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diary - January 2024

math.ucr.edu · 33 words · saved by 1 readers

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

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diary - January 2024

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