The Broken Symmetry of Music: Applying Statistical Physics to Understand the Structure of Music
The ubiquity of music throughout history and across cultures raises a fundamental question: Why is this way of arranging sounds such a powerful medium for human artistic expression? Though there are myriad musical systems and styles, there are certain characteristics that are nearly universal, including a restriction to a discrete set of sound frequencies (pitches). In this talk, I will present a bottom-up approach to a theory of musical harmony, starting from two basic (and conflicting) principles: a system of music is most effective when it 1. minimizes dissonant sounds, and 2. allows sufficient complexity to allow the desired artistic expression. Mathematical statement of these principles allows a direct mapping onto a standard statistical mechanics framework. We can thereby apply all the tools of statistical mechanics to explore the phenomena that emerge from this model of music. In doing so, we will observe ordered phases self-organizing from disordered sound. These ordered phases can replicate existing Western and non-Western systems of music, as well as suggesting new directions to be explored.