### 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 language | English (US) |
---|---|

Title of host publication | Mathematical and Computational Modeling |

Subtitle of host publication | With Applications in Natural and Social Sciences, Engineering, and the Arts |

Publisher | wiley |

Pages | 299-308 |

Number of pages | 10 |

ISBN (Electronic) | 9781118853986 |

ISBN (Print) | 9781118853887 |

DOIs | |

State | Published - May 8 2015 |

### Fingerprint

### 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

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*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

}

TY - CHAP

T1 - Modeling Musical Rhythm Mutations with Geometric Quantization

AU - Toussaint, Godfried

PY - 2015/5/8

Y1 - 2015/5/8

N2 - 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.

AB - 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.

KW - Binarization

KW - Binary rhythms

KW - Clave son

KW - Fume-fume rhythm

KW - Geometric quantization

KW - Musical rhythm mutations

KW - Rhythm similarity

KW - Ternary rhythm

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U2 - 10.1002/9781118853887.ch12

DO - 10.1002/9781118853887.ch12

M3 - Chapter

AN - SCOPUS:85016068515

SN - 9781118853887

SP - 299

EP - 308

BT - Mathematical and Computational Modeling

PB - wiley

ER -