A term applied to music whose composition and/or performance is, to a greater or lesser extent, undetermined by the composer.
PAUL GRIFFITHS
As defined above, the term ‘aleatory’ (‘aleatoric’ is an etymological distortion) applies to all music: it is impossible for a composer to prescribe every aspect in the realization of a composition; even the sound result of a tape playback will depend on the equipment used and the acoustic conditions. However, the term is usually restricted to music in which the composer has made a deliberate withdrawal of control, excluding certain established usages which fall within this category: for example, keyboard improvisation, the cadenza, the ossia, the ad libitum, unmeasured pauses, alternative scorings and the provision of sets of potentially independent pieces (e.g. the Goldberg Variations). Three types of aleatory technique may be distinguished, although a given composition may exhibit more than one of them, separately or in combination: (i) the use of random procedures in the generation of fixed compositions (see §3); (ii) the allowance of choice to the performer(s) among formal options stipulated by the composer (see §4); and (iii) methods of notation which reduce the composer’s control over the sounds in a composition (see §§5–7). The liberty offered by these various means can extend from a choice between two dynamic markings to almost unguided improvisation. Some theoretical considerations and practical consequences are outlined in §§8–9.
Until the mid-20th century Western composers were constantly seeking notational developments that would enable them to determine sounds with greater exactness, an attitude entirely opposed to the aleatory. There were, however, some trivial examples of aleatory music in the 18th century, when schemes were published for generating simple pieces in response to the results of dice throws. These games usually left only one aspect to guided chance: the ordering of bars supplied with the scheme, for instance, or the melody to be placed over a given rhythmic-harmonic pattern. Mozart and Haydn were sometimes claimed as authors, but probably without any more than commercial justification. One might also consider the art of keyboard improvisation as a precursor of aleatory music, but here the creator and the performer are identical; once an improvisation is published for performance by others, it has to be respected as much as any other printed score. In most aleatory music, on the other hand, the creator provides a score which gives a degree of freedom to any performer. Similarly, other improvised musics, such as jazz and folk traditions, were not initially the most important influences on aleatory music.
The first composer to make a significant use of aleatory features was Ives, whose scores include exhortations to freedom, alternatives of an unprecedentedly important character, and unrealizable notations which silently invite the performer to find his own solution. From the 1930s Cowell followed Ives’s lead in such works as the String Quartet no.3 ‘Mosaic’ (1934), which allows the players to assemble the music from fragments provided. He used other ‘elastic’ (his own word) notations to introduce chance or choice into the performance, occasionally instructing the performers to improvise a certain number of bars or ad libitum. His sometime pupil Cage began to use what he called ‘chance operations’ in composition during the early 1950s, notably in the Music of Changes for piano (1951). At first Cage’s work had most influence on his immediate associates: Feldman wrote a number of ‘graph’ pieces, such as the Intersection and Projection series, in which notes are replaced by boxes, determining pitch only relatively; and Brown abandoned all conventional notation in, for example, December 1952, consisting of 31 black rectangles printed on a single sheet.
European composers were more hesitant in taking up aleatory techniques. Such early examples as Stockhausen’s Klavierstück IX (1956) and Boulez’s Piano Sonata no.3 (1956–7) allow the player no more than limited freedom in the ordering of composed sections. By this time Cage had gone much further in abandoning the control exercised by the composer, or even the performer(s), reaching an extreme point in 4' 33'' (1952), whose only sounds – those of the environment – are quite unpredictable. About 1960 purely verbal scores were introduced by LaMonte Young and others, and the following decade saw the pursuit of aleatory methods to a wide range of ends throughout the world. Composers such as Henze and Lutosławski used aleatory incidents in otherwise determined compositions, while Rzewski, Globokar, Stockhausen and others produced scores that give only a few specifications to stimulate improvisation.
After an explosion of interest in the late 1960s, coinciding with a revolutionary period in Western culture generally, aleatory music became a dead or at least dormant issue. Stockhausen returned to conventional notation in his Mantra (1970). Boulez began to write fully determined works again, and even to rescind some of the freedoms of earlier pieces, such as his Improvisation sur Mallarmé III (1959), whose revised score, made in the 1980s, removes alternatives of material and flexibilities of ordering. And though Cage remained true to non-intention, even he went back to staff notation in Cheap Imitation (1969) and many later works. A kind of superficial looseness (represented, for example, by ad libitum repeats of figures, or by ‘time-space’ notation, in which duration is determined by length on the staff) remained as part of the lingua franca of moderate modernism, and improvisation continued as the mainstay of experimental music. But Cage's later music is unusual in the period for the precision of its invitations to chance.
As here defined, aleatory composition involves the use of random procedures in determining musical aspects that are to be notated; unless other aleatory techniques are also used, the resultant score is no less fixed than a conventional composition. Chance procedures in composition have been most fully and diversely exploited by Cage. In producing the Music of Changes, for example, he tossed coins to decide how he should make choices from charts of pitches, durations, intensities and other sound aspects, deriving his chance operations from the ‘I Ching’, the Chinese book of changes. Similar methods were used in assembling Williams Mix for tape (1952) and in notating the parts for 12 radio receivers in Imaginary Landscape no.4 (1951). (The latter work is inevitably unusual, in that the sounds heard in performance are out of the control of both composer and players, depending on the broadcasts that happen to be received.) Other random techniques employed by Cage include placing notes on imperfections in the music paper (Music for Piano, 1952–6) and using templates drawn from maps of the constellations (Atlas eclipticalis, 1961–2). An example of random composing combined with other aleatory features is Cage’s Winter Music (1957), in which from one to 20 pianists may use any quantity of the chance-composed score.
Atlas eclipticalis is one of the few Cage scores from between the mid-1950s and the end of the 1960s to use traditional notation. When Cage returned to such notation, it was with new chance procedures, such as the use of ‘time brackets’ to define not specific durations but rather the intervals during which sounds must start or stop.
Xenakis's principle of ‘stochastic’ composition is different. In such works as ST/4 for string quartet (1956–62), he used a computer in producing music modelled on stochastic processes, where events on the smallest scale are indeterminate though the shape of the whole is defined. Thus randomness is introduced as a necessary part of a willed product, and Xenakis retained the right to modify the computer result. Few composers other than Cage have made much use of true aleatory composition.
By contrast with Cage and his chance operations in composition, other composers have avoided introducing any randomness into their composing or notation, but have permitted the performer some flexibility in realization by means of the provision of alternative orderings. Sometimes, as in Stockhausen’s Klavierstück XI, the player is instructed to pick from the alternatives on the spur of the moment; other works, such as Boulez’s Piano Sonata no.3, suggest a more considered choice. The sonata is in five parts which may be played in any of several permutations, and each part contains sections which may be variously ordered and/or omitted. Fig.1 shows the ‘Troisième texte’, one of the tiniest satellites of Boulez’s mobile-form Structures II for two pianos (1956–61); note that the ordering of events is to some extent free, and that durations and dynamics are variable. Other notable works of mobile form include Boulez’s Pli selon pli for soprano and orchestra (1957–62), Stockhausen’s Momente for soprano, chorus and instruments (1962–4) and Pousseur’s ‘fantaisie variable genre opéra’ Votre Faust (1960–67), which draws the audience, too, into the decision-making. All of these works provide comprehensive rules for the assembling of a performance, whereas when Cage used formal variability, as in Winter Music or the Concert for Piano and Orchestra (1957–8), he left options as open as possible: any amount of the solo part of the Concert may be omitted, as may any or all of the orchestral parts, and the piece may be performed simultaneously with others by the composer.
The types of aleatory music so far described use conventional notation to determine sounds, although, in compositions of mobile form, new signs may be necessary to guide performers in choosing a route. Many composers have introduced new notations which render the sounds themselves indeterminate, frequently by abandoning traditional signs for graphics or texts, each of which is considered below. But it is possible to use conventional notation in an indeterminate manner. An early example is Stockhausen’s Zeitmasse (1955–6), whose tempos depend on the physical capacities of the five wind players: the duration of a single breath, or the fastest speed possible.
The composer can also allow flexibility in the interpretation of conventional symbols by giving alternatives or by specifying sound aspects in only relative terms. Alternative tempos, dynamic degrees and so on have been extensively used by Boulez. Relative notation has often been employed to specify a more or less narrowly defined register rather than a determined pitch, particularly in vocal music. Boulez’s Structures II contains an analogously imprecise notation of durations (fig.1), and Boulez has frequently specified a range of tempo rather than a definite figure, so setting limits to a fluctuating rubato.
Greater indeterminacy is introduced, still with conventional notation, when performers are asked to improvise on the basis of given pitches or rhythms, to interpret a given pitch sequence with any rhythm, to interpret a given rhythm with any pitches, and so on. All these possibilities have been used by composers as different as Kagel and Lutosławski.
The most systematic use of newly invented symbolic notations is to be found in Stockhausen’s ‘process’ compositions, which specify how sounds are to be changed or imitated rather than what they are to be. The first of these compositions was Plus-Minus (1963), whose title indicates the two principal signs that Stockhausen introduced for these purposes: the plus sign means that a sound is to be increased in some ‘parameter’ with respect to some preceding sound (i.e. it may be louder, higher in pitch, longer, more subdivided etc.), and the minus sign has the reverse significance. Fig.2 shows this notation in a fragment of Spiral for solo performer (1969). The number of plus and/or minus signs in any ‘event’ indicates the number of parameters to be changed; other signs refer to articulation (e.g. ‘POLY’ indicates a polyphonic event).
Graphic notation – which may be distinguished from the preceding by the fact that it signifies, if at all, by analogy instead of by symbol – has been employed to supplement conventional notation where the latter proves inadequate. For example, the ‘shape’ of a glissando (i.e. the variation of pitch with time) can be shown by a curved line on a staff; though the aleatory character of such notations is an inevitable concomitant rather than a deliberate addition. A more truly aleatory use of graphics occurs in Stockhausen’s Zyklus for solo percussionist (1959), a compendium of quasi-conventional graphic notation used in conjunction with traditional signs. Fig.3, from Haubenstock-Ramati’s Tableau II for orchestra (1970), shows some examples of this type of graphic notation.
Alternatively, graphics may be used as a total replacement for standard symbols, as in Brown’s December 1952. Logothetis, Cardew (in Treatise, 1963–7) and other composers continued in this direction, raising graphic notation to the level of visual art, but beyond the level of musical intelligibility, since such scores often provide the performer with little or no information as to how the signs are to be interpreted, and the possibilities for sound realization are exceedingly diverse. Fig.4 is an example of graphic notation from Cage's Fontana Mix (1958), a score consisting of transparent sheets to be superposed, and used by the composer originally to make a tape composition. In this case, although the notation looks enigmatic, the rules given with the design offer exact (though chance-determined) means by which sounds are to be chosen and assembled.
Like graphics of this latter sort, verbal texts can be used to give the performer a very large degree of freedom in determining both form and content. The text may be a straightforward instruction for action – often a far from conventionally musical action, as in Young’s Composition 1960 no.5, whose principal requirement is ‘Turn a butterfly (or any number of butterflies) loose in the performance area’. Other text scores are more inscrutable; Young’s Piano Piece for David Tudor no.3, for example, consists of the text: ‘most of them were very old grasshoppers’. More usually, texts have been used to give a more or less clearly stated basis for ensemble improvisation; notable examples include Rzewski’s Love Songs (1968) and Stockhausen’s Aus den sieben Tagen (1968).
Aleatory music implies a quite new inventive role for the performer, and its evolution has been closely linked with the technical innovations and accomplishments of individuals, such as Tudor or Boulez, and of ensembles.
In some respects, compositions of mobile form introduce the fewest new problems, since the material can be fully composed. It is significant that the earliest European efforts in this direction – Stockhausen’s Klavierstück XI and Boulez’s Piano Sonata no.3 – are each for a solo player, who is in a position to make spontaneous or rehearsed decisions about the ordering of the music. When more performers are involved and when the composer does not want an anarchic result, either the performers must make all decisions in advance, as in Stockhausen’s Momente, or else the composer must supply a system of cues and other signals. This was the procedure adopted by Boulez in writing for two pianos (Structures II), for chamber ensemble (‘…explosante-fixe …’) and for orchestra in several works (Pli selon pli, Eclat, Domaines) which expand the conductor’s function.
Where the notation, or lack of it, renders the music still more indeterminate, the performer’s responsibility becomes weightier. It is often difficult for the composer to make his intentions clear without hampering the player more than he wishes, so aleatory scores have frequently to be understood against the background of a composer’s more determinate work or within an implicit cultural milieu; but a performer may choose to take the score out of that background or milieu – as, for example, when the English composer Gavin Bryars made a realization of Stockhausen’s Plus-Minus with fragments from Schubert’s C major String Quintet and a pop song – and so draw attention to the new division of labour between composer and executant.
The common reaction to this problem in the 1960s was the establishment by composers of performing traditions within their own ensembles, of which the Sonic Arts Union (consisting of the four composers Ashley, Behrman, Lucier and Mumma) and the Stockhausen Ensemble were prominent. Such groups were able to develop collective qualities of reaction previously rare outside long-established string quartets, and composers in turn made use of these group characteristics. Sometimes this meant that very little had to be specified in the score – Stockhausen’s Aus den sieben Tagen texts represent an extreme case. Other composers welcomed the extreme variability with which minimally notated scores may be interpreted, and made no attempt to form a tradition of performance. Their interest was, rather, in exciting the players to awareness of their own and their colleagues’ potentialities, a position exemplified by Wolff’s work.
Some performing ensembles dispensed even with this unassuming stimulus from a composer, and engaged in ‘free improvisation’, though most continued to play composed music as well. Among the groups which had some success in this field were Musica Elettronica Viva (Rzewski and others) and New Phonic Art (Globokar and others). It was only at this point that other improvisatory musics had much direct influence on aleatory practice in Western art music, and some players, among them Michel Portal and Barry Guy, involved themselves concurrently in jazz and ‘free improvisation’.
The introduction of chance into a work of art undermines the notion that creation requires, at each moment and on every level, a definite choice on the part of the artist. One implication of Mallarmé’s Un coup de dés, a work that had a great influence on European aleatory composers, is that each creative decision gives rise to a multiplicity of possible continuations, and in the projected Livre he was to provide for alternative continuations to be realized. But in general the Western work of art was, until the mid-20th century, supposed to have an ideal identity, and, in the case of performed arts, a performance might be judged by the extent to which it was held to correspond with that identity.
In the works of most European composers, the operation of aleatory technique does not fundamentally disturb that conception. The composition is still the product of an individual mind, though some aspects are left indefinite; the performer has still to realize the composer’s intentions. (One problem in aleatory music is that of whether the performance should communicate the fact of indeterminacy. The flexible features of a work may not be perceived as such if the listener does not hear frequent different performances, still less if the work is heard most usually in a single recording. In some disc issues, such as that of Pousseur’s Votre Faust, the difficulty has been tackled by having the listener take decisions about operating balance and volume controls during the playing.) And the roots of the aleatory in European music are principally within the European tradition itself. If composers were impressed by the freedom of performance in oriental musics, their reaction was to attempt to establish some equivalent in Western terms. In doing so, they found more immediate stimulus in literary parallels (particularly Mallarmé and Joyce) and in the principle of serialism as it had been developed in Europe up to the mid-1950s. This development had brought about the avoidance of large-scale formal processes, and so the ground was laid for forms in which sections could be moved about without disrupting the whole. In addition, the permutational character of serialism was seen as implying permutable forms. Yet another field of activity within European music which stimulated aleatory innovations was electronic music: first, composers had observed that a sound is partly determinate and partly indeterminate (Boulez was to write of the main parts of his Piano Sonata no.3 as its ‘formants’), and second, there was the desire to achieve in instrumental music what had proved obstinately unobtainable in electronic music, namely variability with performance.
Aleatory music in Europe might, in general, be considered as a matter of choice rather than chance, and the most significant choices have usually remained with the composer, whether he exercised them in notating a score or in directing a performance. In either event, the criteria for judging the result as a work of art are barely altered. Even improvisation groups in Europe customarily retained a traditional regard for achievement, finish and the expression of defined ideas (whether musical or political), although few succeeded in establishing a code of practice, such as exists in most jazz, within which their improvisations may be understood.
Cage’s use of chance was, from the first, more destructive of the traditional notion of a work of art (just as, previously, his ‘automatic’ procedures had been). Influenced by Zen Buddhism as well as by the musics of the east, his aim was to remove the barrier of his discrimination: any sound was to be admitted, freed to ‘be itself’. It was a persistent search for means of avoiding willed choice that led him to investigate procedures that took music out of the control of both composer and performer. Although certain of Cage’s associates, notably Brown and Feldman, found a parallel for their ideas in the work of visual artists (Calder’s mobiles and Pollock’s action paintings, for example), the central Cagean idea was to remove from music any reference to tradition or any trace of subjectivity, and chance, not choice, was the obvious means. This extreme aleatory position was stated at its most exact in Cage’s lecture ‘Indeterminacy’:
Finally I said that the purpose of this purposeless music would be achieved if people learned to listen; that when they listened they might discover that they preferred the sounds of everyday life to the ones they would presently hear in the musical program; that that was alright as far as I was concerned.
P. Boulez: ‘Alea’, Nouvelle revue française (1957), no.59; repr. in Relevés d’apprenti (Paris, 1966), 41; Ger. trans. in Darmstädter Beiträge zur neuen Musik, i (1958), 44; Eng. trans. in Stocktakings from an Apprenticeship (Oxford, 1991), 26–38
P. Boulez: ‘Zu meiner III. Sonate’, Darmstädter Beiträge zur neuen Musik, iii (1960), 27; Eng. trans. in Orientations (London, 1986), 143–54
K. Stockhausen: ‘Musik und Graphik’, Darmstädter Beiträge zur neuen Musik, iii (1960), 5; repr. in Texte, i (Cologne, 1963), 176–88
H.R. Zeller: ‘Mallarmé und der serielle Gedanke’, Die Reihe, vi (1960), p.5; Eng. trans. in Die Reihe, vi (1964), p.5
J. Cage: Silence (Middletown, CN, 1961)
D. Behrman: ‘What Indeterminate Notation Determines’, PNM, iii/2 (1964–5), 58–73
R. Reynolds: ‘Indeterminacy: some Considerations’, PNM, iv/1 (1965–6), 136–40
T.W. Adorno: Vers une musique informelle (Mainz, 1966), 9
E. Brown: On Form (Mainz, 1966), 57; Fr. trans. in Musique en jeu, no.3 (1971), 29
K. Boehmer: Zur Theorie der offenen Form in der neuen Musik (Darmstadt, 1967, 2/1988)
K.H. Eschman: Changing Forms in Modern Music (Boston, MA, 1967)
W. Lutosławski: ‘O roli elementu przypadku w technice komponowania’ [On the role of chance elements in compositional technique], Res facta, i (1967), 35
Source (Sacramento, CA, 1967–) [magazine of short articles on aleatory music, scores and discs]
T.H. O’Beirne: ‘940, 369, 969, 152 Dice-Music Trios’, MT, cix (1968), 911–13
V. Globokar: ‘Réagir …’, Musique en jeu, no.1 (1970), 70–77
R. Kostelanetz, ed.: John Cage (New York, 1970)
L.G. Ratner: ‘Ars combinatoria: Chance and Choice in Eighteenth-Century Music’, Studies in Eighteenth-Century Music: a Tribute to Karl Geiringer, ed. H.C. Robbins Landon and R.E. Chapman (New York and London, 1970), 343–63
D. Charles: ‘L’interprète et le hasard’, Musique en jeu, no.3 (1971), 45–51
C. Deliège: ‘Indétermination et improvisation’, IRASM, ii (1971), 155–91
G.M. Potter: The Role of Chance in Contemporary Music (diss., Indiana U., 1971)
C. Cardew, ed.: Scratch Music (London, 1972)
V. Globokar: ‘Ils improvisent … improvisez … improvisons’, Musique en jeu, no.6 (1972), 13–19
M.E. Keller: ‘Improvisation und Engagement’, Melos, xl (1973), 198–203
M. Nyman: Experimental Music: Cage and Beyond (London, 1974)
I. Stoïanowa: ‘La Troisième sonate de Boulez et le projet mallarméen du Livre’, Musique en jeu, no.16 (1974), 9–28
R. Maconie: The Works of Karlheinz Stockhausen (London, 1976, 2/1990)
W. Zimmermann: Desert Plants: Conversations with 25 American Composers (Vancouver, 1977)
S.A. Hedges: ‘Dice Music in the Eighteenth Century’, ML, lix (1978), 180–7
K. Stockhausen: Texte, iv (Cologne, 1978)
C. Gagne and T. Caras: Soundpieces: Interviews with American Composers (Metuchen, NY, 1982)
D. Jameux: Pierre Boulez (Paris, 1984, Eng. trans., 1991)
P. Boulez and J. Cage: Correspondance et documents, ed. J.-J. Nattiez (Winterthur, 1990; Eng. trans., 1993)
D. Guaccero: ‘L'aléa du son au signe graphique’, Cahiers du CIREM, xviii–xix (1990–91), 9–24
D. Revill: The Roaring Silence: John Cage: a Life (London, 1992)
J. Pritchett: The Music of John Cage (Cambridge, 1993)
E. Schwartz and D. Godfrey: Music since 1945 (New York, 1993)
V. Globokar: Einatmen Ausatmen (Hofheim, 1994)
P. Griffiths: Modern Music and After (Oxford, 1995)
S. Feisst: Der Begriff ‘Improvisation’ in der neuen Musik (Sinzig, 1997)