Term for music whose essential substance is not fully determined. This is quite a wide remit; it would include, for example, concertos and arias allowing room for cadenzas, as well as the long-established practice of the ossia. It would also include much of Ives's music, which includes exhortations to freedom (backed up by his recordings), unusually important alternatives and unrealizable notations that invite the performer to find a solution. Ives's example was important to Cowell, who used what he called ‘elastic’ notations, e.g. providing fragments to be put together by the players (Mosaic Quartet, 1934). Grainger, too, favoured ‘elastic scoring’. But the term ‘aleatory’ is usually confined to music of around 1950–70, though acknowledging also the etymological aptness of counting as aleatory certain 18th-century musical games, which provided for dances to be composed by assembling given bars according to dice throws.
In the post-1950 period there were three distinct schools of aleatory endeavour. One sprang from Cage, and from his many diverse efforts to find, through CHANCE OPERATIONS and INDETERMINACY, ways to achieve music freed from creative will. Another was more concerned with instituting variabilities of form and movement within scores otherwise thoroughly composed (Boulez). The third emerged as a response to the different nature of electronic performance, as well as from the notion of creating a work as a giant image of a sound, requiring some equivalent for elements that could not be predicted (Stockhausen). Boulez's principal aleatory works — his Third Piano Sonata, second book of Structures, Eclat and Pli selon pli - were prompted partly by Asian music, partly by an understanding of serial composition as potentially endless (unlike tonal composition, which is always directed towards a cadence), and partly by Mallarmé's pursuit of ever greater ambiguity in his poetry. Stockhausen's works of this period (the late 1950s and 1960s) increasingly used electronic means, which could not be defined in the old ways, and also became increasingly open to the creative participation of performers, with a corresponding decline in notational exactitude (to the point of using plain symbols or verbal encouragements instead of regular parts). Perhaps the early-music movement, with its insistence on alternative ways of doing things, was also a stimulus to all these composers.
Stockhausen's return to traditional notation in 1970, and Boulez's successive withdrawals of the freedom of Pli selon pli, marked the end of a brief era. For one thing, the complexities of large-scale mobile scores could not survive a period of diminished patronage. But music gained a looseness it has not forgotten.
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