25-odd-limit: Difference between revisions
Jump to navigation
Jump to search
m Fix categorization |
m Proposing separating the lines before the table to be separated in paragraphs, and adding the smallest one that comes closest to consistency |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
{{ | {{Odd-limit navigation|25}} | ||
{{ | {{Odd-limit intro|25}} | ||
* [[1/1]] | * [[1/1]] | ||
| Line 199: | Line 199: | ||
|} | |} | ||
The smallest [[equal division of the octave]] | The smallest [[equal division of the octave]] that comes closest to being [[consistent]] in the 25-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]] (by virtue of it being distinctly consistent through the 27-odd-limit). | |||
[[Category:25-odd-limit| ]] <!-- main article --> | [[Category:25-odd-limit| ]] <!-- main article --> | ||
Latest revision as of 13:55, 8 October 2025
The 25-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 25 and k is an integer. To the 23-odd-limit, it adds 10 pairs of octave-reduced intervals involving 25.
Below is a list of all octave-reduced intervals in the 25-odd-limit.
- 1/1
- 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
- 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
- 20/17, 17/10
- 13/11, 22/13
- 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
- 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
- 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
- 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
- 24/17, 17/12
| Ratio | Size (¢) | Color name | Name | |
|---|---|---|---|---|
| 26/25 | 67.900 | 3ogg | thogugu 2nd | greater tridecimal chroma large tridecimal third-tone |
| 25/24 | 70.672 | yy1 | yoyo unison | classic chromatic semitone |
| 25/23 | 144.353 | 23uyy2 | twethuyoyo 2nd | small vicesimotertial neutral second |
| 28/25 | 196.198 | zgg3 | zogugu 3rd | septimal middle major second sepimal middle whole tone |
| 25/22 | 221.309 | 1uyy2 | luyoyo 2nd | undecimal acute major second undecimal acute whole tone |
| 25/21 | 301.847 | ryy2 | ruyoyo 2nd | septimal quasi-tempered minor third |
| 32/25 | 427.373 | gg4 | gugu 4th | classic diminished fourth |
| 25/19 | 475.114 | 19uyy3 | nuyoyo 3rd | undevicesimal augmented third undevicesimal grave fourth |
| 34/25 | 532.328 | 17ogg5 | sogugu 5th | septendecimal acute fourth |
| 25/18 | 568.717 | yy4 | yoyo 4th | classic narrow tritone classic augmented fourth |
| 36/25 | 631.283 | gg5 | gugu 5th | classic high tritone classic diminished fifth |
| 25/17 | 667.672 | 17uyy4 | suyoyo 4th | septendecimal grave fifth |
| 38/25 | 724.886 | 19ogg6 | nogugu 6th | undevicesimal diminished sixth undevicesimal acute fifth |
| 25/16 | 772.627 | yy5 | yoyo 5th | classic augmented fifth |
| 42/25 | 898.153 | zgg7 | zogugu 7th | septimal quasi-tempered major sixth |
| 44/25 | 978.691 | 1ogg7 | logugu 7th | undecimal grave minor seventh |
| 25/14 | 1003.802 | ryy6 | ruyoyo 6th | septimal middle minor seventh |
| 46/25 | 1055.647 | 23ogg7 | twethogugu 7th | large vicesimotertial neutral seventh |
| 48/25 | 1129.328 | gg8 | gugu octave | classic diminished octave |
| 25/13 | 1132.100 | 3uyy7 | thuyoyo 7th | lesser tridecimal diminished octave |
The smallest equal division of the octave that comes closest to being consistent in the 25-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 (by virtue of it being distinctly consistent through the 27-odd-limit).