Sturmian Canons

  • Clifton Callender
Conference paper

DOI: 10.1007/978-3-642-39357-0_5

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7937)
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

Abstract

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.

Keywords

Sturmian word canon self-similarity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Clifton Callender
    • 1
  1. 1.Florida State UniversityUSA

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