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{{odd-limit intro|23}} It contains all the wonders of [[94edo]]. | |||
* [[1/1]] | * [[1/1]] | ||
| Line 96: | Line 96: | ||
| 23og3 | | 23og3 | ||
| twethogu 3rd | | twethogu 3rd | ||
| vicesimotertial | | vicesimotertial inframinor third | ||
|- | |- | ||
| [[23/19]] | | [[23/19]] | ||
| Line 174: | Line 174: | ||
| 23uy6 | | 23uy6 | ||
| twethuyo 6th | | twethuyo 6th | ||
| vicesimotertial | | vicesimotertial ultramajor sixth | ||
|- | |- | ||
| [[23/13]] | | [[23/13]] | ||
| Line 200: | Line 200: | ||
| vicesimotertial diminished 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]]) | |||
[[Category:23-odd-limit| ]] <!-- main article --> | [[Category:23-odd-limit| ]] <!-- main article --> | ||
Latest revision as of 13:44, 4 June 2025
The 23-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 23 and k is an integer. To the 21-odd-limit, it adds 11 pairs of octave-reduced intervals 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.