Mandos comma

Interval information

Ratio	31104/30625
Factorization	27 × 35 × 5-4 × 7-2
Monzo	[7 5 -4 -2⟩
Size in cents	26.86834 ¢
Name	Mandos comma
FJS name	[math]\displaystyle{ \text{d1}_{5,5,5,5,7,7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	29.8272
Weil norm (log2 max(n, d))	29.8496
Wilson norm (sopfr(nd))	63
Comma size	small
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The mandos comma (ratio: 31104/30625, monzo: [7 5 -4 -2⟩ is a small comma in the 7-limit, measuring about 26.9 cents. It is the difference between a stack of two 36/35 septimal quartertones and a 25/24 classical chromatic semitone.

It is thus also the difference between 36/35 and 875/864, and in terms of other commas, between 64/63 and 4375/4374, and between 128/125 and 245/243. It factors into simpler commas as (126/125)⋅(1728/1715), (2048/2025)⋅(19683/19600), (2430/2401)⋅(3136/3125), or (81/80)⋅(6144/6125).

Temperaments

Tempering out this comma leads to the 7-limit version of the mandos temperament. Mandos has a canonical 11-limit extension that tempers out 176/175 and 243/242, from 31104/30625 = (176/175)²⋅(243/242).

The mandos comma is tempered out in rank-2 temperaments such as myna, modus, and mohajira.