23-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 23-odd-limit is the set of all rational intervals for which neither the numerator nor the denominator of the frequency ratio exceeds 23, once all powers of 2 are removed. To the 21-odd-limit, it adds 11 interval pairs involving 23.

Below is a list of all octave-reduced intervals in the 23-odd-limit. It contains all the wonders of 94edo.

• 1/1
• 24/23, 23/12
• 23/22, 44/23
• 22/21, 21/11
• 21/20, 40/21
• 20/19, 19/10
• 19/18, 36/19
• 18/17, 17/9
• 17/16, 32/17
• 16/15, 15/8
• 15/14, 28/15
• 14/13, 13/7
• 13/12, 24/13
• 12/11, 11/6
• 23/21, 42/23
• 11/10, 20/11
• 21/19, 38/21
• 10/9, 9/5
• 19/17, 34/19
• 9/8, 16/9
• 26/23, 23/13
• 17/15, 30/17
• 8/7, 7/4
• 23/20, 40/23
• 15/13, 26/15
• 22/19, 19/11
• 7/6, 12/7
• 20/17, 17/10
• 13/11, 22/13
• 19/16, 32/19
• 6/5, 5/3
• 23/19, 38/23
• 17/14, 28/17
• 28/23, 23/14
• 11/9, 18/11
• 16/13, 13/8
• 21/17, 34/21
• 26/21, 21/13
• 5/4, 8/5
• 24/19, 19/12
• 19/15, 30/19
• 14/11, 11/7
• 23/18, 36/23
• 9/7, 14/9
• 22/17, 17/11
• 13/10, 20/13
• 30/23, 23/15
• 17/13, 26/17
• 21/16, 32/21
• 4/3, 3/2
• 23/17, 34/23
• 19/14, 28/19
• 15/11, 22/15
• 26/19, 19/13
• 11/8, 16/11
• 18/13, 13/9
• 32/23, 23/16
• 7/5, 10/7
• 24/17, 17/12

Ratio	Size (¢)	Color name		Name
24/23	73.681	23u1	twethu unison	lesser vicesimotertial semitone
23/22	76.956	23o1u2	twetholu 2nd	greater vicesimotertial semitone
23/21	157.493	23or2	twethoru 2nd	vicesimotertial neutral second
26/23	212.253	23u3o2	twethutho 2nd	vicesimotertial whole tone
23/20	241.961	23og3	twethogu 3rd	vicesimotertial inframinor third
23/19	330.761	23o19u3	twethonu 3rd	vicesimotertial supraminor third
28/23	340.552	23uz3	twethuzo 3rd	vicesimotertial neutral third
23/18	424.364	23o4	twetho 4th	vicesimotertial diminished fourth
30/23	459.994	23uy3	twethuyo 3rd	vicesimotertial ultramajor third
23/17	523.319	23o17u4	twethosu 4th	vicesimotertial acute fourth
32/23	571.726	23u4	twethu 4th	vicesimotertial narrow tritone
23/16	628.274	23o5	twetho 5th	vicesimotertial high tritone
34/23	676.681	23u17o5	twethuso 5th	vicesimotertial grave fifth
23/15	740.006	23og6	twethogu 6th	vicesimotertial ultraminor sixth
36/23	775.636	23u5	twethu 5th	vicesimotertial augmented fifth
23/14	859.448	23or6	twethoru 6th	vicesimotertial neutral sixth
38/23	869.239	23u19o6	twethuno 6th	vicesimotertial submajor sixth
40/23	958.039	23uy6	twethuyo 6th	vicesimotertial ultramajor sixth
23/13	987.747	23o3u7	twethothu 7th	vicesimotertial minor seventh
42/23	1042.507	23uz7	twethuzo 7th	vicesimotertial neutral seventh
44/23	1123.044	23u1o7	twethulo 7th	vicesimotertial major seventh
23/12	1126.319	23o8	twetho octave	vicesimotertial diminished octave

94edo is the smallest equal division of the octave to be consistent in the 23-odd limit; the smallest to be distinctly consistent in the same is 282edo.

See also

• 23-limit (prime limit)