256/243 - Revision history

FloraC: /* Temperaments */ update

2026-06-28T11:06:33Z

Temperaments: update

← Older revision		Revision as of 11:06, 28 June 2026
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	== Temperaments ==		== Temperaments ==
	When this ratio is taken as a comma to be tempered in the [[5-limit]], it produces the [[blackwood]] temperament, and it may be called the '''blackwood comma''', named after [[Easley Blackwood Jr]]. Edos tempering it out include [[5edo]], [[10edo]], [[15edo]], [[20edo]], [[25edo]] and [[30edo]]. See [[~~Limmic temperaments~~]] for ~~a number~~ of ~~other~~ temperaments where it is tempered out.		When this ratio is taken as a comma to be tempered in the [[5-limit]], it produces the [[blackwood]] temperament, and it may be called the '''blackwood comma''', named after [[Easley Blackwood Jr]]. Edos tempering it out include [[5edo]], [[10edo]], [[15edo]], [[20edo]], [[25edo]] and [[30edo]].

			See [[Blackwood family]] for the [[family]] of temperaments where it is tempered out.

	== Notation ==		== Notation ==

FloraC: Expand after 2187/2048

2025-11-27T16:36:50Z

Expand after 2187/2048

← Older revision		Revision as of 16:36, 27 November 2025
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	}}		}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = Pythagorean limma, Pythagorean diatonic semitone~~, 3-limit minor 2nd~~, blackwood comma		\| Name = Pythagorean limma, Pythagorean diatonic semitone, blackwood comma
	\| Color name = sw2, sawa 2nd		\| Color name = sw2, sawa 2nd
	\| Sound = jid_256_243_pluck_adu_dr220.mp3		\| Sound = jid_256_243_pluck_adu_dr220.mp3
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	{{Wikipedia\| Semitone #Pythagorean tuning }}		{{Wikipedia\| Semitone #Pythagorean tuning }}

	~~The interval~~ '''256/243''', the '''Pythagorean limma''' or '''Pythagorean diatonic semitone''' or the ~~'''~~3-limit minor ~~2nd'''~~ factors as 2<sup>8</sup>/3<sup>5</sup>, is about 90.2 [[cent]]s in size~~, and is the [[diatonic semitone]] in [[Pythagorean tuning]]~~. It can be generated by stacking five [[4/3]] just perfect fourths and [[~~Octave~~ reduction\|octave-reducing]] the resulting interval, or equivalently by decreasing 4/3 by two [[9/8]] major seconds.		'''256/243''', the '''Pythagorean limma''' or '''Pythagorean diatonic semitone''', is the [[diatonic semitone]] in [[Pythagorean tuning]]. In other words, it is the [[3-limit]] minor second. It factors as 2<sup>8</sup>/3<sup>5</sup>, and is about 90.2 [[cent]]s in size. It can be generated by stacking five [[4/3]] just perfect fourths and [[octave reduction\|octave-reducing]] the resulting interval, or equivalently by decreasing 4/3 by two [[9/8]] major seconds. Unlike the situation in [[meantone]] tunings, it is smaller, not larger, than the corresponding [[chromatic semitone]], which is the Pythagorean augmented unison of [[2187/2048]].

	== Approximation ==		== Approximation ==
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	== Temperaments ==		== Temperaments ==
	When this ratio is taken as a comma to be tempered in the [[5-limit]], it produces the [[blackwood]] temperament, and it may be called the '''blackwood comma''', named after [[Easley Blackwood Jr]]. Edos tempering it out include [[5edo]], [[10edo]], [[15edo]], [[20edo]], [[25edo]] and [[30edo]]. See [[~~limmic~~ temperaments]] for a number of other temperaments where it is tempered out.		When this ratio is taken as a comma to be tempered in the [[5-limit]], it produces the [[blackwood]] temperament, and it may be called the '''blackwood comma''', named after [[Easley Blackwood Jr]]. Edos tempering it out include [[5edo]], [[10edo]], [[15edo]], [[20edo]], [[25edo]] and [[30edo]]. See [[Limmic temperaments]] for a number of other temperaments where it is tempered out.

	== Notation ==		== Notation ==

Squib at 13:44, 28 September 2025

2025-09-28T13:44:49Z

← Older revision		Revision as of 13:44, 28 September 2025
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	{{Wikipedia\| Semitone #Pythagorean tuning }}		{{Wikipedia\| Semitone #Pythagorean tuning }}

	The interval '''256/243''', the '''Pythagorean limma''' or '''Pythagorean diatonic semitone''' or the '''3-limit minor 2nd''' factors as 2<sup>8</sup>/3<sup>5</sup>, is about 90.2 [[cent]]s in size, and is the [[diatonic semitone]] in [[Pythagorean tuning]]. It can be generated by stacking five [[4/3]] just perfect fourths and [[Octave reduction\|octave-reducing]] the resulting interval.		The interval '''256/243''', the '''Pythagorean limma''' or '''Pythagorean diatonic semitone''' or the '''3-limit minor 2nd''' factors as 2<sup>8</sup>/3<sup>5</sup>, is about 90.2 [[cent]]s in size, and is the [[diatonic semitone]] in [[Pythagorean tuning]]. It can be generated by stacking five [[4/3]] just perfect fourths and [[Octave reduction\|octave-reducing]] the resulting interval, or equivalently by decreasing 4/3 by two [[9/8]] major seconds.

	== Approximation ==		== Approximation ==

FloraC: Undo revision 211131 by M1k1 H2tsun2 (talk)

2025-09-27T11:49:25Z

Undo revision 211131 by M1k1 H2tsun2 (talk)

← Older revision		Revision as of 11:49, 27 September 2025
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	}}		}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~Threerish minor second,~~ Pythagorean limma, Pythagorean diatonic semitone, 3-limit minor 2nd, blackwood comma		\| Name = Pythagorean limma, Pythagorean diatonic semitone, 3-limit minor 2nd, blackwood comma
	\| Color name = sw2, sawa 2nd		\| Color name = sw2, sawa 2nd
	\| Sound = jid_256_243_pluck_adu_dr220.mp3		\| Sound = jid_256_243_pluck_adu_dr220.mp3

M1k1 H2tsun2: add it in the first, rather than the other place.

2025-09-27T10:45:17Z

add it in the first, rather than the other place.

← Older revision		Revision as of 10:45, 27 September 2025
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	}}		}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = Pythagorean limma, Pythagorean diatonic semitone, 3-limit minor 2nd, blackwood comma		\| Name = Threerish minor second, Pythagorean limma, Pythagorean diatonic semitone, 3-limit minor 2nd, blackwood comma
	\| Color name = sw2, sawa 2nd		\| Color name = sw2, sawa 2nd
	\| Sound = jid_256_243_pluck_adu_dr220.mp3		\| Sound = jid_256_243_pluck_adu_dr220.mp3

FloraC: Recategorize (the name as a comma is blackwood comma)

2025-04-24T13:02:55Z

Recategorize (the name as a comma is *blackwood comma*)

← Older revision		Revision as of 13:02, 24 April 2025
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	[[Category:Semitone]]		[[Category:Semitone]]
	[[Category:Blackwood]]		[[Category:Blackwood]]
	~~[[Category:Commas named after polymaths]]~~
	~~[[Category:Commas named after controversial individuals]]~~
	[[Category:Commas named after composers]]		[[Category:Commas named after composers]]

TallKite: added a less jargon-y and more musical description for 256/243

2025-02-08T21:53:54Z

added a less jargon-y and more musical description for 256/243

← Older revision		Revision as of 21:53, 8 February 2025
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	}}		}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = Pythagorean limma, Pythagorean diatonic semitone, blackwood comma		\| Name = Pythagorean limma, Pythagorean diatonic semitone, 3-limit minor 2nd, blackwood comma
	\| Color name = sw2, sawa 2nd		\| Color name = sw2, sawa 2nd
	\| Sound = jid_256_243_pluck_adu_dr220.mp3		\| Sound = jid_256_243_pluck_adu_dr220.mp3
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	{{Wikipedia\| Semitone #Pythagorean tuning }}		{{Wikipedia\| Semitone #Pythagorean tuning }}

	The interval '''256/243''', the '''Pythagorean limma''', or '''Pythagorean diatonic semitone''' factors as 2<sup>8</sup>/3<sup>5</sup>, is about 90.2 [[cent]]s in size, and is the [[diatonic semitone]] in [[Pythagorean tuning]]. It can be generated by stacking five [[4/3]] just perfect fourths and [[Octave reduction\|octave-reducing]] the resulting interval.		The interval '''256/243''', the '''Pythagorean limma''' or '''Pythagorean diatonic semitone''' or the '''3-limit minor 2nd''' factors as 2<sup>8</sup>/3<sup>5</sup>, is about 90.2 [[cent]]s in size, and is the [[diatonic semitone]] in [[Pythagorean tuning]]. It can be generated by stacking five [[4/3]] just perfect fourths and [[Octave reduction\|octave-reducing]] the resulting interval.

	== Approximation ==		== Approximation ==

Hstraub: Link to German

2025-01-06T21:18:53Z

Link to German

← Older revision		Revision as of 21:18, 6 January 2025
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			{{interwiki
			\| de = 256/243
			\| en = 256/243
			\| es =
			\| ja =
			}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = Pythagorean limma, Pythagorean diatonic semitone, blackwood comma		\| Name = Pythagorean limma, Pythagorean diatonic semitone, blackwood comma

FloraC: /* Temperaments */ -ahistorical stuff

2024-11-21T10:30:09Z

Temperaments: -ahistorical stuff

← Older revision		Revision as of 10:30, 21 November 2024
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	== Temperaments ==		== Temperaments ==
	When this ratio is taken as a comma to be tempered in the [[5-limit]], it produces the [[blackwood]] temperament, and it may be called the '''blackwood comma'''~~. While the blackwood temperament is~~ named after Easley Blackwood Jr~~, it also coincidentally fits the naming scheme of the [[comptonesque~~]] ~~temperament collection, as Blackwood is the name of a settlement in the old versions of Pandora, a project by Vector~~. Edos tempering it out include [[5edo]], [[10edo]], [[15edo]], [[20edo]], [[25edo]] and [[30edo]]. See [[limmic temperaments]] for a number of other temperaments where it is tempered out.		When this ratio is taken as a comma to be tempered in the [[5-limit]], it produces the [[blackwood]] temperament, and it may be called the '''blackwood comma''', named after [[Easley Blackwood Jr]]. Edos tempering it out include [[5edo]], [[10edo]], [[15edo]], [[20edo]], [[25edo]] and [[30edo]]. See [[limmic temperaments]] for a number of other temperaments where it is tempered out.

	== Notation ==		== Notation ==

BudjarnLambeth at 00:14, 16 November 2024

2024-11-16T00:14:43Z

← Older revision		Revision as of 00:14, 16 November 2024
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	[[Category:Blackwood]]		[[Category:Blackwood]]
	[[Category:Commas named after polymaths]]		[[Category:Commas named after polymaths]]
			[[Category:Commas named after controversial individuals]]
	[[Category:Commas named after composers]]		[[Category:Commas named after composers]]