Forge comma

Interval information

Ratio	1640558367/1638400000
Factorization	2-19 × 314 × 5-5 × 73
Monzo	[-19 14 -5 3⟩
Size in cents	2.279162¢
Name	forge comma
Color name	LLz3g52, lala-trizo-aquingu 2nd
FJS name	[math]\text{d2}^{7,7,7}_{5,5,5,5,5}[/math]
Special properties	reduced
Tenney height (log2 nd)	61.2212
Weil height (log2 max(n, d))	61.2231
Wilson height (sopfr(nd))	126
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.2475 bits
Comma size	unnoticeable
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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.