Editing Aleatoric music (section)

==History==
===Early precedents===
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. (Such dice games are attributed to [[Carl Philipp Emanuel Bach|Carl Phillip Emanuel Bach]], [[Joseph Haydn|Franz Joseph Haydn]], and [[Wolfgang Amadeus Mozart]].) These games consisted of a sequence of musical [[bar (music)|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.{{sfn|Boehmer|1967|p=9–47}}

The French artist [[Marcel Duchamp]] composed two pieces between 1913 and 1915 based on chance operations.{{Clarify|date=June 2017|reason=Do these pieces conform in any way to Meyer-Eppler's definition of 'aleatoric' or are they 'indeterminate', in Cage's conception?}} One of these, ''Erratum Musical'', written with Duchamp's sisters Yvonne and Magdeleine<ref>{{Cite web|url=https://www.toutfait.com/erratum-musical-1913/|title=Erratum Musical, 1913|accessdate=26 January 2022}}</ref> for three voices, was first performed at the Manifestation of Dada on 27 March 1920,<ref>{{Cite web|url=https://digitalcollections.nypl.org/items/fa347ec0-3acb-0133-ccc0-00505686a51c|title=Manifestation Dada|website=NYPL Digital Collections|accessdate=26 January 2022}}</ref> and was eventually published in 1934. Two of his contemporaries, [[Francis Picabia]] and [[Georges Ribemont-Dessaignes]], also experimented with chance composition,{{Clarify|date=June 2017|reason=Do these pieces conform in any way to Meyer-Eppler's definition of 'aleatoric'?}} these works being performed at a Festival Dada staged at the [[Salle Gaveau (Paris)|Salle Gaveau]] concert hall, Paris, on 26 May 1920.{{Citation needed|date=August 2014}} American composer [[John Cage]]'s ''[[Music of Changes]]'' (1951) was "the first composition to be largely determined by random procedures",{{sfn|Randel|2002|p=17}} though his [[Indeterminacy (music)|indeterminacy]] is of a different order from Meyer-Eppler's concept. Cage later asked Duchamp: "How is it that you used chance operations when I was just being born?"{{sfn|Lotringer|1998|p={{Page needed|date=January 2011}}}}

===Modern usage===
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''.{{sfn|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.{{sfn|Farach-Colton|2005}} Some scholars regard the resultant blur as "hardly aleatory, since exact pitches are carefully controlled and any two performances will be substantially the same"{{sfn|Rosner & Wolverton|2001}} although, according to another writer, this technique is essentially the same as that later used by [[Witold Lutosławski]].{{sfn|Fisher|2010}}{{Unreliable source?|date=June 2010|reason=This is a blog. Does it really stand comparison with an article in the New Grove? On the other hand, does this mean that Lutosławski's usage is also not aleatory?}} Depending on the vehemence of the technique, Hovhaness's published scores annotate these sections variously, for example as "Free tempo / humming effect"{{sfn|Hovhaness|1944|p=3}} and "Repeat and repeat ad lib, but not together".{{sfn|Hovhaness|1958|p=2}}

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.{{sfn|Boulez|1957}}

Other early European examples of aleatory music include [[Klavierstücke (Stockhausen)#Klavierstück XI: polyvalent structure|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.{{sfn|Boehmer|1967|p=72}} A form of limited aleatory was used by [[Witold Lutosławski]] (beginning with ''Jeux Vénitiens'' in 1960–61),{{sfn|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.

There has been much confusion of the terms aleatory and indeterminate/chance music. One of Cage's pieces, ''[[HPSCHD]]'', itself composed using chance procedures, uses music from Mozart's ''Musikalisches Würfelspiel'', referred to above, as well as original music.