847/845: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 847/845 | | Ratio = 847/845 | ||
| Monzo = 0 0 -1 1 2 -2 | | Monzo = 0 0 -1 1 2 -2 | ||
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| Sound = | | Sound = | ||
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'''847/845''', the '''cuthbert comma''', is a [[13-limit]] (also 5.7.11.13 [[subgroup]]) [[comma]] measuring about 4.09 | '''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: | ||
* [[66/65]] and [[78/77]] | * [[66/65]] and [[78/77]] | ||
* [[121/120]] and [[169/168]] | * [[121/120]] and [[169/168]] | ||
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[[Category:13-limit]] | [[Category:13-limit]] | ||
[[Category:Small commas]] | [[Category:Small commas]] | ||
[[Category:Cuthbert]] | [[Category:Cuthbert]] | ||
Revision as of 19:51, 27 April 2022
| 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:
- 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 triad.