Archangelic comma

Interval information

Factorization	2301994 × 3-190537
Monzo	[301994 -190537⟩
Size in cents	0.000111619¢
Name	archangelic comma
FJS name	[math]\displaystyle{ \text{27219d18052} }[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	603988
Weil height (log2 max(n, d))	603988
Wilson height (sopfr(nd))	1175600
Comma size	unnoticeable
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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 log₂3 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 (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.