  (1) the  (2) he may t u r n back,  and,  covering  t h e same path, e i t h e r p l a y i t e x a c t l y as before or  permutate the p i t c h , order  and time v a l u e s ,  (3) he may t u r n back,  moving v i a a n . i n t e r s e c t i o n t o a new r o u t e , o r (4) he may jump t o any  other open end and then f o l l o w a new r o u t e .  Presumably the  performance.of P h i c o u l d c o n s i s t s o f two t o four o f these a l t e r natives.  P h i may be f u r t h e r s t r u c t u r e d , by segmenting the sound  path l i n e a r l y , i n t o two o r more sounds, the segments p o s s i b l y being played  repeated l i t e r a l l y o r permutated. simultaneously.,  mixture may be played.  Groups of.sounds may be  o r l i n e a r and simultaneous sounds i n any As ..in., the, networks, o f ..Cassiopeia, the  p i t c h e s a r e l a y e r e d , the h i g h e s t  r e g i s t e r t a k i n g top p o s i t i o n i n  the. network and so. f o r t h down t o t h e lowest r e g i s t e r . performer f o l l o w s the paths, moving from p i t c h t o p i t c h , (group), The  The  (or p i t c h group)  often using i n t e r s e c t i o n s .  composer's use o f t h e terms s t r u c t u r i n g , developing and  permutation would seem t o i n d i c a t e h i s p o i n t o f view.  Certain  elements a r e l e f t u n s p e c i f i e d f o r the performer t o f r e e l y  define,  or the performer may choose c e r t a i n a l t e r n a t i v e s , . b u t i t might be presumed t h a t forethought  be given t o the p i e c e s .  f a m i l i a r i t y w i t h the p i t c h d e s i g n a t i o n ,  Some  p o s s i b l e combinations,  permutations o f combinations o r p o s s i b l e i n t e r p r e t a t i o n s o f the network.might be made. in their  organization.  D e t a i l s a r e g i v e n , t h e freedom e x i s t i n g  In October 1952 the c l e f s i g n s do not appear i n the score but the t r a d i t i o n a l t r e b l e - b a s s r e l a t i o n s h i p i s assumed. and dynamics are determined.  P i t c h events-are g i v e n a v a l u e , but  the exact m e t r i c a l . r e l a t i o n s h i p o f the events The  Pitch  i s indeterminate.  score i s . t o be thought, o f i n terms o f a " d i s c o n t i n u o u s ,  spatial-coordinate."  Events occur a t a p o i n t i n space;  they can  be p l o t t e d i n terms o f a p o i n t on the s t a f f .  The performer  appears t o move through  The score might  "space"  (the s c o r e ) .  appear t o i n d i c a t e t h a t the sounds are j o i n e d , but the composer has simply not i n s e r t e d the r e s t s . chord  The performer  moves from  (note) t o chord without d i r e c t l y j o i n i n g them.  Not o n l y  the s i z e o f the r e s t s but a l s o , i n some c a s e s , . t h e i r placement i s obscure.  There are s p a t i a l gaps.between the sound symbols  ( s i n g l e notes,. chords) interpolation of rests. the performer  i n most i n s t a n c e s , suggestive of p o s s i b l e Although.a  gap might suggest a r e s t ,  need not i n s e r t one r e l a t i v e t o the s i z e o f a gap.  In f a c t , he need not even i n s e r t a r e s t , i t not being  specified  whether there n e c e s s a r i l y a r e r e s t s between a l l events. I n d i v i d u a l p i t c h e s a r e given a r e l a t i v e l y  determined  d u r a t i o n but the tempo o f the p i e c e i s undetermined. c o n s t a n t or v a r i a b l e , c h r o n o l o g i c a l o r i n t u i t i v e .  I t may be  It.might be  supposed t h a t t h i s would a f f e c t the p e r c e p t i o n o f the assigned time v a l u e s , t h a t notated d u r a t i o n s f u n c t i o n . p e r c e p t i b l y o n l y when the speed i s c o n s i s t e n t .  In October 1952  i t i s vague m e t r i c a l r e l a t i o n s h i p s  give r i s e t o indeterminacy.  which  I f r e s t s between the events were  s u p p l i e d by the composer the p i e c e would be determined.  However,  w i t h the f r e e i n s e r t i o n of f r e q u e n t r e s t s , and v a r y i n g tempos, many d i f f e r e n t arrangements  1953  E a r l e Brown: March March 1953  o f m a t e r i a l are p o s s i b l e .  i s s i m i l a r . i n concept, to October 1952.  dynamics and time v a l u e s are again, determined. ( J  = 87)  i s also given.  A s . i n October 1952  Pitch,  A r a t e of speed t h e r e are no  notated r e s t s ; the exact p o s i t i o n o f . t h e otherwise determined events w i t h i n the. composition i s not determined.  While a group  i s i n p r o g r e s s , the group i t s e l f w i l l be r e l a t i v e l y exact i n r e l a t i o n t o the g i v e n tempo, but the exact s i m u l t a n e i t y of or time between f i g u r e s , chords and s i n g l e notes i s t o be determined by the performer.  S i m i l a r c o n s i d e r a t i o n s c o n c e r n i n g the v a l u e s  g i v e n to the spaces between events a r i s e i n March 19 53 as a r i s e i n October 1952.  Exact s i m u l t a n e i t y of events i s s l i g h t l y more 1953,  ambiguous.in.March  In.both, performance  but the o v e r a l l tempo i s more s p e c i f i c .  c o u l d be made d i r e c t l y from the score w i t h -  out p r e - p l a n n i n g or forethought apart from awareness of determined and undetermined  aspects.  to each performance basic material.  The performer c o u l d spontaneously r e a c t  s i t u a t i o n , producing many.versions  o f the same  Dance i s a t r a n s c r i p t i o n i n t o sound symbols of the p l a n of a dance by C a r o l y n Brown. s p a r s e l y l o c a t e d on f o u r s t a v e s .  F o r t y notated The  two  e x i s t i n g i n Dance, determined by the odd sequence c h a r t of the dance, a r e : ^ • ("shorter").  The  pitches  types of and  ("till  floor are  duration  even numbers of inaudible")  the  and  l a t t e r d u r a t i o n i n p a r t i c u l a r i s not  explicit.  Since dynamics are not g i v e n , the a p p l i e d meaning of the  two  d u r a t i o n s would i n p a r t depend upon the f o r c e f u l n e s s w i t h which the note was  struck.  " s h o r t e r " may The  imply  inaudible" implies a sustained  ambiguous.  "length o f  Presumably the t o t a l d u r a t i o n i s  the  purposely  I t i s p o s s i b l e t h a t the s p a t i a l gaps between the  sounds are suggestive  attacks.  note;  a s u s t a i n e d or detached note.  g i v e n d u r a t i o n of the p i e c e i s the  ( o r i g i n a l ) dance."  notated  "Till  of an approximate l e n g t h between  Rests, not being, notated,  performer to  are presumably l e f t  f o r the  insert.  Duration.of  i n d i v i d u a l notes and o f the performance as a  whole, as w e l l as.dynamics and  a t t a c k , are undetermined, but  p i t c h and the g e n e r a l course of events are.determined.  John Cage:. V a r i a t i o n s I .The.score.of V a r i a t i o n s I c o n s i s t s of s i x p i e c e s of t r a n s parent  plastic,  o f four s i z e s .  f i v e c o n t a i n i n g f i v e l i n e s each and The  d o t s , or p o i n t s , r e p r e s e n t  one with  events,  the  dots  size  of the p o i n t i n d i c a t i n g the number of sounds w i t h i n an event.  M u l t i p l e sound events, o r " p l u r a l i t i e s " may be p l a y e d t o g e t h e r or as " c o n s t e l l a t i o n s , " t h a t i s , groupings of sounds. l i n e s o f each square r e p r e s e n t f i v e parameters: frequency, tude,  (2) s i m p l e s t overtone s t r u c t u r e ,  The f i v e  (1) lowest  (3) g r e a t e s t ampli-  (4) l e a s t d u r a t i o n and. (5) e a r l i e s t occurrence w i t h i n a  decided upon time.  Presumably  the performer t a k e s . f i v e r e a d i n g s ,  making f i v e d e t e r m i n a t i o n s f o r each event.  F o r each sound w i t h i n  a p l u r a l i t y , a . d i f f e r e n t p o s i t i o n of a square a d i f f e r e n t square must be used.  (there a r e four) or  The t o t a l . p e r f o r m a n c e . l e n g t h  might be d e c i d e d beforehand. With these i n s t r u c t i o n s the r e s p o n s i b i l i t y o f making a p a r t devolves upon the performer.  A l l aspects are."determined" by  dropping p e r p e n d i c u l a r s from a p o i n t t o a l i n e .  When dropping  p e r p e n d i c u l a r s , d i s t a n c e may be "measured o r simply observed." The measurement may be. d e f i n i t e o r approximate.  Meanings w i l l  have t o be a s s i g n e d . t o r e s u l t i n g measurements; c r i t e r i a have t o be s e t up.  will  Some p l a n n i n g , even o f a g e n e r a l type, might  go i n t o the t a k i n g of. measurements.  That i s , the performer  might  i n t e n t i o n a l l y make a c e r t a i n measurement l a r g e o r s m a l l a c c o r d i n g t o t h e aspect b e i n g determined or h i s . c o n c e p t i o n o f the p i e c e . Making measurements r a t h e r than, f o r example, simply d e t e r mining t h a t the l e a s t d u r a t i o n w i l l be a c e r t a i n v a l u e , suggests a t a k i n g . o f the human w i l l out o f . d e c i s i o n s .  There i s some  element  For instance, the  o f chance in. what the v a l u e w i l l be.  manner i n which the squares and dots a r e t o be arranged i s not specified.  I t c o u l d p o s s i b l y be accomplished  spontaneously.  The  performer's how  c o n c e p t i o n w i l l shape the piece.; i t w i l l  he f e e l s i t should be put t o g e t h e r , how  determine  capriciously  the  measurements w i l l be made. In d e s i g n a t i n g the f i v e parameters of a sound o n l y very g e n e r a l i n d i c a t i o n s are g i v e n .  A measurement taken from one  f o r example, might i n d i c a t e the lowest frequency.  line,  "Lowest"  suggests t h a t a l i m i t or r e s t r i c t i o n i s going to be a p p l i e d . sound may  be any p i t c h but no lower than a c e r t a i n one.  In these  d e t e r m i n a t i o n s , then, t h e r e i s the suggestion t h a t v a r i e t y on one  The  exists  s i d e of a . l i m i t a t i o n . A s i d e from  " e a r l i e s t occurrence" of sounds there i s no  s p e c i f i c o r d e r i n g of m a t e r i a l .  C e r t a i n events.presumably  might  appear any time from the beginning of the p i e c e onward w h i l e the placement of o t h e r events, determined would be more s p e c i f i c .  t o appear towards the  end,  There i s no g i v e n form; a very g e n e r a l  form a r i s e s a f t e r the d e t e r m i n a t i o n s are made. The performer  i s r e s p o n s i b l e f o r making h i s own  part.  By  dropping p e r p e n d i c u l a r s and t a k i n g measurements, aspects of the p i e c e are d e c i d e d , c e r t a i n l i m i t a t i o n s are determined. p o i n t there i s s t i l l amplitude  c o n s i d e r a b l e freedom.  At t h i s  I f o n l y the g r e a t e s t  or l e a s t d u r a t i o n . i s e s t a b l i s h e d , a t some p o i n t the  performer w i l l have.to  f u r t h e r d e f i n e the sounds.  I t i s not  s p e c i f i e d whether t h i s d e f i n i t i o n occurs b e f o r e or d u r i n g performance, by f u r t h e r d e t e r m i n a t i o n s o r spontaneously.  In any  case, a n . i n f i n i t e number of r e a l i z a t i o n s of the score are p o s s i b l e .  John Cage: V a r i a t i o n s I I T h i s score c o n s i s t s of e l e v e n . t r a n s p a r e n t s h e e t s , s i x having a s i n g l e l i n e each, f i v e w i t h one p o i n t each. be p a r t l y superimposed or e n t i r e l y separated.  Sheets  may  Perpendiculars  are dropped from the p o i n t s to the l i n e s and readings are  taken  to determine the f o l l o w i n g : frequency,  dura-  t i o n , p o i n t of occurrence s t r u c t u r e of the event or c o n s t e l l a t i o n ) . of the sheets.  amplitude,  timbre,  i n an e s t a b l i s h e d p e r i o d of time  (number of sounds making.up an  T h i r t y readings may  taking f u r t h e r readings.  aggregate  be taken from one  The p o s i t i o n of the sheets i s a l t e r e d  and  position  before  I t i s not s p e c i f i e d t h a t a l l t h i r t y  readings must be taken b e f o r e changing  sheet p o s i t i o n s .  Any  q u e s t i o n s a r i s i n g are to be answered by dropping p e r p e n d i c u l a r s . The  r e a d i n g i s to be measured "by means of any  C r i t e r i a , as . i n V a r i a t i o n I, w i l l have to be  rule."  "established"; a  c o n s i s t e n t system f o r measuring presumably being chosen. r e s u l t s of the readings w i l l be more determined V a r i a t i o n I. determine.a  The  than i n  For example, i n V a r i a t i o n I I a r e a d i n g c o u l d s p e c i f i c frequency, whereas i n V a r i a t i o n I the  frequency might.be anything above a determined  lowest  frequency.  Thus, by a s s i g n i n g d e f i n i t e meanings to the measurements, the performer  c o u l d come up with, s p e c i f i c answers.  I t c o u l d be  p o s s i b l e by making enough measurements to completely the d e t a i l s .  determine  Or, the measurement c o u l d i n d i c a t e a g e n e r a l range,  or area, w i t h f i n a l d e f i n i t i o n o c c u r r i n g  spontaneously.  Through c a l c u l a t i o n s the performer event  i s to be an "aggregate"  or " c o n s t e l l a t i o n , " t h a t i s , a  s i m u l t a n e i t y or a l i n e a r event. i s not g r a p h i c a l l y i n d i c a t e d . not s p e c i f i e d . determined,  The  must decide whether the  The  number of sounds i n an  Ordering o f the events  sounds might be heard  event  also i s  i n the order they are  or the order might be decided by dropping  perpendi-  culars. The performance may may  be taken.  be any l e n g t h ; any number of  readings  Having t o decide a l l f a c t o r s by c a l c u l a t i o n s  calls  f o r many measurements i n order to produce even a r e l a t i v e l y  short  piece.  I t i s p o s s i b l e , but the performer  to be spontaneously  might leave some aspect  decided d u r i n g . t h e performance.. T h i s might  be a q u e s t i o n f o r a dropped p e r p e n d i c u l a r .  Whatever the  l i t i e s , many s o l u t i o n s should a r i s e ; no two  performances are  l i k e l y to.be i d e n t i c a l .  Again the performer's  possibi-  c o n c e p t i o n shapes  the p i e c e . V a r i a t i o n s I and  II  Both scores are g r a p h i c ; the m a t e r i a l s g i v e n are t o be f u r t h e r developed. o f parameters.  G u i d e l i n e s are g i v e n f o r the  particularization  In both scores dropped p e r p e n d i c u l a r s e s t a b l i s h  a d i s t a n c e , the d i s t a n c e then being g i v e n s i g n i f i c a n c e . p o s s i b l e to determine V a r i a t i o n I I to a g r e a t e r extent V a r i a t i o n I.  It i s than  Both v a r i a t i o n s take form i n three b a s i c , s u c c e s s i v e  stages: 1.  M a t e r i a l s e x i s t i n a g r a p h i c form; g e n e r a l  instructions  are  given.  There are innumerable c h o i c e s a t t h i s  point. A more determined stage f o l l o w s as some a s p e c t s a r e f u r t h e r d e f i n e d , some o r a l l d e t a i l s  established.  The performance i s one r e a l i z a t i o n o f the work.  CHAPTER V CONCLUSIONS D i f f i c u l t i e s a r i s e i n approaching scores from a t h e o r e t i c a l s t a n d p o i n t .  chance and indeterminate The a n a l y s t can o n l y p o i n t  out some o f the q u e s t i o n s posed by the s c o r e s , n o t i n g p o s s i b l e i m p l i c a t i o n s . o f . the i n s t r u c t i o n s and p o s s i b l e s o l u t i o n s t o v a r i o u s aspects o f the s c o r e . performer  I t i s not p o s s i b l e t o suggest  t h a t the  choose any s p e c i f i e d way o f c o n s i d e r i n g the s c o r e .  d i s c u s s i o n o f t h e i n s t r u c t i o n s and suggested  A  s o l u t i o n s may g i v e  r i s e t o a .performer s  spontaneity, p o s s i b l y inducing h i s t r a i n of  thought along c e r t a i n  lines.  1  Some g e n e r a l f e a t u r e s appear to be common t o both and  indeterminate  works.  In b o t h . c a t e g o r i e s d e n i a l o f intended  t e l e o l o g i c a l o r i e n t a t i o n e x i s t s t o some e x t e n t . performer  chance  That i s , the  i s given c h o i c e s and i s r e s p o n s i b l e f o r the f i n a l  d e f i n i t i o n o f the.work.  I t has been assumed t h a t  spontaneity  e x i s t s t o some degree i n . a l l the works d i s c u s s e d . In t h i s study the terms chance and indeterminacy  were  attached t o two d i s t i n c t c a t e g o r i e s , t h e . p i e c e s w i t h i n a category e x h i b i t i n g common f e a t u r e s . focused on t h r e e broad  The d i s c u s s i o n o f the f e a t u r e s  a r e a s : the i n s t r u c t i o n s o f t h e s c o r e s , the  notation, and.possible s o l u t i o n s . The were found  i n s t r u c t i o n s o f the indeterminate t o be r e l a t i v e l y s t r a i g h t f o r w a r d .  scores d i s c u s s e d The performer  u s u a l l y i s g i v e n c l e a r " r u l e s " f o r i n t e r p r e t i n g the s c o r e s .  He  i s made aware of h i s c h o i c e s of the n o t a t i o n  or a l t e r n a t i v e s .  are u s u a l l y f o r the  i n order t o . p o i n t out p u r p o s e f u l  Any  sake of c l a r i f i c a t i o n ,  ambiguity.  The  to be handled..  Nr.  XI  (Pousseur) , Two  Books, o f Study. (Cardew). and  be aware t h a t Brown's "discontinuous,,  spontaneously chosen.by the  score  is  Caracteres  Pour C l a v i e r  (Bussotti)  the performer needs to  spatial-coordinate"  i m p l i e s a l a c k of r e s t s ; the value and to be  the  (Stockhausen) ,  exemplify t h i s approach.. With March 1953  not  instructions  d e a l p r i m a r i l y w i t h the manner of. performance, how 7. K l a v i e r s t u c k  explanations  simply  p o s i t i o n of the r e s t s  are  performer.  In the chance category i n s t r u c t i o n s are needed i n order t o e x p l a i n what i s given are.  i n the  score  how  extensive  the  freedoms  I n s t r u c t i o n s are o f t e n enigmatic; the composer i s c a r e f u l  not to be too e x p l i c i t about any Four Systems, f o r i n s t a n c e , "dimension" but Octet  and  aspect of the n o t a t i o n .  Brown uses terms such as  i s i n d e f i n i t e regarding  In  "active"  t h e i r meaning.  In  '61 Cardew g i v e s p o s s i b l e s o l u t i o n s to s e v e r a l s i g n s ,  makes i t e v i d e n t  and  but  i n h i s "notes" t h a t i t i s the r e s p o n s i b i l i t y of  the performer to determine the d e t a i l s , to i n t e r p r e t the i n whatever manner he chooses.  signs  E x p l a n a t i o n s o f t e n appear to  suggest meanings r a t h e r than to d e l i b e r a t e l y s t a t e them, l e a v i n g the performer to search out  implications.  For  instance,  the  tempo d i r e c t i o n " a s . f a s t as p o s s i b l e to as slow as p o s s i b l e " be g i v e n , but without c o n s i d e r i n g  the  statement i n terms of a  may  c o n c e p t i o n of the p i e c e , l i t t l e  a c t u a l meaning i s obvious.  Implications p o s s i b l y w i l l assert t h e i r i n f l u e n c e subconsciously on the performer, pre-planned  r e s u l t i n g i n c e r t a i n spontaneous r e a c t i o n s not  by him.  meaning i n another,  For example, use of terms having a d e f i n i t e non-musical.field.might  p o s s i b l e m u s i c a l meanings.  immediately  The composer might have j u s t provided  a graphic score and noted t h a t nothing i s determined o c c a s i o n f o r . a performance.  the performer  to d e f i n e .  except  the  Instead t h e r e are o f t e n s e v e r a l  pages of i n s t r u c t i o n s n o t i n g what "may" for  suggest  The  be done and what i s l e f t  r e a d i n g through of the  i n s t r u c t i o n s i n c o n j u n c t i o n w i t h the score should i n f l u e n c e the performer's  response.  Often, however, i t i s what i s not g i v e n  i n the i n s t r u c t i o n s t h a t w i l l d e f i n e what i s g i v e n . ness of the i n s t r u c t i o n s a l l o w s each performer score i n d i v i d u a l l y ; many d i f f e r i n g The performer  The o b l i q u e -  to i n t e r p r e t  the  s o l u t i o n s are l i k e l y to r e s u l t .  w i l l not be l e d to one p a r t i c u l a r s o l u t i o n ; w i t h i n  c e r t a i n l i m i t s whatever comes to mind may  be an  interpretation.  The n o t a t i o n of.works i n the indeterminate category on whole i s " t r a d i t i o n a l . "  The n o t a t i o n may  be a l t e r e d i n some  but r e t a i n s a resemblance t o i t s t r a d i t i o n a l source. ( W o l f f ) , m a t e r i a l i s o r g a n i z e d i n "blocks".but  In  I I (Cacioppo)  way  Duo  traditional  symbols are used to r e p r e s e n t dynamics, m e t r i c v a l u e s and In P i a n o p i e c e  the  pitch.  some of the p i t c h e s are connected  In November 1952 Brown g i v e s the i n d i c a t i o n p o s s i b l e to as slow as p o s s i b l e , i n c l u s i v e . "  "as f a s t  by  as  "networks" but they are s t i l l indeterminate works time may  represented by  "noteheads."  be measured c h r o n o m e t r i c a l l y ; a  s e c t i o n i s sometimes bounded by time l i m i t s or a note may chronometric  have a  v a l u e , as ) = 1 second.  Considerable d i v e r s i f i c a t i o n  occurs i n the n o t a t i o n of the  chance p i e c e s , the degree of departure varying greatly. traditional  In  In November 1952  from t r a d i t i o n a l  notation  Brown r e l i e s b a s i c a l l y  on  symbols; p i t c h e s with a c c i d e n t a l s , m e t r i c . v a l u e s  dynamic signs are l o c a t e d on a f i f t y - l i n e s t a f f . of t r a d i t i o n a l  The  n o t a t i o n might r e a d i l y provoke an  Other scores such as 1953  (Brown) and.Octet  '61  and  familiarity  interpretation. (Cardew) combine  traditional  a n d . n o n - t r a d i t i o n a l symbols.  traditional  symbols might serve as a p l a c e to begin the p e r f o r -  mance, inducing, the performer's set  i n motion, he may  traditional  symbols.  traditional) The  spontaneity.  imagination non-  With.the use of e n t i r e l y  (non-  n o t a t i o n of. Music f o r Piano  #7  graphic  i s . s u g g e s t e d to the  very  general  be chosen c o n s t i t u t e s the  score.  (Kasemets) the approximate number of sounds t o be  played i s i n d i c a t e d by.the symbols, but the nature of sounds depends upon f u r t h e r r e s t r i c t i o n s n e c e s s a r i l y make. "consonant" and December 1952  performer.  (Ichiyanagi) suggests  r e p r e s e n t a t i o n of., a type of sound and  range, from which the sounds may In Timepiece  His  the  evolve p o s s i b l e meanings f o r the  notation often l i t t l e  general ideas —  In these scores  the performer  these must  He must, f o r example, d e f i n e dots and  "dissonant.'.'  dashes,  In the scores Four Systems and  (Brown) the n o t a t i o n does not p r o v i d e even general  solutions.  Terms used i n d e s c r i b i n g the score have a d e f i n e d  meaning i n a mathematical context  and might p o s s i b l y provoke  musical meanings; a l l symbols are to be d e f i n e d by the performer. S p a t i a l d i s t a n c e may  be used i n . g r a p h i c scores as a measurement  s p e c i f y i n g e i t h e r a general.area  of pitch., as i n one  possible  i n t e r p r e t a t i o n . o f Timepiece, an approximate d u r a t i o n of or a r e l a t i v e d u r a t i o n between events, December  events,  as p o s s i b l y used i n  1952.  The p o s s i b l e s o l u t i o n s of indeterminate  works w i l l  involve  e i t h e r the j u x t a p o s i t i o n or the m e t r i c r e l a t i o n s h i p of m a t e r i a l . In Nr.  7 K l a v i e r s t u c k XI  (Stockhausen) the performer's  spontaneity  i d e a l l y c o u l d produce c o u n t l e s s j u x t a p o s i t i o n s o f i t s s e c t i o n s . In C a r a c t e r e s  (Pousseur) the o r d e r i n g i s more l i m i t e d .  There are  c h o i c e s but the.composer wishes only c e r t a i n s o l u t i o n s . of C a r a c t e r e s  c h o i c e s are made b e f o r e the performance; once the  page o r d e r i n g i s chosen.Ib becomes determined. Study  In l b  In Two  Books of  (Cardew) the determined m a t e r i a l f i t s w i t h i n time  but j u x t a p o s i t i o n , i n t e r p o l a t i o n or s u p e r i m p o s i t i o n m a t e r i a l l e a d s to innumerable s o l u t i o n s .  limits,  of the  M a t e r i a l too  difficult  to manage spontaneously might be worked out ahead o f time. t o the complexity  of the groups i n g e n e r a l and t h e i r  i n t e g r a t i o n w i t h i n a time l i m i t , i t would seem t h a t w h i l e i t may  be a f a c t o r , i s not s t r e s s e d .  Owing  necessary spontaneity,  In Pour C l a v i e r  ( B u s s o t t i ) c h o i c e s e x i s t only on c e r t a i n pages; other pages are determined. arrows and  J u x t a p o s i t i o n of m a t e r i a l i s guided by d o t t e d other such means.  lines,  The c h o i c e s , r a t h e r than being  d e c i d e d l y a f f e c t e d by s p o n t a n e i t y , (1) f o l l o w i n g the guided  appear t o be between  a l t e r n a t i v e s and (2) i g n o r i n g the  a l t e r n a t i v e s , p l a y i n g the work a s . i t works might be c o n s i d e r e d viewing  i s l a i d out.  Indeterminate  i n terms of the v i s u a l analogy o f  an o b j e c t from d i f f e r e n t angles.  D i f f e r i n g sequences o f  m u s i c a l m a t e r i a l may o f f e r v a r y i n g e f f e c t s .  With  indeterminate  works the a n a l y s t need o n l y p o i n t out freedoms o r . a l t e r n a t i v e s a v a i l a b l e , n o t i n g the degree of s p o n t a n e i t y  likely.  The performer  must l e a r n the determined m a t e r i a l , a p p l y i n g pre-thought t o t h a t end, final  but a l l o w s p o n t a n e i t y  i n some measure t o g i v e the work i t s  shape. S o l u t i o n s to the a m b i g u i t i e s o f chance p i e c e s may a r i s e  spontaneously, but f o r the sake o f c o n t i n u i t y i t i s l i k e l y some pre-thought w i l l be given to these may not r e a l i z e p r i o r t o attempting given i n a chance score. be made.  solutions.  that  The performer  a s o l u t i o n how l i t t l e i s  Many.small choices.must a t some p o i n t  The performer might d e f i n e terms, impose meanings i n a  g e n e r a l way, s t i l l  a l l o w i n g f o r l a s t minute c h o i c e s • t o be made  d u r i n g the performance.  When the performer begins  t o shape the  p i e c e he w i l l l i k e l y d i s c o v e r how.one d e c i s i o n hinges on another. For i n s t a n c e , when o r d e r i n g i s f r e e the q u e s t i o n o f time between events may p a r t i a l l y w i l l represent  depend upon the order, chosen.  a.drawing out o f the performer's i d e a s .  i d e a o f the composition involved.  Solutions The b a s i c  i s t o make the performer become more  The performer faced with a score such as Four Systems  or Timepiece cannot a u t o m a t i c a l l y o r m e c h a n i c a l l y  reproduce sounds  a c c o r d i n g to the composer's r e l a t i v e l y c l e a r - c u t i n t e n t i o n s .  A  response to the b a s i c ideas i s needed t o produce a s o l u t i o n to a chance work...  The i n t e r p r e t a t i o n may  i s , a d i r e c t performance  be a f i n a l  solution,  from the s c o r e , o r , more l i k e l y ,  that  an  i n t e r m e d i a t e stage where the performer becomes aware of p o s s i b l e s o l u t i o n s , the f i n a l c h o i c e o c c u r r i n g spontaneously i n p e r f o r mance. F i n a l l y , a t h e o r e t i c a l examination of chance and  indeter-  minate works f o r piano h a s . i l l u s t r a t e d - c e r t a i n o f the d i v e r s e means used.to .provoke s p o n t a n e i t y .  I t has a l s o shown how  u n d e r l y i n g p h i l o s o p h y has been a p p l i e d to the works. of  Explication  some of the steps the performer must make p r i o r t o the  performance  and some o f the problems  encountered i n examining  such-scores was.of primary c o n s i d e r a t i o n . aid  the  The study e x i s t s to  the.performer i n the r e a l i z a t i o n of chance and i n d e t e r m i n a t e  works.  Books and A r t i c l e s Anonymous. "Composing by Knucklebone." A p r i l 13, 1962.  Time, 79: 82-83,  Behrman, David. "What Indeterminate N o t a t i o n Determines." P e r s p e c t i v e s of New Music, 3: 58-73, Spring-Summer 1965. B o r e t z , B.  "Music."  The N a t i o n , 194: 107-108, 1962.  Brown, E a r l e . "Form." 10: 57-69, 1966.  Darmstadter Beitr'age zur Neuen Musik,  Boulez, P i e r r e . "Alea." F a l l - W i n t e r 1964.  P e r s p e c t i v e s of New Music, 3: 42-53,  Boulez, P i e r r e . "Sonate, Que Me Veux-tu?" Music, 1: 32-44, Spring 1963. Cage, John. S i l e n c e . P r e s s , 1961.  P e r s p e c t i v e s o f New  Middletown, Conn., Wesleyan  Cage, John. A Year From Monday. U n i v e r s i t y Press, 1963.  University  Middletown, Conn., Wesleyan  Cardew, C o r n e l i u s . "Notation-Interpretation, Etc.." 21-33, Summer 1961.  Tempo, 58:  Charles, Daniel. " E n t r ' a c t e : "Formal" or "Informal" Music?" M u s i c a l Q u a r t e r l y , 51: 144-165, 1965. C o w e l l , Henry. "Current C h r o n i c l e : New York." 38: 123-134, 1952.  Musical Quarterly,  Cross, Anthony. "The S i g n i f i c a n c e o f A l e a t o r i c i s m i n TwentiethCentury Music." Music Review, 29: 306-322, 1968. Dennis, B r i a n . "Metamorphosis 12-21, 1966. Dennis, B r i a n . Dunn, Robert.  "Review."  i n Modern C u l t u r e . "  Tempo, 87: 37-40, Winter 1968.  John Cage Catalogue.  New York, Henmar P r e s s , 1962.  F r a n k l y n , A.F. "Skeletons and Marrow." S p r i n g 1962. Godwin, J .  "Avant-Garde."  Tempo, 78:  Trace, 44: 139-144,  Notes, 24: 349-352, 1967.  Gradenwitz, P e t e r . "The Performer's Role i n the Newest Music." C h e s t e r i a n , 34: 61-64, Autumn 1959. G r u n f e l d , F. "Guggenheim R o u l e t t e . " Jan. 4, 1962. G r u n f e l d , F. "Cage Without Bars." Feb. 4, 1960. Helm, E.  "Review."  Hitchcock, H.W. 1962-1963.  The Reporter, 26: 36-37,  The Reporter, 22: 35,  Music Review, 30: 155-158, May 1969.  "Music Reviews."  Notes, 20: 307-309, Winter  Hitchcock, H.W. "Current C h r o n i c l e : New York." Q u a r t e r l y , 50: 91-98, 1964. H o l l a n d e r , John. "Silence." 141, S p r i n g 1963.  Musical  P e r s p e c t i v e s o f New Music, 1: 137-  Karkoschka, E r h a r d . Das S c h r i f t b i l d der Neuen Musik. Hermann Moeck V e r l a g , 1966. Maren, R. "The M u s i c a l Numbers Game." Mar. 6, 1958.  Celle:  Reporter, 18: 37-39,  Markgraf, Bruce. "John Cage: Ideas and P r a c t i c e s of a Contemporary Speaker." Q u a r t e r l y J o u r n a l o f Speech, 48: 128-135, A p r i l 1962. McGary, K e i t h . "I Have Nothing." Summer 1962.  A n t i o c h . Review,, 22: 248-261,  Metzger, Heinz-Klaus. " A b o r t i v e Concepts i n the Theory and C r i t i c i s m o f Music." Die Reihe, 5: 21-29, 1961. Meyer, Leonard B. "The End of the Renaissance?" 16: 169-186, Summer 1962.  Hudson Review,  Meyer-Eppler, Werner. " S t a t i s t i c and P s y c h o l o g i c Problems of Sound." Die Reihe, 1: 55-61, 1958. Reynolds, Roger. "Indeterminacy: Some C o n s i d e r a t i o n s . " P e r s p e c t i v e s o f New Music, 4: 136-140, F a l l - W i n t e r 1965. Richart., B. "A Modern Composer L e c t u r e s on A r t . " (Jan. 1962), 416.  Commonweal,  R i l e y , Howard. " A l e a t o r i c Procedures i n Contemporary Piano Music." M u s i c a l Times, 107: 311-312, A p r i l 1966.  Rochberg, George. "The New Image o f Music." New Music, 2: 1-10, F a l l - W i n t e r 1963. Rochberg, George. "Indeterminacy i n the New 9-19, January 1960. Sargeant, Winthrop. May 8, 1954. Schonberg, H.C. June 1960.  "Old H o r i z o n s . "  New  "The Far-Out P i a n i s t . "  Snyder, E l l s w o r t h .  "Review."  P e r s p e c t i v e s of Music."  Score, 26:  Yorker, 30:  125,  Harpers, 220: 49-54,  Notes, 25: 482-483, March  1969.  Stuckenschmidt, H.H. "Sessions on Modern Music Held Near Darmstadt." M u s i c a l America, 78: 18, Oct. 1958. T i l b u r y , J . "The Contemporary .150-152, Feb. 1969.  Pianist."  M u s i c a l Times,  110:  Thomson, V i r g i l . "America's M u s i c a l M a t u r i t y : A TwentiethCentury S t o r y . " Yale Review, 51: 66-74, Autumn 1961. Wolff, C h r i s t i a n .  "On Form."  Die Reihe, 7: 26-31,  Wolff, C h r i s t i a n . "Taking Chances." 38-40, May 1969.  1965.  Music and M u s i c i a n s , 17:  Music B u s s o t t i , Sylvano. 1962.  Pour C l a v i e r , C e l l e , Hermann Moeck V e r l a g ,  Brown, E a r l e . F o l i o and Four Systems. Music P u b l i s h e r s , 1961. Cacioppo, George.  Pianopiece I I .  Cacioppo, George.  Cassiopeia.  Cage, John.  V a r i a t i o n s I.  Cage, John.  Variations II.  Cardew, C o r n e l i u s . Jan. 1962.  New New  Octet '61.  Cardew, C o r n e l i u s . Two H i n r i c h s e n , 1966.  New  York, A s s o c i a t e d  Don M i l l s , BMI Canada,  1967.  Don M i l l s , BMI Canada, 19 67. York, Henmar P r e s s , 1960. York, Henmar P r e s s , 1961. M u s i c a l Times, 103: 35-38,  Books of Study f o r P i a n i s t s .  London,  Ichiyanagi, Toshi.  Music f o r Piano #7.  New  York, P e t e r s ,  1963.  Ichiyanagi, Toshi.  Music f o r Piano #2.  New  York, P e t e r s ,  1964.  Kasemets, Udo.  Timepiece.  Pousseur, H e n r i .  Caracteres.  Stockhausen, K a r l h e i n z . U n i v e r s a l , 1957. Wolff, C h r i s t i a n .  Toronto,  Duo  1964.  London, U n i v e r s a l ,  Nr. 7 K l a v i e r s t u c k XI. for Pianists II.  New  1962. London,  York, P e t e r s ,  1962.  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0101738/manifest

Comment

Related Items