Aleatoricmusic (alsoaleatory music orchance music; from theLatin wordalea, meaning "dice") ismusic in which someelement of the composition is left tochance, or some primary element of a composed work's realization is left to the determination of its performer(s), or both. 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 byacousticianWerner Meyer-Eppler at theDarmstadt 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".[1] Through a confusion of Meyer-Eppler's German termsAleatorik (noun) andaleatorisch (adjective), his translator created a new English word, "aleatoric" (rather than using the existing English adjective "aleatory"), which quickly became fashionable and has persisted.[2] More recently, the variant "aleatoriality" has been introduced.[3]
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 theMissa cuiusvis toni ofJohannes Ockeghem. A later genre was theMusikalisches Würfelspiel or musicaldice game, popular in the late 18th and early 19th century. (Such dice games are attributed toCarl Phillip Emanuel Bach,Joseph Haydn, andWolfgang Amadeus Mozart.) These games consisted of a sequence of musicalmeasures, 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.[4]
The French artistMarcel Duchamp composed two pieces between 1913 and 1915 based on chance operations.[clarification needed] One of these,Erratum Musical, written with Duchamp's sisters Yvonne and Magdeleine[5] for three voices, was first performed at the Manifestation of Dada on 27 March 1920,[6] and was eventually published in 1934. Two of his contemporaries,Francis Picabia andGeorges Ribemont-Dessaignes, also experimented with chance composition,[clarification needed] these works being performed at a Festival Dada staged at theSalle Gaveau concert hall, Paris, on 26 May 1920.[citation needed] American composerJohn Cage'sMusic of Changes (1951) was "the first composition to be largely determined by random procedures",[7] though hisindeterminacy 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?"[8]
The earliest significant use of aleatory features is found in many of the compositions of AmericanCharles Ives in the early 20th century.Henry Cowell adopted Ives's ideas during the 1930s, in such works as theMosaic 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 playad libitum.[9] Later American composers, such asAlan Hovhaness (beginning with hisLousadzak 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.[10] Some scholars regard the resultant blur as "hardly aleatory, since exact pitches are carefully controlled and any two performances will be substantially the same"[11] although, according to another writer, this technique is essentially the same as that later used byWitold Lutosławski.[12][unreliable source?] Depending on the vehemence of the technique, Hovhaness's published scores annotate these sections variously, for example as "Free tempo / humming effect"[13] and "Repeat and repeat ad lib, but not together".[14]
In Europe, following the introduction of the expression "aleatory music" by Meyer-Eppler, the French composerPierre Boulez was largely responsible for popularizing the term.[15]
Other early European examples of aleatory music includeKlavierstück XI (1956) byKarlheinz Stockhausen, which features 19 elements to be performed in a sequence to be determined in each case by the performer.[16] A form of limited aleatory was used byWitold Lutosławski (beginning withJeux Vénitiens in 1960–61),[17] 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'sMusikalisches Würfelspiel, referred to above, as well as original music.
Some writers do not make a distinction between aleatory, chance, andindeterminacy in music, and use the terms interchangeably.[9][18][19] From this point of view, indeterminate or chance music can be divided into three groups: (1) the use of random procedures to produce a determinate, fixed score, (2) mobile form, and (3) indeterminate notation, includinggraphic notation and texts.[9]
The first group includes scores in which the chance element is involved only in the process of composition, so that every parameter is fixed before their performance. InJohn Cage'sMusic of Changes (1951), for example, the composer selected duration, tempo, and dynamics by using theI Ching, an ancient Chinese book which prescribes methods for arriving at random numbers.[20] Because this work is absolutely fixed from performance to performance, Cage regarded it as an entirely determinate work made using chance procedures.[21] On the level of detail,Iannis Xenakis used probability theories to define some microscopic aspects ofPithoprakta (1955–56), which is Greek for "actions by means of probability". This work contains four sections, characterized by textural and timbral attributes, such as glissandi and pizzicati. At the macroscopic level, the sections are designed and controlled by the composer while the single components of sound are controlled by mathematical theories.[20][vague]
In the second type of indeterminate music, chance elements involve the performance. Notated events are provided by the composer, but their arrangement is left to the determination of the performer.Karlheinz Stockhausen's Klavierstück XI (1956) presents nineteen events which are composed and notated in a traditional way, but the arrangement of these events is determined by the performer spontaneously during the performance. InEarle Brown'sAvailable forms II (1962), the conductor is asked to decide the order of the events at the very moment of the performance.[22]
The greatest degree of indeterminacy is reached by the third type of indeterminate music, where traditional musical notation is replaced by visual or verbal signs suggesting how a work can be performed, for example ingraphic score pieces. Earle Brown'sDecember 1952 (1952) shows lines and rectangles of various lengths and thicknesses that can read as loudness, duration, or pitch. The performer chooses how to read them. Another example isMorton Feldman'sIntersection No. 2 (1951) for piano solo, written on coordinate paper. Time units are represented by the squares viewed horizontally, while relative pitch levels of high, middle, and low are indicated by three vertical squares in each row. The performer determines what particular pitches and rhythms to play.[22]
Open form is a term sometimes used for 'mobile' or 'polyvalent'musical forms, where the order ofmovements orsections is indeterminate or left up to theperformer.Roman Haubenstock-Ramati composed a series of influential "mobiles" such asInterpolation (1958).
However, "open form" in music is also used in the sense defined by the art historianHeinrich Wölfflin[23] 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 "dynamic, closed" mobile musical composition is Stockhausen'sZyklus (1959).[24]
Stochastic processes may be used in music to compose a fixed piece or may be produced in performance.Stochastic music was pioneered byXenakis, who coined the termstochastic music.[25] Specific examples of mathematics, statistics, and physics applied to music composition are the use of thestatistical mechanics of gases inPithoprakta,statistical distribution of points on a plane inDiamorphoses, minimalconstraints inAchorripsis, thenormal distribution inST/10 andAtrées,Markov chains inAnalogiques,game theory inDuel andStratégie,group theory inNomos Alpha (forSiegfried Palm),set theory inHerma andEonta,[26] andBrownian motion inN'Shima.[27]
Xenakis frequently usedcomputers to produce his scores, such as theST series includingMorsima-Amorsima andAtrées, and foundedCEMAMu.[28][page needed]
Examples of extensive aleatoric writing can be found in small passages fromJohn Williams' score for the filmImages. Other film composers using this technique areMark Snow (X-Files: Fight the Future),John Corigliano, and others.[29] Snow used digital samples of acoustic instruments "to merge starkly electronic timbres with acoustically based sounds, an approach developed extensively in his much celebrated music forThe X-Files (1993–2002, 2016–18). Over the course of the series, Snow's often ambient music dissolved distinctions between sound design and musical score."[30]
Howard Shore employed aleatoriccomposition inThe Lord of the Rings: The Fellowship of the Ring during theFellowship's encounter with theWatcher in the Water outside of the gates ofMoria.[31][32]
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