65/64: Difference between revisions
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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. | == 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 == | ||
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* [[64/63]] | * [[64/63]] | ||
[[Category:Commas with unknown etymology]] | [[Category:Commas with unknown etymology]] <!-- Is it named after Erv Wilson? --> | ||