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

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Welcome to the October 2025 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Patreons, whittle them down to a more manageable number -- based primarily on whether I have anything interesting to say about them, not whether the questions themselves are good -- and sometimes group them together if they are about a similar topic. Enjoy!

Blog post with AMA questions and transcript: https://www.preposterousuniverse.com/podcast/2025/10/13/ama-october-2025/

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Certain features of our universe seem unnatural to us. These include "constants of nature" such as the cosmological constant and the mass of the Higgs boson, as well as features of the initial conditions like the curvature of space and the initial entropy. But they can't truly be "unnatural" -- they are literally features of Nature itself. Some have turned to the anthropic principle and the multiverse, while others look to theism for an explanation. I talk here about my views on the various attitudes one might take toward these apparent fine-tunings, and why it is important to think about them.

Blog post with transcript: https://www.preposterousuniverse.com/podcast/2025/10/06/331-solo-fine-tuning-god-and-the-multiverse/

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Some readings of relevance:

• Livio and Rees, Fine-Tuning, Complexity, and Life in the Multiverse
• Carroll, In What Sense Is the Early Universe Fine-Tuned?
• Barnes, A Reasonable Little Question: A Formulation of the Fine-Tuning Argument
• Goff, Our Improbable Existence Is No Evidence for a Multiverse
• Neal, Puzzles of Anthropic Reasoning Resolved Using Full Non-indexical Conditioning

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