Cloudy comma: Difference between revisions
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- temp data (addressed in misc. 7-limit temps), thereby removing the 11-limit extension as there's no justification for it |
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 16807/16384 | | Ratio = 16807/16384 | ||
| Name = cloudy comma | | Name = cloudy comma | ||
| Color name = | | Color name = Lz<sup>5</sup>3, Laquinzo comma | ||
| Comma = yes | |||
| | |||
}} | }} | ||
'''16807/16384''', the '''cloudy comma''', or systematically the '''5-7-comma''', is a [[medium comma]] in the [[7-limit]] with a size of about 44.1 [[cent]]s. It is the amount by which five [[8/7]]'s fall short of an octave. In the [[2.5.7 subgroup]], it exceeds [[128/125]] by the [[rainy comma]]. | |||
== Temperaments == | |||
[[Tempering out]] this comma splits the octave into 5 equal parts and maps the [[7/4|harmonic seventh]] to [[5edo|4\5]]. In the full 7-limit, this leads to the rank-3 [[cloudy]] temperament. For [[edo]]s ''N'' up to 65, the comma is tempered out if and only if 5 divides ''N''. Examples are [[5edo]], [[10edo]], [[15edo]], [[50edo]], [[55edo]] and [[65edo]]. Rank-2 temperaments tempering it out include [[blackwood]], [[coblack]], [[cloudtone]], [[sengasec]], [[warlock]], [[pentacloud]], [[decic]], [[pentadecal]], and [[quinkee]]. | |||
[[Category: | [[Category:Cloudy]] | ||
[[Category: | [[Category:Commas named for their regular temperament properties]] | ||
Latest revision as of 11:38, 25 June 2026
| Interval information |
reduced harmonic
16807/16384, the cloudy comma, or systematically the 5-7-comma, is a medium comma in the 7-limit with a size of about 44.1 cents. It is the amount by which five 8/7's fall short of an octave. In the 2.5.7 subgroup, it exceeds 128/125 by the rainy comma.
Temperaments
Tempering out this comma splits the octave into 5 equal parts and maps the harmonic seventh to 4\5. In the full 7-limit, this leads to the rank-3 cloudy temperament. For edos N up to 65, the comma is tempered out if and only if 5 divides N. Examples are 5edo, 10edo, 15edo, 50edo, 55edo and 65edo. Rank-2 temperaments tempering it out include blackwood, coblack, cloudtone, sengasec, warlock, pentacloud, decic, pentadecal, and quinkee.