Cathartic - Revision history

FloraC: There's little interesting things left here. Merge into the data page

2026-08-10T14:32:13Z

There's little interesting things left here. Merge into the data page

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-The '''cathartic''' temperament is a rank-3 [[regular temperament]] for the 2.3.5.7.17.19 [[subgroup]] (or any immediate restrictions thereof), defined by [[tempering out]] [[1216/1215]], [[1225/1224]], and [[1445/1444]]. It is generated by a perfect fifth (~[[3/2]]) and an ultramajor second (~[[81/70]]). It is first found and explored by [[Flora Canou]].
+#redirect [[Cathartic family #Cathartic]]
 [[Category:Cathartic| ]] <!-- main article -->
 [[Category:Rank-3 temperaments]]
 [[Category:Cathartic family]]

FloraC: FloraC moved page Canou to Cathartic: Rename (see talk at Cathartic family)

2026-08-10T12:51:58Z

FloraC moved page Canou to Cathartic: Rename (see talk at Cathartic family)

← Older revision	Revision as of 12:51, 10 August 2026
(No difference)

FloraC: Initiate the rename (see talk at Cathartic family)

2026-08-10T12:51:40Z

Initiate the rename (see talk at Cathartic family)

← Older revision		Revision as of 12:51, 10 August 2026
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	The '''~~canou~~''' temperament is a rank-3 [[regular temperament]] for the 2.3.5.7.17.19 [[subgroup]] (or any immediate restrictions thereof), defined by [[tempering out]] [[1216/1215]], [[1225/1224]], and [[1445/1444]]. It is generated by a perfect fifth (~[[3/2]]) and an ultramajor second (~[[81/70]]). It is first found and explored by [[Flora Canou]].		The '''cathartic''' temperament is a rank-3 [[regular temperament]] for the 2.3.5.7.17.19 [[subgroup]] (or any immediate restrictions thereof), defined by [[tempering out]] [[1216/1215]], [[1225/1224]], and [[1445/1444]]. It is generated by a perfect fifth (~[[3/2]]) and an ultramajor second (~[[81/70]]). It is first found and explored by [[Flora Canou]].

	See [[~~Canou~~ family #~~Canou~~]] for more technical data.		See [[Cathartic family #Cathartic]] for more technical data.

	== Overview ==		== Overview ==
	The temperament was at first discovered as [[7-limit]] only, where it tempers out the [[~~canousma~~]], 4802000/4782969 = {{monzo\| 4 -14 3 4 }}. It passes as a [[microtemperament]] with the [[9-odd-limit]] [[~~Minimax~~ tuning\|minimax]] error of 0.98[[¢]] (1/7 ~~canousma~~). Extending it to the 2.3.5.7.17.19 subgroup adds virtually no additional error as the number of minimax error is also characteristic of the [[tonality diamond]] of {1, 3, 5, 7, 9, 15, 17, 19, 21}.		The temperament was at first discovered as [[7-limit]] only, where it tempers out the [[cathartic comma]], 4802000/4782969 = {{monzo\| 4 -14 3 4 }}. It passes as a [[microtemperament]] with the [[9-odd-limit]] [[minimax tuning\|minimax]] error of 0.98[[¢]] (1/7 cathartic comma). Extending it to the 2.3.5.7.17.19 subgroup adds virtually no additional error as the number of minimax error is also characteristic of the [[tonality diamond]] of {1, 3, 5, 7, 9, 15, 17, 19, 21}.

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	\|}		\|}

	The password equates 19/15 with 81/64, 20/19 with 256/243, and 81/80 with 76/75. It characterizes the temperament with a counterpyth fifth and enables 19-odd-limit essentially tempered chords. The aureusma splits the 5/4 major third into a stack of two 19/17's and enables 19-odd-limit essentially tempered chords. The noema equates 35/34 with 36/35 and enables 25-odd-limit essentially tempered chords. Finally, ~~canou~~ tempers out 165376/165375, the decimillisma, the difference between 1216/1215 and 1225/1224.		The password equates 19/15 with 81/64, 20/19 with 256/243, and 81/80 with 76/75. It characterizes the temperament with a counterpyth fifth and enables 19-odd-limit essentially tempered chords. The aureusma splits the 5/4 major third into a stack of two 19/17's and enables 19-odd-limit essentially tempered chords. The noema equates 35/34 with 36/35 and enables 25-odd-limit essentially tempered chords. Finally, cathartic tempers out 165376/165375, the decimillisma, the difference between 1216/1215 and 1225/1224.

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	== Scales ==		== Scales ==
	{{Main\| ~~Canou~~ scales }}		{{Main\| Cathartic scales }}

	Fokker blocks of 9, 14 and 19 tones are among the most useful ~~canou~~ scales.		Fokker blocks of 9, 14 and 19 tones are among the most useful cathartic scales.

	[[Category:~~Canou~~\| ]] <!-- main article -->		[[Category:Cathartic\| ]] <!-- main article -->
	[[Category:Rank-3 temperaments]]		[[Category:Rank-3 temperaments]]
	[[Category:~~Canou~~ family]]		[[Category:Cathartic family]]

Overthink: /* Overview */ avoid subgroup notation

2026-01-09T05:52:50Z

Overview: avoid subgroup notation

← Older revision		Revision as of 05:52, 9 January 2026
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	== Overview ==		== Overview ==
	The temperament was at first discovered as [[7-limit]] only, where it tempers out the [[canousma]], 4802000/4782969 = {{monzo\| 4 -14 3 4 }}. It passes as a [[microtemperament]] with the [[9-odd-limit]] [[Minimax tuning\|minimax]] error of 0.98[[¢]] (1/7 canousma). Extending it to the 2.3.5.7.17.19 subgroup adds virtually no additional error as the number of minimax error is also characteristic of the [[tonality diamond]] of 1.3.5.7.9.15.17.19.21.		The temperament was at first discovered as [[7-limit]] only, where it tempers out the [[canousma]], 4802000/4782969 = {{monzo\| 4 -14 3 4 }}. It passes as a [[microtemperament]] with the [[9-odd-limit]] [[Minimax tuning\|minimax]] error of 0.98[[¢]] (1/7 canousma). Extending it to the 2.3.5.7.17.19 subgroup adds virtually no additional error as the number of minimax error is also characteristic of the [[tonality diamond]] of {1, 3, 5, 7, 9, 15, 17, 19, 21}.

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	:''— It sounds somewhat like a Phrygian scale but the abundance of small intervals of [[28/27]] makes it melodically active.''		:''— It sounds somewhat like a Phrygian scale but the abundance of small intervals of [[28/27]] makes it melodically active.''

	14- and 19-note scales are also highly concise for the temperament. See [[#scales]] for more information.		14- and 19-note scales are also highly concise for the temperament. See [[#scales]] for more information.

	== Interval lattice ==		== Interval lattice ==

FloraC: - parent category

2025-04-29T09:52:55Z

- parent category

← Older revision		Revision as of 09:52, 29 April 2025
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	Fokker blocks of 9, 14 and 19 tones are among the most useful canou scales.		Fokker blocks of 9, 14 and 19 tones are among the most useful canou scales.

	~~[[Category:Temperaments]]~~
	[[Category:Canou\| ]] <!-- main article -->		[[Category:Canou\| ]] <!-- main article -->
	[[Category:Rank-3 temperaments]]		[[Category:Rank-3 temperaments]]
	[[Category:Canou family]]		[[Category:Canou family]]

FloraC: FloraC moved page Canou temperament to Canou: Follow similar pages

2025-04-20T13:03:23Z

FloraC moved page Canou temperament to Canou: Follow similar pages

← Older revision	Revision as of 13:03, 20 April 2025
(No difference)

Lériendil at 23:01, 19 April 2025

2025-04-19T23:01:21Z

← Older revision		Revision as of 23:01, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Canou\| ]] <!-- main article -->		[[Category:Canou\| ]] <!-- main article -->
			[[Category:Rank-3 temperaments]]
	[[Category:Canou family]]		[[Category:Canou family]]

FloraC: Undo revision 109201 by BudjarnLambeth (talk) (that category is for rank-2 temps)

2023-04-25T12:29:20Z

Undo revision 109201 by BudjarnLambeth (talk) (that category is for rank-2 temps)

← Older revision		Revision as of 12:29, 25 April 2023
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	[[Category:Canou\| ]] <!-- main article -->		[[Category:Canou\| ]] <!-- main article -->
	[[Category:Canou family]]		[[Category:Canou family]]
	~~[[Category:Canousmic temperaments]]~~

BudjarnLambeth: Added 1 category

2023-04-25T10:10:42Z

Added 1 category

← Older revision		Revision as of 10:10, 25 April 2023
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	[[Category:Canou\| ]] <!-- main article -->		[[Category:Canou\| ]] <!-- main article -->
	[[Category:Canou family]]		[[Category:Canou family]]
			[[Category:Canousmic temperaments]]

FloraC: /* Interval lattice */

2022-09-07T20:21:59Z

Interval lattice

← Older revision		Revision as of 20:21, 7 September 2022
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	<gallery>		<gallery>
	File:Lattice Orthocanousmic.png		File:Lattice Orthocanousmic.png
			File:Lattice Orthocanousmic Rearranged.png
	</gallery>		</gallery>