Mirwomo comma

Interval information

Ratio	33075/32768
Factorization	2-15 × 33 × 52 × 72
Monzo	[-15 3 2 2⟩
Size in cents	16.14424 ¢
Name	Mirwomo comma
Color name	Lzzyy1, labizoyo unison
FJS name	[math]\displaystyle{ \text{A1}^{5,5,7,7} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	30.0135
Weil norm (log2 max(n, d))	30.0269
Wilson norm (sopfr(nd))	63
Comma size	small
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33075/32768, the mirwomo comma, is a small 7-limit comma measuring about 16.1 cents. It is the difference between the Pythagorean apotome of 2187/2048 and a stack of two septimal quartertones of 36/35.

In terms of other commas, it is the difference between 525/512 and 64/63, or between 81/80 and 6144/6125. It factors into simpler commas as (225/224)⋅(1029/1024), as well as (225/224)²⋅(2401/2400).

Temperaments

Tempering out this comma results in the 7-limit version of the mirwomo temperament. Mirwomo has a canonical 11-limit extension that tempers out 243/242 and 385/384, as 33075/32768 = (243/242)⋅(385/384)² (→ Rastmic rank-3 clan #Mirwomo).

Mirwomo is tempered out in rank-2 temperaments such as miracle, worschmidt, and mohajira. See Mirwomo temperaments for a collection of rank-2 temperaments in which the comma gets tempered out.

Etymology

As is noted above, the mirwomo comma is tempered out in miracle, worschmidt, and mohajira, and so the name is probably a contraction of these three names.