Beyond the Geometry of Music
Posted by John Baez
Yesterday I had a great conversation with Dmitri Tymoczko about groupoids in music theory. But at this Higgs Centre Colloquium, he preferred to downplay groupoids and talk in a way physicists would enjoy more. Click here to watch his talk!
What’s great is that Tymoczkyo not faking it: he’s really found deep ways in which symmetry shows up pervasively in music.
At first he tried to describe them geometrically using orbifolds, which are spaces in which some singular points have nontrivial symmetry groups, like the tip of a cone formed by modding out the plane by the action of the group . But then he realized that the geometry was less important than the symmetry, which you can describe using groupoids. That’s why his talk is called “Beyond the geometry of music”.
I’m helping him with his work on groupoids, and I hope he explains his work to mathematicians someday without pulling his punches. I didn’t get to interview him yesterday, but I’ll try to do that soon.
For now you can read his books A Geometry of Music and Harmony: an Owner’s Manual along with many papers. What I’ve read so far is really exciting.