11-odd-limit: Difference between revisions
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{{odd-limit navigation}} | |||
{{odd-limit intro|11}} | |||
* '''[[12/11]] | * [[1/1]] | ||
* '''[[11/10]] | * '''[[12/11]], [[11/6]]''' | ||
* '''[[11/10]], [[20/11]]''' | |||
* [[10/9]], [[9/5]] | * [[10/9]], [[9/5]] | ||
* [[9/8]], [[16/9]] | * [[9/8]], [[16/9]] | ||
| Line 8: | Line 10: | ||
* [[7/6]], [[12/7]] | * [[7/6]], [[12/7]] | ||
* [[6/5]], [[5/3]] | * [[6/5]], [[5/3]] | ||
* '''[[11/9]] | * '''[[11/9]], [[18/11]]''' | ||
* [[5/4]], [[8/5]] | * [[5/4]], [[8/5]] | ||
* '''[[14/11]] | * '''[[14/11]], [[11/7]]''' | ||
* [[9/7]], [[14/9]] | * [[9/7]], [[14/9]] | ||
* [[4/3]], [[3/2]] | * [[4/3]], [[3/2]] | ||
* '''[[11/8]] | * '''[[11/8]], [[16/11]]''' | ||
* [[7/5]], [[10/7]] | * [[7/5]], [[10/7]] | ||
{| class="wikitable" | {| class="wikitable center-all right-2 left-5" | ||
! Ratio | |||
! Size ([[cents|¢]]) | |||
! colspan="2" | [[Color name]] | |||
! Name | |||
|- | |- | ||
| [[12/11]] | |||
| 150.637 | |||
| 1u2 | |||
| lu 2nd | |||
| lesser undecimal neutral second | |||
|- | |- | ||
| [[11/10]] | |||
| | | 165.004 | ||
| | | 1og2 | ||
| | | logu 2nd | ||
| | | greater undecimal neutral second | ||
|- | |- | ||
| [[11/9]] | |||
| | | 347.408 | ||
| | | 1o3 | ||
| | | ilo 3rd | ||
| | | undecimal neutral third | ||
|- | |- | ||
| [[14/11]] | |||
| | | 417.508 | ||
| | | 1uz4 | ||
| | | luzo 4th | ||
| undecimal major third | |||
|- | |- | ||
| [[11/8]] | |||
| | | 551.318 | ||
| | | 1o4 | ||
| | | ilo 4th | ||
| undecimal superfourth | |||
|- | |- | ||
| [[16/11]] | |||
| | | 648.682 | ||
| | | 1u5 | ||
| | | lu 5th | ||
| undecimal subfifth | |||
|- | |- | ||
| [[11/7]] | |||
| | | 782.492 | ||
| | | 1or5 | ||
| | | loru 5th | ||
| undecimal minor sixth | |||
|- | |- | ||
| [[18/11]] | |||
| | | 852.592 | ||
| | | 1u6 | ||
| | | lu 6th | ||
| undecimal neutral sixth | |||
|- | |- | ||
| [[20/11]] | |||
| | | 1034.996 | ||
| | | 1uy7 | ||
| | | luyo 7th | ||
| | | lesser undecimal neutral seventh | ||
|- | |- | ||
| [[11/6]] | |||
| 1049.363 | |||
| 1o7 | |||
| ilo 7th | |||
| greater undecimal neutral seventh | |||
|} | |} | ||
The smallest [[equal division of the octave]] which is [[consistent]] in the 11-odd-limit is [[22edo]]; that which is distinctly consistent in the same is [[58edo]] (also the smallest EDO to be consistent in the 17-odd-limit). | |||
== See also == | |||
* [[11-limit]] ([[prime limit]]) | |||
* [[diamond11]] – as a scale | |||
[[Category: | [[Category:11-odd-limit| ]] <!-- main article --> | ||
Latest revision as of 14:18, 17 November 2023
The 11-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 11 and k is an integer. To the 9-odd-limit, it adds 5 pairs of octave-reduced intervals involving 11.
Below is a list of all octave-reduced intervals in the 11-odd-limit.
- 1/1
- 12/11, 11/6
- 11/10, 20/11
- 10/9, 9/5
- 9/8, 16/9
- 8/7, 7/4
- 7/6, 12/7
- 6/5, 5/3
- 11/9, 18/11
- 5/4, 8/5
- 14/11, 11/7
- 9/7, 14/9
- 4/3, 3/2
- 11/8, 16/11
- 7/5, 10/7
| Ratio | Size (¢) | Color name | Name | |
|---|---|---|---|---|
| 12/11 | 150.637 | 1u2 | lu 2nd | lesser undecimal neutral second |
| 11/10 | 165.004 | 1og2 | logu 2nd | greater undecimal neutral second |
| 11/9 | 347.408 | 1o3 | ilo 3rd | undecimal neutral third |
| 14/11 | 417.508 | 1uz4 | luzo 4th | undecimal major third |
| 11/8 | 551.318 | 1o4 | ilo 4th | undecimal superfourth |
| 16/11 | 648.682 | 1u5 | lu 5th | undecimal subfifth |
| 11/7 | 782.492 | 1or5 | loru 5th | undecimal minor sixth |
| 18/11 | 852.592 | 1u6 | lu 6th | undecimal neutral sixth |
| 20/11 | 1034.996 | 1uy7 | luyo 7th | lesser undecimal neutral seventh |
| 11/6 | 1049.363 | 1o7 | ilo 7th | greater undecimal neutral seventh |
The smallest equal division of the octave which is consistent in the 11-odd-limit is 22edo; that which is distinctly consistent in the same is 58edo (also the smallest EDO to be consistent in the 17-odd-limit).
See also
- 11-limit (prime limit)
- diamond11 – as a scale