Valentine comma
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Ratio | 1990656/1953125 |
Factorization | 2^{13} × 3^{5} × 5^{-9} |
Monzo | [13 5 -9⟩ |
Size in cents | 32.95158¢ |
Name | valentine comma |
Color name | satritrigu 3rd, sg^{9}3 |
FJS name | [math]\text{dddd3}_{5,5,5,5,5,5,5,5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 41.8222 |
Weil height (log_{2} max(n, d)) | 41.8496 |
Wilson height (sopfr (nd)) | 86 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.49887 bits |
Comma size | medium |
open this interval in xen-calc |
The valentine comma (ratio: 1990656/1953125, monzo: [13 5 -9⟩ is a medium 5-limit comma. It is the amount by which a stack of four 25/24's falls short of 6/5, or a stack of five 25/24's falls short of 5/4. In terms of commas, it is the difference between the lesser diesis (128/125) and the kleisma (15625/15552), and is also equal to one-half of the difference between nine 25/24's and a perfect fifth (3/2). Tempering it out leads to the 5-limit version of valentine temperament.