325/324: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

~~| Ratio = 325/324~~

~~| Monzo = -2 -4 2 0 0 1~~

~~| Cents = 5.33509~~

| Name = marveltwin comma

| Color name =

| Color name = 3oyy1, thoyoyo 1sn,<br>Thoyoyo comma

~~| FJS name = P1<sup>25~~, 13<~~/sup~~>

| Comma = yes

| ~~Sound~~ =

}}

The '''marveltwin comma''', '''325/324''', is a [[13-limit]] (also 2.3.5.13 [[subgroup]]) [[comma]] measuring about 5.3{{cent}}. Its significance is in that it marks the difference between [[16/13]] and a stack of two [[10/9]]'s, or between [[13/9]] and a stack of two [[6/5]]'s. It can also be expressed as ([[25/24]])/([[27/26]]) and ([[100/99]])/([[144/143]]), among other expressions.

~~The '''marveltwin comma'''~~, ~~'''325~~/~~324'''~~, ~~is a~~ [[13-limit]] (~~also 2.3.5.13 subgroup)~~ [[~~comma~~]] ~~measuring about 5.3 cents~~. Tempering it out leads to the rank-~~five~~ [[Marveltwin|marveltwin temperament]], which identifies [[16/13]] by two [[10/9]]'s stacked.

Being a [[triangle-particular|triangle superparticular]], it factors neatly into ([[625/624]])([[676/675]]). Other factorizations are ([[385/384]])([[2080/2079]]), ([[364/363]])([[3025/3024]]), ([[352/351]])([[4225/4224]]), and ([[351/350]])([[4375/4374]]). In the 17-limit it additionally factors into ([[595/594]])([[715/714]]).

== Temperaments ==

Tempering out this comma leads to the rank-5 [[Marveltwin|marveltwin temperament]], which identifies [[16/13]] by two [[10/9]]'s stacked and enables [[marveltwin chords]]. The most significant further temperament is to temper out 625/624 and/or 676/675, equating 26/25 with 25/24~27/26. This in the 2.3.5.13 [[subgroup]] is the rank-2 [[cata]] temperament.

== See also ==

* [[Marveltwin]]

* [[Marveltwin triad]]

* [[Comma]]

* [[List of superparticular intervals]]

~~[[Category:13-limit]]~~

~~[[Category:Small comma]]~~

~~[[Category:Ratio]]~~

[[Category:Marveltwin]]

[[Category:~~Superparticular~~]]

[[Category:Commas with unknown etymology]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
-| Ratio = 325/324
-| Monzo = -2 -4 2 0 0 1
-| Cents = 5.33509
 | Name = marveltwin comma
-| Color name =
+| Color name = 3oyy1, thoyoyo 1sn,<br>Thoyoyo comma
-| FJS name = P1<sup>25, 13</sup>
+| Comma = yes
-| Sound =
 }}
+The '''marveltwin comma''', '''325/324''', is a [[13-limit]] (also 2.3.5.13 [[subgroup]]) [[comma]] measuring about 5.3{{cent}}. Its significance is in that it marks the difference between [[16/13]] and a stack of two [[10/9]]'s, or between [[13/9]] and a stack of two [[6/5]]'s. It can also be expressed as ([[25/24]])/([[27/26]]) and ([[100/99]])/([[144/143]]), among other expressions.
-The '''marveltwin comma''', '''325/324''', is a [[13-limit]] (also 2.3.5.13 subgroup) [[comma]] measuring about 5.3 cents. Tempering it out leads to the rank-five [[Marveltwin|marveltwin temperament]], which identifies [[16/13]] by two [[10/9]]'s stacked.
+Being a [[triangle-particular|triangle superparticular]], it factors neatly into ([[625/624]])([[676/675]]). Other factorizations are ([[385/384]])([[2080/2079]]), ([[364/363]])([[3025/3024]]), ([[352/351]])([[4225/4224]]), and ([[351/350]])([[4375/4374]]). In the 17-limit it additionally factors into ([[595/594]])([[715/714]]).
+== Temperaments ==
+Tempering out this comma leads to the rank-5 [[Marveltwin|marveltwin temperament]], which identifies [[16/13]] by two [[10/9]]'s stacked and enables [[marveltwin chords]]. The most significant further temperament is to temper out 625/624 and/or 676/675, equating 26/25 with 25/24~27/26. This in the 2.3.5.13 [[subgroup]] is the rank-2 [[cata]] temperament.
 == See also ==
 * [[Marveltwin]]
-* [[Marveltwin triad]]
-* [[Comma]]
 * [[List of superparticular intervals]]
-[[Category:13-limit]]
-[[Category:Small comma]]
-[[Category:Ratio]]
 [[Category:Marveltwin]]
-[[Category:Superparticular]]
+[[Category:Commas with unknown etymology]]