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Reassessing the Emergence of Indeterminate Music

Jonathan De Souza


On 11 November 1952, Pierre Boulez arrived in New York for the first time. Though touring as the music director of the Renauld-Barrault theatre company, he had another reason for the visit, a long-awaited reunion with a close friend.1 ‘I am happy to think that at last we are going to see each other again,’ Boulez had written before leaving France, ‘to go on and on nattering. After three years, we have something to talk about. I will have my latest things to show you.’2 Foremost among these ‘latest things’ was a piece for two pianos, Structures 1a (1951–2), embodying the most recent developments in European serialism. Of course, Boulez’s friend, a fellow composer, would also have new music and ideas to share. His name was John Cage.

Cage had appeared at Boulez’s door with scores and records, shortly after his arrival in Paris in the spring of 1949. During his six-month stay in Europe, they had become fast friends. Boulez had helped arrange a performance of Cage’s Sonatas and Interludes (1946–8) and introduced the American to Olivier Messiaen, who asked Cage to demonstrate the prepared piano for his class at the Paris Conservatoire.3 This would be mirrored in 1952 when Boulez would perform at the Peabody Conservatory for a course taught by Cage’s former teacher, Henry Cowell, and his Second Piano Sonata (1947–8) would be programmed beside the work of Cage, Morton Feldman, and Christian Wolff.4 In the years between their visits, however, Boulez and Cage could only write letters, sharing the results of their research, their hopes and frustrations, as they became the artists that we think of today – artists who are often seen in opposition, as representatives of ‘ultra-rationality’ and ‘anti-rationality’.5

This binary understanding of serialism and chance is common, especially in surveys of recent music history. Roger Sutherland, for example, writes that ‘the European serialists and the American experimentalists proceeded from diametrically opposed ideological positions.’6 The English composer Reginald Smith-Brindle also conceives the schism along continental lines:

In the U.S.A. indeterminacy began at a time when European composers were just beginning to wrestle with integral serialism. In fact a whole group of American composers (including such major figures as John Cage, Morton Feldman, Earle Brown, Harry Partch, and Christian Wolff) circumnavigated integral serialism almost completely because they were largely unaware of its existence.7

Not only do these claims dissonate with evidence from the early 1950s, they fail to account for the later appearance of performance indeterminacy on both sides of the Atlantic.8 To better understand this important development, we must reassess the complex relationship between American and European composition in the post-war years.8 After critiquing existing genealogies of indeterminate music, I will discuss two elements central to the creation of this repertory: interdisciplinary influences and the parametric thinking essential to both serialism and chance composition. While the substantial aesthetic differences of Cage, Boulez, and their colleagues cannot be ignored, I feel that, for the moment, we will gain more by exploring their connections than by simply reasserting their independence.

Before entering the post-war milieu, we will review some common explanations of indeterminacy’s origins. Earlier instances of musical indeterminacy are often cited as antecedents to – or, perhaps, justifications of – experimental practices, but their actual relevance to compositional thought in the 1950s is debatable. Still, their prominence in the discourse on aleatory music bears investigation. At the very least, they may remind us that the presence of chance elements in music, which Paul Hindemith called ‘one of the ugliest modern musical diseases’, is not an exclusively modern occurrence.9 They also make it clear that Cage, despite his innovations, should not be uncritically pronounced ‘the inventor of chance music’.11 Most aspects of indeterminacy were present, in a more or less nascent state, long before the 1950s.

Perhaps due to dubious attributions to Haydn and Mozart, examples of chance composition from the eighteenth century remain fairly well known:

From 1757 to 1812 at least twenty musical dice games were published in Europe. […] They offer, two centuries earlier than the twentieth-century ‘advent’ of aleatory music, methods by which chance-determined music may be composed.12

However, referencing these games as a precedent for post-war experimentalism seems to overlook the cultural factors that gave rise to them.13 Coinciding with the period’s growth in music publishing and social changes in music making, these games responded to an intense public fascination with mathematics.14 ‘Without the eighteenth century’s great interest in mathematics,’ notes Stephen Hedges, ‘there would have been no incentive for the creation of such unusual means of composition as dice games.’15 Although amateurs may have principally enjoyed generating simple pieces without knowledge of harmony or counterpoint, the games’ composers and mathematicians were seriously interested in the probabilistic aspects of the games, which presented extensive possibilities for permutation and combination.16 This motivation shows the games to be closer in spirit to the work of Milton Babbitt than either Boulez or Cage. Notwithstanding the obvious technical resemblances and Cage’s use of the Musikalisches Würfelspiel, k294d, in HPSCHD17 (1967–9), connecting eighteenth-century dice-throwing and twentieth-century coin-tossing does not seem historically or aesthetically meaningful. Simply put, a rediscovery of these games did not prompt the rise of indeterminacy. Perhaps more importantly, musical dice games did not involve performance indeterminacy, a more widespread phenomenon than Cage’s methods of chance composition.

Another posited lineage for aleatory music remains within twentieth-century America, identifying Cage as ‘a pupil of the bold but rather naïve experimenter Henry Cowell, an early admirer of [Charles] Ives.’18 In this account, Cage simply ‘continued along certain lines of both Ives and Cowell.’19 It is true that these idiosyncratic composers were among the first to explore indeterminacy in performance. Ives includes a cadenza ‘to play or not to play’ in Scherzo: Over the Pavement (1910, rev. 1926–7) for winds, percussion, and piano, and his symphony, The Unanswered Question (1908, rev. 1930–35), allows the conductor to cue instrumental groups freely.20 Cowell’s pieces in ‘elastic form’, such as the ‘Ritournelle’ from Les mariés de la Tour Eiffel (1939), have flexible duration ‘through the use or omission of bars provided’, and his Mosaic Quartet (1935) is an early example of mobile form, allowing players to perform composed blocks in any order.21 Still, Cage became interested in Ives’s music only after he had already begun to work with performance indeterminacy himself.22 Furthermore, while Cowell’s influence is clear in Cage’s early use of percussion, the prepared piano, and his interest in Asian music and philosophy, this explanation overlooks the chronology of Cage’s development.

Ives and Cowell’s music gave new freedoms to performers but did not involve the random compositional processes found in Cage or the eighteenth-century dice games. Cage’s chance procedures emerged from the use of gamuts23 and charts, during the composition of his Concerto for Prepared Piano (1950–51).24 Works of the following period, such as Music of Changes, do not vary in performance, and it was only in 1957 that Cage turned to performance indeterminacy.25 The systematic use of chance in composition was a more radical break with the preceding generation. After all, in addition to Ives and Cowell, conservative composers distasteful to the avant-garde had occasionally employed performance indeterminacy in their work. As Hugh Davies observes, ‘Even [Ralph] Vaughan Williams used “aleatorism” in indicating a passage in On Wenlock Edge [(1908–9)] where the singer is to be quite independent of his accompaniment.’26 Similar textures appear in Hindemith’s Second String Quartet, Op. 16 (1918), where the second violin repeats a figure without coordination with other parts, and in the music of Darius Milhaud, whom Cage and Boulez repeatedly mock in their letters.27

A third background advocated by the literature involves interrelated issues of notation and improvisation. Some feel that improvised cadenzas or the skeletal indications of figured bass notation form zones of indeterminacy that prefigure contemporary practices.28 While improvisation also gives the performer certain freedoms, the influence of these earlier practices does not appear to be primary: the most prominent composers of this music – Boulez, Cage, Stockhausen, Feldman – are explicitly opposed to improvisation.29 Instead, Cage identifies a form of indeterminacy in Bach’s music that is more related to notation:

In The Art of the Fugue, structure, […] method, […] and form […] are all determined. Frequency and duration characteristics of the material are also determined. Timbre and amplitude characteristics of the material, not being given, are indeterminate.30

This, of course, is a blatant reinterpretation of the past: Bach and his contemporaries would not have perceived these characteristics – or the realisation of a continuo part – as indeterminate, understanding them, rather, as part of broader notational and performance practices.

The standard history of Western musical notation is a narrative of increasing specification. One by one, aspects that had formerly been open – instrumentation, dynamics, tempo, and so on – became fixed in the score.31 As this occurred, the importance of these elements grew: that is, in Bach, ‘extremely wide variations of tempo and dynamics are possible without misrepresenting the substance of the work’, but in Beethoven ‘dynamics must be observed with great fidelity’ due to their ‘structural importance’.32 It is something of a cliché to argue that this movement reached its apex in the overly complex, mathematical rhythms and multitudinous dynamic and articulation markings of post-war serialism. As Michael Parsons puts it, ‘in a totally serial work […] the players’ role is entirely technical, not interpretative.’33

Still, musical notation always leaves aspects of performance unspecified, and the fiction of notational determinacy is linked to ideologies of the musical work. According to Lydia Goehr, the work-concept began to function as a regulative ideal circa 1800, ‘when composition was defined as involving the predetermination of as many structural elements as possible’ and the ideal of performance as notational compliance followed.34 Indeterminate and early music, then, may share this much: they both fail to conform to nineteenth-century models of notation and the musical work.35 Indeterminate music particularly questions the work-concept by questioning ‘formal notions of pre-composition, fixed instrumentation, repeatability, and compliant performance’.36 This challenge emerges from new approaches to composition, notation, and performance, born of a desire to break free from traditional practices and explore fresh musical possibilities.

When Pierre Boulez arrived in New York in 1952, he moved into John Cage’s apartment on the lower East Side. At last, they were together again. In this tiny studio by the river, painted completely white and lacking any furniture except a piano, David Tudor performed Music of Changes (1951) for the two composers.37 Contrary to statements by Joan Peyser and Roger Sutherland, this piece – the first of Cage’s to be fully composed through chance operations – was not a source of division.38 In fact, Boulez’s enthusiasm for the work is clear in his last letter before leaving Paris:

Thank you for the Music of Changes. Which I liked a lot, and which I was so pleased to get. I was absolutely charmed by this development in your style. And I am with you all the way. It is certainly my favourite amongst everything you have done. And I have lent it here to all my young composer friends.39

During his visit, Boulez would also perform Structures 1a with Tudor at Columbia University, another sign of close links between chance composition and integral serialism. Writing in 1951, Boulez tells Cage ‘We are at the same stage of research.’40 What, then, was the focus of this shared inquiry?

On both sides of the Atlantic, composers were determined to move into new musical territory, beyond the confines of tradition and memory. ‘“Post-war” was not going to be just a return to “pre-war”,’ Boulez notes, ‘in music any more than it was in cooking, clothes or drinks…There was to be no return to the fusty habits of the past.’41 While this dissatisfaction extended to both twelve-note and neoclassical mainstreams, the new generation shared a unanimous appreciation for the music of the late Anton Webern.42 Though Michael Nyman claims that American experimentalists were uninterested in the ‘rational, purely technical and procedural aspects of Webern’s music’ or ‘a sterile matching of numbers with sounds’, Boulez’s extensive, post-Webernian theoretical discussions meet nothing but praise from Cage.43 Furthermore, around this time, Cage copied and analysed Webern’s Symphony, Op. 21 (1927–8), with his student, Christian Wolff.44

Both Europeans and Americans appropriated Webern’s music for their own purposes, claiming it as a precursor to their new mode of musical thought. For example, Stockhausen published an analysis positing integral serial organisation in Webern’s Concerto, Op. 24 (1931–4), and Cage attributed his own technique of rhythmic structure to the Viennese composer.45 Many scholars, such as Carl Dahlhaus and Peter Westergaard, attacked these reinterpretations.46 Still, whatever truth their critiques might have, the avant-garde had already made its conceptual leap. The core of their new perspective is expressed by Wolff, writing in the serialist journal, die Reihe: ‘In Webern it becomes clear that music is sound and silence, and that sound consists of pitch, duration, loudness and timbre.’47 This basic, four-part scheme represents a parametric approach to sound that was essential for post-war composition.

‘Until around 1950,’ says Stockhausen, ‘the idea of music as sound was largely ignored.’48 It was an idea that would take on great importance as ‘sound began to emerge as a disproportionate element too immense to be ignored.’49 Conceptualising music as sound was anticipated by Cage’s early interest in noise. Already in 1937, in a talk entitled ‘The Future of Music: Credo’, Cage had redefined music as ‘organization of sound’, predicting advances in technology which would ‘provide complete control of the overtone structure of tones […] and […] make these tones available in any frequency, amplitude, and duration.’50 In this statement, the groundwork for parametric thinking was in place: ‘treating musical objects as divisible, theoretically at least, into parameters pitch, rhythm, duration, timbre’ was now possible.51

While the importance of parametric thinking for integral serialism is clear, it is also central to chance composition. For example, in Music of Changes, Cage composed each event by combining pitch, duration, and dynamic characteristics from three separate charts.52 Paul Griffiths suggests that, in these techniques, Cage created parametric thinking:

Boulez’s reference […] to “duration, amplitude, frequency, and timbre – in other words, the four characteristics of a sound” echoes a statement of sound’s quaternary nature in Cage’s recent essay “Forerunners of Modern Music”, and suggests that the definition of those four parameters, which provided the organizational basis for total serialism, came from Cage. The setting-up of compositional algorithms, another essential feature of total serialism, also has clearer origins in Cage’s principle of rhythmic proportioning than in Boulez’s turmoil of motivic extrapolations. All that was needed was to add the twelve-note principle to these Cageian elements – the four parameters, automatic operation – and [Messiaen’s] Mode de valeurs [one of the first works of integral serialism] would be the almost inevitable result.53

Cage’s influence is clear in Boulez’s letters, particularly in the younger composer’s description of Structures 1a:

I have undertaken a new series of works (currently for two pianos, but it might require three or four). In this series of works, I have attempted to realize the serial organization at all levels: arrangement of the pitches, the dynamics, the attacks, and the durations. […] I’ve taken over your chess-board system for my own purposes.54

Still, we should be careful about attributing the paradigm to any single composer. After all, like Cage’s rhythmic structures, Messiaen’s use of isorhythm involves a degree of independence in the composition of pitch and duration. Furthermore, Edgard Varèse’s work approached the direct organization of sound, and the influence of electronic music, acoustics, and information theorist, Werner Meyer-Eppler, should also be acknowledged.55

Parametric thinking created the fields of new musical possibility for which composers had been searching. The vast distance between Boulez’s parametric approach in Penser la musique aujourd’hui and Schoenberg’s concern with themes and traditional formal models in Fundamentals of Musical Composition shows how far the post-war generation had moved.56 The unpredictable aspects of parametric techniques helped composers eradicate traditional relationships, a desire expressed in Cage’s circle’s ‘necessity to get rid of the glue so that sounds would be themselves.’57 Similarly, Stockhausen, in his ‘point music’ phase, describes Messiaen’s Mode de valeurs (1949) as ‘fantastic music of the stars’ with notes ‘existing for themselves in complete freedom and formulated individually in considerable isolation from each other.’58

Different composers explored this new territory in their own ways. For example, Henri Pousseur composed by developing ‘an interaction between global characteristics laid down by a general parametric structure, and an ordering of single elements which was party to editorial decisions often taken at a later stage.’59 In their respective writings, Cage emphasises the role of silence, while Boulez gives greater weight to the traditional focus of Western music: ‘Pitch and duration seem to me to form the basis of a compositional dialectic, while intensity and timbre belong to second categories.’60 Within a parametric world, composers could employ a wide range of techniques, using parameters independently or in coordination, treating them as a continuum or dividing them into discrete steps.61 Parameters could be governed by total organisation or total chance, in a systematic or free manner, in the service of continuity or discontinuity, tradition or experiment. The musical and personal conflicts that arose between Europeans and Americans grew out of these kinds of issues, these different approaches to a shared parametric framework.

A parametric approach was also crucial for indeterminacy in performance. With this conceptual development, it became possible to ‘decontrol’ only one or two parameters of an event, as Morton Feldman notes:

Up to now the various elements of music (rhythm, pitch, dynamics, etc.) were only recognizable in terms of their formal relationship to each other. As controls were given up, one finds that these elements lose their initial, inherent identity. […] Only by ‘unfixing’ the elements traditionally used to construct a piece of music could the sounds exist in themselves – not as symbols, or memories which were memories of other music to begin with.62

New forms of graphic notation that accompanied indeterminacy were also parametric. For example, in Cage’s Variations II (1961), transparencies with lines and points are superimposed to create a notation: each line represents a parametric axis that determines the characteristics of the sound events represented by each point.63 This piece, like a vast range of post-war composition including serialism, chance, and indeterminacy, is a direct product of a radically new, parametric understanding of music.

While parametric thinking created important new possibilities, aleatory music was not its inevitable result. The aesthetic motivation to compose music with variable performance arose due to a variety of other factors. One of these was dissatisfaction with the first, systematic approaches to parametric composition. Looking back on integral serialism in 1957, Boulez was full of hostility, calling the movement ‘a fetishism of numbers, leading to pure and simple failure.’64 Around the same time, Cage was also critical of his own work from the early 1950s, saying ‘before indeterminacy in performance […] although my choices were controlled by chance operations, I was still making an object.’65 Elsewhere, he makes his shifted priorities explicit: ‘more essential than composing by means of chance operations, it seems to me now, is composing in such a way that what one does is indeterminate of its performance.’66

Cage’s drive towards indeterminacy is often associated with his well-known encounter with Zen Buddhism. This preoccupation, however, should be situated in a broader interdisciplinary climate. In their search for new ideas, post-war composers in Europe and America drew extensively on other arts, science, and philosophy. We should not underestimate the importance of these other domains, free from traditionally musical approaches to work-production and performance. At the beginning of the 1950s, Boulez’s circle, for example, included writers, such as the playwright Armand Gatti, and the novelist Pierre Jouffroy.67 Boulez attributes his adoption of aleatory techniques primarily to the influence of Joyce and Mallarmé, writing that ‘musical considerations have counted less than the literary contacts I have happened to have. […] My current form of thought arose more from reflections about literature than about music.’68

At the same point, Feldman and Cage were closely associated with the contemporary art scene. ‘To understand the intellectual climate in which the music of “chance” first emerged,’ writes Feldman, ‘one must know something of the renaissance happening to painting in the early 1950s in New York City.’69 Feldman states that these artists, including Philip Guston, Mark Rothko, Jasper Johns, Robert Rauschenberg, Willem de Kooning, and Jackson Pollock, ‘were such a strong influence on my creative life, much more so than composers in general.’70 With other painters, particularly Mondrian, they contributed to Feldman’s lifelong concerns with space, colour, and stasis, launching him into a musical equivalent of ‘action painting’:

The new painting made me desirous of a sound world more direct, more immediate, more physical than anything that had existed heretofore. […] The new structure required a concentration more demanding than if the technique were that of still photography, which for me is what precise notation has come to imply.71

Stockhausen’s aleatory compositions were also inspired by an extramusical source. In the early 1950s, following his musical education, he studied communications science and phonetics at the University of Bonn.72 There, Stockhausen analysed the nature of sound, learning that the distribution of characteristic formants in a noise can only be determined statistically. ‘The structures I found in individual sounds, like consonants,’ he explains, ‘I expanded into a larger time-frame, deriving entire musical sections behaving in the same way as a single noise.’73 This statistical method, where defined fields or masses are more important than individual elements, is applied on a still larger scale in Stockhausen’s open form works, such as Klavierstück XI (1956). According to M. J. Grant, this move to aleatory music was ‘a refinement in, rather than a change of, technique’, building on the statistical aspects of serial composition.74

Finally, Cage’s own move into indeterminacy was motivated by his reading of Thoreau and his interest in the social aspects of musical practice. James Pritchett observes, ‘Cage thought that many, if not all, of his post-1957 works were musical analogies to anarchy in one form or another.’75 While the composition of determinate works through chance operations fulfilled his desire to approach Zen nonintention, Cage’s growing social concerns pushed him further:

Music is a social art, social in the sense that it has consisted, formerly, of people telling other people what to do, and those people doing something that other people listen to. What I would like to arrive at, though I may never, what I think would be ideal, would be a situation in which no one told anyone what to do and it all turned out perfectly well anyway.76

For Cage, reducing his control over a notated object was to become less important than reducing his control over other human subjects, in a radical critique of Western musical practice.

When Boulez visited Cage in November 1952, neither one could have predicted where the coming decade would take them, from determinacy to indeterminacy, from friendship to antagonism. There is not space here to discuss the artistic and personal differences that brought about their eventual break. However, it seems safe to say that this conflict coloured the ways in which these composers later represented themselves and, by extension, the way in which the history of their music has often been written. Yet, when we return to the primary sources and encounter the enthusiastic affection of Cage and Boulez’s early letters, commonalities and mutual influence become clear. We then see that the relationship between serialism and chance, between American and European developments in post-war composition, is closer and more complex than polarised accounts acknowledge. The emergence of indeterminate music must be situated in this rich artistic and intellectual climate, where creative individuals engaged in dialogue, where conceptual leaps rethought the past and absorbed diverse, extramusical perspectives. Understanding this context may not only extend our knowledge of indeterminate music: it may also help us deepen our appreciation of conditions conducive to compositional innovation in other places, at other times.


1 Joan Peyser, Boulez (New York: Schirmer Books, 1976), p.80 Back

2 Jean–Jacques Nattiez, ed., The Boulez–Cage Correspondence, trans. Robert Samuels (Cambridge: Cambridge University Press, 1993), p.134 Back

3 Peyser, pp.60–61 Back

4 Ibid., p.83 Back

5 Eric Salzman, Twentieth-Century Music: An Introduction, 4th edn. (Upper Saddle River, NJ: Prentice Hall, 2002), pp.157, 163 Back

6 Roger Sutherland, New Perspectives in Music (London: Sun Tavern Fields, 1994), p.139 Back

7 Reginald Smith Brindle, The New Music: The Avant-Garde since 1945 (Oxford: Oxford University Press, 1975), p.61 Back

8 Following Cage’s original definitions, I will use the term ‘indeterminacy’ to refer to variation in performance and ‘chance’ to denote random compositional procedures. Confusion of terminology often obscures the important distinction between these two phenomena. See James Pritchett, The Music of John Cage (Cambridge: Cambridge University Press, 1993), p.108; John Cage, Silence: Lectures and Writings (Middletown, CT: Wesleyan University Press, 1961), p.36 Back

9 One scholar examining this relationship is M. J. Grant, who argues that serial music is, in essence, an ‘aleatoric process’ and that the statistical implications of open form were part of serialism from its inception. See M. J. Grant, Serial Music, Serial Aesthetics (Cambridge: Cambridge University Press, 2001), pp.131–160 Back

10 Elliott Schwartz and Barney Childs, eds., Contemporary Composers on Contemporary Music (New York: Holt, Rinehart and Winston) 1967, 89. Quoted in David Cope, New Directions in Music, 6th edn. (Madison, WI: WCB Brown & Benchmark, 1993), p.136 Back

11 Aaron Copland, The New Music: 1900–1960 (London: Macdonald, 1968), p.177 Back

12 Stephen A. Hedges, ‘Dice Music in the Eighteenth Century,’ Music & Letters, lix/2 (1978), p.180 Back

13 Cope, p.124; Ramona Cormier, ‘Indeterminacy and Aesthetic Theory,’ Journal of Aesthetics and Art Criticism, xxxiii (1975), p.285; Paul Griffiths, ‘Aleatory,’ Grove Music Online, ed. Laura Macy (http://www.grovemusic.com), §2 (3 July 2006) Back

14 Dexter Edge, ‘Viennese Music Copyists and the Transmission of Music in the Eighteenth Century,’ Revue de musicologie, lxxxiv (1998): 300–301; Robin Moore, ‘The Decline of Improvisation in Western Art Music: An Interpretation of Change,’ International Review of the Aesthetics and Sociology of Music, xxiii/1 (1992): 67–9 Back

15 Hedges, p.180 Back

16 Leonard Ratner, ‘“Ars combinatorial”: Chance and Choice in Eighteenth-century Music,’ Studies in Eighteenth-century Music: A Tribute to Karl Geiringer on his Seventieth Birthday, ed. H. C. Robbins Landon and Roger Chapman (London: Allen & Unwin, 1970), pp.345–50 Back

17 While Mozart’s music had been an inspiration to Cage in the creation of HPSCHD, the inclusion of the musical dice game was suggested by Cage’s collaborator, the composer of computer music, Lejaren Hiller. Pritchett, 160 Back

18 Gerald Abraham, The Concise Oxford History of Music (London: Oxford University Press, 1979), p.853 Back

19 Elliott Antokoletz, Twentieth-Century Music (Englewood Cliffs, NJ: Prentice Hall, 1992), p.475 Back

20 Ibid. Back

21 David Nicholls, ‘Henry Cowell,’ Grove Music Online, ed. Laura Macy (http://www.grovemusic.com), §2 (3 July 2006); Michael Nyman, Experimental Music: Cage and Beyond, 2nd edn. (Cambridge: Cambridge University Press, 1999), p.41 Back

22 John Cage, A Year from Monday: New Lectures and Writings (Middletown, CT: Wesleyan University Press, 1967), pp.37–8 Back

23 ‘In [Cage’s] usage, a gamut is simply a specific collection of musical materials to be used in a piece, defined before the rest of the process of composition continues.’ Pritchett, p.40 Back

24 Ibid., p.62 Back

25 Ibid., p.109; Cage, Silence, 36. Cage himself compares Cowell’s use of formal indeterminacy not to his own techniques but to the work of Boulez and Stockhausen. Ibid., p.71 Back

26 Hugh Davies, ‘Aleatory Procedures,’ The Musical Times, cvii (1966), p.504. The passage to which Davies refers is in the fifth song of the cycle, ‘Bredon Hill’, beginning at the text, ‘Oh, noisy bells, be dumb’. Ralph Vaughan Williams, On Wenlock Edge: A Cycle of Six Songs for Tenor Voice with Accompaniment of Pianoforte and String Quartett [sic] (ad lib) (London: Boosey & Hawkes, 1946), p.38 Back

27 In Hindemith’s quartet, see bb. 458–511 of the final movement. Robin Stowell, ‘Extending the Technical and Expressive Frontiers,’ The Cambridge Companion to the String Quartet, ed. Robin Stowell (Cambridge: Cambridge University Press, 2003), p.149; Davies, p.504; Nattiez, pp.48, 51, 57, 134, 149 Back

28 Cope, pp.124–6; Carol S. Gould and Kenneth Keaton, ‘The Essential Role of Improvisation in Musical Performance,’ The Journal of Aesthetics and Art Criticism, lviii/2 (2000), p.144; Donald J. Grout and Claude V. Palisca, A History of Western Music, 6th edn. (New York and London: W. W. Norton, 2001), p.734 Back

29 Pierre Boulez, Orientations: Collected Writings, ed. Jean-Jacques Nattiez, trans. Martin Cooper (London and Boston: Faber, 1986), p.461; Richard Kostelanetz, ed., John Cage: An Anthology (New York: Da Capo, 1991), p.164; Karlheinz Stockhausen, Stockhausen on Music: Lectures and Interviews, comp. Robin Maconie (London: Marion Boyars, 1989), pp.112–113; Morton Feldman, Give My Regards to Eighth Street: Collected Writings of Morton Feldman, ed. B. H. Friedman, afterword by Frank O’Hara (Cambridge, MA: Exact Change, 2000), p.6. Earle Brown, with his background in jazz, is notably more positive about improvisation. Back

30 Cage, Silence, p.35 Back

31 Richard Rastall, The Notation of Western Music: An Introduction (London: J. M. Dent & Sons, 1983), p.186 Back

32 Roger Smalley, ‘Some Aspects of the Changing Relationship between Composer and Performer in Contemporary Music,’ Proceedings of the Royal Musical Association, xcvi (1969–1970), pp.73–5 Back

33 Michael Parsons, ‘Sounds of Discovery,’ The Musical Times, cix (1968), p.429 Back

34 Lydia Goehr, The Imaginary Museum of Musical Works: An Essay in the Philosophy of Music (Oxford: Clarendon Press, 1992), p.234 Back

35 Ibid., p.268. For Stockhausen’s desire to ‘renounc[e] the composition of single works’, see Karl H. Wörner, Stockhausen: Life and Work, trans. Bill Hopkins (Berkeley, CA: University of California Press, 1973), pp.110–111. For similar statements by Boulez, see Nattiez, p.86 Back

36 Goehr, p.262 Back

37 Peyser, p.82 Back

38 Ibid., p.121; Sutherland, p.120 Back

39 Nattiez, p.133. Emphasis original. Back

40 Ibid., p.97 Back

41 Boulez, Orientations, p.505 Back

42 Nattiez, pp.47–8; Cage, Silence, p.63; Feldman, p.10 Back

43 Nyman, pp.37–8; for Boulez’s discussions, see Nattiez, pp.81–8, 99–103, 119–25; for Cage’s response, see ibid., pp.92, 133 Back

44 David Patterson, ‘Cage and Beyond: An Annotated Interview with Christian Wolff,’ Perspectives of New Music, xxxii/2 (1995), pp.59–60 Back

45 Grant, p.110; Cage, Silence, p.63 Back

46 Grant, p.110; Peter Westergaard, ‘Webern and “Total Organization”: An Analysis of the Second Movement of Piano Variations, Op. 27,’ Perspectives of New Music, i/2 (1963), pp.107–120 Back

47 Grant, p.107 Back

48 Stockhausen, p.88 Back

49 Feldman, pp.34–5 Back

50 Cage, Silence, p.4 Back

51 Grant, p.62 Back

52 Pritchett, p.79. Cage only used three charts because Music of Changes, as a work for solo piano, lacks significant timbral variation. Back

53 Paul Griffiths, Modern Music and After: Directions Since 1945 (Oxford: Oxford University Press, 1995), p.29 Back

54 Nattiez, pp.90–91 Back

55 Grant, p.62 Back

56 Arnold Schoenberg, Fundamentals of Musical Composition, ed. Gerald Strang (London: Faber, 1967), pp.v–vii Back

57 Cage, Silence, p.71 Back

58 Wörner, p.61 Back

59 Grant, p.142 Back

60 Cage, Silence, p.63; Pierre Boulez, Boulez on Music Today, trans. Susan Bradshaw and Richard Rodney Bennett (London: Faber, 1975), p.37 Back

61 Cage, Silence, p.62; Boulez, Boulez on Music Today, pp.85–98 Back

62 Feldman, p.35 Back

63 Cage, Silence, p.69 Back

64 Pierre Boulez, ‘Alea,’ trans. David Noakes and Paul Jacobs, Perspectives on Contemporary Music Theory, ed. Benjamin Boretz and Edward T. Cone (New York: W. W. Norton, 1972), p.46 Back

65 Kostelanetz, John Cage, p.19 Back

66 Cage, Silence, p.69 Back

67 Nattiez, p.5 Back

68 Pierre Boulez, ‘Sonate que me veux-tu?’ Perspectives of New Music, i/2 (1963), p.32 Back

69 Feldman, p.15 Back

70 Ibid., p.115 Back

71 Ibid., p.5 Back

72 Stockhausen, p.46 Back

73 Ibid. Back

74 Grant, p.140 Back

75 Pritchett, p.193 Back

76 Richard Kostelanetz, Conversing with Cage (New York: Limelight Editions, 1988), p.74 Back

©Jonathan De Souza, 2008

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