3-odd-limit

Odd limits:

---

• 1-odd-limit
• 3-odd-limit
• 5-odd-limit
• 7-odd-limit
• 9-odd-limit
• 11-odd-limit
• 13-odd-limit
• 15-odd-limit
• 17-odd-limit
• 19-odd-limit
• 21-odd-limit
• 23-odd-limit
• 25-odd-limit
• 27-odd-limit
• 29-odd-limit
• 31-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 there are only two pitch classes besides the octave. 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)