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 2<sup>111457</sup>/(3/2)<sup>190537</sup>. This difference is inaudible at roughly 0.0001 [[cents]].

This comma was named in direct opposition to the [[satanic comma]] due to ~~being the first~~ [[~~3-limit~~]] ~~comma to have a 3-2~~ [[~~telicity~~]] ~~k-strength greater than 1 after it in the 3/2 convergence series, and, due to actually surpassing it~~ in 3-2 [[telicity]] k-strength.

This comma was named by [[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.~~

Tempering out this comma leads to the [[archangelic family]] of temperaments. It is tempered out in 190537edo, which is a 28-strong 3-2 telic system due to tempering this comma out.

[[Category:Commas named for their regular temperament properties]]

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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]].
+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 in direct opposition to the [[satanic comma]] due to being the first [[3-limit]] comma to have a 3-2 [[telicity]] k-strength greater than 1 after it in the 3/2 convergence series, and, due to actually surpassing it in 3-2 [[telicity]] k-strength.
+This comma was named by [[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.
+Tempering out this comma leads to the [[archangelic family]] of temperaments. It is tempered out in 190537edo, which is a 28-strong 3-2 telic system due to tempering this comma out.
+[[Category:Commas named for their regular temperament properties]]