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, based on H.P Lovecraft's deity Azazoth in his Cthulhu Mythos and Dream Cycle stories; an asleep primordial creator of all existence whose part of its dream is the universe, whose wake would erase reality. This association is an extension of the insane, untenable precision entailed by the temperament, whose relation to insanismic relates insanity unto lovecraftian cosmic horror made math.