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 earliest significant use of aleatory features is found in many of the compositions of American Charles Ives in the early 20th century. Henry Cowell adopted Ives’s ideas during the 1930s, in such works as the Mosaic Quartet (String Quartet No. 3, 1934), which allows the players to arrange the fragments of music in a number of different possible sequences. Cowell also used specially devised notations to introduce variability into the performance of a work, sometimes instructing the performers to improvise a short passage or play ad libitum (Griffiths 2001). Later American composers, such as Alan Hovhaness (beginning with his Lousadzak of 1944) used procedures superficially similar to Cowell's, in which different short patterns with specified pitches and rhythm are assigned to several parts, with instructions that they be performed repeatedly at their own speed without coordination with the rest of the ensemble. Some scholars regard the resultant blur as "hardly aleatory, since exact pitches are carefully controlled and any two performances will be substantially the same" (Rosner and Wolverton 2001) although, according to another writer, this technique is essentially the same as that later used by Witold Lutosławski (Fisher 2010) . Depending on the vehemence of the technique, Hovhaness’s published scores label these sections “spirit murmur” and “controlled chaos”.
In Europe, following the introduction of the expression "aleatory music" by Meyer-Eppler, the French composer Pierre Boulez was largely responsible for popularizing the term (Boulez 1957), using it to describe works that give the performer certain liberties with regard to the sequencing and repetition of parts. The French composer and 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.
Other early European examples of aleatoric music include Klavierstück XI (1956) by Karlheinz Stockhausen, which features 19 elements to be performed in a sequence to be determined in each case by the performer (Boehmer 1967, 72). A form of limited aleatory was used by Witold Lutosławski (beginning with Jeux Vénitiens in 1960–61) (Rae 2001), where extensive passages of pitches and rhythms are fully specified, but the rhythmic coordination of parts within the ensemble is subject to an element of chance. Lutosławski calls these sections '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.
The First Symphony of Alfred Schnittke uses aleatoric techniques as only one of a number of approaches to the 'chaos' of 20th century life (Schnittke also uses Ivesian dissonance to similar effect).
"Open form" chance music
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'" (The Books [n.d.]). On the David Bowie album Low, Brian Eno and Bowie used a die for composing the tonal structure of Warszawa.
Boehmer, Konrad. 1967. Zur Theorie der offenen Form in der neuen Musik. Darmstadt: Edition Tonos. (Second printing 1988.)
The Books (musical group). [n.d.]. "'Read, Eat, Sleep' lyrics". Lyrics Mania website (Accessed 28 January 2010).
Boulez, Pierre. 1957. "Aléa". Nouvelle Revue française, no. 59 (1 November). Reprinted in Pierre Boulez, Relevés d’apprenti, collected and presented by Paule Thévenin, 41–45. Paris: Éditions du Seuil, 1966. ISBN 2020019302. English as "Alea" in Pierre Boulez, Notes of an Apprenticeship, collected and presented by Paule Thévenin, translated from the French by Herbert Weinstock, 35–51. New York: Alfred A. Knopf, 1968. New English translation, as "Alea", in Pierre Boulez, Stocktakings from an Apprenticeship, collected and presented by Paule Thévenin, translated from the French by Stephen Walsh, with an introduction by Robert Piencikowski, 26–38. Oxford: Clarendon Press; New York: Oxford University Press, 1991. ISBN 0193112108.
Fisher, Lynn. 2010. "An Unlikely Musical Pioneer? Early Aleatory Counterpoint". AleaCounterpoint blog site (Accessed 22 June 2010).
Griffiths, Paul. 2001. "Aleatory". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
Lieberman, David. 2006. "Game Enhanced Music Manuscript." In GRAPHITE '06: Proceedings of the 4th International Conference on Computer Graphics and Interactive Techniques in Australasia and South East Asia, Kuala Lumpur (Malaysia), November 29–December 2, 2006, edited by Y. T. Lee, Siti Mariyam Shamsuddin, Diego Gutierrez, and Norhaida Mohd Suaib, 245–50. New York: ACM Press. ISBN 1-59593-564-9.
Meyer-Eppler, Werner. 1957. "Statistic and Psychologic Problems of Sound", translated by Alexander Goehr. Die Reihe 1 ("Electronic Music"): 55–61. Original German edition, 1955, as "Statistische und psychologische Klangprobleme", Die Reihe 1 ("Elektronische Musik"): 22–28.
Pimmer, Hans. 1997. Würfelkomposition: zeitgenössische Recherche: mit Betrachtungen über die Musik 1799. Munich: Akademischer Verlag. ISBN 3929115905.
Prendergast, Mark J. 2000. The Ambient Century: from Mahler to Trance: The Evolution of Sound in the Electronic Age. London: Bloomsbury. ISBN 0747542139.
Rae, Charles Bodman. 2001. "Lutosławski, Witold (Roman)". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
Randel, Don Michael. 2002. The Harvard Concise Dictionary of Music and Musicians. ISBN 0-674-00978-9.
Rosner, Arnold, and Vance Wolverton. 2001. "Hovhaness [Hovaness], Alan [Chakmakjian, Alan Hovhaness]". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
Stone, Susan. 2005. "The Barrons: Forgotten Pioneers of Electronic Music", NPR Music (7 February). (Accessed 23 September 2008)
Wölfflin, Heinrich. 1888. Renaissance und Barock: Eine Untersuchung über Wesen und Entstehung der Barockstils in Italien. Munich: T. Ackermann. English edition: Renaissance and Baroque. Translated by Kathrin Simon, with an introduction by Peter Murray. London: Collins, 1964; Ithaca: Cornell University Press, 1967.