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]]. | 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-strength greater than 1 in the 3/2 convergence series after the satanic comma, and, due to actually surpassing the satanic comma in 3-2 | 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]] [[Telicity #k-Strong Telicity|k-strength]] greater than 1 in the 3/2 convergence series after the satanic comma, and, due to actually surpassing the satanic comma in 3-2 telicity k-strength. | ||
== Temperament == | == 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]] and its multiples. | ||
Revision as of 13:40, 22 December 2022
| Interval information |
reduced subharmonic
The archangelic comma (monzo: [301994 -190537⟩) is the amount by which 190537 perfect fifths fall short of 111457 octaves, in other words 2111457/(3/2)190537. This difference is inaudible at roughly 0.0001 cents.
This comma was named by Aura in direct opposition to the satanic comma due to it being the first 3-limit comma to have a 3-2 telicity k-strength greater than 1 in the 3/2 convergence series after the satanic comma, and, due to actually surpassing the satanic comma in 3-2 telicity k-strength.
Temperament
Tempering out this comma leads to the Archangelic family of temperaments. It is tempered out in 190537edo and its multiples.