65/64

Interval information

Ratio	65/64
Factorization	2-6 × 5 × 13
Monzo	[-6 0 1 0 0 1⟩
Size in cents	26.84138¢
Name	wilsorma
FJS name	[math]\displaystyle{ \text{P1}^{65} }[/math]
Special properties	superparticular, reduced, reduced harmonic
Tenney norm (log2 nd)	12.0224
Weil norm (log2 max(n, d))	12.0447
Wilson norm (sopfr(nd))	30
Open this interval in xen-calc

In 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. It belongs to the 13-prime-limit, which means that the highest prime in the ratio is 13. 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.

See also

• Gallery of just intervals
• 64/63