15-odd-limit: Difference between revisions
m removed self-link, simplified links, transformed inline-HTML list into wiki list |
m Proposing separating the lines before the table to be separated in paragraphs |
||
| (22 intermediate revisions by 9 users not shown) | |||
| Line 1: | Line 1: | ||
{{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]] | ||
* [[15/14]], [[28/15]] | * '''[[16/15]], [[15/8]]''' | ||
* '''[[15/14]], [[28/15]]''' | |||
* [[14/13]], [[13/7]] | * [[14/13]], [[13/7]] | ||
* [[13/12]], [[24/13]] | * [[13/12]], [[24/13]] | ||
| Line 10: | Line 13: | ||
* [[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]] | ||
| Line 21: | Line 24: | ||
* [[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]], [[ | * [[7/5]], [[10/7]] | ||
[[ | {| class="wikitable center-all right-2 left-5" | ||
[[Category: | ! 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 --> | |||