Archangelic comma: Difference between revisions
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Finally! A 3-limit comma that's better than the satanic comma! |
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The '''archangelic comma''' ([[monzo]]: {{monzo| -1054 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| -1054 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 | 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. | ||
== Temperament == | |||
Tempering out this comma leads to the [[Archangelic family]] of temperaments. It is tempered out in [[190537edo]] and its multiples. | |||
Revision as of 13:18, 22 December 2022
| Interval information |
reduced subharmonic
The archangelic comma (monzo: [-1054 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 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.
Temperament
Tempering out this comma leads to the Archangelic family of temperaments. It is tempered out in 190537edo and its multiples.