diary - January 2024

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As my friends are learning about my current obsession with tuning systems, they're starting to ask interesting questions I don't know the answers to. For example, Michael Fourman asked me: if harmonies coming from simple fractions are so natural, do any bird or whale songs feature such harmonies? It turns out an Australian bird called the pied butcherbird has long been a favorite of many composers! Jean-Michel Maujean figured out the frequency ratios that appear in the songs of this bird. He found the 4 most common ratios are close to He notes that 0.607 is close to going down a major sixth (3/5), 0.745 is close to going down a perfect fourth (3/4), 0.815 is kinda close to going down a major third (4/5), 1.34 is close to going up a perfect fourth (4/3). His work looks good — but he shouldn't have bothered comparing the ratios to 12-tone or 18-tone equal temperament. Equal temperament is a system developed for keyboard instruments in the late 1700s. It would be amazing if the birds used

For my June 2025 diary, go here. John Baez August 1, 2025 When bad news gets me down, I often get insomnia. I wake up in the middle of the night, start thinking about how we're all doomed, and can't easily stop. To break out of these doom loops, I do elaborate visualization exercises. They don't really put me to sleep, they just calm me down. Then later I can fall asleep. Here's what I've been doing this week. I visualize this shape made of two interpenetrating tetrahedra, called the 'stella octangula' or 'stellated octahedron'. Notice that these two tetrahedra are 'dual': each corner of…

diary - January 2024

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