3-odd-limit

Odd limit

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← 1-odd-limit  3-odd-limit  5-odd-limit →

The 3-odd-limit is the set of all rational intervals which can be written as 2^k(a/b) where a, b ≤ 3 and k is an integer. To the 1-odd-limit, it adds 1 pairs of octave-reduced interval involving 3.

Below is a list of all octave-reduced intervals in the 3-odd-limit.

• 1/1
• 4/3, 3/2

Ratio	Size (¢)	Color name		Name
4/3	498.045	w4	wa 4th	just perfect fourth
3/2	701.955	w5	wa 5th	just perfect fifth

All edos are consistent in the 3-odd-limit, since every edo maps 3/2 and 4/3 to the nearest step by patent val.

The density of edos consistent in the 3-odd-limit to distance d is expected to be 1/d for d ≥ 1.

See also

• 3-limit (prime limit)