15-odd-limit: Difference between revisions

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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 -->