11-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 11-odd-limit is the set of all rational intervals which can be written as 2^k(a/b) where a, b ≤ 11 and k is an integer. To the 9-odd-limit, it adds 5 pairs of octave-reduced intervals involving 11.

Below is a list of all octave-reduced intervals in the 11-odd-limit.

• 1/1
• 12/11, 11/6
• 11/10, 20/11
• 10/9, 9/5
• 9/8, 16/9
• 8/7, 7/4
• 7/6, 12/7
• 6/5, 5/3
• 11/9, 18/11
• 5/4, 8/5
• 14/11, 11/7
• 9/7, 14/9
• 4/3, 3/2
• 11/8, 16/11
• 7/5, 10/7

Ratio	Size (¢)	Color name		Name
12/11	150.637	1u2	lu 2nd	lesser undecimal neutral second
11/10	165.004	1og2	logu 2nd	greater undecimal neutral second
11/9	347.408	1o3	ilo 3rd	undecimal neutral third
14/11	417.508	1uz4	luzo 4th	undecimal major third
11/8	551.318	1o4	ilo 4th	undecimal superfourth
16/11	648.682	1u5	lu 5th	undecimal subfifth
11/7	782.492	1or5	loru 5th	undecimal minor sixth
18/11	852.592	1u6	lu 6th	undecimal neutral sixth
20/11	1034.996	1uy7	luyo 7th	lesser undecimal neutral seventh
11/6	1049.363	1o7	ilo 7th	greater undecimal neutral seventh

The smallest equal division of the octave which is consistent through to the 11-odd-limit is 22edo; that which is distinctly consistent through to the same is 58edo (also the smallest EDO to be consistent through to the 17-odd-limit).

See also

• 11-limit (prime limit)
• diamond11 – as a scale