Symmetry and Complexity in Music

Abstract: Almost all music is concerned with three fundamental properties: pulse, pitch, and transformed repetition. Many musical transformations are invertible, and hence generate symmetry groups. Symmetry groups in turn give rise to a rich network of mathematical structures including quotient spaces and the fundamental group. This conceptual network originally appeared in conjunction with continuous spaces, but recent work (partly conducted at SFI) has shown it to be universal. My talk will outline this universal structure and explore some of its consequences, not just for making and understanding music, but also for thinking about larger philosophical questions—including some that touch upon AI.