Indeterminacy in music, which began early in the 20th century in the music of Charles Ives, and was continued in the 1930s by Henry Cowell and carried on by his student, the experimental music composer John Cage beginning in 1951 (Griffiths 2001), came to refer to the (mostly American) movement which grew up around Cage. This group included the other members of the so-called New York School: Earle Brown, Morton Feldman and Christian Wolff. Others working in this way included the Scratch Orchestra in the United Kingdom (1968 until the early 1970s) and the Japanese composer Toshi Ichiyanagi (born 1933).
John Cage originally defined indeterminacy as "the ability of a piece to be performed in substantially different ways" (Pritchett 1993, 108). Bryan Simms thus conflates indeterminacy with what Cage called chance composition when he claims that "Any part of a musical work is indeterminate if it is chosen by chance, or if its performance is not precisely specified. The former case is called 'indeterminacy of composition'; the latter is called "indeterminacy of performance" (Simms 1986, 357).
In 1958 Cage gave two lectures in Europe, the first at Darmstadt, titled simply "Indeterminacy" (Cage 1961, 35–40), the second in Brussels called "Indeterminacy: New Aspect of Form in Instrumental and Electronic Music" (given again in an expanded form in 1959 at Teacher's College, Columbia). This second lecture consisted of a number of short stories (originally 30, expanded to ninety in the second version), each story read by Cage in exactly one minute; because of this time limit the speed of Cage's delivery varied enormously (Cage 1961, 260). The second performance and a subsequent recording (Cage 1959) contained music, also by Cage, played by David Tudor at the same time. Subsequently, Cage added still more stories, and published a selection of them, partly as an article, "Indeterminacy" (Cage 1961, 260–73), and partly as scattered interludes throughout his first collection of writings, Silence (Cage 1961).
Between 2007 and 2013, the Dutch artist Iebele Abel developed an electronic instrument called Real-time Indeterminate Synthetic Music Feedback (RT-ISMF). The instrument was designed for empirical research on subjective experiences induced by real-time synthesized music, based on the output of electronic random number generators. The basic idea of this approach was that indeterminate music might evoke unique and exceptional human experience (Abel 2013, 26, 117–19).
Types of indeterminate music
Indeterminate music can be divided into three groups. 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 (Joe and Song 2002, 268). Cage himself, however, regarded Music of Changes as a determinate work, because it is completely fixed from one performance to another (Pritchett 1993, 108). On the level of detail, Iannis Xenakis used probability theories to define some microscopic aspects of Pithoprakta (1955–56), that is the 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, but the single components of sound are generated by mathematical theories (Joe and Song 2002, 268). See: stochastic music.
In the second type of indeterminate music (the only type of indeterminate music according to Cage's definition), 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 (Joe and Song 2002, 269). According to Cage, other examples include Johann Sebastian Bach's Art of Fugue, Morton Feldman's Intersection 3, Earle Brown's Four Systems, and Christian Wolff's Duo for Pianists II (Cage 1961, 35–39).
In this second type of music, control and chance merged in some composers' works in the late 1950s. One type of music in which this might occur is called in sound-mass composition or textural composition, where individual pitches and lines are integrated into complexes of sound ("sound masses").
In sound masses we do not perceive individual pitches, but rather chromatically filled complexes of sound. These sound blocks may result from multiple, minutely notated chromatic lines that fuse into each other (and then the sound masses are dynamic, in constant motion and transformation), as in György Ligeti's Atmosphères (1961), or they may result from more static clusters (blocks of sound made up of adjacent chromatic or microtonal steps), as in Krzysztof Penderecki's Threnody for the Victims of Hiroshima of 1960. … At times, clusters are notated pitch by pitch in conventional notation, whereas at other times they are indicated graphically, usually by means of solid black bands on the score. In sound-mass compositions, musical elements such as texture, density, register, dynamics, and instrumental color replace such musical parameters as rhythm, meter, lines, chords, and harmony, usually considered as "primary" in a more traditional compositional context.[vague] (Roig-Francolí 2008, 280–81)
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 unit are represented by the squares viewed horizontally, while relative pitch levels high, middle and low are indicated by three vertical squares in each row. The performer determines what particular pitches and rhythms to play (Joe and Song 2002, 269).
- Cage, John. 1959. Indeterminacy: New Aspects of Form in Instrumental and Electronic Music. Ninety Stories by John Cage, with Music. John Cage, reading; David Tudor, music (Cage, Solo for Piano from Concert for Piano and Orchestra, with Fontana Mix). Folkways FT 3704 (2 LPs). Reissued 1992 on Smithsonian/Folkways CD DF 40804/5 (2 CDs).
- Abel, Iebele. 2013. Manifestations of Mind in Matter. Princeton: ICRL Press. ISBN 978-1936033072.
- Cage, John. 1961. Silence: Lectures and Writings. Middletown, Conn.: Wesleyan University Press.
- Griffiths, Paul. 2001. "Aleatory". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
- Joe, Jeongwon, and S. Hoon Song. 2002. "Roland Barthes' ’Text’ and Aleatoric Music: Is the Birth of the Reader the Birth of the Listener?". Muzikologija 2:263–81.
- Pritchett, James. 1993. The Music of John Cage. Music in the 20th Century. Cambridge, New York, Melbourne: Cambridge University Press. ISBN 0-521-41621-3 (cloth); ISBN 0-521-56544-8 (pbk).
- Roig-Francolí, Miguel A. 2008. Understanding Post-Tonal Music. Boston: McGraw-Hill. ISBN 0-07-293624-X.
- Simms, Bryan R. 1986. Music of the Twentieth Century: Style and Structure. New York: Schirmer Books; London: Collier Macmillan Publishers. ISBN 0-02-872580-8.
- Childs, Barney. 1974. "Indeterminacy". Dictionary of Twentieth-Century Music, edited by John Vinton. London: Thames and Hudson. ISBN 0-500-01100-1 American edition published under title Dictionary of Contemporary Music (New York: E. P. Dutton, 1974) ISBN 0-525-09125-4.
- Nyman, Michael. 1974. Experimental Music: Cage and Beyond. London: Studio Vista; New York: Schirmer Books. ISBN 0-02-871200-5 Second edition 1999, Cambridge and New York: Cambridge University Press. ISBN 0-521-65297-9 (cloth) ISBN 0-521-65383-5 (pbk).
- Speyer-Carithers, Kirsten. 2005. "The Network of Influence: New York Artists and the Indeterminate Works of John Cage, 1951–1978. Master's thesis. Bowling Green State University.
- Sutherland, Roger. 1994. New Perspectives in Music. London: Sun Tavern Fields. ISBN 0-9517012-6-6.