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 = vishdel 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 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 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~~.

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 ===

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[[Comma list]]: 5632/5625

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

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

[[POTE generator~~|POTE generators~~]]: ~3 = ~~1902~~.1744, ~5 = ~~2786~~.7968

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

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

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

[[Category:~~11-limit~~]]

[[Category:Vishdel]]

[[Category:~~Unnoticeable comma~~]]

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

@@ Line 1: / Line 1: @@
-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 = vishdel 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 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 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.
+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 ===
@@ Line 9: / Line 15: @@
 [[Comma list]]: 5632/5625
-[[Mapping]]: [⟨1 0 0 -9], ⟨0 1 0 2], ⟨0 0 1 4]]
+[[Mapping]]: [{{val| 1 0 0 -9 }}, {{val| 0 1 0 2 }}, {{val| 0 0 1 4 }}]
-[[POTE generator|POTE generators]]: ~3 = 1902.1744, ~5 = 2786.7968
+[[POTE generator]]s: ~3/2 = 702.1744, ~5/4 = 386.7968
-[[Val|Vals]]: 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|Rank-4 temperaments]], where this comma's rank-4 temperament should be added to.
+* [[Rank-4 temperament]], where this comma's rank-4 temperament should be added to.
-[[Category:11-limit]]
+[[Category:Vishdel]]
-[[Category:Unnoticeable comma]]
+[[Category:Commas named by combining multiple temperament names]]