Aesthetics, dynamics, and musical scales: A golden connection

Number theory has recently found a quantity of applications in the natural and applied sciences, and in particular in the study of nonlinear dynamical systems. As our sensory systems are highly nonlinear, it is natural to suppose that number theory also plays an important rôle in the description of perception, including aesthetics. Here we present a mathematical construction, based on number-theoretical properties of the golden mean, that generates meaningful musical scales of different numbers of notes. We demonstrate that ...