On Kepler's geometric approach to consonances

TL;DR

This paper explores Kepler's geometric ideas on musical consonances, using modern mathematics to characterize them through polygons constructible with ruler and compass, revealing a novel link between geometry and music theory.

Contribution

It introduces a new mathematical framework based on Kepler's geometric approach to classify the seven musical consonances using polygons.

Findings

Consonances correspond to polygons with a specific number of edges.

A geometric characterization of consonances aligns with classical music theory.

The approach bridges ancient geometry and modern mathematical music analysis.

Abstract

Kepler's thinking is highly original and the inspiration for discovering his famous third law is based on his rather curious geometric approach in his Harmonices mundi for explaining consonances. In this article we try to use a modern mathematical approach based on Kepler's ideas how to characterize the seven consonances with the help of the numbers of edges of polygons constructible by ruler and compass.