5632/5625: Difference between revisions
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]] | ||