13-odd-limit: Difference between revisions
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{{ | {{Odd-limit navigation|13}} | ||
{{Odd-limit intro|13}} | |||
* [[1/1]] | * [[1/1]] | ||
| Line 40: | Line 40: | ||
| 3o2 | | 3o2 | ||
| tho 2nd | | tho 2nd | ||
| tridecimal supraminor second / tridecimal | | tridecimal supraminor second / tridecimal subneutral second | ||
|- | |- | ||
| [[13/11]] | | [[13/11]] | ||
| Line 58: | Line 58: | ||
| 3og4 | | 3og4 | ||
| thogu 4th | | thogu 4th | ||
| tridecimal | | tridecimal subfourth / tridecimal third-fourth | ||
|- | |- | ||
| [[18/13]] | | [[18/13]] | ||
| Line 64: | Line 64: | ||
| 3u4 | | 3u4 | ||
| thu 4th | | thu 4th | ||
| tridecimal | | tridecimal superfourth | ||
|- | |- | ||
| [[13/9]] | | [[13/9]] | ||
| Line 70: | Line 70: | ||
| 3o5 | | 3o5 | ||
| tho 5th | | tho 5th | ||
| tridecimal | | tridecimal subfifth | ||
|- | |- | ||
| [[20/13]] | | [[20/13]] | ||
| Line 76: | Line 76: | ||
| 3uy5 | | 3uy5 | ||
| thuyo 5th | | thuyo 5th | ||
| tridecimal | | tridecimal superfifth / tridecimal fifth-sixth | ||
|- | |- | ||
| [[13/8]] | | [[13/8]] | ||
| Line 82: | Line 82: | ||
| 3o6 | | 3o6 | ||
| tho 6th | | tho 6th | ||
| tridecimal | | tridecimal subneutral sixth | ||
|- | |- | ||
| [[22/13]] | | [[22/13]] | ||
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| tridecimal submajor seventh | | 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]]. | ||
[[Category: | |||
== See also == | |||
* [[13-limit]] ([[prime limit]]) | |||
* [[Diamond13]] – as a scale | |||
[[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