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. | ||
In terms of other commas, it is the difference between [[176/175]] and [[225/224]]. In the [[13-limit]], it equals ([[676/675]])/([[4225/4224]]) and factors as ([[1001/1000]])⋅([[4096/4095]]). In the [[19-limit]] it factors as ([[1216/1215]])⋅([[2376/2375]]). | |||
[[ | |||
== | == 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]]. | ||
[[ | See [[Vishdelismic clan]] for the [[clan of temperaments]] where it is tempered out. | ||
[[Category:Vishdelismic]] | [[Category:Vishdelismic]] | ||
[[Category:Commas named by combining multiple temperament names]] | [[Category:Commas named by combining multiple temperament names]] | ||
Latest revision as of 12:21, 8 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.
In terms of other commas, it is the difference between 176/175 and 225/224. In the 13-limit, it equals (676/675)/(4225/4224) and factors as (1001/1000)⋅(4096/4095). In the 19-limit it factors as (1216/1215)⋅(2376/2375).
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.
See Vishdelismic clan for the clan of temperaments where it is tempered out.