847/845: Difference between revisions
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Tristanbay (talk | contribs) Corrected a bit of math (847/845 was the product of one of the pairs of superparticulars listed, not the difference) Tags: Mobile edit Mobile web edit |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = cuthbert comma | | Name = cuthbert comma | ||
| Color name = | | Color name = 3uu1oozg1, thuthulolozogu unison | ||
| | | Comma = yes | ||
}} | }} | ||
'''847/845''', the '''cuthbert comma''', is a [[13-limit]] (also 5.7.11.13 [[subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s. In terms of commas, it is the difference between: | '''847/845''', the '''cuthbert comma''', is a [[13-limit]] (also 5.7.11.13 [[subgroup]]) [[comma]] measuring about 4.09{{cent}}. It is the difference between [[7/5]] and a stack of two [[13/11]]'s. In terms of commas, it is the difference between the following superparticular pairs: | ||
* [[66/65]] and [[78/77]] | * [[66/65]] and [[78/77]] | ||
* [[121/120]] and [[169/168]] | * [[121/120]] and [[169/168]] | ||
* [[352/351]] and [[2080/2079]] | * [[352/351]] and [[2080/2079]] | ||
* [[385/384]] and [[4225/4224]] | * [[385/384]] and [[4225/4224]] | ||
Meanwhile, it can be factorized as [[1001/1000]] × [[2200/2197]]. | Meanwhile, it can be factorized as [[1001/1000]] × [[2200/2197]] or [[441/440]] × [[10648/10647]]. | ||
== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma in the 13-limit results in the rank-5 cuthbert temperament and enables the [[cuthbert | [[Tempering out]] this comma in the 13-limit results in the rank-5 cuthbert temperament and enables the [[cuthbert chords]]. | ||
== See also == | == See also == | ||
* [[Small comma]] | * [[Small comma]] | ||
[[Category:Cuthbert]] | [[Category:Cuthbert]] | ||
[[Category:Commas with unknown etymology]] | |||
Latest revision as of 21:16, 7 December 2024
| Interval information |
847/845, the cuthbert comma, is a 13-limit (also 5.7.11.13 subgroup) comma measuring about 4.09 ¢. It is the difference between 7/5 and a stack of two 13/11's. In terms of commas, it is the difference between the following superparticular pairs:
Meanwhile, it can be factorized as 1001/1000 × 2200/2197 or 441/440 × 10648/10647.
Temperaments
Tempering out this comma in the 13-limit results in the rank-5 cuthbert temperament and enables the cuthbert chords.