332 | Dmitri Tymoczko on the Mathematics Behind Music
Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
Sean Carroll
4.7 • 4.7K Ratings
🗓️ 20 October 2025
⏱️ 81 minutes
🧾️ Download transcript
Summary
Music is math that you can dance to. The fact that certain notes sound good when played together, or in succession, is related to the mathematical properties of the frequencies to which they correspond, an idea that goes back as far as Pythagoras himself. These days we have a much more intricate understanding of these relationships and how to manipulate them. I talk to composer and music theorist Dmitri Tymoczko about how different musical scales are constructed and the math underlying what sounds good.
Blog post with transcript: https://www.preposterousuniverse.com/podcast/2025/10/20/332-dmitri-tymoczko-on-the-mathematics-behind-music/
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Dmitri Tymoczko received a Ph.D. in music composition from the University of California, Berkeley. He is currently a professor of music at Princeton University as well as a composer and performer. He has been the recipient of Rhodes and Guggenheim fellowships. As a composer, his works have been performed by multiple groups, and recorded on several albums.
- Personal web site
- Princeton web page
- Mad Musical Science
- Spiral diagrams: rock music, classical music
- Google Scholar publications
- Amazon author page
- Wikipedia
- William Sethares's Tuning Timbre Spectrum Scale
Transcript
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| 0:00.0 | Hello, everyone. Welcome to the Mindscape Podcast. I'm your host, Sean Carroll. Let me start |
| 0:04.4 | today's episode with two quotes from two very different important thinkers in human intellectual |
| 0:10.9 | history. One is from Gottfried Leibniz, who says, music is the pleasure, the human mind experiences |
| 0:18.4 | from counting without being aware that it is counting. |
| 0:22.3 | The other is from Thelonius Monk, the famous jazz composer and pianist, who said all musicians |
| 0:28.7 | are subconsciously mathematicians. |
| 0:31.8 | I learned about the existence of both these quotes from today's guest, Dmitri Tomosco, |
| 0:36.2 | and they express basically exactly the same idea, |
| 0:39.8 | right, that there is something in music, in the playing of music, maybe even in the experiencing |
| 0:46.3 | of music, that is subconsciously mathematical. This connection between math and music is very, |
| 0:52.9 | very well known, and has been explored in great |
| 0:55.8 | details. But there's something else going on. You know, music is not simply abstract mathematics. |
| 1:02.3 | It's not theorems and proofs. It's embodied somehow. You play the notes or you sing the notes, |
| 1:08.5 | and then you hear the notes, you experience the notes. |
| 1:11.6 | So that's physics, as well as mathematics, not to mention psychology and physiology and things |
| 1:17.9 | like that. There's a lot going on in the world of music that intersects with science and with |
| 1:23.2 | mindscapey topics in all sorts of ways. At the same time, there's another famous story that |
| 1:28.1 | may or may not be apocryphal, but I know that I love telling it. I probably told it before |
| 1:31.8 | of Albert Einstein, who loved playing the violin. And he became a celebrity, of course, Einstein. |
| 1:37.5 | So he got to play the violin with real, classically trained musicians, famous musicians. And at one |
| 1:42.8 | point, one of them is playing with |
| 1:44.7 | Einstein and just stops out of frustration and says, Professor, don't you know anything about time? |
... |
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