9-odd-limit: Difference between revisions
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{{odd-limit intro|9}} | |||
* [[1/1]] | * [[1/1]] | ||
* '''[[10/9]], [[9/5]]''' | * '''[[10/9]], [[9/5]]''' | ||
* '''[[9/8]], [[16/9]]''' | * '''[[9/8]], [[16/9]]''' | ||
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* [[7/5]], [[10/7]] | * [[7/5]], [[10/7]] | ||
[[ | {| class="wikitable center-all right-2 left-5" | ||
[[ | ! Ratio | ||
! Size ([[cents|¢]]) | |||
! colspan="2" | [[Color name]] | |||
! Name(s) | |||
|- | |||
| [[10/9]] | |||
| 182.404 | |||
| y2 | |||
| yo 2nd | |||
| classic whole tone <br>minor whole tone | |||
|- | |||
| [[9/8]] | |||
| 203.910 | |||
| w2 | |||
| wa 2nd | |||
| Pythagorean whole tone <br>major whole tone | |||
|- | |||
| [[9/7]] | |||
| 435.084 | |||
| r3 | |||
| ru 3rd | |||
| septimal supermajor third | |||
|- | |||
| [[14/9]] | |||
| 764.916 | |||
| z6 | |||
| zo 6th | |||
| septimal subminor sixth | |||
|- | |||
| [[16/9]] | |||
| 996.090 | |||
| w7 | |||
| wa 7th | |||
| Pythagorean minor seventh | |||
|- | |||
| [[9/5]] | |||
| 1017.596 | |||
| g7 | |||
| gu 7th | |||
| classic minor seventh | |||
|} | |||
The smallest [[equal division of the octave]] which is [[consistent]] in the 9-odd-limit is [[5edo]]; that which is distinctly consistent in the same is [[41edo]]. The {{w|natural density|density}} of edos consistent in the 9-odd-limit is 1/4<ref group="note">Provable in a similar method to the one for the 5-odd-limit.</ref>. | |||
== See also == | |||
* [[Diamond9]] – as a scale | |||
== Notes == | |||
<references group="note"/> | |||
[[Category:9-odd-limit| ]] <!-- main article --> | [[Category:9-odd-limit| ]] <!-- main article --> | ||
Latest revision as of 15:56, 16 August 2025
The 9-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 9 and k is an integer. To the 7-odd-limit, it adds 3 pairs of octave-reduced intervals involving 9.
Below is a list of all octave-reduced intervals in the 9-odd-limit.
| Ratio | Size (¢) | Color name | Name(s) | |
|---|---|---|---|---|
| 10/9 | 182.404 | y2 | yo 2nd | classic whole tone minor whole tone |
| 9/8 | 203.910 | w2 | wa 2nd | Pythagorean whole tone major whole tone |
| 9/7 | 435.084 | r3 | ru 3rd | septimal supermajor third |
| 14/9 | 764.916 | z6 | zo 6th | septimal subminor sixth |
| 16/9 | 996.090 | w7 | wa 7th | Pythagorean minor seventh |
| 9/5 | 1017.596 | g7 | gu 7th | classic minor seventh |
The smallest equal division of the octave which is consistent in the 9-odd-limit is 5edo; that which is distinctly consistent in the same is 41edo. The density of edos consistent in the 9-odd-limit is 1/4[note 1].
See also
- Diamond9 – as a scale
Notes
- ↑ Provable in a similar method to the one for the 5-odd-limit.