![]() At the macroscopic level, the sections are designed and controlled by the composer while the single components of sound are controlled by mathematical theories. The term was devised by the French composer Pierre Boulez to describe works where the performer was given certain liberties with regard to the order and repetition of parts of a musical work. John Cage became a strong proponent of aleatoric techniques, even going so far as to use them in lectures as well as musical compositions. Aleatoric Music or Aleatoric Composition is music where some element of the composition is left to chance. On the level of detail, Iannis Xenakis used probability theories to define some microscopic aspects of Pithoprakta (1955–56), which is Greek for “actions by means of probability.” This work contains four sections, characterized by textural and timbral attributes, such as glissandi and pizzicati. Aleatoric music involves the use of chance in either the composition or performance of the piece. To be clear, the Sonatas and Interludes are not aleatoric works, so the John Cage piece on. ![]() John Cage became a strong proponent of aleatoric techniques, even going so far as to use them in lectures as well as musical compositions. Because this work is absolutely fixed from performance to performance, Cage regarded it as an entirely determinate work made using chance procedures. Aleatoric music involves the use of chance in either the composition or performance of the piece. In John Cage’s Music of Changes (1951), for example, the composer selected duration, tempo, and dynamics by using the I Ching, an ancient Chinese book which prescribes methods for arriving at random numbers. ![]() The first group includes scores in which the chance element is involved only in the process of composition, so that every parameter is fixed before their performance. One composer who wrote aleatoric music was John Cage. From this point of view, indeterminate or chance music can be divided into three groups: (1) the use of random procedures to produce a determinate, fixed score, (2) mobile form, and (3) indeterminate notation, including graphic notation and texts. ![]() Some writers do not make a distinction between aleatory, chance, and indeterminancy in music, and use the terms interchangeably. ![]()
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