24th-octave temperaments - Revision history

FloraC: Switch to Sintel's badness, WE & CWE tunings

2026-05-15T11:47:36Z

Switch to Sintel's badness, WE & CWE tunings

← Older revision		Revision as of 11:47, 15 May 2026
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	== Chromium (5-limit) ==		== Chromium (5-limit) ==
	{{Main\|Chromium}}		{{Main\| Chromium }}
	~~The chromium temperament is defined by equating a stack of 24 [[256/243\|porcupine commas]] with the octave. In 7-limit and higher~~, see [[Landscape microtemperaments#Chromium]].		: ''For extensions, see [[Landscape microtemperaments #Chromium]].''

	~~Subgroup: 2~~.~~3.5~~		The chromium temperament is defined by equating a stack of twenty-four [[250/243\|porcupine commas]] with the octave.

	~~Comma list~~: ~~{{monzo\|-23 120 -72}}~~		[[Subgroup]]: 2.3.5

	{{~~mapping~~\|~~legend=1\|24 37 54\|0 3 5~~}}		[[Comma list]]: {{monzo\| -23 120 -72 }}

	: mapping generators: ~~~256~~/243 ~~= 1\24~~, ~~109418989131512359209/76293945312500000000 = 617.287~~		{{mapping\|legend=1\| 24 1 -6 \| 0 3 5 }}
			: mapping generators: ~250/243, ~{{monzo\| -8 42 -25 }}

	[[~~Support~~]]~~ing~~ [[ET]]s: {{~~EDOs~~\|72, ~~480, 552, 624, 696, 768, 1320~~}}, ...		[[Optimal tuning]]s:
			* [[WE]]: ~250/243 = 50.0000{{c}}, ~{{monzo\| -8 42 -25 }} = 617.2852{{c}}
			: [[error map]]: {{val\| +0.007 -0.093 +0.120 }}
			* [[CWE]]: ~250/243 = 50.0000{{c}}, ~{{monzo\| -8 42 -25 }} = 617.2852{{c}}
			: error map: {{val\| 0.000 -0.099 +0.112 }}

	Badness: ~~0.36784~~		{{Optimal ET sequence\|legend=1\| 72, …, 480, 552, 624, 1320, 1944 }}

			[[Badness]] (Sintel): 169

	{{Navbox fractional-octave}}		{{Navbox fractional-octave}}

2026-05-15T11:41:19Z

Update links

← Older revision		Revision as of 11:41, 15 May 2026
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	Temperaments discussed elswhere include:		Temperaments discussed elswhere include:
			* ''[[Hours]]'' → [[Compton family #Hours\|Compton family]]
	* ''Hours'', → [[Compton family#Hours\|Compton family]]		* ''[[Rabic]]'' → [[Rastmic rank-3 clan #Rabic\|Rastmic rank-3 clan]]
	* ''Rabic'', → [[~~Alphaxenic~~ rank ~~three~~ clan#Rabic\|~~Alphaxenic~~ rank ~~three~~ clan]]

	== Chromium (5-limit) ==		== Chromium (5-limit) ==

2025-02-14T03:55:06Z

← Older revision		Revision as of 03:55, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|24}}		{{Infobox fractional-octave\|24}}
	24edo is otherwise known as the [[quartertone]] tuning, so 24th-octave [[temperament]]s include temperaments where the [[period]] is any [[interval]] which is considered a quartertone.		24edo is otherwise known as the [[quartertone]] tuning, so 24th-octave [[temperament]]s include temperaments where the [[period]] is any [[interval]] which is considered a quartertone.

2024-12-24T05:18:22Z

← Older revision		Revision as of 05:18, 24 December 2024
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	{{Fractional-octave navigation\|24}}		{{Fractional-octave navigation\|24}}
	24edo is otherwise known as the [[quartertone]] tuning, so 24th-octave [[temperament]]s include temperaments where the [[period]] is any [[interval]] which is considered a [[quartertone]].		24edo is otherwise known as the [[quartertone]] tuning, so 24th-octave [[temperament]]s include temperaments where the [[period]] is any [[interval]] which is considered a quartertone.

	Temperaments discussed elswhere include:		Temperaments discussed elswhere include:

2024-12-24T05:18:06Z

Links

← Older revision		Revision as of 05:18, 24 December 2024
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	{{Fractional-octave navigation\|24}}		{{Fractional-octave navigation\|24}}
	24edo is otherwise known as the quartertone tuning, so 24th-octave ~~temperaments~~ include temperaments where the period is any interval which is considered a quartertone.		24edo is otherwise known as the [[quartertone]] tuning, so 24th-octave [[temperament]]s include temperaments where the [[period]] is any [[interval]] which is considered a [[quartertone]].

	Temperaments discussed elswhere include:		Temperaments discussed elswhere include:

2024-12-05T07:21:36Z

navbox

2023-07-07T23:17:46Z

← Older revision		Revision as of 23:17, 7 July 2023
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	{{Fractional-octave navigation\|24}}		{{Fractional-octave navigation\|24}}
	24edo is otherwise known as the quartertone tuning, so 24th-octave temperaments include temperaments where the period is any interval which is considered a quartertone.		24edo is otherwise known as the quartertone tuning, so 24th-octave temperaments include temperaments where the period is any interval which is considered a quartertone.

			Temperaments discussed elswhere include:

			* ''Hours'', → [[Compton family#Hours\|Compton family]]
			* ''Rabic'', → [[Alphaxenic rank three clan#Rabic\|Alphaxenic rank three clan]]

	== Chromium (5-limit) ==		== Chromium (5-limit) ==

2023-07-07T23:15:29Z

Chromium (5-limit)

2023-07-07T15:41:03Z

redundant check

← Older revision		Revision as of 15:41, 7 July 2023
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	Badness: 0.36784		Badness: 0.36784

	~~[[Category:24edo]]~~
	~~[[Category:Temperament collections]]~~

2023-07-07T15:10:08Z

← Older revision		Revision as of 15:10, 7 July 2023
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			{{Fractional-octave navigation\|24}}
	24edo is otherwise known as the quartertone tuning, so 24th-octave temperaments include temperaments where the period is any interval which is considered a quartertone.		24edo is otherwise known as the quartertone tuning, so 24th-octave temperaments include temperaments where the period is any interval which is considered a quartertone.
	~~{{Fractional-octave navigation\|24}}~~

	== Chromium (5-limit) ==		== Chromium (5-limit) ==