  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.
