3645/3584 - Revision history

FloraC: + factorizations & re-organize

2026-07-30T11:00:58Z

+ factorizations & re-organize

← Older revision		Revision as of 11:00, 30 July 2026
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	}}		}}

	The '''aberdiesis'''{{idiosyncratic}} or '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo\|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 29.2 [[cent]]s.		The '''aberdiesis'''{{idiosyncratic}} or '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo\|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 29.2 [[cent]]s. It is the difference between three major whole tones and a small septimal tritone, or in other words, ([[9/8]])<sup>3</sup>/([[7/5]]).

	It ~~is the difference between three major whole tones and a small septimal tritone,~~ or ~~in other words,~~ ([[9/8]])<sup>3</sup>/([[7/5]]).		It factors into simpler commas as ([[81/80]])⋅([[225/224]]) or ([[126/125]])⋅(225/224)<sup>2</sup>. In the [[11-limit]] it further factors into ([[99/98]])⋅([[2835/2816]]), ([[385/384]])⋅([[2187/2156]]), and ([[540/539]])⋅([[2079/2048]]).

	== Temperaments ==		== Temperaments ==
	It is most notably and characteristically tempered out in [[septimal meantone]], where 7/5 is an augmented fourth, as the flat fifth of meantone helps motivate this equivalence.		[[Tempering out]] this comma leads to the rank-3 [[miscellaneous 7-limit temperaments #Aberdietic\|aberdietic]] temperament. It is most notably and characteristically tempered out in [[septimal meantone]], where 7/5 is an augmented fourth, as the flat fifth of meantone helps motivate this equivalence. Other rank-2 temperaments which temper out this comma include [[schism]] and [[pycnic]].

	~~Tempering out this comma leads to the rank-3 [[Miscellaneous 7-limit temperaments #Schismean\|schismean]] temperament~~. Other rank-2 temperaments which temper out this comma include [[schism]] and [[pycnic]].

	== Etymology ==		== Etymology ==
	The name ''schismean'' was given by [[~~User:Xenllium\|~~Xenllium]] in 2022, most likely as a contraction of [[schism]] and [[meantone]]. The name ''aberdiesis'' was given later in 2026 by the observation of [[~~User:FloraC\|~~Fumica]] to observe a pun with the closely-related comma (10/7)/(9/8)<sup>3</sup> = [[64/63\|S8]]/[[81/80\|S9]] = [[5120/5103]], the aberschisma, in light of ~~[[User:Godtone~~\|Godtone]]'s observation that it behaves in almost all ways like a diesis according to a specific intuitively-motivated definition discussed in [[Diesis#Generalization]].		The name ''schismean'' was given by [[Xenllium]] in 2022, most likely as a contraction of [[schism]] and [[meantone]]. The name ''aberdiesis'' was given later in 2026 by the observation of [[Fumica]] to observe a pun with the closely-related comma (10/7)/(9/8)<sup>3</sup> = [[64/63\|S8]]/[[81/80\|S9]] = [[5120/5103]], the aberschisma, in light of {{u\|Godtone}}'s observation that it behaves in almost all ways like a diesis according to a specific intuitively-motivated definition discussed in [[Diesis #Generalization]].

	[[Category:Commas named by combining multiple temperament names]]		[[Category:Commas named by combining multiple temperament names]]

Godtone: this seems like an acceptable fix

2026-07-28T21:55:04Z

this seems like an acceptable fix

← Older revision		Revision as of 21:55, 28 July 2026
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	{{Infobox interval		{{Infobox interval
	\| Name = ~~tritonic diesis~~{{idiosyncratic}}, schismean comma{{idiosyncratic}}		\| Name = aberdiesis{{idiosyncratic}}, schismean comma{{idiosyncratic}}
	\| Color name = Lry-2, Laruyo negative 2nd		\| Color name = Lry-2, Laruyo negative 2nd
	\| Comma = yes		\| Comma = yes
	}}		}}

	The '''~~tritonic diesis~~'''{{idiosyncratic}} or '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo\|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 29.2 [[cent]]s.		The '''aberdiesis'''{{idiosyncratic}} or '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo\|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 29.2 [[cent]]s.

	It is the difference between three major whole tones and a small septimal tritone, or in other words, ([[9/8]])<sup>3</sup>/([[7/5]]).		It is the difference between three major whole tones and a small septimal tritone, or in other words, ([[9/8]])<sup>3</sup>/([[7/5]]).
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	== Etymology ==		== Etymology ==
	The name ''schismean'' was given by [[User:Xenllium\|Xenllium]] in 2022, most likely as a contraction of [[schism]] and [[meantone]]. The name ''~~tritonic diesis~~'' was given later in 2026 by the observation of [[User:~~Godtone~~\|~~Godtone~~]] ~~that it fit~~ a ~~general algorithmic definition discussed in [[Diesis#Generalization]], combined~~ with the ~~observation that the ''septimal tritonic diesis'' of~~ (10/7)/(7/5) = [[50/49]] ~~seemed to suggest~~ the ~~existence of a ''tritonic diesis'' with a focus on the ''tritone'' part as contrasted to the ''septimal'' part~~, ~~hence the expression~~ of ~~it as the amount by which the "literal" tritone~~ [[~~729/512~~\|~~(9/8)<sup>3</sup>~~]] ~~exceeds the LCJI tritone~~ [[~~7/5~~]].		The name ''schismean'' was given by [[User:Xenllium\|Xenllium]] in 2022, most likely as a contraction of [[schism]] and [[meantone]]. The name ''aberdiesis'' was given later in 2026 by the observation of [[User:FloraC\|Fumica]] to observe a pun with the closely-related comma (10/7)/(9/8)<sup>3</sup> = [[64/63\|S8]]/[[81/80\|S9]] = [[5120/5103]], the aberschisma, in light of [[User:Godtone\|Godtone]]'s observation that it behaves in almost all ways like a diesis according to a specific intuitively-motivated definition discussed in [[Diesis#Generalization]].

	[[Category:Commas named by combining multiple temperament names]]		[[Category:Commas named by combining multiple temperament names]]

Godtone: add etymology section, propose alternate name that feels less awkward than current name, link, note connection to septimal meantone

2026-07-26T19:27:08Z

add etymology section, propose alternate name that feels less awkward than current name, link, note connection to septimal meantone

← Older revision		Revision as of 19:27, 26 July 2026
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	{{Infobox interval		{{Infobox interval
	\| Name = schismean comma{{idiosyncratic}}		\| Name = tritonic diesis{{idiosyncratic}}, schismean comma{{idiosyncratic}}
	\| Color name = Lry-2, Laruyo negative 2nd		\| Color name = Lry-2, Laruyo negative 2nd
	\| Comma = yes		\| Comma = yes
	}}		}}

	The '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo\|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 29.2 [[cent]]s~~. It was named by [[User:Xenllium\|Xenllium]] in 2022, most likely as a contraction of [[schism]] and [[meantone]]~~.		The '''tritonic diesis'''{{idiosyncratic}} or '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo\|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 29.2 [[cent]]s.

	It is the difference between three major whole tones and a small septimal tritone, or in other words, (9/8)<sup>3</sup>/(7/5).		It is the difference between three major whole tones and a small septimal tritone, or in other words, ([[9/8]])<sup>3</sup>/([[7/5]]).

	== Temperaments ==		== Temperaments ==
	Tempering out this comma leads to the rank-3 [[Miscellaneous 7-limit temperaments #Schismean\|schismean]] temperament. ~~Rank~~-2 temperaments which temper out this comma include [[schism]], [[meantone]], ~~and~~ [[~~pycnic~~]].		It is most notably and characteristically tempered out in [[septimal meantone]], where 7/5 is an augmented fourth, as the flat fifth of meantone helps motivate this equivalence.

			Tempering out this comma leads to the rank-3 [[Miscellaneous 7-limit temperaments #Schismean\|schismean]] temperament. Other rank-2 temperaments which temper out this comma include [[schism]] and [[pycnic]].

			== Etymology ==
			The name ''schismean'' was given by [[User:Xenllium\|Xenllium]] in 2022, most likely as a contraction of [[schism]] and [[meantone]]. The name ''tritonic diesis'' was given later in 2026 by the observation of [[User:Godtone\|Godtone]] that it fit a general algorithmic definition discussed in [[Diesis#Generalization]], combined with the observation that the ''septimal tritonic diesis'' of (10/7)/(7/5) = [[50/49]] seemed to suggest the existence of a ''tritonic diesis'' with a focus on the ''tritone'' part as contrasted to the ''septimal'' part, hence the expression of it as the amount by which the "literal" tritone [[729/512\|(9/8)<sup>3</sup>]] exceeds the LCJI tritone [[7/5]].

	[[Category:Commas named by combining multiple temperament names]]		[[Category:Commas named by combining multiple temperament names]]

Xenllium at 11:52, 22 January 2026

2026-01-22T11:52:52Z

← Older revision		Revision as of 11:52, 22 January 2026
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	~~{{stub}}~~
	{{Infobox interval		{{Infobox interval
	\| Name = ~~Schismean~~ comma{{idiosyncratic}}		\| Name = schismean comma{{idiosyncratic}}
	\| Color name = Lry-2, Laruyo negative 2nd		\| Color name = Lry-2, Laruyo negative 2nd
	\| Comma = yes		\| Comma = yes
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	Tempering out this comma leads to the rank-3 [[Miscellaneous 7-limit temperaments #Schismean\|schismean]] temperament. Rank-2 temperaments which temper out this comma include [[schism]], [[meantone]], and [[pycnic]].		Tempering out this comma leads to the rank-3 [[Miscellaneous 7-limit temperaments #Schismean\|schismean]] temperament. Rank-2 temperaments which temper out this comma include [[schism]], [[meantone]], and [[pycnic]].

	~~[[Category:7-limit intervals]]~~
	~~[[Category:Small commas]]~~
	[[Category:Commas named by combining multiple temperament names]]		[[Category:Commas named by combining multiple temperament names]]

Xenllium at 11:34, 22 January 2026

2026-01-22T11:34:02Z

← Older revision		Revision as of 11:34, 22 January 2026
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	{{stub}}		{{stub}}
	{{Infobox ~~Interval~~		{{Infobox interval
	\| Name = Schismean comma{{idiosyncratic}}		\| Name = Schismean comma{{idiosyncratic}}
	\| Color name = Lry-2, Laruyo negative 2nd		\| Color name = Lry-2, Laruyo negative 2nd
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	It is the difference between three major whole tones and a small septimal tritone, or in other words, (9/8)<sup>3</sup>/(7/5).		It is the difference between three major whole tones and a small septimal tritone, or in other words, (9/8)<sup>3</sup>/(7/5).

			== Temperaments ==
			Tempering out this comma leads to the rank-3 [[Miscellaneous 7-limit temperaments #Schismean\|schismean]] temperament. Rank-2 temperaments which temper out this comma include [[schism]], [[meantone]], and [[pycnic]].

	[[Category:7-limit intervals]]		[[Category:7-limit intervals]]
	[[Category:Small commas]]		[[Category:Small commas]]
	[[Category:Commas named by combining multiple temperament names]]		[[Category:Commas named by combining multiple temperament names]]

Overthink: changed category

2025-11-06T22:59:04Z

changed category

← Older revision		Revision as of 22:59, 6 November 2025
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	[[Category:7-limit intervals]]		[[Category:7-limit intervals]]
	[[Category:Small commas]]		[[Category:Small commas]]
	[[Category:Commas ~~with unknown etymology~~]]		[[Category:Commas named by combining multiple temperament names]]

Jerdle: It's 29.2 cents, not 23.6.

2025-11-04T18:48:19Z

It's 29.2 cents, not 23.6.

← Older revision		Revision as of 18:48, 4 November 2025
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	}}		}}

	The '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo\|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 23.6 [[cent]]s. It was named by [[User:Xenllium\|Xenllium]] in 2022, most likely as a contraction of [[schism]] and [[meantone]].		The '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo\|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 29.2 [[cent]]s. It was named by [[User:Xenllium\|Xenllium]] in 2022, most likely as a contraction of [[schism]] and [[meantone]].

	It is the difference between three major whole tones and a small septimal tritone, or in other words, (9/8)<sup>3</sup>/(7/5).		It is the difference between three major whole tones and a small septimal tritone, or in other words, (9/8)<sup>3</sup>/(7/5).

Overthink at 03:49, 16 September 2025

2025-09-16T03:49:03Z

← Older revision		Revision as of 03:49, 16 September 2025
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	}}		}}

	The '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo\|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 23.6 [[cent]]s. It was named by [[User:Xenllium\|Xenllium]] in 2022.		The '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo\|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 23.6 [[cent]]s. It was named by [[User:Xenllium\|Xenllium]] in 2022, most likely as a contraction of [[schism]] and [[meantone]].

	It is the difference between three major whole tones and a small septimal tritone, or in other words, (9/8)<sup>3</sup>/(7/5).		It is the difference between three major whole tones and a small septimal tritone, or in other words, (9/8)<sup>3</sup>/(7/5).

BudjarnLambeth at 12:19, 3 November 2024

2024-11-03T12:19:48Z

← Older revision		Revision as of 12:19, 3 November 2024
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	[[Category:7-limit intervals]]		[[Category:7-limit intervals]]
	[[Category:Small commas]]		[[Category:Small commas]]
			[[Category:Commas with unknown etymology]]

Godtone: confusing name given this has almost nothing to do with schismic

2024-07-17T02:29:41Z

confusing name given this has almost nothing to do with schismic

← Older revision		Revision as of 02:29, 17 July 2024
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	{{stub}}		{{stub}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = Schismean comma		\| Name = Schismean comma{{idiosyncratic}}
	\| Color name = Lry-2, Laruyo negative 2nd		\| Color name = Lry-2, Laruyo negative 2nd
	\| Comma = yes		\| Comma = yes
	}}		}}

	The '''schismean comma''' ([[monzo]]: {{monzo\|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 23.6 [[cent]]s. It was named by [[User:Xenllium\|Xenllium]] in 2022.		The '''schismean comma'''{{idiosyncratic}} ([[monzo]]: {{monzo\|-9 6 1 -1}}, [[ratio]]: 3645/3584) is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 23.6 [[cent]]s. It was named by [[User:Xenllium\|Xenllium]] in 2022.

	It is the difference between three major whole tones and a small septimal tritone, or in other words, (9/8)<sup>3</sup>/(7/5).		It is the difference between three major whole tones and a small septimal tritone, or in other words, (9/8)<sup>3</sup>/(7/5).