Well temperament - Revision history

BudjarnLambeth at 12:06, 26 June 2026

2026-06-26T12:06:35Z

← Older revision		Revision as of 12:06, 26 June 2026
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	{{Wikipedia\|Well temperament}}		{{Wikipedia\|Well temperament}}
	A '''well temperament''' (or '''circulating temperament''') is a [[tuning system]] which is regarded as an approximation of an [[equal tuning]], has the same [[equave]] as that equal tuning and preserves the transposability of the equal tuning, but is not exactly the equal tuning being approximated. Historical well temperaments were formed by stacking a combination of pure [[3/2]] and flattened fifths (occasionally also sharpened fifths) and had 12 nearly equal steps.		A '''well temperament''' (or '''circulating temperament''') is a [[tuning system]] which is regarded as an approximation of an [[equal tuning]], has the same [[equave]] as that equal tuning and preserves the transposability of the equal tuning (every key is still 'good enough'), but it is not exactly the equal tuning being approximated. Historical well temperaments were formed by stacking a combination of pure [[3/2]] and flattened fifths (occasionally also sharpened fifths) and had 12 nearly equal steps.

	One of the advantages of these tunings is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.		One of the advantages of these tunings is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.

Tyler Henthorn at 20:18, 24 June 2026

2026-06-24T20:18:17Z

← Older revision		Revision as of 20:18, 24 June 2026
Line 1:		Line 1:
	{{Wikipedia\|Well temperament}}		{{Wikipedia\|Well temperament}}
	A '''well temperament''' (or '''circulating temperament''') is a [[tuning system]] which is regarded as an approximation of an [[equal tuning]], has the same [[equave]] as that equal tuning and preserves the transposability of the equal tuning, but is not exactly the equal tuning being approximated. Historical well temperaments were formed by stacking a combination of pure [[3/2]] and flattened fifths (occasionally also sharpened fifths) and had 12 nearly equal steps.		A '''well temperament''' (or '''circulating temperament''') is a [[tuning system]] which is regarded as an approximation of an [[equal tuning]], has the same [[equave]] as that equal tuning and preserves the transposability of the equal tuning, but is not exactly the equal tuning being approximated. Historical well temperaments were formed by stacking a combination of pure [[3/2]] and flattened fifths (occasionally also sharpened fifths) and had 12 nearly equal steps.

	One of the advantages of these tunings is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.		One of the advantages of these tunings is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.

Lucius Chiaraviglio: occasionally also sharpened fifths

2026-06-24T06:43:17Z

occasionally also sharpened fifths

← Older revision		Revision as of 06:43, 24 June 2026
Line 1:		Line 1:
	{{Wikipedia\|Well temperament}}		{{Wikipedia\|Well temperament}}
	A '''well temperament''' (or '''circulating temperament''') is a [[tuning system]] which is regarded as an approximation of an [[equal tuning]], has the same [[equave]] as that equal tuning and preserves the transposability of the equal tuning, but is not exactly the equal tuning being approximated. Historical well temperaments were formed by stacking a combination of pure [[3/2]] and flattened fifths and had 12 nearly equal steps.		A '''well temperament''' (or '''circulating temperament''') is a [[tuning system]] which is regarded as an approximation of an [[equal tuning]], has the same [[equave]] as that equal tuning and preserves the transposability of the equal tuning, but is not exactly the equal tuning being approximated. Historical well temperaments were formed by stacking a combination of pure [[3/2]] and flattened fifths (occasionally also sharpened fifths) and had 12 nearly equal steps.

	One of the advantages of these tunings is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.		One of the advantages of these tunings is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.

Fredg999: Add (Vincenzo) Galilei's tuning

2025-08-07T19:03:00Z

Add (Vincenzo) Galilei's tuning

← Older revision		Revision as of 19:03, 7 August 2025
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	# six tempered fifths (C–G, D–A, E–B, F–C, G–D and A–E) are flat by 1/6 Pythagorean comma		# six tempered fifths (C–G, D–A, E–B, F–C, G–D and A–E) are flat by 1/6 Pythagorean comma
	# six pure fifths		# six pure fifths

			* [[Galilei's tuning]]
			# eleven [[18/17]] (~99{{cent}}) semitones
			# one (2/1)/(18/17)<sup>11</sup> (~111.5{{cent}}) semitone (B-C)

	== Classification by approaches ==		== Classification by approaches ==

VectorGraphics at 04:48, 23 April 2025

2025-04-23T04:48:30Z

← Older revision		Revision as of 04:48, 23 April 2025
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	# seven [[3/2\|pure]] fifths		# seven [[3/2\|pure]] fifths

	* [[Werck3]] – Werckmeister temperament III		* [[Werck3\|Werckmeister III]] – Werckmeister temperament III
	# four tempered fifths (C–G, D–A, G–D and B–F#) are tuned flat by 1/4 comma (''Werckmeister did not specify whether the syntonic or [[pythagorean comma\|Pythagorean]] comma should be used, so either is acceptable'')		# four tempered fifths (C–G, D–A, G–D and B–F#) are tuned flat by 1/4 comma (''Werckmeister did not specify whether the syntonic or [[pythagorean comma\|Pythagorean]] comma should be used, so either is acceptable'')
	# eight [[3/2\|pure]] fifths		# eight [[3/2\|pure]] fifths

Lériendil: deleted the mmtm stuff

2025-04-13T15:14:02Z

deleted the mmtm stuff

@@ Line 79: / Line 79: @@
 == Relation to regular temperaments ==
 Through the lens of regular temperament theory, a well temperament can be viewed as a result of applying an irregular [[tuning map]] to the abstract intervals of an [[equal temperament]] (i.e. a rank-1 abstract regular temperament), though tuning maps in the technical sense are defined to be regular. However, note that when nejis are considered well temperaments in this sense, the JI ratios the intervals are said to represent and the actual JI ratios of the neji tuning must be distinguished, and the JI ratios that occur in the neji should not be assumed to be consistent with the val.
 == External links ==

Sintel: remove MMTM-isms

2025-03-31T16:05:23Z

remove MMTM-isms

← Older revision		Revision as of 16:05, 31 March 2025
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	* [[Map of Syntonic well temperaments]]		* [[Map of Syntonic well temperaments]]
	* [[Map of tritave well temperaments]]		* [[Map of tritave well temperaments]]

	~~== Other near-equal scales ==~~
	* [[Teleic scales]] – unit step generator, patent tuning alternating [[EdVII\|ed(16/9)]] and ed(9/8)
	* [[Kartvelian scales]] – unit step generator, alternating [[EDF\|edf]] and [[EdIV\|ed(4/3)]]
	* [[Well tempered nonet]]
	* [[Daseian scales]] - unit step generator, patent tuning alternating [[EDO\|edo]]-edo-*[[EDF\|edf]]

	== External links ==		== External links ==

BudjarnLambeth: Add links to orphaned pages

2024-12-02T00:06:47Z

Add links to orphaned pages

@@ Line 79: / Line 79: @@
 == Relation to regular temperaments ==
 Through the lens of regular temperament theory, a well temperament can be viewed as a result of applying an irregular [[tuning map]] to the abstract intervals of an [[equal temperament]] (i.e. a rank-1 abstract regular temperament), though tuning maps in the technical sense are defined to be regular. However, note that when nejis are considered well temperaments in this sense, the JI ratios the intervals are said to represent and the actual JI ratios of the neji tuning must be distinguished, and the JI ratios that occur in the neji should not be assumed to be consistent with the val.
 == Other near-equal scales ==

TallKite: added that well temps are irregular temps

2024-11-08T02:30:36Z

added that well temps are irregular temps

← Older revision		Revision as of 02:30, 8 November 2024
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	One of the advantages of these tunings is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.		One of the advantages of these tunings is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.

	Despite their sharing the word "temperament" in their names, well temperaments and the modern notion of [[regular temperament]]s are two different concepts, ~~though~~ sometimes one can guide construction of the other.		Despite their sharing the word "temperament" in their names, well temperaments and the modern notion of [[regular temperament]]s are two different concepts. In fact, a well temperament is an ''ir''regular temperament. But sometimes one can guide construction of the other.

	== Historical well temperaments ==		== Historical well temperaments ==

Lériendil: section linked to a series of obscure tables w/ no explanation; deemed unnecessary and likely confusing to beginner readers

2024-10-30T13:40:22Z

section linked to a series of obscure tables w/ no explanation; deemed unnecessary and likely confusing to beginner readers

← Older revision		Revision as of 13:40, 30 October 2024
Line 79:		Line 79:
	== Relation to regular temperaments ==		== Relation to regular temperaments ==
	Through the lens of regular temperament theory, a well temperament can be viewed as a result of applying an irregular [[tuning map]] to the abstract intervals of an [[equal temperament]] (i.e. a rank-1 abstract regular temperament), though tuning maps in the technical sense are defined to be regular. However, note that when nejis are considered well temperaments in this sense, the JI ratios the intervals are said to represent and the actual JI ratios of the neji tuning must be distinguished, and the JI ratios that occur in the neji should not be assumed to be consistent with the val.		Through the lens of regular temperament theory, a well temperament can be viewed as a result of applying an irregular [[tuning map]] to the abstract intervals of an [[equal temperament]] (i.e. a rank-1 abstract regular temperament), though tuning maps in the technical sense are defined to be regular. However, note that when nejis are considered well temperaments in this sense, the JI ratios the intervals are said to represent and the actual JI ratios of the neji tuning must be distinguished, and the JI ratios that occur in the neji should not be assumed to be consistent with the val.

	~~== Maps of well temperaments ==~~
	* [[Map of 9&11 well temperaments]]
	* [[Map of Maviloid well temperaments]]
	* [[Map of Porcupine well temperaments]]
	* [[Map of Syntonic well temperaments]]
	* [[Map of pentave well temperaments]]
	* [[Map of tritave well temperaments]]

	== Other near-equal scales ==		== Other near-equal scales ==

← Older revision		Revision as of 04:48, 23 April 2025
Line 23:		Line 23:
	# seven [[3/2\|pure]] fifths		# seven [[3/2\|pure]] fifths

	* [[Werck3]] – Werckmeister temperament III		* [[Werck3\|Werckmeister III]] – Werckmeister temperament III
	# four tempered fifths (C–G, D–A, G–D and B–F#) are tuned flat by 1/4 comma (''Werckmeister did not specify whether the syntonic or [[pythagorean comma\|Pythagorean]] comma should be used, so either is acceptable'')		# four tempered fifths (C–G, D–A, G–D and B–F#) are tuned flat by 1/4 comma (''Werckmeister did not specify whether the syntonic or [[pythagorean comma\|Pythagorean]] comma should be used, so either is acceptable'')
	# eight [[3/2\|pure]] fifths		# eight [[3/2\|pure]] fifths