Aleatoric composition

Aleatoric music (also aleatory music or chance music; from the Latin word alea, meaning "dice") is music in which some element of the composition is left to chance, and/or some primary element of a composed work's realization is left to the determination of its performer(s). The term is most often associated with procedures in which the chance element involves a relatively limited number of possibilities.

The term became known to European composers through lectures by acoustician Werner Meyer-Eppler at the Darmstadt International Summer Courses for New Music in the beginning of the 1950s. According to his definition, “a process is said to be aleatoric […] if its course is determined in general but depends on chance in detail” (Meyer-Eppler 1957, 55). Through a confusion of Meyer-Eppler's German terms Aleatorik (noun) and aleatorisch (adjective), his translator created a new English word, "aleatoric" (rather than using the existing English adjective "aleatory"), which quickly became fashionable and has persisted (Jacobs 1966). More recently, the variant "aleatoriality" has been introduced (Roig-Francolí 2008, 340).

Compositions that could be considered a precedent for aleatory composition date back to at least the late 15th century, with the genre of the catholicon, exemplified by the Missa cuiusvis toni of Johannes Ockeghem. A later genre was the Musikalisches Würfelspiel or musical dice game, popular in the late 18th and early 19th century. (One such dice game is attributed to Wolfgang Amadeus Mozart.) These games consisted of a sequence of musical measures, for which each measure had several possible versions and a procedure for selecting the precise sequence based on the throwing of a number of dice (Boehmer 1967, 9–47).

...
Wikipedia