65/64: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 65/64 | | Ratio = 65/64 | ||
| Monzo = -6 0 1 0 0 1 | | Monzo = -6 0 1 0 0 1 | ||
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| Sound = | | Sound = | ||
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In [[13-limit]] [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8{{cent}}, 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 complement]]s 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. | |||
Tempering it out turns 5/4 and 13/8 into [[ | |||
== See also == | == See also == | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[64/63]] | * [[64/63]] | ||
[[Category:13-limit]] | [[Category:13-limit]] | ||
[[Category: | [[Category:Small commas]] | ||
[[Category:Superparticular]] | [[Category:Superparticular]] | ||
[[Category: | [[Category:Octave-reduced harmonics]] | ||
Revision as of 15:42, 23 March 2022
| Interval information |
reduced,
reduced harmonic
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.