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Why are the frequency ratios of notes in the Pythagorean scales 9/8 and 256/243?

If one uses the following sequence of interval ratios for a major scale, the product of the ratios does, in fact, add up to 2:1 - 9:8, 10:9, 16:15, 9:8, 9:8, 10:9, 16:15. These major and minor ...
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