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The ancient Greeks figured out that if you have a set of strings, it sounds really good if you tune them following the pitch ratios from the natural harmonic series. In such tuning systems, you pick a starting frequency, and then multiply or divide it by ratios of whole numbers to generate more frequencies, the same way you figure out the frequencies of a single string’s harmonics. The best-sounding note combinations (to Western people) are the ones derived from the first few harmonics. In other words, you get the nicest harmony (for Western people) when you multiply and divide your frequencies by ratios of the smallest prime numbers: 2, 3, and 5.
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