332 | Dmitri Tymoczko on the Mathematics Behind Music

Hello, everyone. Welcome to the Windscape Podcast. I'm your host, Sean Carroll. Let me start today's episode with two quotes from, two very different important thinkers in human intellectual history. One is from Gottfried Leibniz, who says, music is the pleasure the human mind experiences from counting without being aware that it is counting. The other is from Thelonious Monk, the famous jazz composer and pianist, who said, all musicians are subconsciously mathematicians. I learned about the existence of both these quotes from today's guest, Dimitri Tomosko, and they express basically exactly the same idea, Right? That there is something in music, in the playing of music, maybe even in the experiencing of music that is subconsciously mathematical. This connection between math and music is very, very well known and has been explored in great details. But there's something else going on, you know, music is not simply abstract mathematics, it's not theorems and proofs, it's embodied somehow. You play the notes or you sing the notes and then you hear the notes, you experience the notes. So that's physics as well as mathematics, not to mention psychology and physiology and things like that. There's a lot going on in the world of music that intersects with science and with mindscape y topics in all sorts of ways. At the same time, there's another famous story that may or may not be apocryphal, but I know that I love telling it. I probably told it before of Albert Einstein who loved playing the violin. And he became a celebrity, of course, Einstein. So he got to play the violin with real classically trained musicians, famous musicians. And at one point, one of them is playing with Einstein and just stops out of frustration and says, Professor, don't you know anything about time? Of course, you can know more about time in its intrinsic nature and its physical reality than any other person alive at the moment without being able to embody that knowledge in keeping time in a piece of music. So the actuality of it, the physicality of it, the reality of it can be different than the knowledge of all this mathematics underlying music. In today's episode, we're gonna be doing a little bit of both. Dimitri Tomosco is a musicologist, a composer, performer, a professor at Princeton, and he's been thinking very deeply about the relationships between mathematics and music. He has a background that includes studying a little bit of physics and philosophy like many Mindscape guests end up doing, and then really thinking about where all this mathematics fits in and get get into very advanced topics mathematically. We're not gonna quite get there in this podcast episode, but, Dimitri has authored books that you can buy. A Geometry of Music is one, and Tonality, a User's Manual, is another one. Thinking about how to put a metric on a space that is defined by what scale or what chords you're playing and thinking about …