Dominant seventh chord - Revision history

Overthink: /* In temperaments */ replace "-" with en dash

2026-01-29T05:57:52Z

In temperaments: replace "-" with en dash

← Older revision		Revision as of 05:57, 29 January 2026
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	In [[meantone]] (including [[12edo]]), on which traditional tonal harmony is built, the interval of a minor seventh represents [[9/5]][[~]][[16/9]], and the tritone between ~5/4 and ~9/5 represents [[36/25]]~[[64/45]]~[[1024/729]], all [[tempered together]] into a single chord:		In [[meantone]] (including [[12edo]]), on which traditional tonal harmony is built, the interval of a minor seventh represents [[9/5]][[~]][[16/9]], and the tritone between ~5/4 and ~9/5 represents [[36/25]]~[[64/45]]~[[1024/729]], all [[tempered together]] into a single chord:

	* (Meantone) 1/1 ‒ [[5/4]] ‒ [[3/2]] ‒ [[9/5]], with steps 5/4, 6/5, 6/5.		* (Meantone) 1/1 – [[5/4]] – [[3/2]] – [[9/5]], with steps 5/4, 6/5, 6/5.

	This chord tempers together [[36:45:54:64]], [[20:25:30:36]], and [[108:135:160:192]], with a resulting [[intervallic odd limit]] of 25 due to the simplest interpretation of its tritone being ~36/25.		This chord tempers together [[36:45:54:64]], [[20:25:30:36]], and [[108:135:160:192]], with a resulting [[intervallic odd limit]] of 25 due to the simplest interpretation of its tritone being ~36/25.
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	[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]], tempers the tritone to ~[[10/7]], making the chord an [[essentially tempered chord]] in the [[9-odd-limit]]. In fact, tempering out the starling comma [[126/125]] alone is enough to convert it to a 9-odd-limit essentially tempered chord:		[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]], tempers the tritone to ~[[10/7]], making the chord an [[essentially tempered chord]] in the [[9-odd-limit]]. In fact, tempering out the starling comma [[126/125]] alone is enough to convert it to a 9-odd-limit essentially tempered chord:

	* (Starling) 1/1 ‒ [[5/4]] ‒ [[3/2]] ‒ [[9/5]]		* (Starling) 1/1 – [[5/4]] – [[3/2]] – [[9/5]]

	However, in [[starling]] the seventh of this chord represents 9/5~[[25/14]], but not 16/9. Septimal meantone tempering is necessary to temper together all three of the sevenths (9/5~16/9~25/14), so either of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])		However, in [[starling]] the seventh of this chord represents 9/5~[[25/14]], but not 16/9. Septimal meantone tempering is necessary to temper together all three of the sevenths (9/5~16/9~25/14), so either of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])

Overthink: /* In just intonation */ add 28:36:42:49, explain 70:90:105:126, reorder limits

2026-01-29T05:56:07Z

In just intonation: add 28:36:42:49, explain 70:90:105:126, reorder limits

← Older revision		Revision as of 05:56, 29 January 2026
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	== In just intonation ==		== In just intonation ==
			In the [[3-limit]]:

	~~In the [[7-limit]]:~~		* [[576:729:864:1024]] is found on the dominant scale degree (V or {{Frac\|3\|2}}) of the [[Pythagorean tuning\|Pythagorean]] diatonic scale.

	* [[4:5:6:7]]~~, the ''harmonic seventh chord'',~~ is ~~a [[concord]] in~~ the ~~7-limit, often used as a tuning target in~~ {{w\|~~Harmonic seventh chord #Barbershop seventh~~\|~~barbershop music~~}}.
	* [[70:90:105:126]] (1/1 - 9/7 - 3/2 - 9/5)

	* [[~~28:35:42:50~~]] ~~is a [[condissonant]] chord, and one of the possible interpretations of the dominant seventh in the starling, marvel, and septimal meantone temperaments~~.

	In the [[5-limit]]:		In the [[5-limit]]:
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	* [[128:160:192:225]], a 5-limit interpretation of an inversion of the {{w\|Neapolitan chord\|''Neapolitan''}} or {{w\|Augmented sixth chord #German sixth\|''German sixth chord''}}, is found rooted at the ♭II ({{Frac\|16\|15}}) and ♭VI ({{Frac\|8\|5}}) of the [[duodene]]. ([[225/128]] is often considered an augmented sixth rather than a minor seventh, but in septimal meantone and [[marvel]] temperament this chord is tuned identically to 4:5:6:7, and in [[12edo]] and its multiples it is tuned identically to 36:45:54:64 and 20:25:30:36.)		* [[128:160:192:225]], a 5-limit interpretation of an inversion of the {{w\|Neapolitan chord\|''Neapolitan''}} or {{w\|Augmented sixth chord #German sixth\|''German sixth chord''}}, is found rooted at the ♭II ({{Frac\|16\|15}}) and ♭VI ({{Frac\|8\|5}}) of the [[duodene]]. ([[225/128]] is often considered an augmented sixth rather than a minor seventh, but in septimal meantone and [[marvel]] temperament this chord is tuned identically to 4:5:6:7, and in [[12edo]] and its multiples it is tuned identically to 36:45:54:64 and 20:25:30:36.)

	In the [[3-limit]]:		In the [[7-limit]]:

			* [[4:5:6:7]], the ''harmonic seventh chord'', is a [[concord]] in the 7-limit, often used as a tuning target in {{w\|Harmonic seventh chord #Barbershop seventh\|barbershop music}}.

			* [[70:90:105:126]] (1/1–9/7–3/2–9/5) is the ''subharmonic seventh chord'', a [[utonal]] [[9-odd-limit]] tetrad which is the inversion of [[6:7:9:10]], the subharmonic sixth chord.

			* [[28:35:42:50]] is a [[condissonant]] chord, and one of the possible interpretations of the dominant seventh in the starling, marvel, and septimal meantone temperaments.

	* [[~~576~~:~~729~~:~~864~~:~~1024~~]] is found on the ~~dominant~~ scale ~~degree (V or {{Frac\|3\|2}})~~ of ~~the~~ [[~~Pythagorean tuning\|Pythagorean~~]] ~~diatonic scale~~.		* [[28:36:42:49]] is a septimal dominant seventh chord. A tempered version of this chord is found in the diatonic scale of [[superpyth]] temperament.

	== See also ==		== See also ==

FloraC: /* In temperaments */ rework to introduce septimal meantone a bit earlier

2024-12-23T13:12:08Z

In temperaments: rework to introduce septimal meantone a bit earlier

← Older revision		Revision as of 13:12, 23 December 2024
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	== In temperaments ==		== In temperaments ==

	In [[meantone]] (including [[12edo]]), on which traditional tonal harmony is built, the interval of a minor seventh represents [[9/5]][[~]][[16/9]], and the tritone between ~5/4 and ~9/5 represents [[36/25]]~[[64/45]]~[[1024/729]], all [[tempered together]] into a single chord:		In [[meantone]] (including [[12edo]]), on which traditional tonal harmony is built, the interval of a minor seventh represents [[9/5]][[~]][[16/9]], and the tritone between ~5/4 and ~9/5 represents [[36/25]]~[[64/45]]~[[1024/729]], all [[tempered together]] into a single chord:

	* (Meantone) 1/~~1 ‒~~ [[5/4]] ‒ [[3/2]] ‒ [[9/5]], with steps 5/4, 6/5, 6/5.		* (Meantone) 1/1 ‒ [[5/4]] ‒ [[3/2]] ‒ [[9/5]], with steps 5/4, 6/5, 6/5.

	This chord tempers together [[36:45:54:64]], [[20:25:30:36]], and [[108:135:160:192]], with a resulting [[intervallic odd limit]] of 25 due to the simplest interpretation of its tritone being ~36/25.		This chord tempers together [[36:45:54:64]], [[20:25:30:36]], and [[108:135:160:192]], with a resulting [[intervallic odd limit]] of 25 due to the simplest interpretation of its tritone being ~36/25.

	In [[~~starling~~]] ~~temperament~~, which ~~tempers out~~ [[~~126/125~~]] ~~and~~ tempers ~~together 9/5~[[25/14]],~~ the ~~~36/25~~ tritone ~~is tempered together with~~ ~[[10/7]], making the chord an [[essentially tempered chord]] in the [[9-odd-limit]]. ~~However~~, ~~note that in~~ starling ~~temperament the seventh of this chord does not also represent the ~16~~/9 ~~seventh.~~		[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]], tempers the tritone to ~[[10/7]], making the chord an [[essentially tempered chord]] in the [[9-odd-limit]]. In fact, tempering out the starling comma [[126/125]] alone is enough to convert it to a 9-odd-limit essentially tempered chord:

	* (Starling) 1/~~1 ‒~~ [[5/4]] ‒ [[3/2]] ‒ [[9/5]]		* (Starling) 1/1 ‒ [[5/4]] ‒ [[3/2]] ‒ [[9/5]]

	[[~~Septimal meantone~~]]~~, which is well-represented by~~ the ~~historically prevalent~~ [[~~quarter-comma meantone~~]], ~~tempers~~ together all three of the sevenths (9/5~16/9~25/14), so either of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])		However, in [[starling]] the seventh of this chord represents 9/5~[[25/14]], but not 16/9. Septimal meantone tempering is necessary to temper together all three of the sevenths (9/5~16/9~25/14), so either of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])

	In [[archytas]] temperament, which tempers out [[64/63]], ~16/9 is equated with ~[[7/4]] rather than 25/14, resulting in an [[Dyadic chord#Essentially tempered dyadic chord\|essentially just]] [[7-odd-limit]] chord that tempers together [[4:5:6:7]] and [[36:45:54:64]]:		In [[archytas]] temperament, which tempers out [[64/63]], ~16/9 is equated with ~[[7/4]] rather than 25/14, resulting in an [[Dyadic chord#Essentially tempered dyadic chord\|essentially just]] [[7-odd-limit]] chord that tempers together [[4:5:6:7]] and [[36:45:54:64]]:

	* (Archytas) 1/1 - [[5/4]] - [[3/2]] - [[7/4]]		* (Archytas) 1/1 – [[5/4]] – [[3/2]] – [[7/4]]

	[[Dominant (temperament)\|Dominant temperament]] combines archytas with meantone, tempering out both 81/80 and 64/63, and as a result also tempers out [[36/35]], equating 4:5:6:7 with all of the 5-limit dominant seventh chords of meantone. Since [[12edo]] is a good tuning of Dominant temperament, this simpler septimal interpretation may also be relevant for dominant seventh chords in music originally composed for 12edo — particularly in performance styles that use more flexible intonation (such as Barbershop).		[[Dominant (temperament)\|Dominant temperament]] combines archytas with meantone, tempering out both 81/80 and 64/63, and as a result also tempers out [[36/35]], equating 4:5:6:7 with all of the 5-limit dominant seventh chords of meantone. Since [[12edo]] is a good tuning of Dominant temperament, this simpler septimal interpretation may also be relevant for dominant seventh chords in music originally composed for 12edo — particularly in performance styles that use more flexible intonation (such as Barbershop).

Fitzgerald Lee: Fixed wikipedia thingy

2024-10-28T10:09:20Z

Fixed wikipedia thingy

← Older revision		Revision as of 10:09, 28 October 2024
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	{{Wikipedia}}		{{Wikipedia\|Dominant seventh chord}}
	A '''dominant seventh chord''' is a [[tetrad]] comprising a root, [[major]] third, fifth, and [[minor]] seventh.		A '''dominant seventh chord''' is a [[tetrad]] comprising a root, [[major]] third, fifth, and [[minor]] seventh.

TallKite: /* In just intonation */ added 1/(9:7:6:5)

2024-09-27T23:25:29Z

In just intonation: added 1/(9:7:6:5)

← Older revision		Revision as of 23:25, 27 September 2024
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	* [[4:5:6:7]], the ''harmonic seventh chord'', is a [[concord]] in the 7-limit, often used as a tuning target in {{w\|Harmonic seventh chord #Barbershop seventh\|barbershop music}}.		* [[4:5:6:7]], the ''harmonic seventh chord'', is a [[concord]] in the 7-limit, often used as a tuning target in {{w\|Harmonic seventh chord #Barbershop seventh\|barbershop music}}.
			* [[70:90:105:126]] (1/1 - 9/7 - 3/2 - 9/5)

	* [[28:35:42:50]] is a [[condissonant]] chord, and one of the possible interpretations of the dominant seventh in the starling, marvel, and septimal meantone temperaments.		* [[28:35:42:50]] is a [[condissonant]] chord, and one of the possible interpretations of the dominant seventh in the starling, marvel, and septimal meantone temperaments.

FloraC: /* In temperaments */ marvel is wrong (thanks to bcmills for catching this)

2024-09-12T15:29:35Z

In temperaments: marvel is wrong (thanks to bcmills for catching this)

← Older revision		Revision as of 15:29, 12 September 2024
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	* (Starling) 1/1 ‒ [[5/4]] ‒ [[3/2]] ‒ [[9/5]]		* (Starling) 1/1 ‒ [[5/4]] ‒ [[3/2]] ‒ [[9/5]]

	Similarly, in [[marvel]] temperament, which tempers out [[225/224]] and tempers together 16/9~25/14 (but ''not'' 9/5), the ~64/45 tritone is tempered together with ~10/7, again resulting in a 9-odd-limit essentially tempered chord:		[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]], tempers together all three of the sevenths (9/5~16/9~25/14), so either of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])

	* (Marvel) 1/1 ‒ [[5/4]] ‒ [[3/2]] ‒ [[16/9]]

	[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]]), tempers together all three of ~~these~~ sevenths (9/5~16/9~25/14), so ~~any~~ of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])

	In [[archytas]] temperament, which tempers out [[64/63]], ~16/9 is equated with ~[[7/4]] rather than 25/14, resulting in an [[Dyadic chord#Essentially tempered dyadic chord\|essentially just]] [[7-odd-limit]] chord that tempers together [[4:5:6:7]] and [[36:45:54:64]]:		In [[archytas]] temperament, which tempers out [[64/63]], ~16/9 is equated with ~[[7/4]] rather than 25/14, resulting in an [[Dyadic chord#Essentially tempered dyadic chord\|essentially just]] [[7-odd-limit]] chord that tempers together [[4:5:6:7]] and [[36:45:54:64]]:
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	[[Dominant (temperament)\|Dominant temperament]] combines archytas with meantone, tempering out both 81/80 and 64/63, and as a result also tempers out [[36/35]], equating 4:5:6:7 with all of the 5-limit dominant seventh chords of meantone. Since [[12edo]] is a good tuning of Dominant temperament, this simpler septimal interpretation may also be relevant for dominant seventh chords in music originally composed for 12edo — particularly in performance styles that use more flexible intonation (such as Barbershop).		[[Dominant (temperament)\|Dominant temperament]] combines archytas with meantone, tempering out both 81/80 and 64/63, and as a result also tempers out [[36/35]], equating 4:5:6:7 with all of the 5-limit dominant seventh chords of meantone. Since [[12edo]] is a good tuning of Dominant temperament, this simpler septimal interpretation may also be relevant for dominant seventh chords in music originally composed for 12edo — particularly in performance styles that use more flexible intonation (such as Barbershop).
	<!-- Note: 12edo also supports Mint temperament via Dominant, but I'm intentionally omitting it here for simplicity. It's easy enough to find via [[36/35]].-->		<!-- Note: 12edo also supports Mint temperament via Dominant, but I'm intentionally omitting it here for simplicity. It's easy enough to find via [[36/35]].-->

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

Bcmills: add categories for tempered chords

2024-09-08T04:16:54Z

add categories for tempered chords

← Older revision		Revision as of 04:16, 8 September 2024
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	[[Category:Dominant seventh chords\| ]] <!-- main article -->		[[Category:Dominant seventh chords\| ]] <!-- main article -->
	[[Category:Just intonation chords]]		[[Category:Just intonation chords]]
			[[Category:Essentially tempered chords]]
			[[Category:9-odd-limit chords]]

Bcmills: add 28:35:42:50

2024-09-01T19:43:51Z

add 28:35:42:50

← Older revision		Revision as of 19:43, 1 September 2024
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	* [[4:5:6:7]], the ''harmonic seventh chord'', is a [[concord]] in the 7-limit, often used as a tuning target in {{w\|Harmonic seventh chord #Barbershop seventh\|barbershop music}}.		* [[4:5:6:7]], the ''harmonic seventh chord'', is a [[concord]] in the 7-limit, often used as a tuning target in {{w\|Harmonic seventh chord #Barbershop seventh\|barbershop music}}.

			* [[28:35:42:50]] is a [[condissonant]] chord, and one of the possible interpretations of the dominant seventh in the starling, marvel, and septimal meantone temperaments.

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

Bcmills at 19:36, 1 September 2024

2024-09-01T19:36:58Z

← Older revision		Revision as of 19:36, 1 September 2024
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	[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]]), tempers together all three of these sevenths (9/5~16/9~25/14), so any of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])		[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]]), tempers together all three of these sevenths (9/5~16/9~25/14), so any of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])

	In [[archytas]] temperament, which tempers out [[64/63]], ~16/9 is equated with ~[[7/4]] rather than 25/14, resulting in an [[essentially just]] [[7-odd-limit]] chord that tempers together [[4:5:6:7]] and [[36:45:54:64]]:		In [[archytas]] temperament, which tempers out [[64/63]], ~16/9 is equated with ~[[7/4]] rather than 25/14, resulting in an [[Dyadic chord#Essentially tempered dyadic chord\|essentially just]] [[7-odd-limit]] chord that tempers together [[4:5:6:7]] and [[36:45:54:64]]:

	* (Archytas) 1/1 - [[5/4]] - [[3/2]] - [[7/4]]		* (Archytas) 1/1 - [[5/4]] - [[3/2]] - [[7/4]]

Bcmills: Mention Archytas and Dominant.

2024-09-01T18:51:26Z

Mention Archytas and Dominant.

← Older revision		Revision as of 18:51, 1 September 2024
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	[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]]), tempers together all three of these sevenths (9/5~16/9~25/14), so any of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])		[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]]), tempers together all three of these sevenths (9/5~16/9~25/14), so any of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])

			In [[archytas]] temperament, which tempers out [[64/63]], ~16/9 is equated with ~[[7/4]] rather than 25/14, resulting in an [[essentially just]] [[7-odd-limit]] chord that tempers together [[4:5:6:7]] and [[36:45:54:64]]:

			* (Archytas) 1/1 - [[5/4]] - [[3/2]] - [[7/4]]

			[[Dominant (temperament)\|Dominant temperament]] combines archytas with meantone, tempering out both 81/80 and 64/63, and as a result also tempers out [[36/35]], equating 4:5:6:7 with all of the 5-limit dominant seventh chords of meantone. Since [[12edo]] is a good tuning of Dominant temperament, this simpler septimal interpretation may also be relevant for dominant seventh chords in music originally composed for 12edo — particularly in performance styles that use more flexible intonation (such as Barbershop).
			<!-- Note: 12edo also supports Mint temperament via Dominant, but I'm intentionally omitting it here for simplicity. It's easy enough to find via [[36/35]].-->

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