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This is a list of 15-odd-limit intervals. It has proven helpful for showing JI properties of medium-sized [[EDO|edo]] systems (~15 .. 41 steps).
{{Odd-limit navigation|15}}
{{Odd-limit intro|15}}
This collection of intervals has proven to be useful for illustrating certain characteristics of medium-sized [[edo]]s (~15 to 41 steps).


<ul><li>[[16/15|16/15]], [[15/8|15/8]]</li><li>[[15/14|15/14]], [[28/15|28/15]]</li><li>[[14/13|14/13]], [[13/7|13/7]]</li><li>[[13/12|13/12]], [[24/13|24/13]]</li><li>[[12/11|12/11]], [[11/6|11/6]]</li><li>[[11/10|11/10]], [[20/11|20/11]]</li><li>[[10/9|10/9]], [[9/5|9/5]]</li><li>[[9/8|9/8]], [[16/9|16/9]]</li><li>[[8/7|8/7]], [[7/4|7/4]]</li><li>[[15/13|15/13]], [[26/15|26/15]]</li><li>[[7/6|7/6]], [[12/7|12/7]]</li><li>[[13/11|13/11]], [[22/13|22/13]]</li><li>[[6/5|6/5]], [[5/3|5/3]]</li><li>[[11/9|11/9]], [[18/11|18/11]]</li><li>[[16/13|16/13]], [[13/8|13/8]]</li><li>[[5/4|5/4]], [[8/5|8/5]]</li><li>[[14/11|14/11]], [[11/7|11/7]]</li><li>[[9/7|9/7]], [[14/9|14/9]]</li><li>[[13/10|13/10]], [[20/13|20/13]]</li><li>[[4/3|4/3]], [[3/2|3/2]]</li><li>[[15/11|15/11]], [[22/15|22/15]]</li><li>[[11/8|11/8]], [[16/11|16/11]]</li><li>[[18/13|18/13]], [[13/9|13/9]]</li><li>[[7/5|7/5]], [[10/7|10/7]]</li></ul>      [[Category:15-limit-diamond]]
* [[1/1]]
[[Category:just_interval]]
* '''[[16/15]], [[15/8]]'''
* '''[[15/14]], [[28/15]]'''
* [[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]]
* '''[[15/13]], [[26/15]]'''
* [[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]]
* '''[[15/11]], [[22/15]]'''
* [[11/8]], [[16/11]]
* [[18/13]], [[13/9]]
* [[7/5]], [[10/7]]
 
{| class="wikitable center-all right-2 left-5"
! Ratio
! Size ([[cents|¢]])
! colspan="2" | [[Color name]]
! Name(s)
|-
| [[16/15]]
| 111.731
| g2
| gu 2nd
| classic diatonic semitone
|-
| [[15/14]]
| 119.443
| ry1
| ruyo unison
| septimal diatonic semitone
|-
| [[15/13]]
| 247.741
| 3uy2
| thuyo 2nd
| tridecimal supermajor second / tridecimal second-third
|-
| [[15/11]]
| 536.951
| 1uy4
| luyo 4th
| undecimal acute fourth
|-
| [[22/15]]
| 663.049
| 1og5
| logu 5th
| undecimal grave fifth
|-
| [[26/15]]
| 952.259
| 3og7
| thogu 7th
| tridecimal subminor seventh / tridecimal sixth-seventh
|-
| [[28/15]]
| 1080.557
| zg8
| zogu octave
| small septimal major seventh
|-
| [[15/8]]
| 1088.269
| y7
| yo 7th
| just major seventh
|}
The smallest edo which is consistent in the 15-odd-limit is [[29edo]].
 
The one that is distinctly consistent in the same is [[111edo]].
 
== See also ==
* [[Arto and tendo theory]]
* [[Diamond15]] – as a scale
 
[[Category:15-odd-limit| ]] <!-- main article -->

Latest revision as of 13:45, 8 October 2025

← 13-odd-limit  15-odd-limit  17-odd-limit →

The 15-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 15 and k is an integer. To the 13-odd-limit, it adds 4 pairs of octave-reduced intervals involving 15.

Below is a list of all octave-reduced intervals in the 15-odd-limit. This collection of intervals has proven to be useful for illustrating certain characteristics of medium-sized edos (~15 to 41 steps).

Ratio Size (¢) Color name Name(s)
16/15 111.731 g2 gu 2nd classic diatonic semitone
15/14 119.443 ry1 ruyo unison septimal diatonic semitone
15/13 247.741 3uy2 thuyo 2nd tridecimal supermajor second / tridecimal second-third
15/11 536.951 1uy4 luyo 4th undecimal acute fourth
22/15 663.049 1og5 logu 5th undecimal grave fifth
26/15 952.259 3og7 thogu 7th tridecimal subminor seventh / tridecimal sixth-seventh
28/15 1080.557 zg8 zogu octave small septimal major seventh
15/8 1088.269 y7 yo 7th just major seventh

The smallest edo which is consistent in the 15-odd-limit is 29edo.

The one that is distinctly consistent in the same is 111edo.

See also

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