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 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).
Compositions that could be considered a precedent for aleatoric 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).
American composer John Cage's Music of Changes (1951) is the first piece to be conceived largely through random procedures (Randel 2002, 17), though for just this reason his indeterminacy is of a different order from Meyer-Eppler's concept.
The French composer Pierre Boulez was largely responsible for popularizing the term, using it to describe works that give the performer certain liberties with regard to the sequencing and repetition of parts, an approach pioneered by avant-garde American composer-theorist Henry Cowell in his Mosaic Quartet (String Quartet No. 3, 1935). Another composer, the French broadcaster Pierre Schaeffer, developed the term jeu (French for play) in reference to a technique of allowing random sounds to enter into a musical composition.
Early examples of aleatoric music include Klavierstück XI (1956) by Karlheinz Stockhausen, which features 19 elements to be performed in changing sequences. Witold Lutosławski began using aleatory with Jeux vénitiens in 1960–61, which contains passages where the pitches and rhythms are fully specified, but the rhythmic coordination of parts within the ensemble is subject to an element of chance (Rae 2001). Lutosławski calls this 'ad libitum'. In some works by Krzysztof Penderecki characteristic sequences are repeated quickly, producing a kind of oscillating sound.
There has been considerable confusion of the terms aleatory and indeterminate/chance music. One of Cage's pieces, HPSCHD, (see also his books of changes for more musical examples) itself composed using chance procedures, uses music from Mozart's Musikalisches Würfelspiel, referred to above, as well as original music. Still, both the aesthetic aims as well as the number of elements controlled by chance make the two methods clearly different.
Open form is a term sometimes used for mobile or polyvalent musical forms, where the order of movements or sections is indeterminate or left up to the performer. Roman Haubenstock-Ramati composed a series of influential "mobiles" such as Interpolation (1958).
However, "open form" in music is also used in the sense defined by the art historian Heinrich Wölfflin (Renaissance und Barock, 1888) to mean a work which is fundamentally incomplete, represents an unfinished activity, or points outside of itself. In this sense, a "mobile form" can be either "open" or "closed". An example of a closed mobile musical composition is Stockhausen's Zyklus (1959). Terry Riley's In C (1964) was composed of 53 short sequences; each member of the ensemble can repeat a given sequence as many times as desired before going on to the next, making the details of each performance of In C unique though, because the overall course is fixed, it is a closed form.
Randomness has also been used in popular music, but general randomness is quite a different thing from the aleatory. Duo, The Books refer to Aleatoric Music in the words near the end of their song "Read, Eat, Sleep", repeating samples of the word 'aleatoric', and then with a sample saying "By digitising thunder and traffic noises, Georgia was able to compose 'Aleatoric Music'." On the David Bowie album Low, Brian Eno and Bowie used a die for composing the tonal structure of the title track.