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Dynamical Systems, Celestial Mechanics, and Music: Pythagoras Revisited

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I am every day more and more convinced of the Truth of Pythagoras’s Saying, that Nature is sure to act consistently, and with a constant Analogy in all her Operations: From whence I conclude that the same Numbers, by means of which the Agreement of Sounds affects our Ears with Delight, are the very same which please our Eyes and Mind. We shall therefore borrow all our Rules for the Finishing our Proportions, from the Musicians, who are the greatest Masters of this Sort of Numbers, and from those Things wherein Nature shows herself most excellent and compleat.

—Leon Battista Alberti (1407–1472), De Re Aedificatoria

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Notes

  1. Obtained without performing the arithmetic mean with the lower fifth of the F (8/9); it is necessary to include as a note the naturally generated interval between the Pythagorean F and G; this is a whole tone, 3/2 / 4/3 = 9/8.

  2. Quoted in [41, p. 109]; translation from the French by the authors.

  3. Translation from the Italian by the authors.

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Authors and Affiliations

  1. Instituto Andaluz de Ciencias de la Tierra, CSIC-Universidad de Granada, Armilla, 18100, Granada, Spain

    Julyan H. E. Cartwright

  2. Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071, Granada, Spain

    Julyan H. E. Cartwright

  3. Istituto per la Microelettronica e i Microsistemi, Area della Ricerca CNR di Bologna, 40129, Bologna, Italy

    Diego L. González

  4. Dipartimento di Scienze Statistiche “Paolo Fortunati”, Università di Bologna, 40126, Bologna, Italy

    Diego L. González

  5. Departament de Física, Universitat de les Illes Balears, 07071, Palma de Mallorca, Spain

    Oreste Piro

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Chapter V of Book IX of Alberti’s Ten Books of Architecture, translated by James Leoni.

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Cartwright, J.H.E., González, D.L. & Piro, O. Dynamical Systems, Celestial Mechanics, and Music: Pythagoras Revisited. Math Intelligencer 43, 25–39 (2021). https://doi.org/10.1007/s00283-020-10025-x

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