Indeterminacy

Indeterminacy is a controversial approach to musical composition that has been the subject of a great deal of debate over many decades.

Music can be said to be indeterminate if an element of the composition or performance is left to chance. Indeterminacy in music can be split into two types, indeterminate with respect to composition, or with respect to performance. Both have been explored in great depth by many prominent composers, such as John Cage and Karlheinz Stockhausen. The methods may not be as popular today as they once were, but their influence on the way composers approach music is undeniable.

An example of indeterminate composition is The Music of Changes by John Cage. This is one of Cage’s earliest fully indeterminate works. The form, materials, sounds and silences are all determined by chance events using coin tosses and other methods. Although no two performances will ever be the same, the fundamentals of the music are all predetermined, hence the piece is said to be determinate with respect to its composition. Another example is Indices by Earle Brown, which used tables of random numbers to generate the content. (Cox & Warner 2004)

John Cage later looks back and criticises pieces that are indeterminate with respect to composition, including his own work. He claims that though chance operations brought about the determinations of these compositions, they allow no freedom for the performance. He goes as far as to say that this “gives the work the alarming aspect of a Frankenstein monster” (Cox & Warner 2004, p. 179). Cage insists that true indeterminacy must be achieved through the performance, and suggests Stockhausen has successfully achieved this in Klavierstuck XI (Cox & Warner 2004). While the note-to-note procedure is determined, the sequence of the parts is not, allowing for new expressive content in each performance (Cardew 1974).

Pierre Boulez was influenced by aleatoric methods and they are featured in much of his work since 1956. However Boulez is distinct from Cage and Stockhausen in the way he uses chance in his compositions. The third formant, ‘Constellation-Miroir,’ allows the performer to determine the order of some of the fragments of music. This was a much more conservative approach, as Boulez believed that choices must be made consciously rather than totally by chance. (Johnson, 1989)

Cage however, wanted to move past this aleatoric style, and had the “desire to strip his work of subjectivity” (Cardew, 1974 p167) and this inevitably led to more and more extreme work. Eventually he wrote the ultimate indeterminate work 4’33”. The piece is possibly Cage’s most famous work and constitutes four minutes and thirty-three seconds of silence. According to Cage however, there is no such thing as silence, and this is where the indeterminacy lies. The content 4’33” isn’t in the score or the composition, but in the inevitable external sounds heard by the audience.

Cage and other twentieth century composers pushed indeterminacy in music to the extremes. Although few of their specific techniques have survived to be used in more recent compositions, they succeeded in challenging accepted practices in musical composition, and opened the doors to greater innovation and experimentation. Consequently, echoes of their work and ideas can still be heard in music today.

References:

Cardew, C (1974). Stockhausen Serves Imperialism. London: Latimer New Dimensions Limited.

Cox, C. Warner, D (2004). Audio Culture: Readings in Modern Music. New York: Continuum. P176-186.

Griffiths, P. (1989). Edgard Varese and Karlheinz Stockhausen. In: Raeburn, M and Kendall, A Heritage of Music: Music in the Twentieth Century. Oxford: Oxford University Press. P279-289.

Johnson, S. J. (1989). Olivier Messiaen and Pierre Boulez. In: Raeburn, M and Kendall, A Heritage of Music: Music in the Twentieth Century. Oxford: Oxford University Press. P269-278.