- Cite this paper as:
- Callender C. (2013) Sturmian Canons. In: Yust J., Wild J., Burgoyne J.A. (eds) Mathematics and Computation in Music. MCM 2013. Lecture Notes in Computer Science, vol 7937. Springer, Berlin, Heidelberg
Sturmian words are balanced, almost periodic, self-similar and hierarchical infinite sequences that have been studied in music theory in connection with diatonic scale theory and related subjects. Carey and Camplitt (1996) give a brief but suggestive rhythmic example in which these properties are made manifest in a particularly visceral manner. The present paper expands upon this example, considering the properties of canons based on Sturmian words, or Sturmian canons. In particular, a Sturmian word of irrational slope a with a hierarchical periodicity of p gives rise to p-tuple canons, the voices and relations of which are determined by the terms of the continued fraction expansion of a.
KeywordsSturmian word canon self-similarity
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