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Created page with "{{odd-limit navigation}} This is a list of '''27-odd-limit''' intervals. To 25-odd-limit, it adds 9 interval pairs involving 27. * 1/1 * '''28/27, 27/14''..." |
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The smallest [[equal division of the octave]] that comes closest to being [[consistent]] in the 27-odd-limit is [[217edo]] (misses [[23/14]], [[23/21]], [[28/23]], [[42/23]]). | |||
[[ | The one which is truly consistent is [[282edo]] (by virtue of it being consistent through the 29-odd-limit) | ||
[[Category: | |||
The one which is distinctly consistent in the same is [[388edo]]. | |||
[[Category:27-odd-limit| ]] <!-- main article --> | |||
Latest revision as of 13:57, 8 October 2025
The 27-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 27 and k is an integer. To the 25-odd-limit, it adds 9 pairs of octave-reduced intervals involving 27.
Below is a list of all octave-reduced intervals in the 27-odd-limit.
- 1/1
- 28/27, 27/14
- 27/26, 52/27
- 26/25, 25/13
- 25/24, 48/25
- 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
- 27/25, 50/27
- 13/12, 24/13
- 25/23, 46/25
- 12/11, 11/6
- 23/21, 42/23
- 11/10, 20/11
- 21/19, 38/21
- 10/9, 9/5
- 19/17, 34/19
- 28/25, 25/14
- 9/8, 16/9
- 26/23, 23/13
- 17/15, 30/17
- 25/22, 44/25
- 8/7, 7/4
- 23/20, 40/23
- 15/13, 26/15
- 22/19, 19/11
- 7/6, 12/7
- 27/23, 46/27
- 20/17, 17/10
- 13/11, 22/13
- 32/27, 27/16
- 19/16, 32/19
- 25/21, 42/25
- 6/5, 5/3
- 23/19, 38/23
- 17/14, 28/17
- 28/23, 23/14
- 11/9, 18/11
- 27/22, 44/27
- 16/13, 13/8
- 21/17, 34/21
- 26/21, 21/13
- 5/4, 8/5
- 34/27, 27/17
- 24/19, 19/12
- 19/15, 30/19
- 14/11, 11/7
- 23/18, 36/23
- 32/25, 25/16
- 9/7, 14/9
- 22/17, 17/11
- 13/10, 20/13
- 30/23, 23/15
- 17/13, 26/17
- 21/16, 32/21
- 25/19, 38/25
- 4/3, 3/2
- 27/20, 40/27
- 23/17, 34/23
- 19/14, 28/19
- 34/25, 25/17
- 15/11, 22/15
- 26/19, 19/13
- 11/8, 16/11
- 18/13, 13/9
- 25/18, 36/25
- 32/23, 23/16
- 7/5, 10/7
- 38/27, 27/19
- 24/17, 17/12
| Ratio | Size (¢) | Color name | Name | |
|---|---|---|---|---|
| 28/27 | 62.961 | z2 | zo 2nd | septimal third-tone |
| 27/26 | 65.337 | 3u1 | thu unison | lesser tridecimal chroma small tridecimal third-tone |
| 27/25 | 133.238 | gg2 | gugu 2nd | large limma acute semitone |
| 27/23 | 277.591 | 23u2 | twethu 2nd | vicesimotertial augmented second |
| 32/27 | 294.135 | w3 | wa 3rd | Pythagorean minor third |
| 27/22 | 354.547 | 1u3 | lu 3rd | rastmic neutral third |
| 34/27 | 399.090 | 17o4 | iso 4th | septendecimal major third quasi-tempered major third |
| 27/20 | 519.551 | g4 | gu 4th | acute fourth wolf fourth |
| 38/27 | 591.648 | 19o5 | ino 5th | undevicesimal narrow tritone |
| 27/19 | 608.352 | 19u4 | inu 4th | undevicesimal high tritone |
| 40/27 | 680.449 | y5 | yo 5th | grave fifth wolf fifth |
| 27/17 | 800.910 | 17u5 | su 5th | septendecimal minor sixth quasi-tempered minor sixth |
| 44/27 | 845.453 | 1o6 | ilo 6th | rastmic neutral sixth |
| 27/16 | 905.865 | w6 | wa 6th | Pythagorean major sixth |
| 46/27 | 922.409 | 23o7 | twetho 7th | vicesimotertial diminished seventh |
| 50/27 | 1066.762 | yy7 | yoyo 7th | grave major seventh |
| 52/27 | 1134.663 | 3o8 | tho octave | greater tridecimal diminished octave |
| 27/14 | 1137.039 | r7 | ru 7th | septimal supermajor seventh |
The smallest equal division of the octave that comes closest to being consistent in the 27-odd-limit is 217edo (misses 23/14, 23/21, 28/23, 42/23).
The one which is truly consistent is 282edo (by virtue of it being consistent through the 29-odd-limit)
The one which is distinctly consistent in the same is 388edo.