2197/2187 - Revision history

Overthink: sectioning

2026-05-01T00:31:38Z

sectioning

← Older revision		Revision as of 00:31, 1 May 2026
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	}}		}}

	The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogous to [[tempering out]] the diesis, which divides the octave into three sharp [[5/4]]'s, tempering out the threedie divides the [[tritave]] into three slightly flat [[13/9]]'s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.		The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]].

			== Temperaments ==
			Analogous to [[tempering out]] the diesis, which divides the octave into three sharp [[5/4]]'s, tempering out the threedie divides the [[tritave]] into three slightly flat [[13/9]]'s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.

	It factors into simpler commas in the [[2.3.5.13 subgroup]] as ([[325/324]])([[676/675]]), and tempering out both of them leads to the 2.3.5.13 [[kleismic]] temperament (also known as ''cata''). It can also be expressed in the [[2.3.7.13 subgroup]] as ([[169/168]])/([[729/728]]), i.e. {{S\|13}}/S27.		It factors into simpler commas in the [[2.3.5.13 subgroup]] as ([[325/324]])([[676/675]]), and tempering out both of them leads to the 2.3.5.13 [[kleismic]] temperament (also known as ''cata''). It can also be expressed in the [[2.3.7.13 subgroup]] as ([[169/168]])/([[729/728]]), i.e. {{S\|13}}/S27.

	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]

Overthink: mention kleismic

2026-03-26T04:19:24Z

mention kleismic

← Older revision		Revision as of 04:19, 26 March 2026
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	The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogous to [[tempering out]] the diesis, which divides the octave into three sharp [[5/4]]'s, tempering out the threedie divides the [[tritave]] into three slightly flat [[13/9]]'s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.		The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogous to [[tempering out]] the diesis, which divides the octave into three sharp [[5/4]]'s, tempering out the threedie divides the [[tritave]] into three slightly flat [[13/9]]'s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.

	It factors into simpler commas in the 2.3.5.13 subgroup as ([[325/324]])([[676/675]]), or can be expressed in the 2.3.7.13 subgroup as ([[169/168]])/([[729/728]]), i.e. ~~S13~~/S27.		It factors into simpler commas in the [[2.3.5.13 subgroup]] as ([[325/324]])([[676/675]]), and tempering out both of them leads to the 2.3.5.13 [[kleismic]] temperament (also known as ''cata''). It can also be expressed in the [[2.3.7.13 subgroup]] as ([[169/168]])/([[729/728]]), i.e. {{S\|13}}/S27.

	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]

BudjarnLambeth at 23:57, 15 November 2024

2024-11-15T23:57:14Z

← Older revision		Revision as of 23:57, 15 November 2024
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	It factors into simpler commas in the 2.3.5.13 subgroup as ([[325/324]])([[676/675]]), or can be expressed in the 2.3.7.13 subgroup as ([[169/168]])/([[729/728]]), i.e. S13/S27.		It factors into simpler commas in the 2.3.5.13 subgroup as ([[325/324]])([[676/675]]), or can be expressed in the 2.3.7.13 subgroup as ([[169/168]])/([[729/728]]), i.e. S13/S27.

			[[Category:Commas with unknown etymology]]

Lériendil at 19:33, 25 July 2024

2024-07-25T19:33:41Z

← Older revision		Revision as of 19:33, 25 July 2024
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	The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogous to [[tempering out]] the diesis, which divides the octave into three sharp [[5/4]]'s, tempering out the threedie divides the [[tritave]] into three slightly flat [[13/9]]'s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.		The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogous to [[tempering out]] the diesis, which divides the octave into three sharp [[5/4]]'s, tempering out the threedie divides the [[tritave]] into three slightly flat [[13/9]]'s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.

	It factors into simpler commas as ([[325/324]])([[676/675]]), or can be expressed as ([[169/168]])/([[729/728]]), i.e. S13/S27.		It factors into simpler commas in the 2.3.5.13 subgroup as ([[325/324]])([[676/675]]), or can be expressed in the 2.3.7.13 subgroup as ([[169/168]])/([[729/728]]), i.e. S13/S27.

Lériendil at 19:33, 25 July 2024

2024-07-25T19:33:13Z

← Older revision		Revision as of 19:33, 25 July 2024
Line 7:		Line 7:
	The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogous to [[tempering out]] the diesis, which divides the octave into three sharp [[5/4]]'s, tempering out the threedie divides the [[tritave]] into three slightly flat [[13/9]]'s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.		The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogous to [[tempering out]] the diesis, which divides the octave into three sharp [[5/4]]'s, tempering out the threedie divides the [[tritave]] into three slightly flat [[13/9]]'s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.

	It factors into simpler commas as ([[325/324]])([[676/675]]).		It factors into simpler commas as ([[325/324]])([[676/675]]), or can be expressed as ([[169/168]])/([[729/728]]), i.e. S13/S27.

FloraC: Cleanup and +factorization into simpler commas.

2024-04-02T05:46:31Z

Cleanup and +factorization into simpler commas.

← Older revision		Revision as of 05:46, 2 April 2024
Line 5:		Line 5:
	}}		}}

	The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. ~~Analogously~~ to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.		The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogous to [[tempering out]] the diesis, which divides the octave into three sharp [[5/4]]'s, tempering out the threedie divides the [[tritave]] into three slightly flat [[13/9]]'s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.

			It factors into simpler commas as ([[325/324]])([[676/675]]).

TallKite at 20:29, 11 January 2023

2023-01-11T20:29:18Z

← Older revision		Revision as of 20:29, 11 January 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = threedie		\| Name = threedie
	\| Color name = s3o<sup>3</sup>2, Satritho comma		\| Color name = s3o<sup>3</sup>2, satritho 2nd,<br>Satritho comma
	\| Comma = yes		\| Comma = yes
	}}		}}

	The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.		The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.

TallKite: added color name

2022-12-29T01:57:19Z

added color name

← Older revision		Revision as of 01:57, 29 December 2022
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	{{Infobox Interval		{{Infobox Interval
	\| Name = threedie		\| Name = threedie
			\| Color name = s3o<sup>3</sup>2, Satritho comma
	\| Comma = yes		\| Comma = yes
	}}		}}

	The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.		The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.

Plumtree: Normalising usage of Infobox Interval

2022-10-25T12:09:22Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 12:09, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 2197/2187~~
	~~\| Monzo = 0 -7 0 0 0 3~~
	~~\| Cents = 7.89798~~
	\| Name = threedie		\| Name = threedie
	\| ~~Color name =~~		\| Comma = yes
	~~\| FJS name = dd2<sup>13,13,13</sup>~~
	~~\| Sound~~ =
	}}		}}

	The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.		The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.

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

Fredg999: Misc. edits, categories

2022-03-21T14:44:50Z

Misc. edits, categories

← Older revision		Revision as of 14:44, 21 March 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 2197/2187		\| Ratio = 2197/2187
	\| Monzo = 0 -7 0 0 0 3		\| Monzo = 0 -7 0 0 0 3
Line 10:		Line 9:
	}}		}}

	The '''threedie''', '''2197/2187''', is a 3.13 analog of the 2.5 [[128/125\|diesis]]. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.		The '''threedie''', '''2197/2187''', is a 3.13-[[subgroup]] analog of the 2.5-subgroup [[128/125\|diesis]]. Measuring about 7.9{{cent}}, it is a [[small comma]]. Analogously to tempering the diesis, which divides the octave into three sharp 5/4s, tempering the threedie divides the [[tritave]] into three slightly flat 13/9s, since (13/9)<sup>3</sup>/3 = 2197/2187. Furthermore, tempering out the threedie divides [[9/8]] into three instances of [[27/26]]. [[596edo]] provides the optimal patent val for the corresponding rank-5 temperament.

	[[Category:13-limit]]		[[Category:13-limit]]
	~~[[Category:Interval ratio]]~~
	[[Category:Small commas]]		[[Category:Small commas]]