Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: Voice Leading as Vector
Speaker: Dmitri Tymoczko, Princeton University
Date: Thursday, December 3, 2015 5:00pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
In my talk I will describe what I believe to be one of the most general and fundamental connections between music and mathematics, a kind of "translation manual" that allows us to associate basic concepts in music theory with ideas from contemporary geometry. The most fundamental entries in this translation manual associate chords with points in an orbifold, voice leadings with vectors (or, given the structure of the spaces, homotopy classes of paths in the orbifold), and scales with metrics. Using this translation manual we can translate back and forth between the visual and the musical realms, creating spatial representations that allow us to understand not just particular pieces but also more general constraints on musical styles. But even without these visual representations, a focus on vectors or voice leadings opens the door to new statistical understanding of even the most basic questions about traditional music.