65/64: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = wilsorma | | Name = wilsorma | ||
| | | Color name = 3oy1, thoyo 1sn,<br>Thoyo comma | ||
| | | Comma = yes | ||
}} | }} | ||
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]]. | 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 [[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. | ||
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 "{{invert|13}}" (a turned "13"). If the base note is C, then [[13/8]] is represented by C–Ab13. | |||
Tempering it out leads to the rank-2 2.5.13 '''wilsormatic''' temperament, which has a generator tuned to abut 370-375 cents that represents both 5/4 and 16/13, or the rank-5 '''wilsormic''' temperament. | |||
== See also == | == See also == | ||
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* [[64/63]] | * [[64/63]] | ||
[[Category: | [[Category:Commas with unknown etymology]] | ||
{{todo|research|comment=Is it named after Erv Wilson?}} | |||