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{{ | {{Odd-limit navigation|9}} | ||
[[File:9-odd-limit.png|480px|thumb|right|9-odd-limit intervals within an octave]] | |||
{{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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| classic minor seventh | | classic minor seventh | ||
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The smallest [[equal division of the octave]] which is [[consistent]] in the 9-odd-limit is [[5edo]]. | |||
The one 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 19:33, 18 June 2026
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.
The one 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.