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]]. | |||
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 | == Notation == | ||
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. | |||
== Temperaments == | |||
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 in the 13-limit. However, it is natural to equate [[14/13]] and [[15/14]] with 13/12[[~]]16/15, thus leading to the [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] temperament [[negri]], which splits the perfect fourth [[4/3]] into four equal parts, each being one step of the 12::16 segment of the [[harmonic series]]. | |||
== See also == | == See also == | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[64/63]] | * [[64/63]] | ||
[[Category: | [[Category:Commas with unknown etymology]] <!-- Is it named after Erv Wilson? --> | ||
Latest revision as of 06:55, 12 July 2026
| Interval information |
Thoyo comma
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.
Notation
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.
Temperaments
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 in the 13-limit. However, it is natural to equate 14/13 and 15/14 with 13/12~16/15, thus leading to the 2.3.5.7.13-subgroup temperament negri, which splits the perfect fourth 4/3 into four equal parts, each being one step of the 12::16 segment of the harmonic series.