5632/5625: Difference between revisions
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Rework following the pattern established by 1375/1372 |
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'''5632/5625''', the '''vishdelisma''' or '''vishdelic comma''', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] (specifically [[2.3.5.11 subgroup|2.3.5.11-subgroup]]) [[comma]] with a size of about 2.15 [[cent]]s. It is the amount that the [[11/1|11th harmonic]] overshoots two [[3/2|perfect fifths]], four [[5/4|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]]. | '''5632/5625''', the '''vishdelisma''' or '''vishdelic comma''', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] (specifically [[2.3.5.11 subgroup|2.3.5.11-subgroup]]) [[comma]] with a size of about 2.15 [[cent]]s. It is the amount that the [[11/1|11th harmonic]] overshoots two [[3/2|perfect fifths]], four [[5/4|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]]. | ||
== | == Temperaments == | ||
[[Tempering out]] this comma in the full 11-limit gives the rank-4 [[vishdelismic]] temperament, or in the 2.3.5.11 subgroup, the rank-3 '''vishdelic''' temperament. | [[Tempering out]] this comma in the full 11-limit gives the rank-4 [[vishdelismic]] temperament, or in the 2.3.5.11 subgroup, the rank-3 '''vishdelic''' temperament. | ||
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{{Mapping|legend=1| 1 0 0 -9 | 0 1 0 2 | 0 0 1 4 }} | {{Mapping|legend=1| 1 0 0 -9 | 0 1 0 2 | 0 0 1 4 }} | ||
: mapping generators: ~2, ~3, ~5 | |||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1199.8976{{c}}, ~3/2 = 702.1145{{c}}, ~5/4 = 386.7638{{c}} | |||
: [[error map]]: {{val| -0.102 +0.057 +0.245 -0.136 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1309{{c}}, ~5/4 = 386.7770{{c}} | |||
: error map: {{val| 0.000 +0.176 +0.463 +0.052 }} | |||
{{Optimal ET sequence|legend=1| 31, 34, 53, 65, 87, 118, 152, | {{Optimal ET sequence|legend=1| 31, 34, 53, 65, 87, 118, 152, 270, 335, 605, 940, 1092, 1362c, 1697c, 2302c }} | ||
[[Badness]] (Sintel): 0.183 | |||
[[Category:Vishdelismic]] | [[Category:Vishdelismic]] | ||
[[Category:Commas named by combining multiple temperament names]] | [[Category:Commas named by combining multiple temperament names]] | ||
Revision as of 12:38, 5 September 2026
| Interval information |
vishdelic comma
5632/5625, the vishdelisma or vishdelic comma, is an unnoticeable 11-limit (specifically 2.3.5.11-subgroup) comma with a size of about 2.15 cents. It is the amount that the 11th 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.
Temperaments
Tempering out this comma in the full 11-limit gives the rank-4 vishdelismic temperament, or in the 2.3.5.11 subgroup, the rank-3 vishdelic temperament.
Vishdelic
Subgroup: 2.3.5.11
Comma list: 5632/5625
Mapping: [⟨1 0 0 -9], ⟨0 1 0 2], ⟨0 0 1 4]]
- mapping generators: ~2, ~3, ~5
- WE: ~2 = 1199.8976 ¢, ~3/2 = 702.1145 ¢, ~5/4 = 386.7638 ¢
- error map: ⟨-0.102 +0.057 +0.245 -0.136]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.1309 ¢, ~5/4 = 386.7770 ¢
- error map: ⟨0.000 +0.176 +0.463 +0.052]
Optimal ET sequence: 31, 34, 53, 65, 87, 118, 152, 270, 335, 605, 940, 1092, 1362c, 1697c, 2302c
Badness (Sintel): 0.183