325/324: Difference between revisions

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{{Infobox Interval

~~| 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 ~~can be expressed as ([[10/9]])<sup>2</sup>/(~~[[16/13]]~~), (~~[[25/18]]~~)/(~~[[18/13]]~~), (~~[[25/24]]~~)/(~~[[27/26]]) and ~~([[100/99]])/(~~[[~~144~~/~~143~~]]~~), among other expressions~~.

The '''marveltwin comma''', '''325/324''', is a [[small comma|small]] [[13-limit]] (also 2.3.5.13 [[subgroup]]) [[superparticular ratio|superparticular]] [[comma]] measuring about 5.3 [[cent]]s. Its significance is in that it marks the difference between [[16/13]] and a stack of two [[10/9]]'s, and [[13/9]] and a stack of two [[6/5]]'s. It can also be expressed as the difference between [[1053/1024]] and a stack of two [[81/80]]'s.

~~It factors into ([[625/624]])([[676/675]])~~, ~~([[385/384]])(~~[[~~2080~~/~~2079~~]]~~), (~~[[~~364~~/~~363~~]]~~)([[3025/3024]]), ([[352/351]])([[4225/4224]]), or (~~[[~~351~~/~~350~~]])([[~~4375~~/~~4374~~]]).

In terms of other superparticular ratios, it is the difference between:

* [[25/24]] and [[27/26]]

* [[100/99]] and [[144/143]]

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]])

* ([[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]]

* [[List of superparticular intervals]]

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

~~[[Category:Small commas]]~~

~~[[Category:Superparticular]]~~

[[Category:Marveltwin]]

[[Category:Commas with unknown etymology]]

~~{{todo|add color name}}~~

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| 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 can be expressed as ([[10/9]])<sup>2</sup>/([[16/13]]), ([[25/18]])/([[18/13]]), ([[25/24]])/([[27/26]]) and ([[100/99]])/([[144/143]]), among other expressions.
+The '''marveltwin comma''', '''325/324''', is a [[small comma|small]] [[13-limit]] (also 2.3.5.13 [[subgroup]]) [[superparticular ratio|superparticular]] [[comma]] measuring about 5.3 [[cent]]s. Its significance is in that it marks the difference between [[16/13]] and a stack of two [[10/9]]'s, and [[13/9]] and a stack of two [[6/5]]'s. It can also be expressed as the difference between [[1053/1024]] and a stack of two [[81/80]]'s.
-It factors into ([[625/624]])([[676/675]]), ([[385/384]])([[2080/2079]]), ([[364/363]])([[3025/3024]]), ([[352/351]])([[4225/4224]]), or ([[351/350]])([[4375/4374]]).
+In terms of other superparticular ratios, it is the difference between:
+* [[25/24]] and [[27/26]]
+* [[100/99]] and [[144/143]]
-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]])
+* ([[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]]
 * [[List of superparticular intervals]]
-[[Category:13-limit]]
-[[Category:Small commas]]
-[[Category:Superparticular]]
 [[Category:Marveltwin]]
+[[Category:Commas with unknown etymology]]
-{{todo|add color name}}