Aleatoric Music. Music in which either composition or method of performance is determined by elements of chance or unpredictability. Terms such as chance music, indeterminate music, or aleatoric music are applied to many works written after World War II, the pioneers being Cage, Lutoslawski, Stockhausen, and Xenakis, each of whom approached the technique in his own way.
Many composers have approached electronic composition by applying some indeterminate techniques with, for example, the use of voltage-controlled equipment. By setting up a simple program to allow the equipment to run almost automatically (the Moog, Arp, and Putney synthesizers, etc), the composer generates musical material determined by random combinations of various electronic units and is able to interrupt the program at will to change any result.
More often, however, aleatoric music refers to the method of performance rather than to compositional procedure. In Cage's Music of Changes or Stockhausen's Zyklus for percussion, the musical components are in some way predetermined, leaving to the performer the choice of which components to play or in what order. A major exponent of "Cagean" chance music in Canada is Udo Kasemets, who uses performance charts or other controlled-improvisation means. In Trigon, he calls for 1, 3, 9, or 27 participants playing in various media, musical and non-musical, up to 81 in number, each performance being a new realization that he has notated precisely. The same is true of Cascando, which spawned the precisely notated pieces Stereosonic Vocophony, Synersonic Octet, and Synersonophony: Vocosonic Poem: Sonophonic Interlude: Stereosonovocophony. In his desire for greater indeterminacy, Kasemets uses as material "any dictionary, any subject in any language" for his work Wordmusic/Interface. Other composers who have written in this genre are Claude Vivier, Don Druick, and Alex Pauk.
Trends in Aleatoric Composition
The majority of composers, however, have allowed for some choices in an otherwise precisely notated score. R. Murray Schafer, in such works as Threnody (for chorus, narrators, orchestra, and electronic tape) and Divan i Shams i Tabriz (for orchestra and electronic tape), uses graphic notation, a visual representation of the sound desired, without predetermining either the pitch or the exact duration. Often electronic tape is used in conjunction with this type of instrumental or choral music, in which case the overall or macro-time is predetermined by the material on tape but with some freedom in the micro-time of events and the pitch. In a sense, the indeterminate compositional procedure applied to the creation of the tape is carried over to the instrumental writing, sometimes including some choices to be made by the performers or conductor. Composers who have used this technique extensively with tape include Anhalt, Aitken, Ford, Tremblay, and Truax. Composers who generally have excluded tape but otherwise call for the same techniques include Beckwith, Beecroft, Buczynski, Cherney, Fodi, Garant, Hawkins, Huse, and Joachim. Later works of Weinzweig (Around the Stage and after) and Pentland (Trio con Alea and after) show a trend toward the use of these procedures.
Stochastic music - a term coined by Xenakis to describe music determined by the mathematical laws of chance, such as the theory of probability or games theory - is, in a sense, an outgrowth of total serialization. Although serialization is a predetermining procedure for each musical parameter (dynamics, rhythm, articulation, etc), the combination of all parameters is often subject to random ordering. Boulez' Structures is an attempt at total serialization.
Serge Garant modified this idea in Asymétries I and II by leaving some of the choices within each parameter to his intuition, to give apparent, if not actual, randomness. This was a frequent compositional procedure both internationally and in Canada in the late 1950s and early 1960s in works by Fodi, Huse, Joachim, Somers, and others.
At the turn of the 21st century, the aleatoric technique has lost favour with many composers, and is applied sparingly by others in combination with other techniques. A notable example is Schafer's Falling into Light (2003) for six choirs, children's choir and percussion.