# 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:

• 4/3 is a ratio of 3 because the largest odd factor is 3.
• 5/3 is a ratio of 5 because the largest odd factor is 5.
• 8/5 is also a ratio of 5, because the largest odd factor is still 5.
• 10/3 is also a ratio of 5, because the largest odd factor is still 5.
• 16/9 and 9/7 are both ratios of 9.
• etc.
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