325/324 - Revision history

FloraC: Ordinary analysis doesn't need list form

2026-02-02T10:11:26Z

Ordinary analysis doesn't need list form

← Older revision		Revision as of 10:11, 2 February 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	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:		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.

	* [[16/13]] and two [[10/9]]'s		In terms of other superparticular ratios, it is the difference between:
	* [[13/8]] and [[81/50]] ([[8/5]] * [[81/80]])
	* [[13/9]] and two [[6/5]]'s
	* [[1053/1024]] and two [[81/80]]'s
	* [[25/24]] and [[27/26]]		* [[25/24]] and [[27/26]]
	* [[100/99]] and [[144/143]]		* [[100/99]] and [[144/143]]

	Being a [[triangle-particular\|triangle superparticular]], it factors neatly into ([[625/624]])([[676/675]]). Other factorizations are:		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]])

	* ([[385/384]])([[2080/2079]])		In the 17-limit it additionally factors into ([[595/594]])⋅([[715/714]]).
	* ([[364/363]])([[3025/3024]])
	* ([[352/351]])([[4225/4224]])
	* ([[351/350]])([[4375/4374]])
	* ([[595/594]])([[715/714]]) ~~In the 17-limit~~.

	== Temperaments ==		== 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 ==		== See also ==

Eufalesio: Made the equivalences easier to read

2026-02-01T18:52:56Z

Made the equivalences easier to read

← Older revision		Revision as of 18:52, 1 February 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	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{{cent}}. Its significance is in that it marks the difference between:

	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]]).		* [[16/13]] and two [[10/9]]'s
			* [[13/8]] and [[81/50]] ([[8/5]] * [[81/80]])
			* [[13/9]] and two [[6/5]]'s
			* [[1053/1024]] and two [[81/80]]'s
			* [[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]])
			* ([[595/594]])([[715/714]]) In the 17-limit.

	== Temperaments ==		== Temperaments ==

BudjarnLambeth at 00:00, 16 November 2024

2024-11-16T00:00:23Z

← Older revision		Revision as of 00:00, 16 November 2024
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	[[Category:Marveltwin]]		[[Category:Marveltwin]]
			[[Category:Commas with unknown etymology]]

FloraC: +17-limit factorization

2024-09-28T10:47:34Z

+17-limit factorization

← Older revision		Revision as of 10:47, 28 September 2024
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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 [[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.

	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]]).		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 ==		== Temperaments ==

FloraC: These expressions say too little. Rework into verbal descriptions. Decompose 25/18 (precisely 36/25) into a stack of two 6/5's.

2024-09-28T10:45:53Z

These expressions say too little. Rework into verbal descriptions. Decompose 25/18 (precisely 36/25) into a stack of two 6/5's.

← Older revision		Revision as of 10:45, 28 September 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	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 [[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.

	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]]).		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]]).

Godtone: make link go to table of triangle-(super)particulars

2024-03-13T22:41:19Z

make link go to table of triangle-(super)particulars

← Older revision		Revision as of 22:41, 13 March 2024
Line 6:		Line 6:
	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 [[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.

	Being a [[~~square superparticular~~\|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]]).		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]]).

	== Temperaments ==		== Temperaments ==

FloraC: Expand

2024-03-13T07:04:17Z

Expand

← Older revision		Revision as of 07:04, 13 March 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	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 [[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.

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

	Tempering it out leads to the rank-~~five~~ [[Marveltwin\|marveltwin temperament]], which identifies [[16/13]] by two [[10/9]]'s stacked.		== 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 ==		== See also ==
	* [[Marveltwin]]		* [[Marveltwin]]
	* [[Marveltwin triad]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	[[Category:Marveltwin]]		[[Category:Marveltwin]]

TallKite at 21:23, 11 January 2023

2023-01-11T21:23:00Z

← Older revision		Revision as of 21:23, 11 January 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = marveltwin comma		\| Name = marveltwin comma
	\| Color name = 3oyy1, Thoyoyo comma		\| Color name = 3oyy1, thoyoyo 1sn,<br>Thoyoyo comma
	\| Comma = yes		\| Comma = yes
	}}		}}

TallKite: added color name

2022-12-29T01:53:03Z

added color name

← Older revision		Revision as of 01:53, 29 December 2022
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	{{Infobox Interval		{{Infobox Interval
	\| Name = marveltwin comma		\| Name = marveltwin comma
			\| Color name = 3oyy1, Thoyoyo comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T15:04:10Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 15:04, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 325/324~~
	~~\| Monzo = -2 -4 2 0 0 1~~
	~~\| Cents = 5.33509~~
	\| Name = marveltwin comma		\| Name = marveltwin comma
	\| ~~Color name =~~		\| Comma = yes
	~~\| FJS name = P1<sup>25, 13</sup>~~
	~~\| 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 [[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.
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	~~[[Category:13-limit]]~~
	~~[[Category:Small commas]]~~
	~~[[Category:Superparticular]]~~
	[[Category:Marveltwin]]		[[Category:Marveltwin]]

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