Theory IV Class Notes Indeterminacy Page 1 of 6

Indeterminacy, Chance, and Aleatory Music The terms indeterminacy, chance, aleatoric, random, and improvisatory (total, controlled, or otherwise) have been applied to music in which one or more aspect of a composition are left to chance. One composer may use completely random operations, while another may use freedom in only one parameter. Indeterminacy can be partial or total, and it can affect a small part of a composition or the whole. Elements that can be “indeterminate” are pitch, note durations, form, sound material, and expression (dynamics, timbre, etc.) We will give a few examples from Reginald Smith Brindle The New Music (Oxford University Press, 1975). An early example is Morton Feldman’s Projection I for solo cello (1950). The timbre is indicated (diamond = harmonic, P = pizzicato, and A = arco) and relative pitch is shown as a square or rectangle in three relative ranges — low, medium, or high.

In Stockhausen’s Zeitmasse (“tempi”), written for wind quintet in 1956, the flute and bassoon play in exact time (eighth = 112) while the oboe plays “as slow as possible”, the English horn “slow – quickening,” and the clarinet begins after a pause of imprecise duration.

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In this example from Sylvano Bussotti’s Sette Foglie (for flute and piano), the pitches are notated using traditional symbols, but in reality note-durations depend on the space occupied on the written page. This is sometimes called “proportional notation.”

Berio’s Circles uses indeterminate notation to indicate rapid cascades of sounds for marimba and xylophone.

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Composers have also used “graphic scores” to suggest directions for improvisation by the performer. In these cases much of the final result is left to chance. Two examples are shown below.

A large number of works are based merely on successions of sounds of imprecise duration, where instruments begin together and then play on in their own time. An example is Morton Feldman’s Durations.

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An example of indeterminate or “open” form can be found in Earle Brown’s Four Systems and various pieces in Folio (1952). The music can be played forwards or backwards, or upside down, or on designs that can be played in any position, by any number of players. Compositions heard in class.

• Excerpts from Folio When the Spirit Catches You … (2003)

• John Cage Aria with Fontana Mix (performance directions attached).

• Excerpts from John Cage’s Indeterminacy. This consists of 90 short stories narrated by the composer and accompanied by David Tudor on synthesizer and piano. Each story is told in one minute, so the speed of delivery depends on the length of the story. The complete texts can be seen on the web site

< http://www.lcdf.org/indeterminacy/index.cgi >

The performance directions and first page of the score for Cage’s Aria are reproduced below.

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