21-odd-limit: Difference between revisions
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The smallest [[equal division of the octave]] which is consistent in the 21-odd-limit is [[94edo]] (by virtue of it being consistent through the 23-odd-limit) | The smallest [[equal division of the octave]] which is consistent in the 21-odd-limit is [[94edo]] (by virtue of it being consistent through the 23-odd-limit). | ||
The one which is distinctly consistent in the same is [[282edo]] (by virtue of it being distinctly consistent through the 23-odd-limit as well). | |||
[[Category:21-odd-limit| ]] <!-- main article --> | [[Category:21-odd-limit| ]] <!-- main article --> | ||
Latest revision as of 13:49, 8 October 2025
The 21-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 21 and k is an integer. To the 19-odd-limit, it adds 6 pairs of octave-reduced intervals involving 21.
Below is a list of all octave-reduced intervals in the 21-odd-limit.
- 1/1
- 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
- 11/10, 20/11
- 21/19, 38/21
- 10/9, 9/5
- 19/17, 34/19
- 9/8, 16/9
- 17/15, 30/17
- 8/7, 7/4
- 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
- 17/14, 28/17
- 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
- 9/7, 14/9
- 22/17, 17/11
- 13/10, 20/13
- 17/13, 26/17
- 21/16, 32/21
- 4/3, 3/2
- 19/14, 28/19
- 15/11, 22/15
- 26/19, 19/13
- 11/8, 16/11
- 18/13, 13/9
- 7/5, 10/7
- 24/17, 17/12
| Ratio | Size (¢) | Color name | Name(s) | |
|---|---|---|---|---|
| 22/21 | 80.537 | 1or1 | loru unison | undecimal chromatic semitone |
| 21/20 | 84.467 | zg2 | zogu 2nd | septimal chromatic semitone / greater septimal chroma |
| 21/19 | 173.268 | 19uz2 | nuzo 2nd | small undevicesimal whole tone |
| 21/17 | 365.825 | 17uz3 | suzo 3rd | septendecimal submajor third |
| 26/21 | 369.747 | 3or3 | thoru 3rd | tridecimal submajor third |
| 21/16 | 470.781 | z4 | zo 4th | septimal sub-fourth |
| 32/21 | 729.219 | r5 | ru 5th | septimal super-fifth |
| 21/13 | 830.253 | 3uz6 | thuzo 6th | tridecimal supraminor sixth |
| 34/21 | 834.175 | 17or6 | soru 6th | septendecimal supraminor sixth |
| 38/21 | 1026.732 | 19or7 | noru 7th | large undevicesimal minor seventh |
| 40/21 | 1115.533 | ry7 | ruyo 7th | large septimal major seventh |
| 21/11 | 1119.463 | 1uz8 | luzo octave | undecimal diminished octave |
The smallest equal division of the octave which is consistent in the 21-odd-limit is 94edo (by virtue of it being consistent through the 23-odd-limit).
The one which is distinctly consistent in the same is 282edo (by virtue of it being distinctly consistent through the 23-odd-limit as well).