gutkin libre

DaviD Gutkin

Notation Games: On Autonomy and Play in Avant-Garde Musical Scores

Introduction

In his 1938 study of the ludic principle, Homo Ludens, historian Johann Huizinga set play apart from daily life, the ordinary world, and the real itself.1 Three decades later, in Les jeux et les hommes, sociologist Ro-ger Caillois reinscribed the opposition between the ludic and the everyday, going so far as to write that play and ordinary life are constantly and uni-versally antagonistic to each other2. The characteristics ascribed to the notion of play in these two foundational texts of ludic studies bear a notable resemblance to post-Enlightenment claims about the autonomy of art, and indeed Huizinga borrowed Kants terminology from the Critique of Judgment in describing the disinterestedness3 of play. Moreover, a par-ticular vexation in the conception of autonomy advanced by these scholars of play might be likewise discerned in contemporaneous philosophies of art: in both midcentury ludic and aesthetic theory, autonomy tended to be dialectically enmeshed with its opposite. Huizinga and Caillois interpreted play as a dynamic force that shapes the very world that it is said to suspend. Huizinga, for example, noted that his study is not on the play element in culture but on the play element of culture.4 Likewise, Caillois wrote that he had not simply attempted a sociology of games but had laid the found-ations for a sociology derived from games.5 For both writers, plays socio-cultural character and power is wedded to its unsullied separation from

1 Huizinga, Johan: Homo Ludens: A Study of the Play Element in Culture, Boston 1955, p. 7-9, 19, Chapter 1 passim.

2 Caillois, Roger: Man, Play and Games, trans. Meyer Barash, Urbana/Chicago 2001 [1961], p. 63.

3 Huizinga 1955, p. 7. 4 No page number (Foreword). Huizinga writes, For many years the conviction has

grown upon me that civilization arises and unfolds in and as play. Traces of such an opinion are to be found in my writings ever since 1903. I took it as the theme for my annual address as Rector of Leyden University in 1933, and afterwards for my lectures in Zrich, Vienna, and London, in the last instance under the title: The Play Element of Culture. Each time my hosts wanted to correct it to in Culture, and each time I protested and clung to the genitive, because it was not my object to define the place of play among all the other manifestations of culture, but rather to ascertain how far culture itself bears the character of play. Nevertheless, Huizingas English-language translator chose to write in culture for the title.

5 Caillois 2001, p. 58.

168 DaviD Gutkin 169notation Games

art was already premised on a philosophy of play.9 However, rather than ad-ducing the many points of historical confluence between play and art, and probing the matter of priority and influence enterprises far beyond the scope of this essay in what follows I explore a delimited field of the ludic-aesthetic intersection that falls at a late stage in the modernist investment in autonomy: namely, as found in mid-twentieth-century music-notational practice. In particular, I interpret musical notation as a privileged form of mediation between two seemingly opposed midcentury artistic tendencies: on the one hand, an impetus toward the intensified autonomization of art, and on the other hand, the anti-aesthetic embrace of everyday life. I seek to show how, over the course of about two decades, a network of avant-garde composers grappled with these competing (anti-)aesthetic visions. We will see that for composers such as Pierre Boulez, Iannis Xenakis, John Cage, and Cornelius Cardew (and for their commentators), play and game function as recurring tropes in the attempt to stake out a position on the continuum of autonomy.

In an accompanying appendix I include two examples of what I call listening exercises aural-visual analyses that play on themes introduced in the body of this article. One centers on Boulezs Structures Ia and the other on Earle Browns December 1952.

I From the Closed Score to Open-Ended Play

During the early 1950s, numerous young composers of the postwar avant-garde in Europe and the United States employed serial principles derived from Arnold Schoenbergs twelve-tone technique with the aim of genera-ting cohesive, autonomous musical forms. Many of these same composers wrote scores (in Western staff notation) of such detail that they left little room for interpretation and seemed to call for machine-like performers.10

9 For example, the play drive [Spieltrieb] was central to Friedrich Schillers concep-tion of art as expounded in his Letters on the Aesthetic Education of Man. And before Schiller, Kant could write of arts purposiveness without purpose in part because he posited that art was purposive only in play. See Guillory, John: Cultural Capital: The Problem of Literary Canon Formation, Chicago/London 1995, p. 318. For his part, Huizinga describes the constitutive role of play for the civilizing process in general, and devotes a chapter to the relationship between play-forms in art, and another chapter to play in poetry.

10 Of this period, Cornelius Cardew writes: The indeterminacies of traditional notation became to such an extent accepted that it was forgotten that they existed, and of what sort they were. The results of this can be seen in much of the pointillist music of the 50s (Boulez, Berio, Goeyvaerts, Pousseur, Stockhausen, [Herman] Van San, etc.). The music seemed to exclude all possibility of interpretation in any real sense; the utmost differentiation, refinement and exactitude were demanded of the players. Cardew, Cornelius: Notation Interpretation, Etc., in: Tempo, no. 58, summer 1961, p. 22.

the instrumental obligations of life, a paradox of autonomy that Theodor Adorno never ceased pointing to in his writings on aesthetics. To take but one of his many formulations of the principle, in Aesthetic Theory Adorno wrote that art becomes social by its opposition to society, and it occupies this position only as autonomous art.6

But what is really intended by the rhetoric of autonomy? What, pre-cisely, are we said to be gaining autonomy from in play or in art? Some-times it is a question of autonomy from use value, other times from the marketplace, society, politics, subjectivity, history, or everyday life.7 The matter becomes additionally opaque if we grant that all these concepts are less than self-evident even, or perhaps especially, everyday life. (As Si-tuationist raconteur Guy Debord memorably commented in 1961: The very existence of everyday life has been disputed from its very inception.8) More troublesome yet in these modernist discourses is the dialectical pi-vot between the autonomous and its social-quotidian-worldly counterpart (however that is designated). The process by which those play activities and mentalities bounded by Huizingas magic circle become the prin-ciples of culture, or by which Adornos autonomous art becomes social remain murky despite these authors sustained efforts at its elucidation. I believe this dialectic of autonomy continues to comprise one of the major theoretical problems that must be elaborated in comprehending and his-toricizing the modernist project. The present essay is intended as a step in this direction.

As an opening gambit, I want to suggest that since play and art seem to function as twin paradigms within the rhetoric of autonomy, we should more closely inspect this very doubling. Although I observed that twen-tieth-century ludic theory picked up on Enlightenment aesthetics, we could also show that the late eighteenth-centurys disinterested conception of

6 Adorno, Theodor W.: Aesthetic Theory, trans. Robert Hullot-Kentor, Minneapolis, MN 1998, p. 225. The complement to this statement would be that the idea of auto-nomous art only came about in tandem with arts commodification.

7 In a recent study of the concept of autonomy in modernist literature and criticism, Andrew Goldstone asks what modernist writers, in particular times and places, most urgently seek autonomy from. He lays out four basic possibilitiesof ever-mo-re-extensive claims for literary autonomy: elevating the cultivation of aesthetic form over mimetic realism; distinguishing the autonomous artistic work from the less inde-pendent artist who makes it; rejecting any political or communal affiliation for artist and artistic practice alike; or, finally, disavowing reference to reality altogether. The books four central chapters are correspondingly titled Autonomy from Labor, Au-tonomy from the Person, Expatriation as Autonomy, and Literature without Ex-ternal Reference. Goldstone, Andrew: Fictions of Autonomy: Modernism from Wilde to de Man, New York 2013, p. 4.

8 Debord, Guy: Perspectives for Conscious Changes in Everyday Life, in: Situationist International Anthology, ed. and trans. Ken Knabb, Berkeley, CA 2007, p. 90. Origi-nally published in Internationale Situationniste #6 (August 1961).


ference. When the young Boulez titled his 1952 polemic Schoenberg is Dead, he was not simply reporting the news. Schoenberg, Boulez charged, did not advance twelve-tone composition to its logical conclusion the se-rialization of all sonic parameters and thus remained attached to historical anachronisms.14 In a few scores from the early 1950s, notably Structures I for two pianos (1952), Boulez applied the principle of serial organization to pitch, duration, dynamics, and attack (all of which had to be scrupulously notated) with the aim of engendering a self-consistent music autonomous even from History (ex. 1). In Boulezs words, the piece was his most ex-treme exercise in ridding his music of foreign bodies especially stylis-tic reminiscences15, a rhetoric of pathology resembling Cailloiss nearly contemporaneous claim that play should not be contaminated by the real world16.

While the self-enclosed musical work was notated in a score that left little room for performative interpretation or play, observers perceived a semblance of the ludic in Boulezs compositional process itself. In a 1957 article published in the premiere European organ for serialist discourse, Die Reihe, music theorist Herbert Eimert suggested that the intersection of mechanical automatism and subjective choice that the serial composer must negotiate in his recourse to systematic operations17 resembles the re-lationship in games between pre-given rules and the decisions of the play-ers. According to Eimert, both serialism and games sublimate arbitrary (or irrational) subjectivity into a non-arbitrary hidden machinery.18 Fellow composer Gyrgi Ligeti alleged, in a 1952 article, that Boulezs system its-elf was flawed interesting as a game, he wrote, but fundamentally arbit-

14 Boulez, Pierre: Schoenberg is Dead, in: Notes of an Apprenticeship, ed. Paul Theve-nin, trans. Herbert Weinstock, New York 1968, p. 209-14.

15 Boulez, Pierre: On my Structures for Two Pianos (1952), in: Sonus, trans. Otta Laske, vol. 24, no. 2, Spring 2004, p. 78.

16 Caillois 2001, p. 44. 17 This might include creating matrices of pitch rows, manipulating these rows to derive

series for other parameters such as duration, and further systematizing the relation-ship between different musical parameters through mechanistic means.

18 Eimerts statement reads: Hidden machinery is at work hereone might say that this combination of dream and exact thinking is the patterns, the artistically colou-red pattern, for the aforementioned functions of system and choice. But even if we stay on strictly theoretical ground: games, too, are neither purely arbitrary nor wholly mechanical; they are not even a cross between the two. In serial music this becomes clear as soon as one sees clearly that while the composer is still bound to the elements intelligible to him, he is at the same time carrying out compositional strategy. Ei-mert, Herbert: The Composers Freedom of Choice, in: Die Reihe, vol. 3, 1957, p. 2. For more on the subject of compositional techniques (including serialism), me-chanics, and games see: Krones, Hartmut: Spiel, Kombination und Mechanik in der Musik(geschichte), in: Arnold Schnbergs Schachzge: Dodekaphonie und Spiele-Kon-struktionen, ed. Christian Meyer, Wien 2006, p. 59-84.

In order to make sense of the connection between these compositional and notational tendencies it is necessary to back up a bit and briefly set the stage for this relatively late phase of musical modernism.

Owing to its ephemerality and supposedly non-representational cha-racter, music was widely regarded within nineteenth-century aesthetic dis-course from E. T. A. Hoffmann to Walter Pater as the most emblemati-cally non-functional and autonomous of the arts. Music was even conceived of as autonomous from the phenomenal world as such, following the ap-pearance around 1800 of the concept of an ideal musical work.11 Yet the transcendence imputed to musical works the idea that they exist beyond sonic instantiation was predicated on an increased authority accorded to their material representation: the notated score.12 And in fact, from the ear-ly nineteenth century onwards, Western composers employed increasingly detailed and regulative notations that stipulated not only pitch and rhythm, but ever finer qualities of dynamics, tempo, and articulation.

As notation became even more nuanced in the scores of early twen-tieth-century modernists, the Romantic conception of musical autonomy gradually gave way to a less overtly transcendent philosophy of formal autonomy, exemplified by Arnold Schoenbergs pithy description of his twelve-tone musical technique as composition with twelve notes related only to one another.13 The postwar heirs to twelve-tone composition, prominently including Pierre Boulez and Karlheinz Stockhausen, sought even more fervently a music of autonomous forms purified of external re-

11 According to Lydia Goehrs landmark study, The Imaginary Museum of Musical Works, in the early nineteenth century, art music in the West began to be conceived no longer as an activity of ever-changing performances but as a repertoire of discrete, repeatab-le, and highly determinate works. While almost all musicologists would now concur that the concept of a musical work was indeed a thoroughly historical phenomenon and thus came about at some point there is significant controversy about when this was, and whether Goehrs periodization is correct. See, for example, The Musical Work: Reality or Invention?, ed. Michael Talbot, Liverpool 2000.

12 In order to be true to the composers work, performers were increasingly expected to strictly adhere to its notational representation. An early instance of this werktreue paradigm can be seen in E. T. A. Hoffmanns seminal 1813 essay on Beethovens ins-trumental music: The true artist lives only in the work that he has understood as the composer meant it and that he then performs. He is above putting his own personality forward in any way, and all his endeavors are directed toward a single end that all the wonderful and enchanting pictures and apparitions that the composer has sealed into his work with magic power may be called into active life, shining in a thousand colors, and that they may surround mankind in luminous sparkling circles and, enkindling its imagination, its innermost soul, may bear it in rapid flight into the faraway spirit realm of sound. Hoffmann, E. T. A.: Beethovens Instrumental Music, in: Source Rea-dings in Music History, ed. Oliver Strunk and Leo Treitler, New York 1998, p. 1197f.

13 Schoenberg, Arnold: Composition with Twelve Tones (1941), in: Style and Idea, ed. Leonard Stein, trans. Leo Black, Berkeley/Los Angeles 1975, p. 218. This sentiment resembles Stravinskys aesthetic thought during the period, as well as roughly con-temporaneous developments in New Critical literary theory.


rary.19 Unsurprisingly, Boulez was said to be extremely upset about Ligetis analysis. Following arbitrary rules as if they were not arbitrary may be done with playful self-awareness in the case of the game-player but not in the case of the serialist, for whom the development of compositional method was understood to follow a necessary telos.20 Another common criticism of Structures I still heard today is that its construction is more interesting than its sound; it is held to be overly intellectual blackboard music or paper music.21 Structures I has thus been regarded as only so many games played on the page. And because of their complexity, these games can never quite be realized in performance anyway. In this reading, the culmination of the process inaugurated in the nineteenth century is the autonomous musical work as a hyper-determinate score that must remain silent. (See, however, my Listening Exercise 1 in the appendix.)

The emergence of radically indeterminate, so-called graphic scores in the 1950s represented, in many respects, a reaction against hyper-deter-minate notation and the serial compositional principles associated with it. Placing the fixed musical work in question, a number of composers pro-minently, Cage, Morton Feldman, and Earle Brown began to develop a constellation of variously indeterminate notational practices that someti-mes dispensed with conventional notational signs entirely. With Projection 1 (1950), Morton Feldman sketched rectangular shapes on graph paper to indicate indeterminate pitches (with stipulations only of high, middle, and low registers), while durations were represented spatially. Far more enig-matically, for the score December 1952, Earle Brown drew thirty-one ver-tical and horizontal line segments across a large sheet of paper, providing

19 With that phrase Ligeti is specifically describing Boulezs series of dynamic levels. Elsewhere, he critiques Boulezs arbitrary derivation of durations. The selection of dynamic proportions according to this diagonal process is interesting as a game, but is even less functional than the duration-permutation described [previously]; it is not derived from the musical material, but from a numerical abstraction. Ligeti, Gyr-gi: Decision and Automatism in Structure Ia, trans. Leo Black, in: Die Reihe, vol. 4, 1958, p. 41. At the same time, Ligeti did not attack Structures Ia on sonic grounds, and in fact he is one of the few commentators to have found anything interesting to say about how it sounds.

20 In 1952, Boulez notoriously declared, Anyone who has not felt I do not say under-stand but felt the necessity of the dodecaphonic [twelve-tone] language is USEL-ESS. Boulez, Pierre: Eventuellement, in: Notes of an Apprenticeship, ed. Paul The-venin, trans. Herbert Weinstock, New York 1968, p. 113.

21 Morton Feldman (for whom Boulez was a kind of bte noire and cipher for all that was wrong with European composition) implicitly makes this accusation: If one hears what one composes by that I mean not just paper music how can one not be seduced by the sensuality of sound? Feldman, Morton: Sound, Noise, Varse, Bou-lez, in: Audio Cultures: Readings in Modern Music, eds. Christoph Cox and Daniel Warner, New York/London 2004, p. 15.

Ex.1: Pierre Boulez, Structures Ia, measures 49-54


chestra does indeed correspond to a work, but a special kind that he calls an aleamorphic work. The notation of an aleamorphic work functions like the constitutive rules of a game. Just as any two tennis matches will differ from each other, while both being instances of the game called tennis, each instantiation of an aleamorphic work may consist of different sound-events while still constituting a genuine instance of the work as long as the stipulated set of rules has been followed.24

But it must be conceded that Tormeys rule-instantiation model does not fare so well when confronted with a score such as Browns December 1952 that is to say, a score that does not seem to impose even a mini-mum criterion for identity between performances (other than, perhaps, a common intention to perform it). Although a performance might be un-convincing, how could it fail to yield a genuine instance of the work De-cember 1952?25 Or consider, for instance, Piece 3 from Sylvano Bussottis Five Piano Pieces for David Tudor (1959): the score is comprised of around one-hundred hand-drawn, irregular horizontal lines which form a rectang-le. Scattered among and within these lines are little figurations: an arc, a parallelogram, a profusion of dots (ex. 3). There are no instructions for performance. Although very far removed in conception and notation from Boulezs Structures I, these scores by Brown and Bussotti also verge on silence, although for opposite reasons. Not only do they not represent au-tonomous works in much detail, they indicate no sounds in particular.26

mark to mark. Nothing can be determined to be a true copy of Cages autograph dia-gram or to be a performance of it. Goodman, Nelson: Languages of Art: An Approach to a Theory of Symbols, Indianapolis, IN 1976 [1968]), p. 189-90.

24 Tormey, Alan: Indeterminacy and Identity in Art, in: Monist, vol. 58, no. 2, 1974, p. 206f. 25 But even if it is only as ciphers of intentionality, scores like Browns and Bussottis are

certainly operative in some way. While they include no clear identity constraints, the-se scores do nevertheless condition and frame performance. Caillois observes that a fictive element is often appended to free play (e.g., children playing cops and robbers) in which the sentiment as if takes on and performs the same function as do rules. (Caillois 2001, p. 8) Doesnt the performer of December 1952 constrain improvisation not by explicit rules but by a fictive guise? The performer plays as if it is these signs (and, by extension, the work December 1952) that are being instantiated and the audience, if it is cooperative, plays along. By this I do not at all intend to denigrate such scores nor the performances they yield, although I recognize that my position draws perilously close to the reactionary dogma that modern art has been a variation on the tale of the emperors new clothes.

26 David Tudor, the dedicatee, could not even decide which parts of the notation to look at. He asked: Should everything be interpreted? Black and white? Only black? Only white? All lines? Eventually Tudor decided that all lines must be sound. Bussot-ti disagreed. He stated that he had drawn the score according to no specific musi-cal application or possibilities of execution. The performer, he continued, need not utilize all graphics but only those that his or her eye encountered in the moment of performance. For more on this, see my Drastic or Plastic?: Threads from Karlheinz Stockhausens Musik und Graphik, 1959, in: Perspectives of New Music , vol. 50, nos. 1&2, 2012, p. 272.

hardly any guidelines for their sonic realization (ex. 2).22 Other scores of the period liberally mixed traditional and idiosyncratic notations, such as Cages mammoth Concert for Piano and Orchestra (1957-58), which em-ploys eighty-four notational forms accompanied by an extensive key to interpretation.

According to the definition of notation that philosopher Nelson Goodman proposed in his 1968 book Languages of Art, such scores (one of his actual examples is notation BB from Cages Concert for Piano and Orchestra) satisfy neither the syntactic nor semantic requirements of nota-tional schemes and systems, nor are they strictly allographic.23 That is, they do not yield works as repeatable identities. Against Goodman, philosopher Alan Tormey argued that a score such as Cages Concert for Piano and Or-

22 In addition to the supplementary notebook sketch (shown in example 2) Brown provided the following lengthy, and somewhat technical sounding, but nevertheless rather loose indications: The composition may be performed in any direction from any point in the defined space for any length of time and may be performed from any of the four rational positions in any sequence. In a performance utilizing only three dimensions as active (vertical, horizontal, and time), the thickness of the event indica-tes the relative intensity and/or (where applicable instrumentally) clusters. Where all four dimensions are active, the relative thickness and length of events are functions of their conceptual position on a plane perpendicular to the vertical and horizontal plane of the score. In the latter case all of the characteristics of sound and their relationships to each other are subject to continual transformation and modification. It is primarily intended that performances be made directly from this graphic implication (one for each performer) and that no further preliminary defining of the events, other than an agreement as to total performance time, take place. Further defining of the events is not prohibited however, provided that the imposed determinate-system is implicit in the score and in these notes. Brown, Earle: Prefatory Note, in: Folio and Four Sys-tems, New York/London: 1961.

23 The Stanford dictionary of philosophy has a good summary of Goodmans very pre-cise but complex formulations: the syntactic requirements for a notational scheme are disjointness (each mark belongs to no more than one character) and finite dif-ferentiation, or articulation (in principle, it is always possible to determine to which character a mark belongs); the semantic requirements for a notational system of which all notational schemes are not necessarily members are 1) the characters are correlated to the field of reference unambiguously (with no character being correlated to more than one class of reference, or compliance class), 2) what a character refers to the compliance class must not intersect the compliance class of another charac-ter (i.e., the characters must be semantically disjoint), and 3) it is always possible to determine to which symbol an item in the field of reference complies (i.e., the system must be, semantically, finitely differentiated). See http://plato.stanford.edu/entries/goodman-aesthetics/#TheSymSysLanArt for clarification of this terminology. On Cages notation BB from the Concert for Piano and Orchestra Goodman writes: Now I am by no means pronouncing upon whether adoption of a system like that described might nevertheless be a good idea () Nor am I quibbling about the proper use of such words as notation, score, and work. That matters little more than the pro-per use of a fork. What does matter is that the system in question furnishes no means of identifying a work from performance to performance or even of a character from


Ex.3: Sylvano Bussotti, Piece 3 from Five Piano Pieces for David Tudor

In fact, during the 1950s composers began discussing notations increa-sing propensity to dispense with the representation of sound, and at times spoke of notations transformation into a field of autonomous graphics. Around the same period, musical scores, especially graphically elaborate ones, were increasingly displayed in galleries and sold as fine art. It is thus an ironic development in the history of musical autonomy that the most radical attempts to negate the ideal, autonomous musical work yielded a type of score that resembled the very model of the work-concept: namely, the plastic or pictorial art object.27

27 Stockhausen discusses the notational shift into autonomous graphics in a series of lec-tures titled Musik und Graphik delivered in 1959 at the Darmstadt Ferienkurse. I consider more fully the ironic developments in the history of graphic notation in the concluding section of Drastic or Plastic, p. 282-286.

Ex.2: Earle Brown, December 1952 and diagram from Prefatory Note


music, on the other hand, was to allow for external conflict between opposing musicians whereby one partys move would influence and con-dition that of the other.31 In pursuit of this heteronomous music, Xenakis began to experiment with ideas drawn from the recently emerging mathe-matical and economic field of game theory in two game scores, Duel (1959) and Stratgie (1962). In both pieces there are two separate orchestras each equipped with its own conductor. Each conductor makes moves in what, according to game theory, would be categorized as a zero-sum game.32 Eve-ry move is conveyed by the conductor to his or her respective orchestra, resulting in a specified sound (the music) which simultaneously informs the competing conductor of the move just played (ex. 4). (In a sense, the conductors are the players of the game and the orchestras are the games pieces.) According to Xenakis, audiences followed the musical games in-tently aided by a display board and even cheered good moves.33

Xenakis game scores reflected his entirely serious, formal interest in game theory, but they also represented a self-consciously comic attempt to transpose the high sphere of avant-garde music into the more common world of games and spectator sports. (Xenakis stipulated that at the end of the game, a winner should be announced and a trophy presented by the judge.) But while the playfully agonistic and ritualistic environment created by these performances was at odds with the dominant ethos of solemn and intellectualized postwar musical modernism, a separation from the every-day clearly remained if as the ludic theorists insisted games stand apart from ordinary life.34

31 Xenakis, Iannis: Formalized Music: Thought and Mathematics in Composition, Bloo-mington/London 1971, p. 110-111.

32 Wikipedia defines zero-sum game as follows: In game theory and economic the-ory, a zero-sum game is a mathematical representation of a situation in which a participants gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s). If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero. http://en.wikipedia.org/wiki/Zero-sum_game (accessed: 2014/12/19)

33 Although it scarcely suffices as a substitute for the spectator experience, a 1966 recor-ding of Stratgie played by conductors Seiji Ozawa and Hiroshi Wakasugi with the Yomiuri Nippon Symphony Orchestra can be found on the LP: Ligeti / Ichiyanagi / Takemitsu / Xenakis Orchestral Space (Varese Sarabande Label, 1978). This record is out-of-print and hard to find, so the reader might instead try: https://www.youtube.com/watch?v=Ipwbze36uj0 (accessed: 2014/12/19)

34 The socio-economic backgrounds of the musicians and audiences involved with Xenakiss work may have been fairly homogenous. Nevertheless, his game pieces as well as some of his later ritualistic happenings/events seem to suggest a bid for a more popular or communal avant-gardism.

II Autonomy and Everyday Life

By the mid-1950s, some of the composers who had been most intensively involved in the serial project themselves began to experiment with alter-natives to the closed work. Boulez, for example, came to incorporate in-determinate properties into his Third Piano Sonata (1955-57). The score is precisely notated but can be navigated by the player in multiple ways. Boulez compared it both to a maze and to a map of a city; the basic elements retain their identity but the potential passageways offered to the performer are multiple. The literary theorist Hans Rudolph Zeller made a related analogy: to a game.28 It is worth noting that Boulez conceived of the Third Sonatas interactive, game-like dimension as a shift away from the au-tonomously aesthetic a new perspective supposedly indebted to his study of non-Western musical cultures. Nothing I found [in the music of Afri-ca and the Far East] was based on the masterpiece, he wrote, on the closed cycle, on passive contemplation or narrowly aesthetic pleasure. In these civilizations music is a way of existence in the world of which it forms an integral part and with which it is indissolubly linked an ethical rather than simply aesthetic category.29 Nevertheless, neither Boulezs open-form score, nor more radically indeterminate graphic scores, did much to transform the social fact of avant-garde musics relative autonomy. These experiments did not shatter the regime of the aesthetic and make art a way of existence. Audiences at Darmstadt still sat in dimmed rooms and ob-served the paradigmatic behaviors of nineteenth-century concert etiquette. Equally to the point, audiences and composers of avant-garde music still came, by and large, from a narrow slice of the European and Euro-Ameri-can class system (and, predominantly, one side of the gender divide).30 But what of a score that is not just like a game but really is a game? Would that narrow the distance between the avant-garde and the everyday world?

During the late 1950s, Iannis Xenakis began to develop what he called heteronomous music, which he opposed to autonomous music. In au-tonomous music, Xenakis wrote, virtually everything is written into the score. Even if the composer allows for instances of indeterminacy and improvisation, the only conflict is internal and shut up inside the score. The role of the performers is still only that of controlling the output (sound) by comparison with the input (the notation). Heteronomous

28 Zeller, Hans Rudolph: Mallarm and Serialist Thought, in: Die Reihe, vol. 6, 1960, p. 18.29 Pierre Boulez, Sonate, que me veux-tu?, in: Orientations: Collected Writings, ed.

Jean-Jacques Nattiez, trans Martin Cooper, Cambridge, MA 1986, p. 145. Boulez would also cite Mallarms Un Coup de Ds Jamais NAbolira Le Hasard as an ins-piration for his experimentation with open-form works. He was surely responding, as well, to the chance and indeterminate compositional and notational techniques of Cage and the American experimental circle. See also Ala, in: Orientations.

30 Thanks to Len Gutkin for suggesting this very important last point.


Far more than Boulez or even Xenakis, it was John Cage (and his stu-dents, notably Alan Kaprow35) who sought to dissolve the barrier separa-ting the autonomously aesthetic from quotidian activities and the everyday world. Everything we do is music, Cage famously proclaimed. So perhaps it is not surprising that he objected to the characterization of his composi-tional methods (including chance techniques and indeterminate notation) as game-like; he was bound to be opposed to any kind of activity that was said to stand apart from the world. Asked about his criticism of the term play Cage once responded: I read part of that book called Homo Ludens, do you know it? It discusses man as the playing one and the whole business of setting up rules whereby a game may be played, furthermore setting up a place in which to play in all kinds of ways producing separation from the rest of the world. All of that annoys me.36 But given Cages compositio-nal and notational techniques, the comparison with games is unavoidable: for Music of Changes (1951) he flipped coins and, in consultation with the I Ching, transcribed the results in exacting notation; for the aforementi-oned Concert for Piano and Orchestra he drew playful notations and accom-panied them with lengthy lists of rules; and for Reunion (1968), he even

35 Kaprow often described his art-life activities (doing life, consciously) in terms of play and games. Having once characterized the Happening as a game, an adventure, a number of activities engaged in by participants for the sake of playing, Kaprow la-ter drew a finer distinction between game and play: The critical difference between gaming and playing cannot be ignored. Both involve free fantasy and apparent spon-taneity, both may have clear structures, both may (but neednt) require special skills that enhance the playing. Play, however, offers satisfaction, not in some stated practical outcome, some immediate accomplishment, but rather in continuous participation as its own end. Taking sides, victory, and defeat, all irrelevant in play, are the chief requi-sites of game. In play one is carefree; in a game one is anxious about winning. With a nod to Huizinga, Kaprow suggests that the artist absorb this ideal of non-producti-ve, non-competitive activity and reinvent him or herself as the player. Kaprow, Alan: Education of the un-artist part 2, in: Essays on the Blurring of Art and Life, ed. Jeff Kelley, Berkeley and Los Angeles 1993, p. 122, 125f.

36 Kostelanetz, Richard: Conversing with Cage, New York 2003, p. 280. The full state-ments reads: Yes, I dont like it. I mean I dont like the idea that that is what art is. The reason I dont is because myI read part of that book called Homo Ludens, do you know it? It discusses man as the playing one and the whole business of setting up rules whereby a game may be played, furthermore setting up a place in which to play in all kinds of ways producing separation from the rest of the world. All of that annoys me. And then invention, you see, which Im so involved in, is bad because it changes the rules. And thats what I mean when I refer to spoilsport because an inventor sim-ply ruins the game. But I dont think were playing games. I like to play games, but I dont think of art as being that. I think that we should treat politics and economics, as they are now dying, as games, and I think we should treat this new thing coming into being as inviting celebration. Now I dont think that it is we who are celebrating. I think that it is it thats celebrating. I prefer that notion to the notion of games.

Ex.4: Iannis Xenakis, Matrix for Stratgie, COPYRIGHT 1967 BY BOOSEY & HAWKES MUSIC PUBLISHERS LIMITED

Mit freundlicher Genehmigung von Boosey & Hawkes Bote & Bock GmbH, Berlin


the form of all possible facts. Wittgensteins seminal text inspired Cor-nelius Cardews monumental graphic score, Treatise (1963-67), comprised of 193 pages of finely drawn lines, bulbous shapes, and other pictorially elegant geometric figurations, with only the occasional vestige of conventi-onal notational symbols and no accompanying directions (ex. 5). Just what did this music-notational epic have to do with the Tractatus?

In fact, Wittgenstein invoked musical notation in an important pas-sage of the Tractatus: The gramophone record, the musical thought, the score, the waves of sound, all stand to one another in that pictorial internal relation which holds between language and the world. To all of them the logical structure is common. (Like the two youths, their two horses and their lilies in the story. They are all in a certain sense one.)39 But it would appear that Cardews score stands in no clear relation to any sonic content. And yet it was precisely as a self-contained symbolic system that was to be in need of no supplementary clarification that Cardews notation was indebted to Wittgensteins conception of the logical proposition.

39 Section 4.014. These thoughts begin: At first glance the proposition say as it stands printed on paper does not seem to be a picture of the reality of which it treats. But nor does the musical score appear at first sight to be a picture of a musical piece; nor does our phonetic spelling (letters) seem to be a picture of our spoken language. And yet these symbolisms prove to be pictures even in the ordinary sense of what they represent. [4.011] A bit later Wittgenstein writes: In the fact that there is a general rule by which the musician is able to read the symphony out of the score, and there is a rule by which one could reconstruct the symphony from the line on a gramophone record and from this again by means of the first rule construct the score, herein lies the internal similarity between these things which at first sight seem to be entirely different. [4.0141] Wittgenstein, Ludwig: Tractatus Logico-Philosophicus, trans. C. K. Ogden, New York 2003 [1922], p. 39-41.

Ex.5: Cornelius Cardew, Treatise, page 145

played a game of chess against Marcel Duchamp in which the pieces and board were equipped with sound-yielding circuitry, rendering them both instrument and score.

So, why so much game playing in Cages version of life? For Cage, game-like procedures seemed to serve a purpose related to that of auto-matic serial processes: they allowed for the negation of tradition and sub-jectivity, except that these negations were aimed not at transcending the world but at stripping away the conventionalized detritus that prevents its being encountered in itself . Here the fundamental arbitrariness of games was not necessarily problematic (as it was for the young Boulez) because Cages systems were not meant to be self-contained, but rather to open back onto the very contingency of phenomenal existence from which they derived. This might be observed in Cages flipping of coins to engender notation or in his transformation of imperfections found in sheets of paper (the surface of notational inscription itself) into sounds for his Music for Piano series (1952-1962). Of course, listening to or playing Cages scores still does not yield what we generally think of as ordinary experiences of the everyday world. Borrowing a phrase from Michel de Certeau, we could say that Cages compression of the immanent and the ludic produced a kind of pseudo-autonomous hagiographic everydayness.37

III: Notation and the Form of the World

A kind of counterpart to the Cageian attempt to fuse the autonomous and the worldly might be seen in the vision of a total world doubled in its own autonomous representation. Although many writers have played with the idea of representational totality, it has usually been as a thought game (e.g., Jorge Luis Borgess Library of Babel) or an exercise in futility (e.g., Gertrude Steins ambition in The Making of Americans to describe every kind of person who has lived).38 Perhaps philosophers are more hubristic than novelists. In his Tractatus Logico-Philosophicus, Ludwig Wittgentstein sought to articulate all that can be known about the world by showing

37 De Certeau used the phrase pejoratively: Far from arbitrarily assuming the privilege of speaking in the name of the ordinary (it cannot be spoken), or claiming to be in that general place (that would be a false mysticism), or, worse, offering up a hagiographic everydayness for its edifying value, it is a matter of restoring historicity to the mo-vement which leads analytical procedures back to their frontiers, to the point where they are changed, indeed disturbed, by the ironic and mad banality that speaks in the everyman in the sixteenth century and that has returned in the final stages of Freuds knowledge. Certeau, Michel de: The Practice of Everyday Life, vol. 1, trans. Steven Rendall, Berkeley/Los Angeles 1984, p. 5.

38 In a rather less playful vein, Lukacs described the epic as a form that should represent what Hegel called a totality of objects. See esp. Lukcs, Georg: The Historical Novel, trans Hannah Mitchell and Stanley Mitchell, Boston 1962, p. 93.


Cardew described a 1966 performance of Treatise that he participated in with the improvisation collective AMM as the turning point, and said: I now regard Treatise as a transition between my early preoccupations with problems of music notation and my present concerns improvisation and a musical life.44 Perhaps the trajectory of Cardews thought,45 from his early concern with self-consistent notational systems to his later dedication to improvisational performance and a musical life, recalls Wittgensteins own philosophical evolution: Having renounced the metaphysical concep-tion of an autonomous and pure logical language, the philosopher concei-ved of language-games whose rules were indissociable from use, and thus comprised a form of life.

Conclusion

I have tried to show how in the course of about two decades a group of composers grappled with the tensions inherent in the multifaceted concept of autonomy. Since musical notation was inextricably bound up with this concept, it inevitably comprised one of the central elements in these nego-tiations. But why were ludic techniques and tropes so pervasive? We should observe that play and game are notoriously open-ended words. (Spiel meaning both play and game was Wittgensteins paradigmatic example

44 Cardew 1971, p x-xi. Cardew writes: However I would have been a great deal loster if it hadnt been for the performance of January 1966 () Joining AMM was the turning point, both in the composition of Treatise and in everything I have thought about mu-sic up to now. Before that, Treatise had been an elaborate attempt at graphic notation of music; after that time it became simply graphic music (which I can only define as a graphic score that produces in the reader, without any sound, something analogous to the experience of music), a network of nameless lines and spaces pursuing their own geometry untethered to themes and modulations, 12-note series and their transforma-tions, the rules or laws of musical composition and all the other figments of the musi-cological imagination. / Up to the time of this performance, improvisation had always terrified me; I thought it must be something like composing, but accelerated a million times, a feat of which I knew I was incapable. With the AMM improvisers I discovered that anyone can play, me too, provided, as a Chinese musician of the 16th century put it, the thoughts are serious, the mind peaceful and the will resolute, and what comes out in such play is vital and direct, rather than a translation or interpretation of intel-lect, attitude, notation, inspiration or what have you.

45 There was, in fact, a final turn in Cardews philosophical and political development, and once again notation was a source of contention. In 1971, Cardew writes, he found himself tippedinto the maelstrom of class struggle. No longer was a musical life achieved through experimental modes of improvisation a sufficient goal. To ad-dress real problems in the real world music had to be political, useful, and populist. At the same time, he turned against Treatise and decided that it was in fact no better than Bussottis aestheticized scores. Treatise, he concluded, was a particularly strik-ing outbreak ofa disease of notation, namely the tendency for musical notations to become aesthetic objects in their own right.

According to the Tractatus, an adequately notated logical proposition would be internally consistent, self-evident, and, admitting no supple-mentary metalanguage, fundamentally self-contained. But it would not therefore be divorced from the world. It would describe the scaffolding of the world but treat of nothing. In a gloss on this passage, Cardew wrote of his score-in-process: Reference. What is the reference of the network? This is meaningless. Something things should be referable to the network.40 Indeed Cardew took Wittgensteins hard-to-imagine con-cept of logical notation as an ideal. Thus, Treatise was to be a self-contained symbolic system without need of any additional directions. That it does not describe or prescribe any particular sounds no pitches, no rhythms is the point, since, according to the Tractatus, logical propositions reflect (and are reflected within) the world not as specific empirical things but as formal (or logical) possibilities.

For all the apparent attention to graphic elegance, Cardew sharply distinguished between his notational project and what he described as Bussottis non-functional aesthetic notations[n]otation for its own sake.41 Even though the notation in Treatise designates no specific sound or action, the score was not intended as only a vague stimulus for perfor-mance. Cardew writes: The score must govern the music. It must have authority, and not merely be an arbitrary jumping-off point for improvisa-tion, with no internal consistency.42 A player might decide, for example, that circular shapes always correspond to harmonics, and would then have to determine some sort of rule that makes sonic sense of the variation in circle size, the position of the circles on the page, and so on. Writing about this kind of interpretive decision, Cardew, in his private notes on Treati-se, paraphrases Wittgenstein on the role of arbitrary yet binding rules in games: And if e.g. you play a game you hold by its rules. And it is an inte-resting fact that people set up rules for pleasure and then hold by them.43

After five years of struggling with Treatise Cardew eventually recog-nized insurmountable contradictions in his project. But instead of thinking of the score as a failure he began to understand it as a transitional endea-vor that led him to a new conception of music. On a 1970 radio broadcast

40 Wittgenstein 2003, p. 131 [6.124]. Cardew, Cornelius: Treatise Handbook, including Bun no. 2 Volo Solo, New York 1971, p. iv.

41 A musical notation that looks beautiful is not a beautiful notation, because it is not the function of a musical notation to look beautiful (functionalism). Any attempts in this direction (Bussotti) could be called aesthetic notations. Notation for its own sake, but in a different sense from say, pure mathematics. Cardew, Cornelius: Nota-tion, Interpretation, Etc., in: Tempo 58, Summer 1961, p. 29.

42 Cardew 1971, p. iv. 43 Ibid., vii. Cardew presents the line as a direct quotation of Wittgenstein. I cant locate

this exact phrase in any English translation of Wittgenstein, but it is certainly close to a number of statements from Philosophical Investigations. Cardew read German well, and it may have been his own translation.


mathematically coherent, that the structures should lay themselves bare to the ear. Although Boulez was in part guilty of fostering this interpreta-tion with scientistic writings (and with titles like Structures), his aesthe-tics stemmed equally from a poetics of violence, indebted in particular to Antonin Artaud. The autonomous system was not meant to be heard as such, nor was the ascetic rigidity of the movements construction me-ant to translate into a clarity of perception.48 Rather, the sonic experience should have triggered what Boulez called the disintegration of conventio-nal listening49, a kind of frenzied dissociation resulting from the calculated short-circuiting of memory and historical reference a music of difference and infinite play, paradoxically engendered by a theoretically closed system. When I listened to the piece closely, I found that the critics were right but for the wrong reasons. Structures I is a failure, not because it sounds ran-dom but because it sounds too logical, traditional, and even good a value judgment only possible on the basis of historical criteria.

Pulling myself away from the score, I was surprised to discover that I heard a coherent, even quasi-traditional musical rhetoric in Structures Ia (the first and most heavily serially automated movement of the piece). From this realization I set out to discover what else I might hear if, instead of thinking about the serial processes that I had been trained to recognize in the score, I allowed myself to form a detailed and quite personal auditory understanding of the work. I then elucidated this process by returning to the score and mapping my listening back onto it. The following is a con-densed and fragmentary representation of this listening exercise.

Boulez divides Structures Ia into eleven sections, each separated by a brief pause. I describe moments from the first three sections, and then I consider one aspect of the whole movement.

Section 1: From the very beginning I cant help but hear something that I am sure Boulez would not want me to hear in such a way: a direc-tionally rhyming melody two 2-note ascending phrases followed by two 2-note descending ones (ex. 6). Boulez sought to suppress principle and subsidiary lines in his dense polyphony but how can these not emerge?

48 On the contrary, railing against Mondrians austere, constructivist tendencies, Boulez (in a letter to John Cage) held up Klees paintings as preferable: His [Mondrians] works are the most denuded of mystery that have ever been in the world.It is against the facility of a Mondrian that I rise up. After this Boulez writes: For the rest, genu-ine works are those in which one can never come to an end (infinite [infrangible?] nucleus of the night.); and when all is said, one still has said nothing, and one will never say anything. Boulez, Pierre. The Boulez-Cage Correspondence, ed. and col-lected Jean-Jacques Nattiez, trans. Robert Samuels, Cambridge 1993, p. 116f.

49 Boulez 2004, p. 83.

of a word that resists regulative definition.)46 Perhaps it was partially owing to some fundamental ambiguities in the idea of game/play encompassing, as it does, a continuum of activities that run from the hyper-regulated to the entirely improvised, and dichotomously describing both abstract rules and embodied actions that the ludic was useful both to those composers who aimed to construct purified autonomous systems and to those who would endeavor to open these up to the world. Further elaboration of this conjecture would be a topic for another essay.

What I have most wanted to thematize here were the complex super-impositions and oscillations conjoining the transcendently autonomous and the immanently quotidian. In each case some vestige of the autono-my concept was retained. Cardews improvisational musical life is also, presumably, not everyday life (although the problematic denotation of that last phrase grows increasingly clear). Nevertheless, we can identify a gene-ral trajectory since the midcentury away from the autonomy principle, and therefore away from aesthetics as such.

Appendix: Two Listening Exercises

ExErcisE 1:

What would be different has not begun as yet. (Th. W. Adorno)

As I observed above, Structures I has often been regarded as only so many numerical games.47 A corollary of which is that the piece has been consi-dered as suitable for score-based, but not sonic, analysis. When Structures I is in fact listened to, a common observation is that despite its systematic construction, it sounds as chaotic as works composed through chance ope-rations, such as John Cages contemporaneous Music of Changes (1951). But I believe the critique of sonic randomness is founded on a misappre-hension, namely the assumption that the work should sound objective or

46 Wittgenstein famously argued for the inadequacy of regulative linguistic definitions by showing that no single characteristic is common to all activities we call games (board-games, card-games, ball-games, athletic games but also singing and dancing games). Thus, he suggests that it is not with ideal definitions but in a wonderfully recur-sive move with the language-games that comprise real linguistic practices that we should begin. Wittgenstein, Ludwig: Philosophical Investigations, trans. G. E. M. Ans-combe, P. M. S. Hacker, and Joachim Schulte, Malden/Oxford 2009 [1953], 36e.

47 Dominique Jameaux also argues against the disparaging classification of Structures Ia as blackboard music. Jameaux, Dominique: Pierre Boulez, trans. Susan Bradshaw, Cambridge, Mass. 1991, p. 283.


Ex.7: Pierre Boulez, Structures Ia, measures 8-11Ex.9: Pierre Boulez, Structures Ia, measures 114f.

Ex.8: Pierre Boulez, Structures Ia, measures 32f.

Section 2: The atonality fissures into competing harmonic regions as clusters of white-key harmonies (a, d, a, e) are punctuated by sequence of black-key open intervals (b-flat, e-flat, g-sharp) (ex. 7). This harmonic con-flict is mirrored in a temporal one. Time seems to get out of sync with itself it moves backwards and forwards, or, better, forwards at different speeds.

Section 3: Although Boulez wrote that his durational system was con-ceived without reference to pulse, something like a pulse emerges. And, even more surprising, strains of tonality, with the pitches g, a-flat, and e sounding to me like scale degrees 2, 3, and 7 in f-minor (ex. 8). And other motives pop out of the welter of activity.

Because of the construction of Boulezs initial row, sections 1-5 end with a tritone that most dissonant interval of Western tonal music. This tritone acts, paradoxically, as both an element of tension (bearing the vesti-gial trace of its dissonant function in tonality and, given its structural recur-rence, stability. It also exemplifies the rhyming trope. The disappearance of the tritone in its concluding role during the second half of the movement (sections 6-11) almost makes its role as a motive even clearer. The trito-ne seems doubly unresolved; disappearance is not a resolution but a new

tension. But in the final moments of the piece so-mething really interesting happens. The three pitches (d, a, e) before the final pitch resolve the linge-ring idea of the tritone, for-ming two open fifths (the interval that the tritone strains toward in tonal mu-sic) in a crystal clear high register. But the ultimate e-flat, in a sharply contrasting bass register, forms yet ano-ther tritone with the still ringing a (ex. 9). It is a perfect moment funny and even poignant, and brings the work to an architecturally coherent close.

Ex.6: Pierre Boulez, Structures Ia, measures 1-7


Instead, by attempting this, you constantly highlight particular areas in ra-pid oscillation. 2) Conversely, look closely. The lines are not so perfect. They have subtly rough (trilling?) edges.

References

Adorno, Theodor W.: Aesthetic Theory. Trans. Robert Hullot-Kentor Minneapolis, MN 1998.

Boulez, Pierre: Schoenberg is Dead, in Notes of an Apprenticeship, ed. Paul Thevenin, trans. Herbert Weinstock, New York 1968, p. 209-14.

Alea, in Notes of an Apprenticeship, ed. Paul Thevenin, trans. Herbert Weinstock, New York 1968, p. 26-38.

Possibly in Notes of an Apprenticeship, ed. Paul Thevenin, trans. Her-bert Weinstock, New York 1968, p. 111-140.

On My Structures for Two Pianos (1952), trans. Otta Laske, in Sonus, volume 24, no. 2, Spring 2004, p. 77-87.

Form in Orientations, ed. Jean-Jacques Nattiez, trans. Martin Cooper, Cambridge, MA 1986, p. 90-96.

Sonate, que me veux-tu? in Orientations, trans Martin Cooper, Cam-bridge, MA 1986 p. 143-154.

Caillois, Roger: Man, Play and Games, trans. Meyer Barash, Urbana/Chi-cago 2001 [1961].

Cardew, Cornelius: Notation Interpretation, Etc., Tempo, no. 58, sum-mer 1961, p. 21-33.

Cardew, Cornelius: Treatise Handbook, London: Edition Peters, 1971.de Certeau, Michel: The Practice of Everyday Life volume 1, trans. Steven

Rendall, Berkeley/Los Angeles 1984. Eimert, Herbert: The Composers Freedom of Choice, in Die Reihe, vol.

3, 1957, p. 1-9. Goehr, Lydia: The Imaginary Museum of Musical Works: An Essay in Musical

Philosophy, Oxford/New York 1992. Hoffmann, E. T. A.: Beethovens Instrumental Music, in: Source Rea-

dings in Music History, ed. Oliver Strunk and Leo Treitler, New York 1998, p. 1193-1197.

Huizinga, Johan: Homo Ludens: A Study of the Play Element in Culture. Boston 1955.

Kaprow, Allan: Essays on the Blurring of Art and Life, ed. Jeff Kelley, Berke-ley/Los Angeles 1993.

Kostelanetz, Richard: Conversing with Cage. New York 2003.

With this exercise I discovered that I cannot but hear sound structures in reference to past experience and hence in a semiotic system of ingrained, if contingent, meaning. My being-in-history has rendered me necessarily inadequate to the task of encountering the work (no less in history itself, of course) on its own autonomous terms. In a sense, it is not only that I have analyzed Structures Ia but that it has analyzed me; it has functioned as an aesthetically elevated Rohrschach test to expose my own personal idiosyncrasies and my more general cultural inheritance.

ExErcisE 2:

My procedure is simple: I listened to four performances of December 1952 while looking at the score. (David Tudor, Michael Daugherty, David Ar-den, ensemble conducted by Brown) My aim was not exactly to figure out employed by the four different interpreters, but to discover what sound illuminates about this notation-image, and vice versa. These meditations on the score are only a haphazard assortment of impressions. It is a somewhat self-indulgent exercise.

What to do with the swaths of white space, the unmarked paper around the lines? Is it silence? That is what Tudors performance tells me, but Daughertys suggests otherwise. Here the space is rendered percussive, an electronic resonance beneath pitched articulation. What could make this space active? The lines do give the white space a kind of shape. Even Tudors silence has a shape.

I had thought the lines were sparse sort of elegant and restrained in their subtle differences of length and width. Also, they stayed still for Tudor and Arden. One then another, maybe a line overlaps here and there. The ensembles performance showed otherwise. There is an active relati-onship between lines. In fact I noticed something strange while focusing on individual lines: a small border of light, or space whiter than the paper appears an optical illusion. It only works for a couple lines at a time, and only if those lines are close to each other. I imagine the complex relation-ships that might form between the shifting simultaneities of illuminated lines within the ensembles collective vision. I think there were 23 perfor-mers in the ensemble. At a given moment were they ever all focusing on a different line, or all on the same line? I suppose they wouldnt have known.

People speak of accurate performances of traditionally notated mu-sic. Ardens realization here is something else altogether: realistic.

Daughertys interpretation is striking for its apparent distance from what I see. Why so much sonic continuity? I simplistically associated the hanging resonances with white space, but where are these extended me-lodic trill figures to be found on the page? I have two ideas. 1) Step back from the score and try to take the whole thing in at once without focusing on any particular area. Unless you are about four feet away it cant be done.

192 DaviD Gutkin

Krones, Hartmut: Spiel, Kombination und Mechanik in der Musik(geschichte), Journal of the Arnold Schnberg Center, (7) 2005, p. 59-84.

Ligeti, Gyrgi: Decision and Automatism in Structure Ia, in Die Reihe vol. 4, 1958, p. 36-62 .

Pater, Walter: The School of Giorgione, Fortnightly Review, 1877. Schoenberg, Arnold: Composition with Twelve Tones (1) (1941), in Style

and Idea, ed. Leonard Stein, trans. Leo Black, Berkeley/Los Angeles 1975, p. 214-244.

Tormey, Alan: Indeterminacy and Identity in Art, Monist, vol. 58, no. 2, 1974, p. 203-215.

Wittgenstein, Ludwig: Philosophical Investigations, trans. G.E.M. Anscom-be, P.M.S. Hacker and Joachim Schulte, Oxford 2009.

Xenakis, Iannis: Formalized Music: Thought and Mathematics in Compositi-on, Bloomington, IN/London 1971.