Forge comma
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Ratio | 1640558367/1638400000 |
Factorization | 2^{-19} × 3^{14} × 5^{-5} × 7^{3} |
Monzo | [-19 14 -5 3⟩ |
Size in cents | 2.2791622¢ |
Name | forge comma |
Color name | LLz^{3}g^{5}2, lala-trizo-aquingu 2nd |
FJS name | [math]\text{d2}^{7,7,7}_{5,5,5,5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 61.2212 |
Weil height (log_{2} max(n, d)) | 61.2231 |
Wilson height (sopfr (nd)) | 126 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.2475 bits |
Comma size | unnoticeable |
open this interval in xen-calc |
The forge comma is the 7-limit unnoticeable comma 1640558367/1638400000, which measures roughly 2.28 cents. It's notable as the amount by which a stack consisting of an octave, a 6561/4096 Pythagorean augmented fifth, and a 5/4 major third, exceeds a stack of three 100/63 quasi-tempered minor sixths. It also is the interval separating the amity comma from the gamelisma and is the sum of the landscape comma and the schisma. This comma was first found as the 7-limit comma linking 12edo, 34edo and 159edo. The various 11-limit families that temper out this comma are named after various metal objects made in a forge, hence the Forge as the name of this collection of temperaments.