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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]] systems (∼15 to 41 steps). To [[13-odd-limit]], it adds four additional interval pairs involving 15.
{{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).


* '''[[16/15]]''', '''[[15/8]]'''
* [[1/1]]
* '''[[16/15]], [[15/8]]'''
* '''[[15/14]], [[28/15]]'''
* '''[[15/14]], [[28/15]]'''
* [[14/13]], [[13/7]]
* [[14/13]], [[13/7]]
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* [[9/8]], [[16/9]]
* [[9/8]], [[16/9]]
* [[8/7]], [[7/4]]
* [[8/7]], [[7/4]]
* '''[[15/13]]''', '''[[26/15]]'''
* '''[[15/13]], [[26/15]]'''
* [[7/6]], [[12/7]]
* [[7/6]], [[12/7]]
* [[13/11]], [[22/13]]
* [[13/11]], [[22/13]]
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* [[13/10]], [[20/13]]
* [[13/10]], [[20/13]]
* [[4/3]], [[3/2]]
* [[4/3]], [[3/2]]
* '''[[15/11]]''', '''[[22/15]]'''
* '''[[15/11]], [[22/15]]'''
* [[11/8]], [[16/11]]
* [[11/8]], [[16/11]]
* [[18/13]], [[13/9]]
* [[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)
|-
|-
! | Ratio
| [[16/15]]
! | Cents Value
| 111.731
! colspan="2" |[[Kite's color notation|Color Name]]
| g2
! | Name
| gu 2nd
| classic diatonic semitone
|-
|-
| | [[16/15]]
| [[15/14]]
| | 111.731
| 119.443
| | g2
| ry1
| | gu 2nd
| ruyo unison
| | classic diatonic semitone
| septimal diatonic semitone
|-
|-
| | [[15/14]]
| [[15/13]]
| | 119.443
| 247.741
| | ry1
| 3uy2
| | ruyo unison
| thuyo 2nd
| | septimal diatonic semitone
| tridecimal supermajor second / tridecimal second-third
|-
|-
| | [[15/13]]
| [[15/11]]
| | 247.741
| 536.951
| | 3uy2
| 1uy4
| | thuyo 2nd
| luyo 4th
| | tridecimal supermajor second /<br>tridecimal second-third
| undecimal acute fourth
|-
|-
| | [[15/11]]
| [[22/15]]
| | 536.951
| 663.049
| | 1uy4
| 1og5
| | luyo 4th
| logu 5th
| | undecimal acute fourth
| undecimal grave fifth
|-
|-
| | [[22/15]]
| [[26/15]]
| | 663.049
| 952.259
| | 1og5
| 3og7
| | logu 5th
| thogu 7th
| | undecimal grave fifth
| tridecimal subminor seventh / tridecimal sixth-seventh
|-
|-
| | [[26/15]]
| [[28/15]]
| | 952.259
| 1080.557
| | 3og7
| zg8
| | thogu 7th
| zogu octave
| | tridecimal subminor seventh /<br>tridecimal sixth-seventh
| small septimal major seventh
|-
|-
| | [[28/15]]
| [[15/8]]
| | 1080.557
| 1088.269
| | zg8
| y7
| | zogu octave
| yo 7th
| | small septimal major seventh
| just 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-limit-diamond]]
[[Category:15-odd-limit| ]] <!-- main article -->
[[Category:Just interval]]
[[Category:Odd limit]]
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