Archangelic comma
Factorization | 2^{301994} × 3^{-190537} |
Monzo | [301994 -190537⟩ |
Size in cents | 0.00011161901¢ |
Name | archangelic comma |
FJS name | [math]\text{27219d18052}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 603988 |
Weil height (log_{2} max(n, d)) | 603988 |
Wilson height (sopfr (nd)) | 1175600 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.19982 bits |
Comma size | unnoticeable |
open this interval in xen-calc |
The archangelic comma (monzo: [301994 -190537⟩) is the amount by which 190537 perfect fifths fall short of 111457 octaves, in other words 2^{111457}/(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 and its multiples (571611edo, 762148edo, 1714833edo, 1905370edo, and 4191814edo just to name a few), with 190537edo itself being a 28-strong 3-2 telic system due to tempering this comma out.