65/64
| Interval information |
Thoyo comma
reduced,
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
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.
This interval is the 13th-partial chroma (13-limit formal comma) in Ben Johnston's notation, denoted simply with the number "13", while its reciprocal is denoted as "13" (a turned "13"). If the base note is C, then 13/8 is represented by C–Ab13.