7-odd-limit: Difference between revisions
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{{ | {{Odd-limit navigation|7}} | ||
{{ | [[File:7-odd-limit.png|480px|thumb|right|7-odd-limit intervals within an octave]] | ||
{{Odd-limit intro|7}} | |||
* [[1/1]] | * [[1/1]] | ||
| Line 26: | Line 27: | ||
| z3 | | z3 | ||
| zo 3rd | | zo 3rd | ||
| septimal | | septimal subminor third | ||
|- | |- | ||
| [[7/5]] | | [[7/5]] | ||
| Line 32: | Line 33: | ||
| zg5 | | zg5 | ||
| zogu 5th | | zogu 5th | ||
| narrow tritone / Huygens tritone | | narrow tritone / Huygens tritone / septimal diminished fifth | ||
|- | |- | ||
| [[10/7]] | | [[10/7]] | ||
| Line 38: | Line 39: | ||
| ry4 | | ry4 | ||
| ruyo 4th | | ruyo 4th | ||
| high tritone / Euler's tritone | | high tritone / Euler's tritone / septimal augmented fourth | ||
|- | |- | ||
| [[12/7]] | | [[12/7]] | ||
| Line 50: | Line 51: | ||
| z7 | | z7 | ||
| zo 7th | | zo 7th | ||
| harmonic seventh | | harmonic seventh / septimal subminor seventh | ||
|} | |} | ||
The smallest [[equal division of the octave]] which is [[consistent]] in the 7-odd-limit is [[4edo]] | The smallest [[equal division of the octave]] which is [[consistent]] in the 7-odd-limit is [[4edo]]. | ||
The one which is distinctly consistent in the same is [[27edo]]. | |||
The {{w|natural density|density}} of edos consistent in the 7-odd-limit is 1/2<ref group="note">Provable in a similar method to the one for the [[5-odd-limit]].</ref>. | |||
== See also == | == See also == | ||
* [[7-limit]] ([[prime limit]]) | * [[7-limit]] ([[prime limit]]) | ||
* [[Diamond7]] – as a scale | * [[Diamond7]] – as a scale | ||
== Notes == | |||
<references group="note"/> | |||
[[Category:7-odd-limit| ]] <!-- main article --> | [[Category:7-odd-limit| ]] <!-- main article --> | ||
Latest revision as of 17:05, 5 August 2026
The 7-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 7 and k is an integer. To the 5-odd-limit, it adds 3 pairs of octave-reduced intervals involving 7.
Below is a list of all octave-reduced intervals in the 7-odd-limit.
| Ratio | Size (¢) | Color name | Name(s) | |
|---|---|---|---|---|
| 8/7 | 231.174 | r2 | ru 2nd | septimal supermajor second |
| 7/6 | 266.871 | z3 | zo 3rd | septimal subminor third |
| 7/5 | 582.512 | zg5 | zogu 5th | narrow tritone / Huygens tritone / septimal diminished fifth |
| 10/7 | 617.488 | ry4 | ruyo 4th | high tritone / Euler's tritone / septimal augmented fourth |
| 12/7 | 933.129 | r6 | ru 6th | septimal supermajor sixth |
| 7/4 | 968.826 | z7 | zo 7th | harmonic seventh / septimal subminor seventh |
The smallest equal division of the octave which is consistent in the 7-odd-limit is 4edo.
The one which is distinctly consistent in the same is 27edo.
The density of edos consistent in the 7-odd-limit is 1/2[note 1].
See also
- 7-limit (prime limit)
- Diamond7 – as a scale
Notes
- ↑ Provable in a similar method to the one for the 5-odd-limit.