Aleatory Quiz

John Cage and Karlheinz Stockhausen, c. 1958

John Cage and Karlheinz Stockhausen, c. 1958

It’s Aleatory Week in my Music Theory IV class, and I always give a fun aleatory quiz for the occasion. Aleatory (derived from the Latin alea, meaning “dice”) is “a term applied to music whose composition and/or performance is, to a greater or lesser extent, undetermined by the composer.” (Grove Music) Aleatory is thus synonymous with the term indeterminacy. Two broad types of aleatory music can be distinguished: music in which elements of the compositional construction are determined by chance (resulting in fixed compositions), and music in which elements of the performance are undetermined by the composer and must be determined by the performer(s) (e.g. through the use of graphic notation or “mobile form”). Certainly it is possible for these two types to be combined in a single work.

The below quiz contains six excerpts from the following three piano works: Pierre Boulez’s Piano Sonata No.2 (1947-48), Karlheinz Stockhausen’s Klavierstückeset 1 (Nos.1-4) (1952), and John Cage’s Music of Changes (1951). Only the Cage work is aleatory. It is a composition in which each element was determined by the use of chance procedures. “Each detail of his score was determined by the toss of three coins six times, which directed him to a specific number in I Ching (the Oriental “Book of Changes”); this in turn sent him to a numbered position on one of twenty-six charts he had devised. Thus a single pitch was determined. The procedure was then repeated in the determination of duration, timbre, and other parameters.” (Watkins, Soundings, p.560) Cage’s Music of Changes is then aleatory of the first type described above – that is, chance operations were used in constructing its fixed, carefully notated score.

The quiz, then, essentially requires the listener to aurally identify Cage’s chance music from among the other two highly-controlled works. Each of the three works listed above are represented at least once on the quiz. If you are up for a real challenge, try to distinguish the Boulez excerpts from the Stockhausen excerpts as well. (No fair cheating with your Shazam app!) Answers are posted at the bottom of the page.

Number 1
Number 2
Number 3
Number 4
Number 5
Number 6

The obvious point of this quiz is the ironic fact that aleatory of the kind represented by Cage’s Music of Changes often produced results that are strikingly similar to works of composers in the modernist avant-garde, composers that came to loathe Cage’s aleatory. Boulez, who initially recognized an aesthetic affinity between Cage and himself, eventually attacked Cage mercilessly (without naming him) stating that the adoption of chance procedures only “conceal[s] a fundamental weakness in compositional technique… It is an artificial paradise, comfortably arranged, whose dreams are, I suspect, never very miraculous: a narcotic which protects against the needle-prick of invention.” (Boulez, “Alea” 1957, tr. Stephen Walsh)

# Answers (highlight boxes below to reveal answers)
1 Cage, Music of Changes
2 Boulez, Piano Sonata No. 2, mvmt 4
3 Stockhausen, Klavierstück II
4 Boulez, Piano Sonata No. 2, mvmt 4
5 Cage, Music of Changes
6 Stockhausen, Klavierstück I



About Luke Dahn

Composer and music theorist Luke Dahn is Visiting Assistant Professor of Music Theory at the University of Utah. He is also co-founder and artistic co-director of Ensemble Périphérie, and lives in Salt Lake City with his wife Yu Jueng and daughter Mae.
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