Azazoth comma: Difference between revisions

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{{Infobox Interval|Monzo=20 16 -12 -5 -1|Name=~~Insomniac~~ 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 3 [[ragisma]]~~<nowiki/>~~s and an [[olympia]], or alternatively, between a stack of ~~4 162/125 (~~[[~~major third]] + [[128~~/125~~|diesis~~]]), 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]]~~<nowiki/>~~s.

{{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 ==

Tempering it out alone in the 11-limit results in the rank-4 temperament [[Catalog of rank-4 temperaments#Azazoth ( ~~%5B−20 −16~~ 12 5 1⟩ )|azazoth]], with its 13-limit extension as one of the least-badness 13-limit temperaments with extremely small error.

[[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 [[~~Ragismic family#Raglympic|~~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~~]].

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]]

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-{{Infobox Interval|Monzo=20 16 -12 -5 -1|Name=Insomniac 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 3 [[ragisma]]<nowiki/>s and an [[olympia]], or alternatively, between a stack of 4 162/125 ([[major third]] + [[128/125|diesis]]), 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]]<nowiki/>s.
+{{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 ==
-Tempering it out alone in the 11-limit results in the rank-4 temperament [[Catalog of rank-4 temperaments#Azazoth ( %5B−20 −16 12 5 1⟩ )|azazoth]], with its 13-limit extension as one of the least-badness 13-limit temperaments with extremely small error.
+[[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 [[Ragismic family#Raglympic|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]].
+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]]

Azazoth comma: Difference between revisions

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