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 [[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]].

== Temperament ==

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.

[[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.

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

=== Vishdelic ===

[[Subgroup]]: 2.3.5.11

[[Comma list]]: 5632/5625

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

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

[[Optimal tuning]] ([[POTE]]): ~3/2 = 702.1744{{c}}, ~5/4 = 386.7968{{c}}

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

{{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:Vishdelismic]]

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

@@ Line 1: / Line 1: @@
 {{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 [[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]].
 == Temperament ==
-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.
+[[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.
-=== 118 & 65 & 152 ===
+=== Vishdelic ===
 [[Subgroup]]: 2.3.5.11
 [[Comma list]]: 5632/5625
-[[Mapping]]: [{{val| 1 0 0 -9 }}, {{val| 0 1 0 2 }}, {{val| 0 0 1 4 }}]
+{{Mapping|legend=1| 1 0 0 -9 | 0 1 0 2 | 0 0 1 4 }}
-[[POTE generator]]s: ~3/2 = 702.1744, ~5/4 = 386.7968
+[[Optimal tuning]] ([[POTE]]): ~3/2 = 702.1744{{c}}, ~5/4 = 386.7968{{c}}
-{{Optimal ET sequence|legend=1| 31, 34, 53, 65, 87, 118, 152, 183, 217, 270}}
+{{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:Vishdelismic]]
 [[Category:Commas named by combining multiple temperament names]]

5632/5625: Difference between revisions

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