325/324: Difference between revisions

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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 [[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.

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]]).

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

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

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

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.

[[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 ==

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 }}
-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 [[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.
-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]]).
+In terms of other superparticular ratios, it is the difference between:
+* [[25/24]] and [[27/26]]
+* [[100/99]] and [[144/143]]
+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.
+[[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 ==