65/64
Ratio | 65/64 |
Factorization | 2^{-6} × 5 × 13 |
Monzo | [-6 0 1 0 0 1⟩ |
Size in cents | 26.841376¢ |
Name | wilsorma |
Color name | 3oy1, thoyo 1sn, Thoyo comma |
FJS name | [math]\text{P1}^{5,13}[/math] |
Special properties | superparticular, reduced, reduced harmonic |
Tenney height (log_{2} nd) | 12.0224 |
Weil height (log_{2} max(n, d)) | 12.0447 |
Wilson height (sopfr (nd)) | 30 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.34087 bits |
Comma size | small |
S-expression | S13 × S14 × S15 |
open this interval in xen-calc |
In 13-limit just intonation, 65/64, the wilsorma, is a superparticular interval of around 26.8 ¢, nearly a quarter of a semitone or eighth of a tone. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between 5/4 and 16/13; 8/5 and 13/8; 13/12 and 16/15; 15/8 and 24/13, 13/10 and 32/25; 20/13 and 25/16, and of course, infinitely many other pairs of just intervals. It differs from the septimal comma 64/63 by 4096/4095 and from the syntonic comma 81/80 by 325/324.
Tempering it out turns 5/4 and 13/8 into octave complements of one another. This is particularly useful in many 13-limit magic family extensions, as it means they are very simply mapped to plus and minus one generator.
Ben Johnston's notation denotes this interval simply with the number "13", and its reciprocal as 13 (a turned 13).