250/243 - Revision history

Lucius Chiaraviglio: /* Approximation */ 24edo itself does not qualify as a chromium tuning

2026-05-28T02:17:52Z

Approximation: 24edo itself does not qualify as a chromium tuning

← Older revision		Revision as of 02:17, 28 May 2026
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	== Approximation ==		== Approximation ==
	250/243 is very close to one step of [[24edo]], which is the quarter tone that is exactly the half of [[12edo]] semitone. Therefore, if 250/243 is not tempered and instead is treated as an identity where it is equated with 1/24th of the octave, it serves as the period in the [[chromium]] temperament. Thus in the framework of this temperament and the tuning systems associated with it, [[Eliora]] proposes the name ''chromium quartertone''.		250/243 is very close to one step of [[24edo]], which is the quarter tone that is exactly the half of [[12edo]] semitone. Therefore, if 250/243 is not tempered and instead is treated as an identity where it is equated with 1/24th of the octave, it serves as the period in the [[chromium]] temperament. (However, note that 24edo itself maps 250/243 inconsistently, and so chromium temperament starts at [[72edo]].) Thus in the framework of this temperament and the tuning systems associated with it, [[Eliora]] proposes the name ''chromium quartertone''.

	[[Category:Porcupine]]		[[Category:Porcupine]]
	[[Category:Commas named after compositions]]		[[Category:Commas named after compositions]]

TallKite: updated the comma color name

2026-04-29T04:07:41Z

updated the comma color name

← Older revision		Revision as of 04:07, 29 April 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = porcupine comma, maximal diesis		\| Name = porcupine comma, maximal diesis
	\| Color name = y<sup>3</sup>1, triyo 1sn,<br>~~Triyo comma~~		\| Color name = y<sup>3</sup>1, triyo 1sn,<br>y<sup>3</sup>M, triyoma
	\| Comma = yes		\| Comma = yes
	}}		}}

Eliora: start by mentioning first how 250/243 is close to 24edo step, then explain chromium

2025-03-14T02:03:35Z

start by mentioning first how 250/243 is close to 24edo step, then explain chromium

← Older revision		Revision as of 02:03, 14 March 2025
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	== Approximation ==		== Approximation ==
	~~If we do~~ not ~~temper out this interval~~ and instead ~~use it~~ as an identity of ~~some sort~~, it serves as the period in the [[chromium]] temperament~~, where it is mapped to 1/24th of the octave - exact quarter-tone or half a standard semitone~~. Thus in the framework of this temperament and the tuning systems associated with it, [[Eliora]] proposes the name ''chromium quartertone''.		250/243 is very close to one step of [[24edo]], which is the quarter tone that is exactly the half of [[12edo]] semitone. Therefore, if 250/243 is not tempered and instead is treated as an identity where it is equated with 1/24th of the octave, it serves as the period in the [[chromium]] temperament. Thus in the framework of this temperament and the tuning systems associated with it, [[Eliora]] proposes the name ''chromium quartertone''.

	[[Category:Porcupine]]		[[Category:Porcupine]]
	[[Category:Commas named after compositions]]		[[Category:Commas named after compositions]]

Eliora: explain how it's a niche use of the name I proposed

2025-03-14T02:01:44Z

explain how it's a niche use of the name I proposed

← Older revision		Revision as of 02:01, 14 March 2025
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	== Approximation ==		== Approximation ==
	If we do not temper out this interval and instead use it as an identity of some sort, it serves as the period in the [[chromium]] temperament, where it is mapped to 1/24th of the octave. Thus [[Eliora]] proposes the name ''chromium quartertone''.		If we do not temper out this interval and instead use it as an identity of some sort, it serves as the period in the [[chromium]] temperament, where it is mapped to 1/24th of the octave - exact quarter-tone or half a standard semitone. Thus in the framework of this temperament and the tuning systems associated with it, [[Eliora]] proposes the name ''chromium quartertone''.

	[[Category:Porcupine]]		[[Category:Porcupine]]
	[[Category:Commas named after compositions]]		[[Category:Commas named after compositions]]

ArrowHead294 at 01:54, 4 December 2024

2024-12-04T01:54:26Z

← Older revision		Revision as of 01:54, 4 December 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''250/243''' is known as the '''porcupine comma''' or the '''maximal diesis'''. Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9\|minor whole tones]] exceed a minor third, that is, (10/9)<sup>2</sup>/(6/5). It is also the difference between [[25/24]] and [[81/80]], the two smallest [[5-limit]] [[superparticular]] ratios, and between three syntonic commas and the [[2187/2048\|Pythagorean apotome]], putting it on the [[Syntonic-chromatic equivalence continuum]].		'''250/243''' is known as the '''porcupine comma''' or the '''maximal diesis'''. Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9\|minor whole tones]] exceed a minor third, that is, (10/9)<sup>2</sup>/(6/5). It is also the difference between [[25/24]] and [[81/80]], the two smallest [[5-limit]] [[superparticular]] ratios, and between three syntonic commas and the [[2187/2048\|Pythagorean apotome]], putting it on the [[Syntonic–chromatic equivalence continuum]].

	== Temperaments ==		== Temperaments ==

BudjarnLambeth at 07:18, 3 November 2024

2024-11-03T07:18:02Z

← Older revision		Revision as of 07:18, 3 November 2024
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	[[Category:Porcupine]]		[[Category:Porcupine]]
			[[Category:Commas named after compositions]]

ArrowHead294 at 23:12, 17 August 2024

2024-08-17T23:12:15Z

← Older revision		Revision as of 23:12, 17 August 2024
Line 10:		Line 10:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''250/243''' is known as the '''porcupine comma''' or the '''maximal diesis'''. Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9\|minor whole tones]] exceed a minor third, that is, (10/9)<sup>2</sup>/(6/5). It is also the difference between [[25/24]] and [[81/80]], the two smallest [[5-limit]] [[superparticular]] ratios, and an [[apotome]] ~~minus three syntonic commas~~, putting it on the [[Syntonic-chromatic equivalence continuum]].		'''250/243''' is known as the '''porcupine comma''' or the '''maximal diesis'''. Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9\|minor whole tones]] exceed a minor third, that is, (10/9)<sup>2</sup>/(6/5). It is also the difference between [[25/24]] and [[81/80]], the two smallest [[5-limit]] [[superparticular]] ratios, and between three syntonic commas and the [[2187/2048\|Pythagorean apotome]], putting it on the [[Syntonic-chromatic equivalence continuum]].

	== Temperaments ==		== Temperaments ==

Yourmusic Productions: More relationships.

2023-10-01T10:04:02Z

More relationships.

← Older revision		Revision as of 10:04, 1 October 2023
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''250/243''' is known as the '''porcupine comma''' or the '''maximal diesis'''. Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9\|minor whole tones]] exceed a minor third, that is, (10/9)<sup>2</sup>/(6/5).		'''250/243''' is known as the '''porcupine comma''' or the '''maximal diesis'''. Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9\|minor whole tones]] exceed a minor third, that is, (10/9)<sup>2</sup>/(6/5). It is also the difference between [[25/24]] and [[81/80]], the two smallest [[5-limit]] [[superparticular]] ratios, and an [[apotome]] minus three syntonic commas, putting it on the [[Syntonic-chromatic equivalence continuum]].

	== Temperaments ==		== Temperaments ==

TallKite at 20:39, 11 January 2023

2023-01-11T20:39:35Z

← Older revision		Revision as of 20:39, 11 January 2023
Line 7:		Line 7:
	{{Infobox Interval		{{Infobox Interval
	\| Name = porcupine comma, maximal diesis		\| Name = porcupine comma, maximal diesis
	\| Color name = y<sup>3</sup>1, Triyo comma		\| Color name = y<sup>3</sup>1, triyo 1sn,<br>Triyo comma
	\| Comma = yes		\| Comma = yes
	}}		}}

FloraC: De-bold the neologism. The original names are pretty established and not subject to changes. Section into "temperaments" and "approximation"

2022-11-06T02:24:26Z

De-bold the neologism. The original names are pretty established and not subject to changes. Section into "temperaments" and "approximation"

← Older revision		Revision as of 02:24, 6 November 2022
Line 10:		Line 10:
	\| Comma = yes		\| Comma = yes
	}}		}}
			'''250/243''' is known as the '''porcupine comma''' or the '''maximal diesis'''. Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9\|minor whole tones]] exceed a minor third, that is, (10/9)<sup>2</sup>/(6/5).

	~~'''250/243''' is known as~~ the ~~'''~~porcupine ~~comma,''' '''maximal diesis''' or~~ the ~~'''chromium quartertone'''~~.		== Temperaments ==
			Tempering it out leads to the [[5-limit]] [[porcupine]] temperament. See [[porcupine family]] for the family of rank-2 temperaments where it is tempered out.

	== ~~Theory~~ ==		== Approximation ==
	~~Measuring about 49{{cent}},~~ it ~~is a [[medium comma]]. It is the amount by which two [[10/9\|minor whole tones]] exceed a minor third~~, ~~that is, (10/9)<sup>2</sup>/(6/5). Tempering~~ it ~~out leads to [[5-limit]] [[Porcupine family\|porcupine temperament]].~~		If we do not temper out this interval and instead use it as an identity of some sort, it serves as the period in the [[chromium]] temperament, where it is mapped to 1/24th of the octave. Thus [[Eliora]] proposes the name ''chromium quartertone''.

	It serves as a period in the [[chromium]] temperament, where it is mapped to 1/24th of the octave.

	[[Category:Porcupine]]		[[Category:Porcupine]]

	~~{{todo\|improve layout}}~~