847/845: Difference between revisions
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'''847/845''', the '''cuthbert comma''', is a [[13-limit]] (also 5.7.11.13 | '''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. It is also the difference between [[125/121]] and [[175/169]]. | ||
In the 5.7.11.13 subgroup, it is the simplest comma of its size (and the smallest of its complexity) by an extremely large margin. For comparison, [[637/625]] is about as simple but much larger, and [[2941225/2924207]] is significantly more complex yet still twice as large. | |||
In terms of full 13-limit commas, it is the difference between the following superparticular pairs: | In terms of full 13-limit commas, it is the difference between the following superparticular pairs: | ||
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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 chords]]. | [[Tempering out]] this comma in the 13-limit results in the rank-5 cuthbert temperament and enables the [[cuthbert chords]]. | ||
Tempering it out in the 5.7.11.13 subgroup leads to an extremely efficient rank-3 temperament. | |||
== See also == | == See also == | ||