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 [9 -2 -4 0 1⟩, and a size of~~ 2.~~1531 cents~~. ~~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 = vishdelisma, vishdelic comma

| Color name = s1og<sup>4</sup>2, saloquadgu 2nd

| Comma = yes

}}

'''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.

~~== Temperament ==~~

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]]).

~~Tempering this comma out gives~~ the ~~rank~~-~~4 vishdel temperament~~. ~~Below however, is a rank~~-~~3 subgroup temperament since the vishdel comma doesn't have any sevens in~~ it.

==~~= 118 & 65 & 152 =~~==

== Temperaments ==

[[~~Subgroup~~]]: 2.3.5.11

[[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]].

[[~~Comma list~~]]~~: 5632/5625~~

See [[Vishdelismic clan]] for the [[clan of temperaments]] where it is tempered out.

[[~~Mapping]]~~: ~~[⟨1 0 0 -9], ⟨0 1 0 2], ⟨0 0 1 4~~]]

[[Category:Vishdelismic]]

[[Category:Commas named by combining multiple temperament names]]

[[~~POTE generator|POTE generators]]~~: ~~~3 = 1902.1744, ~5 = 2786.7968~~

~~[[Val|Vals]]: 31, 34, 53, 65, 87, 118, 152, 183, 217, 270~~

~~== See also ==~~

* [[Unnoticeable comma]]

* [[Rank-4 temperament~~|Rank-4 temperaments~~]]~~, where this comma's rank-4 temperament should be added to.~~

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-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 [[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 = vishdelisma, vishdelic comma
+| Color name = s1og<sup>4</sup>2, saloquadgu 2nd
+| Comma = yes
+}}
+'''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.
-== Temperament ==
+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]]).
-Tempering this comma out gives the rank-4 vishdel temperament. Below however, is a rank-3 subgroup temperament since the vishdel comma doesn't have any sevens in it.
-=== 118 & 65 & 152 ===
+== Temperaments ==
-[[Subgroup]]: 2.3.5.11
+[[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]].
-[[Comma list]]: 5632/5625
+See [[Vishdelismic clan]] for the [[clan of temperaments]] where it is tempered out.
-[[Mapping]]: [⟨1 0 0 -9], ⟨0 1 0 2], ⟨0 0 1 4]]
+[[Category:Vishdelismic]]
+[[Category:Commas named by combining multiple temperament names]]
-[[POTE generator|POTE generators]]: ~3 = 1902.1744, ~5 = 2786.7968
-[[Val|Vals]]: 31, 34, 53, 65, 87, 118, 152, 183, 217, 270
-== See also ==
-* [[Unnoticeable comma]]
-* [[Rank-4 temperament|Rank-4 temperaments]], where this comma's rank-4 temperament should be added to.