5632/5625: Difference between revisions
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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]]. | {{Infobox Interval | ||
| Ratio = 5632/5625 | |||
| Name = vishdel comma | |||
| Color name = s1og<sup>4</sup>2, saloquadgu 2nd | |||
| Comma = yes | |||
}} | |||
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 also the amount by which four major thirds falls short of [[11/9]] plus an octave. It is tempered out in 11-limit extensions of temperaments such as [[vishnu]], [[grendel]], [[quasiorwell]], [[hemithirds]], and [[decoid]]. | |||
== Temperament == | == Temperament == | ||
Tempering this comma out gives the rank-4 vishdel temperament. Below | Tempering this comma out in the full 11-limit gives the rank-4 vishdel temperament. Below is the rank-3 subgroup temperament as the vishdel comma doesn't have any 7's. | ||
=== 118 & 65 & 152 === | === 118 & 65 & 152 === | ||
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[[POTE generator]]s: ~3/2 = 702.1744, ~5/4 = 386.7968 | [[POTE generator]]s: ~3/2 = 702.1744, ~5/4 = 386.7968 | ||
{{Optimal ET sequence|legend=1| 31, 34, 53, 65, 87, 118, 152, 183, 217, 270}} | |||
== See also == | == See also == | ||
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* [[Rank-4 temperament]], where this comma's rank-4 temperament should be added to. | * [[Rank-4 temperament]], where this comma's rank-4 temperament should be added to. | ||
[[Category:Vishdel]] | [[Category:Vishdel]] | ||
[[Category:Commas named by combining multiple temperament names]] | |||
Latest revision as of 03:40, 30 October 2025
| Interval information |
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 also the amount by which four major thirds falls short of 11/9 plus an octave. It is tempered out in 11-limit extensions of temperaments such as vishnu, grendel, quasiorwell, hemithirds, and decoid.
Temperament
Tempering this comma out in the full 11-limit gives the rank-4 vishdel temperament. Below is the rank-3 subgroup temperament as the vishdel comma doesn't have any 7's.
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 ET 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.