Harrison's comma
(Redirected from 59049/57344)
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| 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{n\cdot d}[/math]) |
~4.78701 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.