French sixth chord - Revision history

FloraC: Undo revision 176740 by MisterShafXen (talk). This was just false

2025-01-17T15:07:20Z

Undo revision 176740 by MisterShafXen (talk). This was just false

← Older revision		Revision as of 15:07, 17 January 2025
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	* [[72:90:100:125]], another possible interpretation of the meantone chord, is found in [[Euler-Fokker genus\|genus]] 3²·5³.		* [[72:90:100:125]], another possible interpretation of the meantone chord, is found in [[Euler-Fokker genus\|genus]] 3²·5³.

	== ~~In equal temperaments~~==		== See also ==

	~~12edo: 0 4 6 10, 0-400-600-1000c.~~		* [[Dominant seventh flat five chord]], a chord that is enharmonically equivalent to a French sixth in 12edo.

	~~17edo: 0 5 7 12, 0-353-494-847c.~~

	~~17b Val: 0 6 9 15, 0-424-635-1059c.~~
	~~==See also ==~~

	*[[Dominant seventh flat five chord]], a chord that is enharmonically equivalent to a French sixth in 12edo.

	[[Category:French sixth chords\| ]] <!-- main article -->		[[Category:French sixth chords\| ]] <!-- main article -->

MisterShafXen at 14:59, 17 January 2025

2025-01-17T14:59:44Z

← Older revision		Revision as of 14:59, 17 January 2025
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	* [[72:90:100:125]], another possible interpretation of the meantone chord, is found in [[Euler-Fokker genus\|genus]] 3²·5³.		* [[72:90:100:125]], another possible interpretation of the meantone chord, is found in [[Euler-Fokker genus\|genus]] 3²·5³.

	== ~~See also~~ ==		== In equal temperaments==

	* [[Dominant seventh flat five chord]], a chord that is enharmonically equivalent to a French sixth in 12edo.		12edo: 0 4 6 10, 0-400-600-1000c.

			17edo: 0 5 7 12, 0-353-494-847c.

			17b Val: 0 6 9 15, 0-424-635-1059c.
			==See also ==

			*[[Dominant seventh flat five chord]], a chord that is enharmonically equivalent to a French sixth in 12edo.

	[[Category:French sixth chords\| ]] <!-- main article -->		[[Category:French sixth chords\| ]] <!-- main article -->

Bcmills at 04:16, 8 September 2024

2024-09-08T04:16:05Z

← Older revision		Revision as of 04:16, 8 September 2024
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	* [[128:160:180:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at ♭II ({{Frac\|16\|15}}) and ♭VI ({{Frac\|8\|5}}) in the [[duodene]].		* [[128:160:180:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at ♭II ({{Frac\|16\|15}}) and ♭VI ({{Frac\|8\|5}}) in the [[duodene]].
	* [[72:90:100:125]], another possible interpretation of the meantone chord, is found in [[Euler-Fokker genus\|genus]] 3²·5³.		* [[72:90:100:125]], another possible interpretation of the meantone chord, is found in [[Euler-Fokker genus\|genus]] 3²·5³.

			== See also ==

			* [[Dominant seventh flat five chord]], a chord that is enharmonically equivalent to a French sixth in 12edo.

	[[Category:French sixth chords\| ]] <!-- main article -->		[[Category:French sixth chords\| ]] <!-- main article -->

Bcmills: direct link to Euler-Fokker genus

2024-08-31T01:27:51Z

direct link to Euler-Fokker genus

← Older revision		Revision as of 01:27, 31 August 2024
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	* [[128:160:180:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at ♭II ({{Frac\|16\|15}}) and ♭VI ({{Frac\|8\|5}}) in the [[duodene]].		* [[128:160:180:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at ♭II ({{Frac\|16\|15}}) and ♭VI ({{Frac\|8\|5}}) in the [[duodene]].
	* [[72:90:100:125]], another possible interpretation of the meantone chord, is found in [[genus]] 3²·5³.		* [[72:90:100:125]], another possible interpretation of the meantone chord, is found in [[Euler-Fokker genus\|genus]] 3²·5³.

	[[Category:French sixth chords\| ]] <!-- main article -->		[[Category:French sixth chords\| ]] <!-- main article -->

Bcmills at 18:13, 25 August 2024

2024-08-25T18:13:38Z

← Older revision		Revision as of 18:13, 25 August 2024
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	or [[20:25:28:35]] (step sizes 5/4, 28/25, and 5/4). Since the [[28/25]] interval in this chord also represents [[9/8]] in septimal meantone and [[marvel]], and [[10/9]] in septimal meantone and [[starling]], this chord is an [[essentially tempered chord]] in those temperaments in the [[9-odd-limit]].		or [[20:25:28:35]] (step sizes 5/4, 28/25, and 5/4). Since the [[28/25]] interval in this chord also represents [[9/8]] in septimal meantone and [[marvel]], and [[10/9]] in septimal meantone and [[starling]], this chord is an [[essentially tempered chord]] in those temperaments in the [[9-odd-limit]].

	<!-- Note: The close approximation of the 7-limit chord in meantone is specific to quarter-comma meantone. Many other meantones, such as 12edo and 19edo, do not approximate it nearly as closely, although they may nonetheless support the septimal meantone interpretation that unifies it with the French sixth. -->		<!-- Note: The close approximation of the 7-limit chord in meantone is specific to quarter-comma meantone. Many other meantones, such as 12edo and 19edo, do not approximate it nearly as closely, although they may nonetheless support the septimal meantone interpretation that unifies it with the French sixth. -->

Bcmills: /* In just intonation */

2024-08-24T14:01:30Z

In just intonation

← Older revision		Revision as of 14:01, 24 August 2024
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	* [[128:160:180:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at ♭II ({{Frac\|16\|15}}) and ♭VI ({{Frac\|8\|5}}) in the [[duodene]].		* [[128:160:180:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at ♭II ({{Frac\|16\|15}}) and ♭VI ({{Frac\|8\|5}}) in the [[duodene]].
	* [[72:90:100:125]] is another possible interpretation of the meantone chord, is found in [[genus]] 3²·5³.		* [[72:90:100:125]], another possible interpretation of the meantone chord, is found in [[genus]] 3²·5³.

	[[Category:French sixth chords\| ]] <!-- main article -->		[[Category:French sixth chords\| ]] <!-- main article -->

Bcmills: /* In just intonation */

2024-08-24T14:00:18Z

In just intonation

← Older revision		Revision as of 14:00, 24 August 2024
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	== In just intonation ==		== In just intonation ==

			In the [[7-limit]]:
			* [[20:25:28:35]] is a [[condissonant]] chord corresponding to an interpretation of the French sixth found in starling and marvel temperaments.

	In the [[5-limit]]:		In the [[5-limit]]:

	* [[128:160:180:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at ♭II ({{Frac\|16\|15}}) and ♭VI ({{Frac\|8\|5}}) in the [[duodene]].		* [[128:160:180:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at ♭II ({{Frac\|16\|15}}) and ♭VI ({{Frac\|8\|5}}) in the [[duodene]].
			* [[72:90:100:125]] is another possible interpretation of the meantone chord, is found in [[genus]] 3²·5³.

	[[Category:French sixth chords\| ]] <!-- main article -->		[[Category:French sixth chords\| ]] <!-- main article -->

Bcmills: mention both marvel and starling, since they temper the 7-limit chord to different 5-limit interpretations of the meantone chord

2024-08-24T13:15:34Z

mention both marvel and starling, since they temper the 7-limit chord to different 5-limit interpretations of the meantone chord

← Older revision		Revision as of 13:15, 24 August 2024
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	* ([[Septimal meantone chords\|Septimal meantone]]) 1 – 5/4 – 7/5 – 7/4		* ([[Septimal meantone chords\|Septimal meantone]]) 1 – 5/4 – 7/5 – 7/4

	or [[20:25:28:35]] (step sizes 5/4, 28/25, and 5/4). Since the [[28/25]] interval in this chord also represents [[10/9]], in septimal meantone (and~~, more generally, in~~ [[starling]] ~~temperaments)~~ this chord is an [[essentially tempered chord]] in the [[9-odd-limit]].		or [[20:25:28:35]] (step sizes 5/4, 28/25, and 5/4). Since the [[28/25]] interval in this chord also represents [[9/8]] in septimal meantone and [[marvel]], and [[10/9]] in septimal meantone and [[starling]], this chord is an [[essentially tempered chord]] in those temperaments in the [[9-odd-limit]].
	<!-- Note: The close approximation of the 7-limit chord is specific to quarter-comma meantone. Many other meantones, such as 12edo and 19edo, do not approximate it nearly as closely, although they may nonetheless support the septimal meantone interpretation that unifies it with the French sixth. -->
			<!-- Note: The close approximation of the 7-limit chord in meantone is specific to quarter-comma meantone. Many other meantones, such as 12edo and 19edo, do not approximate it nearly as closely, although they may nonetheless support the septimal meantone interpretation that unifies it with the French sixth. -->

	== In just intonation ==		== In just intonation ==

Bcmills: /* In temperaments */ clarify conventional / septimal meantone distinction; refer to starling instead of marvel for the general essentially-tempered chord (marvel doesn't get that close!)

2024-08-24T05:28:23Z

In temperaments: clarify conventional / septimal meantone distinction; refer to starling instead of marvel for the general essentially-tempered chord (marvel doesn't get that close!)

← Older revision		Revision as of 05:28, 24 August 2024
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	However, in the historically prevalent [[quarter-comma meantone]], the augmented sixth is tuned only a few cents shy of a just [[7/4]], and the augmented fourth is only a few cents shy of [[7/5]], so the meantone French sixth chord can be considered to also approximate the [[septimal meantone]] chord:		However, in the historically prevalent [[quarter-comma meantone]], the augmented sixth is tuned only a few cents shy of a just [[7/4]], and the augmented fourth is only a few cents shy of [[7/5]], so the meantone French sixth chord can be considered to also approximate the [[septimal meantone]] chord:

	* ([[~~Didymic chords#~~Septimal meantone chords\|~~Meantone~~]]) 1 – 5/4 – 7/5 – 7/4		* ([[Septimal meantone chords\|Septimal meantone]]) 1 – 5/4 – 7/5 – 7/4

	or [[20:25:28:35]] (step sizes 5/4, 28/25, and 5/4). Since the [[28/25]] interval in this chord also represents [[9/8]], in septimal meantone (and, more generally, in [[~~marvel~~]] temperaments) this chord is an [[essentially tempered chord]] in the [[9-odd-limit]].		or [[20:25:28:35]] (step sizes 5/4, 28/25, and 5/4). Since the [[28/25]] interval in this chord also represents [[10/9]], in septimal meantone (and, more generally, in [[starling]] temperaments) this chord is an [[essentially tempered chord]] in the [[9-odd-limit]].
	<!-- Note: The close approximation of the 7-limit chord is specific to quarter-comma meantone. Many other meantones, such as 12edo and 19edo, do not approximate it nearly as closely, although they may nonetheless support the septimal meantone interpretation that unifies it with the French sixth. -->		<!-- Note: The close approximation of the 7-limit chord is specific to quarter-comma meantone. Many other meantones, such as 12edo and 19edo, do not approximate it nearly as closely, although they may nonetheless support the septimal meantone interpretation that unifies it with the French sixth. -->

Bcmills: add links and categories for meantone chords

2024-08-22T03:19:16Z

add links and categories for meantone chords

← Older revision		Revision as of 03:19, 22 August 2024
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	A '''French sixth chord''' is a [[tetrad]] comprising a root, major third, augmented fourth, and augmented sixth.		A '''French sixth chord''' is a [[tetrad]] comprising a root, major third, augmented fourth, and augmented sixth.

	== In ~~meantone~~ ==		== In temperaments ==

	In 5-limit meantone, the traditional foundation of tonal harmony, the augmented sixth represents both [[225/128]] and [[125/72]], and the augmented fourth represents all of [[45/32]], [[25/18]], and [[729/512]], so the 5-limit meantone French sixth chord,		In 5-limit [[meantone]], the traditional foundation of tonal harmony, the augmented sixth represents both [[225/128]] and [[125/72]], and the augmented fourth represents all of [[45/32]], [[25/18]], and [[729/512]], so the 5-limit meantone French sixth chord,

	* (Meantone) 1 – 5/4 – 25/18 – 125/72		* (Meantone) 1 – 5/4 – 25/18 – 125/72
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	However, in the historically prevalent [[quarter-comma meantone]], the augmented sixth is tuned only a few cents shy of a just [[7/4]], and the augmented fourth is only a few cents shy of [[7/5]], so the meantone French sixth chord can be considered to also approximate the [[septimal meantone]] chord:		However, in the historically prevalent [[quarter-comma meantone]], the augmented sixth is tuned only a few cents shy of a just [[7/4]], and the augmented fourth is only a few cents shy of [[7/5]], so the meantone French sixth chord can be considered to also approximate the [[septimal meantone]] chord:

	* (Meantone) 1 – 5/4 – 7/5 – 7/4		* ([[Didymic chords#Septimal meantone chords\|Meantone]]) 1 – 5/4 – 7/5 – 7/4

	or [[20:25:28:35]] (step sizes 5/4, 28/25, and 5/4). Since the [[28/25]] interval in this chord also represents [[9/8]], in septimal meantone (and, more generally, in [[marvel]] temperaments) this chord is an [[essentially tempered chord]] in the [[9-odd-limit]].		or [[20:25:28:35]] (step sizes 5/4, 28/25, and 5/4). Since the [[28/25]] interval in this chord also represents [[9/8]], in septimal meantone (and, more generally, in [[marvel]] temperaments) this chord is an [[essentially tempered chord]] in the [[9-odd-limit]].
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	* [[128:160:180:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at ♭II ({{Frac\|16\|15}}) and ♭VI ({{Frac\|8\|5}}) in the [[duodene]].		* [[128:160:180:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at ♭II ({{Frac\|16\|15}}) and ♭VI ({{Frac\|8\|5}}) in the [[duodene]].

			[[Category:French sixth chords\| ]] <!-- main article -->
	[[Category:Just intonation chords]]		[[Category:Just intonation chords]]
	[[Category:~~French sixth~~ chords\| ]] <!-- ~~main article -->~~		[[Category:Essentially tempered chords]]
			[[Category:9-odd-limit chords]]