Dynamical systems, celestial mechanics, and music: Pythagoras revisited
| Autor: | Diego L. González, Julyan H. E. Cartwright, Oreste Piro |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Dynamical systems theory
General Mathematics Mathematics - History and Overview History and Overview (math.HO) 010102 general mathematics Pythagorean theorem Physics - History and Philosophy of Physics FOS: Physical sciences Nonlinear Sciences - Chaotic Dynamics 01 natural sciences Kepler Celestial mechanics symbols.namesake History and Philosophy of Science Music theory Musica universalis Calculus Galileo (satellite navigation) symbols FOS: Mathematics History and Philosophy of Physics (physics.hist-ph) 0101 mathematics Chaotic Dynamics (nlin.CD) Copernicus |
| Zdroj: | Digital.CSIC. Repositorio Institucional del CSIC instname |
| DOI: | 10.48550/arxiv.2104.00998 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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