Harrison's comma
(Redirected from 59049/57344)
Jump to navigation
Jump to search
Ratio | 59049/57344 |
Factorization | 2^{-13} × 3^{10} × 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 (log_{2} nd) | 31.657 |
Weil height (log_{2} 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.