847/845: Difference between revisions
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'''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]] | ||
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== 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 == | ||
Revision as of 07:51, 21 May 2023
| 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:
- 66/65 and 78/77
- 121/120 and 169/168
- 352/351 and 2080/2079
- 385/384 and 4225/4224
- 441/440 and 10648/10647
Meanwhile, it can be factorized as 1001/1000 × 2200/2197.
Temperaments
Tempering out this comma in the 13-limit results in the rank-5 cuthbert temperament and enables the cuthbert chords.