Dynamical systems, celestial mechanics, and music: Pythagoras revisited

TL;DR

This paper explores the historical and modern connections between Pythagorean ideas, dynamical systems, and music, highlighting how principles of proportion and resonance underpin both celestial mechanics and musical theory.

Contribution

It reviews 25 years of research linking dynamical systems theory with music and celestial mechanics, emphasizing Pythagorean influence across disciplines.

Findings

Historical links between Pythagoras and musical scales.

Modern dynamical systems explain resonances in physics and music.

Pythagorean concepts underpin Musica Universalis and nonlinear resonances.

Abstract

Gioseffo Zarlino reintroduced the Pythagorean paradigm into Renaissance musical theory. In a similar fashion, Nicolaus Copernicus, Galileo Galilei, Johannes Kepler, and Isaac Newton reinvigorated Pythagorean ideas in celestial mechanics; Kepler and Newton explicitly invoked musical principles. Today, the theory of dynamical systems allows us to describe very different applications of physics, from the orbits of asteroids in the Solar System to the pitch of complex sounds. Our aim in this text is to review the overarching aims of our research in this field over the past quarter of a century. We demonstrate with a combination of dynamical systems theory and music theory the thread running from Pythagoras to Zarlino that allowed the latter to construct musical scales using the ideas of proportion known to the former, and we discuss how the modern theory of dynamical systems, with the study of resonances in nonlinear systems, returns to Pythagorean ideas of a Musica Universalis.