Sur le th\'eor\`eme des trois distances et la construction des gammes

TL;DR

This paper explores the connection between a classical diophantine approximation theorem, known as the three gap theorem, and the construction of musical scales, highlighting interdisciplinary links between mathematics and music theory.

Contribution

It clarifies the relationship between the three gap theorem and musical scale construction, providing insights into their mathematical and musical interplay.

Findings

The three gap theorem explains the spacing in certain musical scales.

Mathematical principles can inform musical scale design.

Interdisciplinary connections between number theory and music are demonstrated.

Abstract

We explain the link between the so-called "three gap theorem" and the construction of musical scales. Nous expliquons le lien entre un th\'eor\`eme classique d'approximation diophantienne (le th\'eor\`eme des trois distances), et la construction des gammes en musique.