Symmetry and Complexity in Music

Explore the mathematical foundations underlying music through an examination of pulse, pitch, and transformed repetition in this 45-minute conference talk by Dmitri Tymoczko from Princeton University at the Santa Fe Institute. Discover how musical transformations generate symmetry groups that create rich networks of mathematical structures, including quotient spaces and the fundamental group. Learn about recent research conducted at SFI demonstrating the universal nature of these mathematical concepts that originally appeared in continuous spaces. Examine the consequences of this universal structure for both music creation and comprehension, while considering broader philosophical questions that extend into artificial intelligence applications.