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>. | 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 [[ | 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 == | == Temperament == | ||
Tempering out this comma leads to the [[ | 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]] | |||
Latest revision as of 21:57, 14 August 2025
| 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 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, which is a 28-strong 3-2 telic system due to tempering this comma out.