Music in which deliberate use is made of chance or indeterminacy; the term chance music is preferred by many composers. The indeterminate aspect may affect the act of composition, the performance, or both. In the first instance, some random process, such as throwing dice (the original meaning of aleatory being "according to the throw of a die"), is used to fix certain compositional decisions: e.g., the choice of pitches or rhythmic values. In the second, the performer (or performers) makes certain compositional decisions in a given realization of a piece: e.g., the number of segments played or the order in which they are played or the specific pitches or durations used.
Although aleatory music, especially in its more extreme forms, is principally a phenomenon of the later 20th century, precedents are found throughout Western musical history. Medieval theorists, for example, occasionally recommend the permutation of a given succession of pitches as a mechanical aid to melodic invention; and musical dice games, in which choices are made among a number of available possibilities with the aid of dice, were popular in the 18th century. In the early 20th century, Charles Ives at times allowed the performer certain alternatives (for example, the number of times a measure is to be played, or even whether or not an entire section will be played), and such tendencies were later developed further by Henry Cowell, especially in his String Quartet no. 3 of 1935, known as the Mosaic Quartet, which consists of a number of separate segments that have to be "assembled" by the players. The terms open form and mobile form have since been applied to works of this type. It should also be noted that the use of chance played a significant role in the work of Marcel Duchamp, as well as other artists and writers associated with the Dada movement.
The major figure in the evolution of modern aleatory music is John Cage, whose Music of Changes, a piano piece composed in 1951, was the first composition to be largely determined by random procedures. For this work, Cage tossed coins and used the results to choose configurations from the I Ching, a Chinese book of oracles, which in turn led to the selection of pitches, durations, dynamics, etc. Cage, along with Morton Feldman and Earle Brown (with whom he was in close association during the early 1950s), had an important influence on a number of younger composers and artists working in America, including those involved with the Fluxus movement in New York (Nam June Paik), the ONCE group in Ann Arbor (Robert Ashley, Gordon Mumma, Roger Reynolds), and the San Francisco Tape Center (Pauline Oliveros, Morton Subotnick), all active during the 1960s.
Cage visited Europe several times during the 1950s, and his ideas also had a significant impact on a number of younger European composers of the time, including Pierre Boulez and Karlheinz Stockhausen. But whereas Cage's own approach to indeterminacy has always been essentially unsystematic, even mystical, in character, the Europeans tended to a more theoretical conception of aleatory music with a more limited range of choices. In Stockhausen's Zyklus for one percussionist, for example, all pitches and timbres are strictly specified; choice is allowed only in the temporal placement of individual events (and even these must be placed within certain carefully prescribed boundaries) and in the determination of a starting point and the "direction" (i.e., whether backward or forward) in which the piece will be played.
The degree of leeway left to a performer may vary widely in aleatory music and is closely tied to the notational system used. Certain scores by Brown, Robert Moran, and Anestis Logothetis, for example, are purely graphic, containing no traditional notation at all. The performer is thus allowed to interpret the "score" more or less freely, with little if any specific instruction. Other works, such as LaMonte Young's "instructive" scores and Stockhausen's Aus den sieben Tagen, are completely verbal. More commonly, however, one finds a mixture of traditional and graphic notation, with some elements specified while others are left to the performer's choice (e.g., Brown's Available Forms). The incorporation of indeterminate processes in computer music applications, dating back to the "stochastic" works of Iannis Xenakis, has contributed to its continued importance in more recent music. See also Notation.
Bibliography: Pierre Boulez, "Alea," Nouvelle revue française, no. 59 (1957); trans. in PNM 3 (1964/65): 42–53. John Cage, "Indeterminacy," in his Silence (Middletown, Conn.: Wesleyan U Pr, 1961), pp. 35–40. Roger Reynolds, "Indeterminacy: Some Considerations," PNM 4 (1965/66): 136–40. Leonard G. Ratner, "Ars combinatoria: Chance and Choice in 18th-Century Music," Geiringer, 1970, pp. 343–63. Michael Nyman, Experimental Music: Cage and Beyond (London: Cassell and Collier Macmillan, 1974). Terence J. O'Grady, "Aesthetic Value in Indeterminate Music," MQ 67 (1981): 366–81. James Pritchett, The Music of John Cage (New York: Cambridge U Pr, 1993). R.P.M.
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