5632/5625: Difference between revisions
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m FloraC moved page Vishdel comma to 5632/5625 over redirect: 4-digit ratios |
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The vishdel comma is an [[11-limit]] [[unnoticeable comma]] with a ratio of 5632/5625, a monzo of | The '''vishdel comma''' is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''5632/5625''', a monzo of {{monzo| 9 -2 -4 0 1 }}, and a size of 2.1531 [[cent]]s. It is the amount that the [[11/1|eleventh harmonic]] overshoots two [[3/2|perfect fifths]], four [[5/4|major thirds]], and an [[2/1|octave]] combined. It is tempered out in 11-limit extensions of temperaments such as [[vishnu]], [[grendel]], [[quasiorwell]], [[hemithirds]], and [[decoid]]. | ||
== Temperament == | == Temperament == | ||
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[[Comma list]]: 5632/5625 | [[Comma list]]: 5632/5625 | ||
[[Mapping]]: [ | [[Mapping]]: [{{val| 1 0 0 -9 }}, {{val| 0 1 0 2 }}, {{val| 0 0 1 4 }}] | ||
[[POTE generator | [[POTE generator]]s: ~3/2 = 702.1744, ~5/4 = 386.7968 | ||
[[ | [[Optimal GPV sequence]]: 31, 34, 53, 65, 87, 118, 152, 183, 217, 270 | ||
== See also == | == See also == | ||
* [[Unnoticeable comma]] | * [[Unnoticeable comma]] | ||
* [[Rank-4 temperament | * [[Rank-4 temperament]], where this comma's rank-4 temperament should be added to. | ||
[[Category:11-limit]] | [[Category:11-limit]] | ||
[[Category:Unnoticeable comma]] | [[Category:Unnoticeable comma]] | ||
[[Category:Vishdel]] | |||
Revision as of 03:25, 1 October 2022
The vishdel comma is an 11-limit unnoticeable comma with a ratio of 5632/5625, a monzo of [9 -2 -4 0 1⟩, and a size of 2.1531 cents. It is the amount that the eleventh harmonic overshoots two perfect fifths, four major thirds, and an octave combined. It is tempered out in 11-limit extensions of temperaments such as vishnu, grendel, quasiorwell, hemithirds, and decoid.
Temperament
Tempering this comma out gives the rank-4 vishdel temperament. Below however, is a rank-3 subgroup temperament since the vishdel comma doesn't have any sevens in it.
118 & 65 & 152
Subgroup: 2.3.5.11
Comma list: 5632/5625
Mapping: [⟨1 0 0 -9], ⟨0 1 0 2], ⟨0 0 1 4]]
POTE generators: ~3/2 = 702.1744, ~5/4 = 386.7968
Optimal GPV sequence: 31, 34, 53, 65, 87, 118, 152, 183, 217, 270
See also
- Unnoticeable comma
- Rank-4 temperament, where this comma's rank-4 temperament should be added to.