7-odd-limit: Difference between revisions
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Density of edos |
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{{odd-limit navigation}} | |||
{{odd-limit intro|7}} | |||
* [[1/1]] | |||
* '''[[8/7]], [[7/4]]''' | * '''[[8/7]], [[7/4]]''' | ||
* '''[[7/6]], [[12/7]]''' | * '''[[7/6]], [[12/7]]''' | ||
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* '''[[7/5]], [[10/7]]''' | * '''[[7/5]], [[10/7]]''' | ||
[[ | {| class="wikitable center-all right-2 left-5" | ||
[[Category: | ! Ratio | ||
! Size ([[cents|¢]]) | |||
! colspan="2" | [[Color name]] | |||
! Name(s) | |||
|- | |||
| [[8/7]] | |||
| 231.174 | |||
| r2 | |||
| ru 2nd | |||
| septimal supermajor second | |||
|- | |||
| [[7/6]] | |||
| 266.871 | |||
| z3 | |||
| zo 3rd | |||
| septimal minor third | |||
|- | |||
| [[7/5]] | |||
| 582.512 | |||
| zg5 | |||
| zogu 5th | |||
| narrow tritone / Huygens tritone | |||
|- | |||
| [[10/7]] | |||
| 617.488 | |||
| ry4 | |||
| ruyo 4th | |||
| high tritone / Euler's tritone | |||
|- | |||
| [[12/7]] | |||
| 933.129 | |||
| r6 | |||
| ru 6th | |||
| septimal supermajor sixth | |||
|- | |||
| [[7/4]] | |||
| 968.826 | |||
| z7 | |||
| zo 7th | |||
| harmonic seventh | |||
|} | |||
The smallest [[equal division of the octave]] which is [[consistent]] in the 7-odd-limit is [[4edo]]; that 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 == | |||
* [[7-limit]] ([[prime limit]]) | |||
* [[Diamond7]] – as a scale | |||
== Notes == | |||
<references group="note"/> | |||
[[Category:7-odd-limit| ]] <!-- main article --> | |||
Latest revision as of 15:56, 16 August 2025
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 minor third |
| 7/5 | 582.512 | zg5 | zogu 5th | narrow tritone / Huygens tritone |
| 10/7 | 617.488 | ry4 | ruyo 4th | high tritone / Euler's tritone |
| 12/7 | 933.129 | r6 | ru 6th | septimal supermajor sixth |
| 7/4 | 968.826 | z7 | zo 7th | harmonic seventh |
The smallest equal division of the octave which is consistent in the 7-odd-limit is 4edo; that 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.