Archangelic comma: Difference between revisions

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The '''archangelic comma''' ([[monzo]]: {{monzo| 301994 -190537 }}) is the amount by which 190537 [[perfect fifth]]s fall short of 111457 [[octave]]s, in other words 2111457/(3/2)190537. This difference is inaudible at roughly 0.0001 [[cents]].

This comma was named by [[User:Aura|Aura]] in direct opposition to the [[satanic comma]] due to ~~it being the first [[3-limit]] comma to have a~~ 3-2 ~~[[Telicity #k-Strong Telicity|~~telicity k-strength~~]] greater than 1 in the log23 convergence series after~~ the satanic comma, ~~and, due to actually surpassing~~ the ~~satanic~~ comma in ~~3-2 telicity k-strength~~.

This comma was named by [[User:Aura|Aura]] in direct opposition to the [[satanic comma]] due to 190537edo actually surpassing 665edo in 3-2 telicity k-strength. However, it is opposite the satanic comma in other ways, such as the fact that tempering this comma results in a stretched fifth rather than a compressed fifth.

== Temperament ==

Tempering out this comma leads to the [[Archangelic family]] of temperaments. It is tempered out in [[190537edo]] and its multiples ([[571611edo]], [[762148edo]], [[1714833edo]], [[1905370edo]], and [[4191814edo]] just to name a few), with 190537edo itself being an 28-strong 3-2 telic system due to tempering this comma out.

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 The '''archangelic comma''' ([[monzo]]: {{monzo| 301994 -190537 }}) is the amount by which 190537 [[perfect fifth]]s fall short of 111457 [[octave]]s, in other words 2<sup>111457</sup>/(3/2)<sup>190537</sup>.  This difference is inaudible at roughly 0.0001 [[cents]].
-This comma was named by [[User:Aura|Aura]] in direct opposition to the [[satanic comma]] due to it being the first [[3-limit]] comma to have a 3-2 [[Telicity #k-Strong Telicity|telicity k-strength]] greater than 1 in the log<sub>2</sub>3 convergence series after the satanic comma, and, due to actually surpassing the satanic comma in 3-2 telicity k-strength.
+This comma was named by [[User:Aura|Aura]] in direct opposition to the [[satanic comma]] due to 190537edo actually surpassing 665edo in 3-2 telicity k-strength.  However, it is opposite the satanic comma in other ways, such as the fact that tempering this comma results in a stretched fifth rather than a compressed fifth.
 == Temperament ==
 Tempering out this comma leads to the [[Archangelic family]] of temperaments.  It is tempered out in [[190537edo]] and its multiples ([[571611edo]], [[762148edo]], [[1714833edo]], [[1905370edo]], and [[4191814edo]] just to name a few), with 190537edo itself being an 28-strong 3-2 telic system due to tempering this comma out.