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Interval information
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,
Tenney height (log2 nd) 12.0224
Weil height (log2 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).

See also