English

Algebraic Structures in Microtonal Music

Sound 2025-06-24 v1 Audio and Speech Processing History and Overview

Abstract

We will discuss how certain group theory structures are found in music theory. Western music splits the octave into 12 equal tones called half-steps. We can take this division further and split the octave into 24 equal tones by splitting each half-step in two, called a quarter-step. By assigning each of these 24 notes a number, we can discuss musical actions mathematically. In this paper, we analyze 24-tone microtonal music and explore how musical and harmonic structures in this system can be interpreted in terms of group-theoretic structures. This work extends the study by Crans, Fiore, and Satyendra.

Cite

@article{arxiv.2506.17778,
  title  = {Algebraic Structures in Microtonal Music},
  author = {Veronica Flynn and Carmen Rovi},
  journal= {arXiv preprint arXiv:2506.17778},
  year   = {2025}
}

Comments

17 pages, 12 figures. The content should be accessible for students in a first course of Abstract Algebra. A musical background is not necessary. Comments welcome!

R2 v1 2026-07-01T03:27:57.722Z