Aleatoricmusic (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 the 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".Through a confusion of Meyer-Eppler's German terms Aleatorik (noun) and aleatorisch (adjective), his translator created a new English word, "aleatoric" (rather than using the existing English adjective "aleatory"), which quickly became fashionable and has persisted. More recently, the variant "aleatoriality" has been introduced.
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. (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.
The French artist Marcel 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 for three voices, was first performed at the Manifestation of Dada on 27 March 1920, and was eventually published in 1934. Two of his contemporaries, Francis Picabia and Georges Ribemont-Dessaignes, also experimented with chance composition,[ clarification needed ] these works being performed at a Festival Dada staged at the Salle Gaveau concert hall, Paris, on 26 May 1920.[ citation needed ] American composer John Cage's Music of Changes (1951) was "the first composition to be largely determined by random procedures", though his 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?"
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. [ unreliable source? ] Depending on the vehemence of the technique, Hovhaness's published scores annotate these sections variously, for example as "Free tempo / humming effect" and "Repeat and repeat ad lib, but not together".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" although, according to another writer, this technique is essentially the same as that later used by Witold Lutosławski.
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.
Other early European examples of aleatory 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.A form of limited aleatory was used by Witold Lutosławski (beginning with Jeux Vénitiens in 1960–61), 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.
Some writers do not make a distinction between aleatory, chance, and indeterminacy in music, and use the terms interchangeably.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, including graphic notation and texts.
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. In John Cage's Music of Changes (1951), for example, the composer selected duration, tempo, and dynamics by using the I Ching , an ancient Chinese book which prescribes methods for arriving at random numbers. [ vague ]Because this work is absolutely fixed from performance to performance, Cage regarded it as an entirely determinate work made using chance procedures. On the level of detail, Iannis Xenakis used probability theories to define some microscopic aspects of Pithoprakta (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.
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. In Earle Brown's Available forms II (1962), the conductor is asked to decide the order of the events at the very moment of the performance.
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 in graphic score pieces. Earle Brown's December 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 is Morton Feldman's Intersection 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.
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 Wölfflinto 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's Zyklus (1959).
Stochastic processes may be used in music to compose a fixed piece or may be produced in performance. Stochastic music was pioneered by Xenakis, who coined the term stochastic music.Specific examples of mathematics, statistics, and physics applied to music composition are the use of the statistical mechanics of gases in Pithoprakta, statistical distribution of points on a plane in Diamorphoses , minimal constraints in Achorripsis, the normal distribution in ST/10 and Atrées, Markov chains in Analogiques, game theory in Duel and Stratégie, group theory in Nomos Alpha (for Siegfried Palm), set theory in Herma and Eonta , and Brownian motion in N'Shima.
Xenakis frequently used computers to produce his scores, such as the ST series including Morsima-Amorsima and Atrées, and founded CEMAMu. [ page needed ]
Examples of extensive aleatoric writing can be found in small passages from John Williams' score for the film Images . Other film composers using this technique are Mark Snow ( X-Files: Fight the Future ), John Corigliano, and others.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 for The 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."
Howard Shore employed aleatoric composition in The Lord of the Rings: The Fellowship of the Ring during the Fellowship's encounter with the Watcher in the Water outside of the gates of Moria.
David Eugene Tudor was an American pianist and composer of experimental music.
John Milton Cage Jr. was an American composer and music theorist. A pioneer of indeterminacy in music, electroacoustic music, and non-standard use of musical instruments, Cage was one of the leading figures of the post-war avant-garde. Critics have lauded him as one of the most influential composers of the 20th century. He was also instrumental in the development of modern dance, mostly through his association with choreographer Merce Cunningham, who was also Cage's romantic partner for most of their lives.
Giannis Klearchou Xenakis was a Romanian-born Greek-French avant-garde composer, music theorist, architect, performance director and engineer.
Aleatoricism or aleatorism, the noun associated with the adjectival aleatory and aleatoric, is a term popularised by the musical composer Pierre Boulez, but also Witold Lutosławski and Franco Evangelisti, for compositions resulting from "actions made by chance", with its etymology deriving from alea, Latin for "dice". It now applies more broadly to art created as a result of such a chance-determined process. The term was first used "in the context of electro-acoustics and information theory" to describe "a course of sound events that is determined in its framework and flexible in detail", by Belgian-German physicist, acoustician, and information theorist Werner Meyer-Eppler. In practical application, in compositions by Mozart and Kirnberger, for instance, the order of the measures of a musical piece were left to be determined by throwing dice, and in performances of music by Pousseur, musicians threw dice "for sheets of music and cues". However, more generally in musical contexts, the term has had varying meanings as it was applied by various composers, and so a single, clear definition for aleatory music is defied. Aleatory should not be confused with either indeterminacy, or improvisation.
Stochastic refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselves, these two terms are often used synonymously. Furthermore, in probability theory, the formal concept of a stochastic process is also referred to as a random process.
Electroacoustic music is a genre of popular and Western art music in which composers use technology to manipulate the timbres of acoustic sounds, sometimes by using audio signal processing, such as reverb or harmonizing, on acoustical instruments. It originated around the middle of the 20th century, following the incorporation of electric sound production into compositional practice. The initial developments in electroacoustic music composition to fixed media during the 20th century are associated with the activities of the Groupe de recherches musicales at the ORTF in Paris, the home of musique concrète, the Studio for Electronic Music in Cologne, where the focus was on the composition of elektronische Musik, and the Columbia-Princeton Electronic Music Center in New York City, where tape music, electronic music, and computer music were all explored. Practical electronic music instruments began to appear in the early 20th century.
Graphic notation is the representation of music through the use of visual symbols outside the realm of traditional music notation. Graphic notation became popular in the 1950s, and can be used either in combination with or instead of traditional music notation. Graphic notation was influenced by contemporary visual art trends in its conception, bringing stylistic components from modern art into music. Composers often rely on graphic notation in experimental music, where standard musical notation can be ineffective. Other uses include pieces where an aleatoric or undetermined effect is desired. One of the earliest pioneers of this technique was Earle Brown, who, along with John Cage, sought to liberate performers from the constraints of notation and make them active participants in the creation of the music.
French classical music began with the sacred music of the Roman Catholic Church, with written records predating the reign of Charlemagne. It includes all of the major genres of sacred and secular, instrumental and vocal music. French classical styles often have an identifiably national character, ranging from the clarity and precision of the music of the late Renaissance music to the sensitive and emotional Impressionistic styles of the early 20th century. Important French composers include Pérotin, Machaut, Du Fay, Ockeghem, Josquin, Lully, Charpentier, Couperin, Rameau, Leclair, Grétry, Méhul, Auber, Berlioz, Alkan, Gounod, Offenbach, Franck, Lalo, Saint-Saëns, Delibes, Bizet, Chabrier, Massenet, Widor, Fauré, d'Indy, Chausson, Debussy, Dukas, Vierne, Duruflé, Satie, Roussel, Hahn, Ravel, Honegger, Milhaud, Poulenc, Auric, Messiaen, Françaix, Dupré, Dutilleux, Xenakis, Boulez, Guillou, Grisey, and Murail.
Metastaseis is an orchestral work for 61 musicians by Iannis Xenakis. His first major work, it was written in 1953–54 after his studies with Olivier Messiaen and is about 8 minutes in length. The work was premiered at the 1955 Donaueschingen Festival with Hans Rosbaud conducting. This work was originally a part of a Xenakis trilogy titled Anastenaria but was detached by Xenakis for separate performance.
Pierre Boulez composed three piano sonatas: the First Piano Sonata in 1946, the Second Piano Sonata in 1947–48, and the Third Piano Sonata in 1955–57 with further elaborations up to at least 1963, though only two of its movements have been published.
Indeterminacy is a composing approach in which some aspects of a musical work are left open to chance or to the interpreter's free choice. John Cage, a pioneer of indeterminacy, defined it as "the ability of a piece to be performed in substantially different ways".
Experimental music is a general label for any music or music genre that pushes existing boundaries and genre definitions. Experimental compositional practice is defined broadly by exploratory sensibilities radically opposed to, and questioning of, institutionalized compositional, performing, and aesthetic conventions in music. Elements of experimental music include indeterminate music, in which the composer introduces the elements of chance or unpredictability with regard to either the composition or its performance. Artists may also approach a hybrid of disparate styles or incorporate unorthodox and unique elements.
Evryali is a piece for solo piano composed by Iannis Xenakis in 1973. It is based on a technique Xenakis invented in early 1970s, called arborescences—proliferations of melodic lines created from a generative contour. The title refers to the name of one of the Gorgon sisters, and is also Greek for open sea.
Herma is a piece for solo piano composed by Iannis Xenakis in 1961. About ten minutes long, it is based on a formulation of the algebraic equations of Boolean algebra, and is also an example of what Xenakis called symbolic music.
Pithoprakta (1955–56) is a piece by Iannis Xenakis for string orchestra, two trombones, xylophone, and wood block, premièred by conductor Hermann Scherchen in Munich in March 1957. A typical performance of the piece lasts about 10 minutes.
Alea III is a Boston, Massachusetts-based music ensemble that is devoted to the promotion, performance, and teaching of contemporary classical music.
Komboï is a 1981 stochastic composition for amplified harpsichord and percussion by Greek composer Iannis Xenakis. It is one of the two compositions for harpsichord and percussion written by Xenakis, the other one being Oophaa.
Jeux vénitiens is a 1961 composition by Polish composer Witold Lutosławski, under commission from the Krakow Philharmonic. It premiered April 21, 1961 in Venice. Another performance occurred at Warsaw Autumn in 1961.
Lousadzak, Op. 48, is a 1944 concerto for piano and string orchestra by the American-Armenian composer Alan Hovhaness. The work is known for its use of aleatory that is said to have impressed fellow composers Lou Harrison and John Cage, and anticipated "many soon-to-be-hip" aleatory techniques.
Eonta is a composition for piano, two trumpets, and three tenor trombones by Iannis Xenakis. It was written in 1963–64, and was premiered on December 16, 1964, by the Ensemble du Domaine Musical, with Yuji Takahashi on piano and Pierre Boulez conducting. Its duration is approximately 18 minutes.