Cloudy comma

Interval information

Ratio	16807/16384
Factorization	2-14 × 75
Monzo	[-14 0 0 5⟩
Size in cents	44.12953¢
Name	cloudy comma
Color name	Lz53, Laquinzo comma
FJS name	[math]\displaystyle{ \text{d3}^{7,7,7,7,7} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	28.0368
Weil norm (log2 max(n, d))	28.0735
Wilson norm (sopfr(nd))	63
Comma size	medium
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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.