Dynamical Systems: A Golden Gate from Auditory Physiology to Musical Aesthetics?

Julyan H.E. Cartwright, Diego L. González, Oreste Piro and Domenico Stanzial
Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings (2003)
Pages 331–338


From antiquity humanity has sought through scientific enquiry a rational explanation of nature. All artworks were considered an imitation of nature, the same purpose has pervaded the history of the arts. The Pythagoreans were the first to put into mathematical terms the rules for aesthetics, borrowing them from music [1]. Later there arose the concepts of eurhythmy or commodulation: the application of rhythmical movements or harmonious proportions in a piece of music; a painting; a sculpture; a building; a dance. Throughout the Middle Ages, mathematical ideas of proportion lived side by side with the body of artistic activity, but during the Renaissance, the natural sciences and mathematics began a process of separation from the arts, both theoretically as well as in practical terms [2]. One of the reasons for the divorce was that all efforts failed to give a rational basis to the role played by numerical proportions in the aesthetics of an artwork. This lack of scientific rationale caused a rejection of works on numerical proportion in aesthetics by the scientific community, which began to consider writings in this area esoteric and unscientific. The divergence between arts and sciences grew wider in the twentieth century, with the end of the last movements retaining the ancient mathematical roots of art: neoclassicism and cubism. From this point on, the tendency of artists has been to consider that the mathematical design of an artwork implies an unacceptable constraint to creativity. If, in the future, the gulf between arts and sciences is to be reduced, this may come about through being able to understand in an objective fashion the phenomena that take place in our perceptual and nervous systems when we look at a painting [3], or listen to music. Some of these phenomena may be rooted in the fundamental role in the theory of nonlinear dynamical systems played by a particular number: the golden mean.