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Encyclopedia of Microtonal Music Theory

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ratio-of

[Harry Partch 1974, Genesis of a Music, 2nd ed.; adapted by Joe Monzo]

"Ratios of R" are those ratios with odd factors no larger than R, in which R is present as an odd factor.

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[Paul Erlich, private communication with Joe Monzo]

n/d is a ratio of R if and only if the larger of (the largest odd factor of n) and (the largest odd factor of d) is R. Some examples:

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