13-odd-limit: Difference between revisions
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{{ | {{Odd-limit navigation|13}} | ||
{{Odd-limit intro|13}} | |||
* '''[[14/13]] | * [[1/1]] | ||
* '''[[13/12]] | * '''[[14/13]], [[13/7]]''' | ||
* '''[[13/12]], [[24/13]]''' | |||
* [[12/11]], [[11/6]] | * [[12/11]], [[11/6]] | ||
* [[11/10]], [[20/11]] | * [[11/10]], [[20/11]] | ||
| Line 10: | Line 11: | ||
* [[8/7]], [[7/4]] | * [[8/7]], [[7/4]] | ||
* [[7/6]], [[12/7]] | * [[7/6]], [[12/7]] | ||
* '''[[13/11]] | * '''[[13/11]], [[22/13]]''' | ||
* [[6/5]], [[5/3]] | * [[6/5]], [[5/3]] | ||
* [[11/9]], [[18/11]] | * [[11/9]], [[18/11]] | ||
* '''[[16/13]] | * '''[[16/13]], [[13/8]]''' | ||
* [[5/4]], [[8/5]] | * [[5/4]], [[8/5]] | ||
* [[14/11]], [[11/7]] | * [[14/11]], [[11/7]] | ||
* [[9/7]], [[14/9]] | * [[9/7]], [[14/9]] | ||
* '''[[13/10]] | * '''[[13/10]], [[20/13]]''' | ||
* [[4/3]], [[3/2]] | * [[4/3]], [[3/2]] | ||
* [[11/8]], [[16/11]] | * [[11/8]], [[16/11]] | ||
* '''[[18/13]] | * '''[[18/13]], [[13/9]]''' | ||
* [[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(s) | |||
|- | |- | ||
| [[14/13]] | |||
| 128.298 | |||
| 3uz2 | |||
| thuzo 2nd | |||
| tridecimal large semitone | |||
|- | |- | ||
| [[13/12]] | |||
| | | 138.573 | ||
| | | 3o2 | ||
| | | tho 2nd | ||
| | | tridecimal supraminor second / tridecimal subneutral second | ||
|- | |- | ||
| [[13/11]] | |||
| | | 289.210 | ||
| | | 3o1u3 | ||
| | | tholu 3rd | ||
| | | tridecimal minor third | ||
|- | |- | ||
| [[16/13]] | |||
| | | 359.472 | ||
| | | 3u3 | ||
| | | thu 3rd | ||
| tridecimal supra-neutral third | |||
|- | |- | ||
| [[13/10]] | |||
| | | 454.214 | ||
| | | 3og4 | ||
| | | thogu 4th | ||
| | | tridecimal subfourth / tridecimal third-fourth | ||
|- | |- | ||
| [[18/13]] | |||
| | | 563.382 | ||
| | | 3u4 | ||
| | | thu 4th | ||
| | | tridecimal superfourth | ||
|- | |- | ||
| [[13/9]] | |||
| | | 636.618 | ||
| | | 3o5 | ||
| | | tho 5th | ||
| tridecimal subfifth | |||
|- | |- | ||
| [[20/13]] | |||
| | | 745.786 | ||
| | | 3uy5 | ||
| | | thuyo 5th | ||
| | | tridecimal superfifth / tridecimal fifth-sixth | ||
|- | |- | ||
| [[13/8]] | |||
| | | 840.528 | ||
| | | 3o6 | ||
| | | tho 6th | ||
| | | tridecimal subneutral sixth | ||
|- | |- | ||
| [[22/13]] | |||
| | | 910.790 | ||
| | | 3u1o6 | ||
| | | thulo 6th | ||
| tridecimal major sixth | |||
|- | |- | ||
| [[24/13]] | |||
| | | 1061.427 | ||
| | | 3u7 | ||
| | | thu 7th | ||
| tridecimal supra-neutral seventh | |||
|- | |- | ||
| [[13/7]] | |||
| 1071.702 | |||
| 3or7 | |||
| thoru 7th | |||
| tridecimal submajor seventh | |||
|} | |} | ||
The smallest [[equal division of the octave]] which is [[consistent]] in the 13-odd-limit is [[26edo]]. | |||
<span data-darkreader-inline-color="">The smallest one which is distinctly consistent in the same is</span> [[87edo]]. | |||
== See also == | |||
* [[13-limit]] ([[prime limit]]) | |||
* [[Diamond13]] – as a scale | |||
[[Category: | [[Category:13-odd-limit| ]] <!-- main article --> | ||
Latest revision as of 13:42, 8 October 2025
The 13-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 13 and k is an integer. To the 11-odd-limit, it adds 6 pairs of octave-reduced intervals involving 13.
Below is a list of all octave-reduced intervals in the 13-odd-limit.
- 1/1
- 14/13, 13/7
- 13/12, 24/13
- 12/11, 11/6
- 11/10, 20/11
- 10/9, 9/5
- 9/8, 16/9
- 8/7, 7/4
- 7/6, 12/7
- 13/11, 22/13
- 6/5, 5/3
- 11/9, 18/11
- 16/13, 13/8
- 5/4, 8/5
- 14/11, 11/7
- 9/7, 14/9
- 13/10, 20/13
- 4/3, 3/2
- 11/8, 16/11
- 18/13, 13/9
- 7/5, 10/7
| Ratio | Size (¢) | Color name | Name(s) | |
|---|---|---|---|---|
| 14/13 | 128.298 | 3uz2 | thuzo 2nd | tridecimal large semitone |
| 13/12 | 138.573 | 3o2 | tho 2nd | tridecimal supraminor second / tridecimal subneutral second |
| 13/11 | 289.210 | 3o1u3 | tholu 3rd | tridecimal minor third |
| 16/13 | 359.472 | 3u3 | thu 3rd | tridecimal supra-neutral third |
| 13/10 | 454.214 | 3og4 | thogu 4th | tridecimal subfourth / tridecimal third-fourth |
| 18/13 | 563.382 | 3u4 | thu 4th | tridecimal superfourth |
| 13/9 | 636.618 | 3o5 | tho 5th | tridecimal subfifth |
| 20/13 | 745.786 | 3uy5 | thuyo 5th | tridecimal superfifth / tridecimal fifth-sixth |
| 13/8 | 840.528 | 3o6 | tho 6th | tridecimal subneutral sixth |
| 22/13 | 910.790 | 3u1o6 | thulo 6th | tridecimal major sixth |
| 24/13 | 1061.427 | 3u7 | thu 7th | tridecimal supra-neutral seventh |
| 13/7 | 1071.702 | 3or7 | thoru 7th | tridecimal submajor seventh |
The smallest equal division of the octave which is consistent in the 13-odd-limit is 26edo.
The smallest one which is distinctly consistent in the same is 87edo.
See also
- 13-limit (prime limit)
- Diamond13 – as a scale