5632/5625: Difference between revisions

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{{Infobox Interval

| Ratio = 5632/5625

| Name = ~~vishdel~~ comma

| Name = vishdelisma, vishdelic comma

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

| Comma = yes

}}

~~The~~ '''~~vishdel~~ comma''' is an [[11-limit]] [[~~unnoticeable~~ comma]] with ~~a ratio of '''5632/5625''', a monzo of {{monzo| 9 -2 -4 0 1 }}, and~~ a size of 2.~~1531~~ [[cent]]s. 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~~]].

'''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 in~~ the ~~full 11~~-limit ~~gives the rank-4 vishdel temperament~~. ~~Below is~~ the ~~rank~~-~~3 subgroup temperament~~ as ~~the vishdel comma doesn't have any 7's~~.

==~~= 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]]: [{{val| 1 0 0 -9 }}, {{val| 0 1 0 2 }}, {{val| 0 0 1 4 }}]~~

[[Category:Vishdelismic]]

~~[[POTE generator]]s: ~3/2 = 702.1744, ~5/4 = 386.7968~~

~~{{Optimal ET sequence|legend=1| 31, 34, 53, 65, 87, 118, 152, 183, 217, 270}}~~

~~== See also ==~~

* [[Unnoticeable comma]]

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

[[Category:~~Vishdel~~]]

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

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 {{Infobox Interval
 | Ratio = 5632/5625
-| Name = vishdel comma
+| Name = vishdelisma, vishdelic comma
 | Color name = s1og<sup>4</sup>2, saloquadgu 2nd
 | Comma = yes
 }}
-The '''vishdel comma''' is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''5632/5625''', a monzo of {{monzo| 9 -2 -4 0 1 }}, and a size of 2.1531 [[cent]]s. 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]].
+'''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 in the full 11-limit gives the rank-4 vishdel temperament. Below is the rank-3 subgroup temperament as the vishdel comma doesn't have any 7's.
-=== 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]]: [{{val| 1 0 0 -9 }}, {{val| 0 1 0 2 }}, {{val| 0 0 1 4 }}]
+[[Category:Vishdelismic]]
-[[POTE generator]]s: ~3/2 = 702.1744, ~5/4 = 386.7968
-{{Optimal ET sequence|legend=1| 31, 34, 53, 65, 87, 118, 152, 183, 217, 270}}
-== See also ==
-* [[Unnoticeable comma]]
-* [[Rank-4 temperament]], where this comma's rank-4 temperament should be added to.
-[[Category:Vishdel]]
 [[Category:Commas named by combining multiple temperament names]]