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Aleatoric (or aleatory) music or composition, is music where some element of the composition is left to chance. 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. The term was intended by Boulez to distinguish his work from works composed through the application of chance operations by John Cage.
An early genre of composition that could be considered a precedent for aleatoric compositions were the Musikalische Würfelspiele or Musical Dice Games, 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.
Music related to the aleatoric idea may be found in works of John Cage, who was in part inspired by his friend Morton Feldman who was making experiments with chance in music in the 1950s. Cage used the I Ching in the composition of his music in order to introduce an element of chance over which he would have no control. The first time he used it was in the Music of Changes for solo piano in 1951, to determine the sequence of notes or groups of notes that should be used and the precise timing of their occurrences. He used chance in other ways as well; Imaginary Landscape No. 4 (1951) is written for twelve radio receivers. Each radio has two players, one to control the frequency the radio is tuned to, the other to control the volume level. Cage wrote very precise instructions in the score about how the performers should set their radios and change them over time, but he could not control the actual sound coming out of them, which was dependent on whatever radio shows were playing at that particular place and time of performance.
One of Cage's other pieces, HPSCHD, itself composed using chance procedures, uses music from Mozart's Musikalisches Würfelspiel, referred to above, as well as original music.
Other aleatoric composers include Henry Brant, Witold Lutoslawski and Lukas Foss.
The term "aleatory" is not always applied to music where the composer does not maintain full control over the piece. In pieces where certain decisions are left up to the performer, but are not a matter of chance, the terms indeterminate music or limited aleatory are sometimes used. For example, a composer may indicate to the player a certain melodic idea by drawing a wavy line across the staff, ornamented with arrows perhaps, approximately where the notes should fall, but will not actually notate the melody, or indicate a tempo.
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Douglas Hofstadter, writing in Gödel, Escher, Bach, punningly characterises some of the musical compositions of John Cage by using the acronym CAGE to stand for Composition of Aleatorically Generated Elements, in contrast to a Beautiful Aperiodic Crystal of Harmony (or BACH).
Some aleatoric music, such as that of the Mangabros, is inspired by the book The Dice Man by Luke Rhinehart.
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