Harrison's comma

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(Redirected from 59049/57344)
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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
open this interval in xen-calc

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.