Modeling Musical Rhythm Mutations with Geometric Quantization

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

A mathematical analysis of musical rhythm presupposes what exactly a musical rhythm is and how it is represented. In the music literature, there are more than 50 ways to define musical rhythm. This chapter is concerned with transforming rhythms from one category of rhythms to another. Two classes of rhythms are referred to as binary and ternary. Several binarization algorithms that result from geometric quantization schemes are examined using the transformation of the fume-fume into the clave son as a case study. The chapter sheds some light on the likelihood of musical rhythm mutation between these two rhythms and that it suggests psychological experiments to determine which binarization algorithm is the better predictor of human perceived similarity. There are many ways to measure rhythm similarity. One natural approach is to sum the discrepancies between all the corresponding pairs of onsets.

Original languageEnglish (US)
Title of host publicationMathematical and Computational Modeling
Subtitle of host publicationWith Applications in Natural and Social Sciences, Engineering, and the Arts
Publisherwiley
Pages299-308
Number of pages10
ISBN (Electronic)9781118853986
ISBN (Print)9781118853887
DOIs
StatePublished - May 8 2015

Fingerprint

Geometric Quantization
Binarization
rhythm
Fumes
mutations
Mutation
Mathematical Analysis
Music
Modeling
Ternary
Discrepancy
Predictors
Likelihood
Binary
fumes
Experiment
Experiments
Similarity
applications of mathematics
music

Keywords

  • Binarization
  • Binary rhythms
  • Clave son
  • Fume-fume rhythm
  • Geometric quantization
  • Musical rhythm mutations
  • Rhythm similarity
  • Ternary rhythm

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Chemistry(all)
  • Computer Science(all)

Cite this

Toussaint, G. (2015). Modeling Musical Rhythm Mutations with Geometric Quantization. In Mathematical and Computational Modeling: With Applications in Natural and Social Sciences, Engineering, and the Arts (pp. 299-308). wiley. https://doi.org/10.1002/9781118853887.ch12

Modeling Musical Rhythm Mutations with Geometric Quantization. / Toussaint, Godfried.

Mathematical and Computational Modeling: With Applications in Natural and Social Sciences, Engineering, and the Arts. wiley, 2015. p. 299-308.

Research output: Chapter in Book/Report/Conference proceedingChapter

Toussaint, G 2015, Modeling Musical Rhythm Mutations with Geometric Quantization. in Mathematical and Computational Modeling: With Applications in Natural and Social Sciences, Engineering, and the Arts. wiley, pp. 299-308. https://doi.org/10.1002/9781118853887.ch12
Toussaint G. Modeling Musical Rhythm Mutations with Geometric Quantization. In Mathematical and Computational Modeling: With Applications in Natural and Social Sciences, Engineering, and the Arts. wiley. 2015. p. 299-308 https://doi.org/10.1002/9781118853887.ch12
Toussaint, Godfried. / Modeling Musical Rhythm Mutations with Geometric Quantization. Mathematical and Computational Modeling: With Applications in Natural and Social Sciences, Engineering, and the Arts. wiley, 2015. pp. 299-308
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