Get 20M+ Full-Text Papers For Less Than $1.50/day. Subscribe now for You or Your Team.

Learn More →

Exploring the space of perfectly balanced rhythms and scales

Exploring the space of perfectly balanced rhythms and scales Periodic scales and meters typically embody “organizational principles” – their pitches and onset times are not randomly distributed, but structured by rules or constraints. Identifying such principles is useful for understanding existing music and for generating novel music. In this article, we identify and discuss a novel organizational principle for scales and rhythms that we feel is of both theoretical interest and practical utility: perfect balance. When distributed around the circle, perfectly balanced rhythms and scales have their “centre of gravity” at the centre of the circle. The present article serves as a repository of the theorems and definitions crucial to perfect balance. It also further explores its mathematical ramifications by linking the existing theorems to algebraic number theory and computational optimizations. In the Online Supplement, http://www.dynamictonality.com/perfect_balance_files/, we provide audio samples of perfectly balanced rhythmic loops and microtonal scales, computational routines, and video demonstrations of some of the concepts. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis and Composition" Taylor & Francis

Exploring the space of perfectly balanced rhythms and scales


Abstract

Periodic scales and meters typically embody “organizational principles” – their pitches and onset times are not randomly distributed, but structured by rules or constraints. Identifying such principles is useful for understanding existing music and for generating novel music. In this article, we identify and discuss a novel organizational principle for scales and rhythms that we feel is of both theoretical interest and practical utility: perfect balance. When distributed around the circle, perfectly balanced rhythms and scales have their “centre of gravity” at the centre of the circle. The present article serves as a repository of the theorems and definitions crucial to perfect balance. It also further explores its mathematical ramifications by linking the existing theorems to algebraic number theory and computational optimizations. In the Online Supplement, http://www.dynamictonality.com/perfect_balance_files/, we provide audio samples of perfectly balanced rhythmic loops and microtonal scales, computational routines, and video demonstrations of some of the concepts.

Loading next page...
 
/lp/taylor-francis/exploring-the-space-of-perfectly-balanced-rhythms-and-scales-fdmQpmM38h

References (50)

Publisher
Taylor & Francis
Copyright
© 2018 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1745-9745
eISSN
1745-9737
DOI
10.1080/17459737.2017.1395915
Publisher site
See Article on Publisher Site

Abstract

Periodic scales and meters typically embody “organizational principles” – their pitches and onset times are not randomly distributed, but structured by rules or constraints. Identifying such principles is useful for understanding existing music and for generating novel music. In this article, we identify and discuss a novel organizational principle for scales and rhythms that we feel is of both theoretical interest and practical utility: perfect balance. When distributed around the circle, perfectly balanced rhythms and scales have their “centre of gravity” at the centre of the circle. The present article serves as a repository of the theorems and definitions crucial to perfect balance. It also further explores its mathematical ramifications by linking the existing theorems to algebraic number theory and computational optimizations. In the Online Supplement, http://www.dynamictonality.com/perfect_balance_files/, we provide audio samples of perfectly balanced rhythmic loops and microtonal scales, computational routines, and video demonstrations of some of the concepts.

Journal

"Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis and Composition"Taylor & Francis

Published: Sep 2, 2017

Keywords: perfect balance; evenness; scales; rhythm and meter; consonance and dissonance; 00A65; 05B30; 11R18; 97N80; 90C25 2012 Computing Classification Scheme : sound and music computing; user interface design; convex optimization

There are no references for this article.