Rainy comma

Interval information

Ratio	2100875/2097152
Factorization	2-21 × 53 × 75
Monzo	[-21 0 3 5⟩
Size in cents	3.070674¢
Name	rainy comma
Color name	Quinzotriyo comma
FJS name	[math]\displaystyle{ \text{M2}^{5,5,5,7,7,7,7,7} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	42.0026
Weil norm (log2 max(n, d))	42.0051
Wilson norm (sopfr(nd))	92
Comma size	unnoticeable
Open this interval in xen-calc

2100875/2097152, the rainy comma, is an unnoticeable 7-limit (specifically 2.5.7-subgroup) comma of about 3.07 cents. It is the amount by which five 8/7's fall short of three 5/4's, i.e. the amount by which 16807/16384 exceeds 128/125. It factors into simpler commas as (2401/2400)⋅(65625/65536).

Temperaments

Tempering out this comma in the 2.5.7 subgroup leads to the rainy temperament, or in the 7-limit an unnamed expansion thereof. It is tempered out by notable tunings such as 31edo, 94edo, 109edo, 140edo, 171edo and even 311edo.

Etymology

This comma was named by +merlan #flirora in 2021.