Azazoth comma: Difference between revisions
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{{Infobox Interval|Monzo=20 16 -12 -5 -1|Name= | {{Infobox Interval | ||
| Monzo = 20 16 -12 -5 -1 | |||
| Name = Azazoth comma | |||
| Color name = luquinru-aquadtriguma, 1ur^5g^12M | |||
| Comma = yes}} | |||
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 [[ragisma]]s 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 [[pontigailimma]]s. | |||
== Temperaments == | == Temperaments == | ||
Tempering | [[Tempering out]] this comma alone in the 11-limit results in the rank-4 temperament [[Catalog of rank-4 temperaments #Azazoth ({{lbrack}}-20 -16 12 5 1⟩)|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 [[ | 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. | |||
[[Category:Commas with unknown etymology]] | |||
Latest revision as of 11:21, 24 October 2026
| Interval information |
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.