Harrison's comma

Interval information

Ratio	59049/57344
Factorization	2-13 × 310 × 7-1
Monzo	[-13 10 0 -1⟩
Size in cents	50.724102¢
Name	Harrison's comma
Color name	Lr-2, Laru comma
FJS name	[math]\text{d}{-2}_{7}[/math]
Special properties	reduced
Tenney height (log2 nd)	31.657
Weil height (log2 max(n, d))	31.6993
Wilson height (sopfr(nd))	63
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.46451 bits
Comma size	medium
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59049/57344, or Harrison's comma, is the amount by which ten 3/2's exceed 7/4 (all octave-reduced). In other words, (3/2)¹⁰ = 7 ⋅ 59049/57344. It factors into simpler commas as (81/80)²(225/224), that is, two syntonic commas and a marvel comma.

Tempering out this comma will map the 7/4 to the augmented sixth (e.g. C-A♯), and the only notable 7-limit temperament that does that is septimal meantone.