Aleatoric Music Explained: 5 Examples of Indeterminate Music

Aleatoric music is a form of music that is subject to improvisation or structured randomness. It relies on a composer making chance decisions while writing the piece, or more commonly, a performer improvising while playing a piece. Also known as aleatory music, indeterminate music, or chance music, it combines scripted instructions from a composer—typically via sheet music—and improvisation by the musician playing the piece.

Aleatoric music played an integral role in mid-to-late twentieth-century classical music. Composers like John Cage, Karlheinz Stockhausen, Pierre Boulez, and Witold Lutoslawski wrote open-form pieces designed to be interpreted by individual players. This introduced the element of chance to a traditionally scripted form of musical composition.

Aleatoric music thrived in the mid-to-late twentieth century, but its roots date farther back.

• Early aleatoric compositions: In the Renaissance and Baroque periods of music, composers wrote out pieces with figured bass notation, which left a degree of performance choices to the composer. In the Classical era, composers such as Wolfgang Amadeus Mozart used a musical dice game called Musikalisches Würfelspiel that applied the use of chance to the content of specific musical measures. Yet by the time the piece was completed, the music was set, with no space for improvised passages by a performer.
• Twentieth-century adaptations: Aleatoric music did not play a role in Classical or Romantic-era performances, but by the twentieth century, it had found its way into classical music. American composers Charles Ives, Henry Cowell, and Alan Hovhaness included small sections in pieces where performers could improvise.
• Full embrace from John Cage: In 1951, American composer John Cage debuted Music of Changes, which embraced the concept of indeterminacy—the notion that the same piece of music could be played in different ways depending on the performer’s choices.
• Broader acceptance within the avant-garde: Cage's music inspired many twentieth-century classical music composers to try their own hand at aleatory music. Pierre Boulez composed pieces with only a limited number of possibilities for players—all of which were tightly scripted. Europeans like Witold Lutoslawski and Karlheinz Stockhausen—along with Americans like Terry Riley and Earle Brown—wrote works with scripted musical parts and phrases but let the performers decide the sequence of performance.
• Graphic notation: As aleatoric music caught on, new forms of music notation evolved to describe it. Morton Feldman, George Crumb, Krzysztof Penderecki, Anthony Braxton, and John Cage himself were among the composers who expressed their aleatoric music using graphic illustrations rather than traditional five-line staves.

Aleatoric music comes from the Latin word alea, which means "dice." Several pieces exemplify this notion of musical performance as a roll of the dice.

1. 1. Music of Changes by John Cage (1951): This piece, considered the foundational aleatoric work of the twentieth century, employs the ancient Chinese text I Ching to derive random numbers representing tempo, dynamics, and note duration.
2. 2. Concerto for 2 Pianos by Alan Hovhaness (1954): This Hovhaness piece combines concepts from European fugue and Indian raga—a style that inherently involves improvisation.
3. 3. Klavierstück XI by Karlheinz Stockhausen (1956): The score to this piece is printed on a single page and contains 19 musical fragments in traditional notation. They are to be played in a particular order, but the performer may start at any place in the cycle.
4. 4. Pithoprakta by Iannis Xenakis (1956): With a title translating to "actions through probability," this aleatoric piece is conceptually inspired by the physics of gas molecules. Such composition via physical or mathematical principles is sometimes called stochastic music.
5. 5. In C by Terry Riley (1964): Riley helped bring aleatory to a subset of classical music called minimalism. This piece for an indeterminate number of players—Riley suggests "about 35"—contains 53 numbered musical phrases that performers play and repeat at their own discretion.

In the spirit of John Cage, many composers use the terms "aleatoric music" and "indeterminate music" interchangeably. There are four types of indeterminate music composition.

1. 1. Music composed with chance procedures: Some forms of indeterminate music are fixed for performers, but the composers use chance operations to compose sections of a piece. In the Classical era, for instance, Wolfgang Amadeus Mozart used a musical dice game called Musikalisches Würfelspiel to help him choose how to write certain measures within his pieces.
2. 2. Mobile form: In mobile form, the aleatory elements of a piece are bequeathed upon a performer. A composer provides notation for performers to work with, and the performers may choose how and when to perform that notated music once in the concert hall.
3. 3. Indeterminate notation: In indeterminately notated music, composers eschew the traditional five-line staff with treble clefs, bass clefs, alto clefs, and tenor clefs. Instead, they use graphic notation or text notation to give the players guidance on what to do. This format leads to even more performer discretion than the mobile form of aleatory music.
4. 4. Improvisation over a form: In pop, rock, and jazz music, performers often improvise over a song form. A jazzy saxophone break in a New York club or a screaming guitar solo at a rock festival represents a form of aleatoric music. This is all the more true when a backing band extends or alters a song form to fit the solo. Electronic music played in clubs can take on a similar aleatory quality, as DJs often alter song forms from one performance to another.

A small number of films have used aleatoric music as part of their musical score. John Williams's partially aleatoric score for Robert Altman's Images earned him an Academy Award nomination. X-Files composer Mark Snow occasionally used aleatory in the score to the long-running TV show. Radiohead guitarist and avant-garde composer Jonny Greenwood has used aleatoric techniques in scores for Paul Thomas Anderson films.

Become a better musician with the MasterClass Annual Membership. Gain access to exclusive video lessons taught by the world’s best, including Herbie Hancock, Itzhak Perlman, St. Vincent, Sheila E., Timbaland, Tom Morello, and more.