Azazoth comma

Interval information

Factorization	220 × 316 × 5-12 × 7-5 × 11-1
Monzo	[20 16 -12 -5 -1⟩
Size in cents	0.06797276 ¢
Name	Azazoth comma
Color name	luquinru-aquadtriguma, 1ur^5g^12M
FJS name	[math]\displaystyle{ \text{ddd1}_{5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	90.7187
Weil norm (log2 max(n, d))	90.7188
Wilson norm (sopfr(nd))	194
Comma size	unnoticeable
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The azazoth comma is a 11-limit interval. It is an extremely small comma, one of the smallest 11-limit commas. It is the difference between a stack of three ragismas and an olympia, or alternatively, between a stack of four 162/125 (triptolemaic diminished fourths), and a stack of 11/4 plus a cloudy comma. It factors into the 13-limit as the product of a chalmersia and two pontigailimmas.

Temperaments

Tempering out this comma alone in the 11-limit results in the rank-4 temperament azazoth, with its 13-limit extension as one of the least-badness 13-limit temperaments with extremely small error.

It is trivially tempered out in raglympic as the ragisma and olympia are also tempered out; and all of its temperaments also support it, like abigail, alphatrillium, brahmagupta, ponta, hitchcock or mineral.

Etymology

This comma was named by Eufalesio in 2026.