5632/5625: Difference between revisions
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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 | '''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 by which a stack of four [[5/4]] major thirds falls short of [[11/9]] plus an [[octave]]. Equivalently, it is the amount by which [[11/8]] overshoots a stack of two [[75/64]] classical augmented seconds. | ||
== Temperaments == | == 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. It is tempered out in 11-limit extensions of temperaments such as [[vishnu]], [[grendel]], [[quasiorwell]], [[hemithirds]], and [[decoid]]. | ||
=== Vishdelic === | === Vishdelic === | ||
Revision as of 12:48, 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 by which a stack of four 5/4 major thirds falls short of 11/9 plus an octave. Equivalently, it is the amount by which 11/8 overshoots a stack of two 75/64 classical augmented seconds.
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. It is tempered out in 11-limit extensions of temperaments such as vishnu, grendel, quasiorwell, hemithirds, and decoid.
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