4:5:6:7 - Revision history

Pailiaq at 04:29, 26 May 2026

2026-05-26T04:29:07Z

← Older revision		Revision as of 04:29, 26 May 2026
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	Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[16/15\|15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The 15/16 can step up by 16/15 to reach [[1/1]], and the 21/16 down by [[21/20]] to reach 5/4, resolving to the [[4:5:6]] chord on the tonic.		Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[16/15\|15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The 15/16 can step up by 16/15 to reach [[1/1]], and the 21/16 down by [[21/20]] to reach 5/4, resolving to the [[4:5:6]] chord on the tonic.

			{{chord edo approximation}}

	== Audio of close voicings ==		== Audio of close voicings ==
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	Plausible [[chord homonym\|homonyms]]: none.		Plausible [[chord homonym\|homonyms]]: none.

	~~{{chord edo approximation}}~~

	Notable extensions (7-limit):		Notable extensions (7-limit):

Pailiaq at 04:28, 26 May 2026

2026-05-26T04:28:41Z

← Older revision		Revision as of 04:28, 26 May 2026
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	Plausible [[chord homonym\|homonyms]]: none.		Plausible [[chord homonym\|homonyms]]: none.

			{{chord edo approximation}}

	Notable extensions (7-limit):		Notable extensions (7-limit):

FloraC: Fixes

2025-12-26T19:28:30Z

Fixes

← Older revision		Revision as of 19:28, 26 December 2025
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	It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126\|1–9/7–3/2–9/5]].		It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126\|1–9/7–3/2–9/5]].

	Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The [[15/16]] can step up by [[16/15]] to reach [[1/1]], and the [[21/16]] down by [[21/20]] to reach [[5/4]], resolving to the [[4:5:6]] chord on the tonic.		Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[16/15\|15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The 15/16 can step up by 16/15 to reach [[1/1]], and the 21/16 down by [[21/20]] to reach 5/4, resolving to the [[4:5:6]] chord on the tonic.

	== Audio of close voicings ==		== Audio of close voicings ==
	[[File:SculpEufaDem4-5-6-7-onD.mp3\|none\|thumb\|4:5:6:7, Root position]]		[[File:SculpEufaDem4-5-6-7-onD.mp3\|none\|thumb\|4:5:6:7, Root position]]
	[[File:SculpEufaDem5-6-7-8-onD.mp3\|none\|thumb\|5:6:7:8, 1st inversion]]		[[File:SculpEufaDem5-6-7-8-onD.mp3\|none\|thumb\|5:6:7:8, 1st inversion]]
	~~[[Category:Dominant seventh chords\|#]]~~
	[[File:SculpEufaDem6-7-8-10-onD.mp3\|none\|thumb\|6:7:8:10, 2nd inversion]]		[[File:SculpEufaDem6-7-8-10-onD.mp3\|none\|thumb\|6:7:8:10, 2nd inversion]]
	[[File:SculpEufaDem7-8-10-12-onD.mp3\|none\|thumb\|7:8:10:12, 3rd inversion]]		[[File:SculpEufaDem7-8-10-12-onD.mp3\|none\|thumb\|7:8:10:12, 3rd inversion]]
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	* [[5:6:7]]		* [[5:6:7]]

			[[Category:Dominant seventh chords\|#]]
	[[Category:German sixth chords\|#]] <!-- 1-digit first number -->		[[Category:German sixth chords\|#]] <!-- 1-digit first number -->

Overthink: better wording

2025-12-26T02:23:46Z

better wording

← Older revision		Revision as of 02:23, 26 December 2025
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	It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126\|1–9/7–3/2–9/5]].		It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126\|1–9/7–3/2–9/5]].

	Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The [[15/16]] can step up by [[16/15]] to reach [[1/1]], and the [[21/16]] down by [[21/20]] to reach [[5/4]], to ~~reach~~ the [[4:5:6]] chord on the tonic.		Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The [[15/16]] can step up by [[16/15]] to reach [[1/1]], and the [[21/16]] down by [[21/20]] to reach [[5/4]], resolving to the [[4:5:6]] chord on the tonic.

	== Audio of close voicings ==		== Audio of close voicings ==

Overthink: Use as dominant seventh

2025-12-26T02:23:09Z

Use as dominant seventh

← Older revision		Revision as of 02:23, 26 December 2025
Line 4:		Line 4:

	It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126\|1–9/7–3/2–9/5]].		It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126\|1–9/7–3/2–9/5]].

			Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The [[15/16]] can step up by [[16/15]] to reach [[1/1]], and the [[21/16]] down by [[21/20]] to reach [[5/4]], to reach the [[4:5:6]] chord on the tonic.

	== Audio of close voicings ==		== Audio of close voicings ==

Overthink: /* Related chords */ fix typo

2025-11-24T23:53:27Z

Related chords: fix typo

← Older revision		Revision as of 23:53, 24 November 2025
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	Melodic inversion: 1/(7:6:5:4) = [[60:70:84:105]] = 1–7/6–7/5–7/4, and its homonym 1/(12:10:8:7) = [[70:84:105:120]] = 1–6/5–3/2–12/7.		Melodic inversion: 1/(7:6:5:4) = [[60:70:84:105]] = 1–7/6–7/5–7/4, and its homonym 1/(12:10:8:7) = [[70:84:105:120]] = 1–6/5–3/2–12/7.

	Plausible [[chord homonym\|~~homonyns~~]]: none.		Plausible [[chord homonym\|homonyms]]: none.

	Notable extensions (7-limit):		Notable extensions (7-limit):

TallKite at 21:07, 24 November 2025

2025-11-24T21:07:32Z

← Older revision		Revision as of 21:07, 24 November 2025
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	\|-		\|-
	\| 4:5:6:7		\| 4:5:6:7
	\| ~~Basic~~		\| basic
	\| Isodifferential		\| Isodifferential
	\|-		\|-

FloraC: Cleanup

2025-11-24T09:38:16Z

Cleanup

← Older revision		Revision as of 09:38, 24 November 2025
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	'''4:5:6:7''', the ''harmonic seventh chord'', is the simplest [[tetrad]] in [[7-limit]] harmony. It is often used as a tuning target for the [[dominant seventh chord]] in barbershop music (→ [[Wikipedia: Harmonic seventh chord #Barbershop seventh]]), and also for the German augmented sixth chord in [[septimal meantone]].		'''4:5:6:7''', the ''harmonic seventh chord'', is the simplest [[tetrad]] in [[7-limit]] harmony. It is often used as a tuning target for the [[dominant seventh chord]] in barbershop music (→ [[Wikipedia: Harmonic seventh chord #Barbershop seventh]]), and also for the German augmented sixth chord in [[septimal meantone]].

	It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126\|~~1 - 9~~/~~7 - 3~~/~~2 - 9~~/5]].		It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126\|1–9/7–3/2–9/5]].

	== Audio of close voicings ==		== Audio of close voicings ==
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	== Notable voicings ==		== Notable voicings ==
	Sorted by [[Wilson norm~~#Example\|Wilson Height~~]]. AOV and CAOV stand for [[Odd limit#Proposed extensions\|all-odd voicing]] and ''condensed'' AOV respectively. This list is only a brief overview, see [[Voicings of 4:5:6:7]] for a more comprehensive list.		Sorted by [[Wilson norm]]. AOV and CAOV stand for [[Odd limit #Proposed extensions\|all-odd voicing]] and ''condensed'' AOV respectively. This list is only a brief overview, see [[Voicings of 4:5:6:7]] for a more comprehensive list.

	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	!Voices		! Voices
	![[EFR]]		! [[EFR]]
	![[Kite's thoughts on hi-lo notation\|Hi-lo name]]		! [[Kite's thoughts on hi-lo notation\|Hi-lo name]]
	!Special properties		! Special properties
	\|-		\|-
	\| rowspan="5" \|4 voices		\| rowspan="5" \|4 voices
	\|1:3:5:7		\| 1:3:5:7
	\|hi37loR		\| hi37loR
	\|AOV, [[Isodifferential chord\|isodifferential]]		\| AOV, [[Isodifferential chord\|isodifferential]]
	\|-		\|-
	\|2:3:5:7		\| 2:3:5:7
	\|hi37		\| hi37
	\|CAOV		\| CAOV
	\|-		\|-
	\|3:4:5:7		\| 3:4:5:7
	\|lo5		\| lo5
	\|		\|
	\|-		\|-
	\|4:5:6:7		\| 4:5:6:7
	\|~~basic~~		\| Basic
	\|~~isodifferential~~		\| Isodifferential
	\|-		\|-
	\|4:6:7:10		\| 4:6:7:10
	\|hi3		\| hi3
	\|		\|
	\|}		\|}

	== Related chords ==		== Related chords ==
	Melodic inversion: 7:6:5:4 = [[60:70:84:105]] = 1/~~1 - 7~~/~~6 - 7/5 - 7~~/4, and its homonym 12:10:8:7 = [[70:84:105:120]] = 1/~~1 - 6/5 - 3~~/~~2 - 12~~/7.		Melodic inversion: 1/(7:6:5:4) = [[60:70:84:105]] = 1–7/6–7/5–7/4, and its homonym 1/(12:10:8:7) = [[70:84:105:120]] = 1–6/5–3/2–12/7.

	Plausible [[~~Chord~~ homonym\|homonyns]]: none.		Plausible [[chord homonym\|homonyns]]: none.

	Notable extensions (7-limit):		Notable extensions (7-limit):
	* [[4:5:6:7:9]] – adds 9/4		* [[4:5:6:7:9]] – adds 9/4
	* [[12:15:18:21:28]] – adds 7/3 to make the 7-limit Hendrix chord		* [[12:15:18:21:28]] – adds 7/3 to make the 7-limit Hendrix chord

	Notable restrictions:		Notable restrictions:

	* [[4:5:6]]		* [[4:5:6]]
	* [[4:5:7]]		* [[4:5:7]]

TallKite at 09:31, 24 November 2025

2025-11-24T09:31:36Z

← Older revision		Revision as of 09:31, 24 November 2025
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	== Notable voicings ==		== Notable voicings ==
	AOV and CAOV stand for [[Odd limit#Proposed extensions\|all-odd voicing]] and ''condensed'' AOV respectively.		Sorted by [[Wilson norm#Example\|Wilson Height]]. AOV and CAOV stand for [[Odd limit#Proposed extensions\|all-odd voicing]] and ''condensed'' AOV respectively. This list is only a brief overview, see [[Voicings of 4:5:6:7]] for a more comprehensive list.
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	!Voices		!Voices
	!~~Voicing~~		![[EFR]]
	![[Kite's thoughts on hi-lo notation\|Hi-lo name]]		![[Kite's thoughts on hi-lo notation\|Hi-lo name]]
	!Special properties		!Special properties

TallKite: major rewrite

2025-11-20T16:17:31Z

major rewrite

← Older revision		Revision as of 16:17, 20 November 2025
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	{{Infobox Chord\|4:5:6:7\|ColorName=yo zo-7 or y,z7, har-7 or h7}}		{{Infobox Chord\|4:5:6:7\|ColorName=yo zo-7 or y,z7, har-7 or h7}}
	{{Wikipedia\|Harmonic seventh chord}}		{{Wikipedia\|Harmonic seventh chord}}
	'''4:5:6:7''', the ''harmonic seventh chord'', is the simplest [[tetrad]] in [[7-limit]] harmony. It is often used as a tuning target for the [[dominant seventh chord]] in barbershop music (→ [[Wikipedia: Harmonic seventh chord #Barbershop seventh ]]), and also for the German augmented sixth chord in [[septimal meantone]].		'''4:5:6:7''', the ''harmonic seventh chord'', is the simplest [[tetrad]] in [[7-limit]] harmony. It is often used as a tuning target for the [[dominant seventh chord]] in barbershop music (→ [[Wikipedia: Harmonic seventh chord #Barbershop seventh]]), and also for the German augmented sixth chord in [[septimal meantone]].

	It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get ~~the subharmonic sixth~~ chord~~. The intervals~~ [[25/24]] ~~and~~ [[49/~~48]] thus serve as chromas, and they are equated when [[50~~/~~49]] is tempered out, such as in [[pajara~~]].		It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126\|1 - 9/7 - 3/2 - 9/5]].

	== ~~Rotations around the octave~~ ==		== Audio of close voicings ==
	[[File:SculpEufaDem4-5-6-7-onD.mp3\|none\|thumb\|4:5:6:7 "Root position"]]		[[File:SculpEufaDem4-5-6-7-onD.mp3\|none\|thumb\|4:5:6:7, Root position]]
	[[File:SculpEufaDem5-6-7-8-onD.mp3\|none\|thumb\|5:6:7:8 "1st inversion"]]		[[File:SculpEufaDem5-6-7-8-onD.mp3\|none\|thumb\|5:6:7:8, 1st inversion]]
	[[Category:Dominant seventh chords\|#]]		[[Category:Dominant seventh chords\|#]]
	[[File:SculpEufaDem6-7-8-10-onD.mp3\|none\|thumb\|6:7:8:10 "2nd inversion"]]		[[File:SculpEufaDem6-7-8-10-onD.mp3\|none\|thumb\|6:7:8:10, 2nd inversion]]
	[[File:SculpEufaDem7-8-10-12-onD.mp3\|none\|thumb\|7:8:10:12 "3rd inversion"]]		[[File:SculpEufaDem7-8-10-12-onD.mp3\|none\|thumb\|7:8:10:12, 3rd inversion]]

	== ~~Voicings and rotations around two octaves~~ ==		== Notable voicings ==
	{\| class="wikitable ~~sortable" style="text-align:center;~~"		AOV and CAOV stand for [[Odd limit#Proposed extensions\|all-odd voicing]] and ''condensed'' AOV respectively.
			{\| class="wikitable"
	\|+		\|+
	! ~~style="width:120px;" {{diagonal split header\|Rotation\|Voicing}}~~		!Voices
	! ~~style="width:120px;" \| Root~~		!Voicing
	~~! style="width:120px;" \| '3~~		![[Kite's thoughts on hi-lo notation\|Hi-lo name]]
	~~! style="width:120px;" \| '5~~		!Special properties
	~~! style="width:120px;" \| '7~~
	~~! style="width:120px;" \| '3'5~~
	! ~~style="width:120px;" \| '3~~'7
	~~! style="width:120px;"~~ \| ~~'''<nowiki/>'5'7'''~~
	! ~~style="width:120px;" \| '3'5'7~~
	\|-		\|-
	~~! style="width:120px;" \| On 1~~		\| rowspan="5" \|4 voices
	\| ~~data-sort-value~~="~~004-005-006-007" \| ''4:~~5~~:6:7''~~		\|1:3:5:7
	~~\| data-sort-value="004-005-007-012~~" \| 4~~:5:7:12~~		\|hi37loR
	\| ~~data-sort-value="004-006-007-010" \| 4~~:~~6:7:10~~		\|AOV, [[Isodifferential chord\|isodifferential]]
	~~\| data-sort-value="004-005-006-014" \| 4~~:5~~:6:14~~
	~~\| data-sort-value="004-007-010-012" \| 4~~:7~~:10:12~~
	~~\| data-sort-value="004-005-012-014" \| 4:5:12:14~~
	\| ~~data-sort-value="002-003-005-007" \| 2:3:5:7~~
	\| ~~data-sort-value="002-005-006-007"~~ \| ~~2:5:6:7~~
	\|-		\|-
	~~! style="width:120px;" \| On 3~~		\|2:3:5:7
	\| ~~data-sort-value="006-007-016-020" \| 6:7:16~~:20		\|hi37
	~~\| data-sort-value="003-004-005-007" \|~~ 3:4:5:7		\|CAOV
	\| ~~data-sort-value="006-007-010-016" \| 6:7:10:16~~
	~~\| data-sort-value="003-007-008-010" \| 3:7:8:10~~
	~~\| data-sort-value="003-004-007-010" \| 3:4:7:10~~
	~~\| data-sort-value="006-007-008-010" \| ''6:7:8:10''~~
	\| ~~data-sort-value="003-005-007-008" \| 3:5:7:8~~
	~~\| data-sort-value="006-007-008-020" \| 6:7:8:20~~
	\|-		\|-
	~~! style="width:120px;" \| On 5~~		\|3:4:5:7
	\| ~~data-sort-value="005-006-007-016" \| 5:6~~:7:16		\|lo5
	~~\| data-sort-value="005-007-012-016" \|~~ 5:7~~:12:16~~		\|
	\| ~~data-sort-value="005-008-012-014" \| 5:8:12:14~~
	\| ~~data-sort-value="005-006-014-016" \| 5:6:14:16~~
	~~\| data-sort-value="005-006-008-014" \| 5:6:8:14~~
	~~\| data-sort-value="005-012-014-016" \| 5:12:14:16~~
	~~\| data-sort-value="005-007-008-012" \| 5:7:8:12~~
	~~\| data-sort-value="005-006-007-008" \| ''5:6:7:8''~~
	\|-		\|-
	~~! style="width:120px;" \| On 7~~		\|4:5:6:7
	\| ~~data-sort-value="007-016-020-024" \| 7~~:16:20:24		\|basic
	\| ~~data-sort-value="007-012-016-020" \| 7:12:16:20~~		\|isodifferential
	\| ~~data-sort-value="007-010-016-024" \| 7:10:16:24~~		\|-
	\| ~~data-sort-value="007-008-010~~-~~012" \| ''7:8:10:12''~~		\|4:6:7:10
	\| ~~data-sort-value="007-010-012-016" \| 7~~:10:~~12:16~~		\|hi3
	~~\| data-sort-value="007-008-010-024" \|~~ 7:8:10~~:24~~		\|
	\| ~~data-sort-value="007-008-012-020" \| 7:8:12:20~~
	\| ~~data-sort-value="007-008-020-024" \| 7:8:20:24~~
	\|}		\|}

	~~Enumerations in italics map to an existing octave~~-~~reduced rotation~~.		== Related chords ==
			Melodic inversion: 7:6:5:4 = [[60:70:84:105]] = 1/1 - 7/6 - 7/5 - 7/4, and its homonym 12:10:8:7 = [[70:84:105:120]] = 1/1 - 6/5 - 3/2 - 12/7.

	~~== Related chords ==~~		Plausible [[Chord homonym\|homonyns]]: none.
	~~Chords related to this triad~~ (7-limit ~~except where noted~~):
	* [[60:70:84:105]] – chord inversion		Notable extensions (7-limit):
	* [[4:5:6:7:9]] – adds 9/4 ~~(two octave spanning pentad)~~		* [[4:5:6:7:9]] – adds 9/4
	* [[12:14:18:21]] – ~~substitutes~~ 5/4 ~~with~~ 7/6		* [[12:15:18:21:28]] – adds 7/3 to make the 7-limit Hendrix chord
			Notable restrictions:

			* [[4:5:6]]
			* [[4:5:7]]
			* [[4:6:7]]
			* [[5:6:7]]

	[[Category:German sixth chords\|#]] <!-- 1-digit first number -->		[[Category:German sixth chords\|#]] <!-- 1-digit first number -->

← Older revision		Revision as of 19:28, 26 December 2025
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	It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126\|1–9/7–3/2–9/5]].		It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126\|1–9/7–3/2–9/5]].

	Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The [[15/16]] can step up by [[16/15]] to reach [[1/1]], and the [[21/16]] down by [[21/20]] to reach [[5/4]], resolving to the [[4:5:6]] chord on the tonic.		Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[16/15\|15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The 15/16 can step up by 16/15 to reach [[1/1]], and the 21/16 down by [[21/20]] to reach 5/4, resolving to the [[4:5:6]] chord on the tonic.

	== Audio of close voicings ==		== Audio of close voicings ==
	[[File:SculpEufaDem4-5-6-7-onD.mp3\|none\|thumb\|4:5:6:7, Root position]]		[[File:SculpEufaDem4-5-6-7-onD.mp3\|none\|thumb\|4:5:6:7, Root position]]
	[[File:SculpEufaDem5-6-7-8-onD.mp3\|none\|thumb\|5:6:7:8, 1st inversion]]		[[File:SculpEufaDem5-6-7-8-onD.mp3\|none\|thumb\|5:6:7:8, 1st inversion]]
	~~[[Category:Dominant seventh chords\|#]]~~
	[[File:SculpEufaDem6-7-8-10-onD.mp3\|none\|thumb\|6:7:8:10, 2nd inversion]]		[[File:SculpEufaDem6-7-8-10-onD.mp3\|none\|thumb\|6:7:8:10, 2nd inversion]]
	[[File:SculpEufaDem7-8-10-12-onD.mp3\|none\|thumb\|7:8:10:12, 3rd inversion]]		[[File:SculpEufaDem7-8-10-12-onD.mp3\|none\|thumb\|7:8:10:12, 3rd inversion]]
Line 61:		Line 60:
	* [[5:6:7]]		* [[5:6:7]]

			[[Category:Dominant seventh chords\|#]]
	[[Category:German sixth chords\|#]] <!-- 1-digit first number -->		[[Category:German sixth chords\|#]] <!-- 1-digit first number -->

← Older revision		Revision as of 16:17, 20 November 2025
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	{{Infobox Chord\|4:5:6:7\|ColorName=yo zo-7 or y,z7, har-7 or h7}}		{{Infobox Chord\|4:5:6:7\|ColorName=yo zo-7 or y,z7, har-7 or h7}}
	{{Wikipedia\|Harmonic seventh chord}}		{{Wikipedia\|Harmonic seventh chord}}
	'''4:5:6:7''', the ''harmonic seventh chord'', is the simplest [[tetrad]] in [[7-limit]] harmony. It is often used as a tuning target for the [[dominant seventh chord]] in barbershop music (→ [[Wikipedia: Harmonic seventh chord #Barbershop seventh ]]), and also for the German augmented sixth chord in [[septimal meantone]].		'''4:5:6:7''', the ''harmonic seventh chord'', is the simplest [[tetrad]] in [[7-limit]] harmony. It is often used as a tuning target for the [[dominant seventh chord]] in barbershop music (→ [[Wikipedia: Harmonic seventh chord #Barbershop seventh]]), and also for the German augmented sixth chord in [[septimal meantone]].

	It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get ~~the subharmonic sixth~~ chord~~. The intervals~~ [[25/24]] ~~and~~ [[49/~~48]] thus serve as chromas, and they are equated when [[50~~/~~49]] is tempered out, such as in [[pajara~~]].		It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction\|octave-reduced]] version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is [[70:84:105:120\|1–6/5–3/2–12/7]], sometimes called the ''subharmonic sixth chord''. The harmonic seventh chord can be modified by inflecting the [[5/4]] down by [[25/24]] and [[7/4]] down by [[49/48]] to get this chord, or by inflecting both up by [[36/35]] to get the ''subharmonic seventh chord'' [[70:90:105:126\|1 - 9/7 - 3/2 - 9/5]].

	== ~~Rotations around the octave~~ ==		== Audio of close voicings ==
	[[File:SculpEufaDem4-5-6-7-onD.mp3\|none\|thumb\|4:5:6:7 "Root position"]]		[[File:SculpEufaDem4-5-6-7-onD.mp3\|none\|thumb\|4:5:6:7, Root position]]
	[[File:SculpEufaDem5-6-7-8-onD.mp3\|none\|thumb\|5:6:7:8 "1st inversion"]]		[[File:SculpEufaDem5-6-7-8-onD.mp3\|none\|thumb\|5:6:7:8, 1st inversion]]
	[[Category:Dominant seventh chords\|#]]		[[Category:Dominant seventh chords\|#]]
	[[File:SculpEufaDem6-7-8-10-onD.mp3\|none\|thumb\|6:7:8:10 "2nd inversion"]]		[[File:SculpEufaDem6-7-8-10-onD.mp3\|none\|thumb\|6:7:8:10, 2nd inversion]]
	[[File:SculpEufaDem7-8-10-12-onD.mp3\|none\|thumb\|7:8:10:12 "3rd inversion"]]		[[File:SculpEufaDem7-8-10-12-onD.mp3\|none\|thumb\|7:8:10:12, 3rd inversion]]

	== ~~Voicings and rotations around two octaves~~ ==		== Notable voicings ==
	{\| class="wikitable ~~sortable" style="text-align:center;~~"		AOV and CAOV stand for [[Odd limit#Proposed extensions\|all-odd voicing]] and ''condensed'' AOV respectively.
			{\| class="wikitable"
	\|+		\|+
	! ~~style="width:120px;" {{diagonal split header\|Rotation\|Voicing}}~~		!Voices
	! ~~style="width:120px;" \| Root~~		!Voicing
	~~! style="width:120px;" \| '3~~		![[Kite's thoughts on hi-lo notation\|Hi-lo name]]
	~~! style="width:120px;" \| '5~~		!Special properties
	~~! style="width:120px;" \| '7~~
	~~! style="width:120px;" \| '3'5~~
	! ~~style="width:120px;" \| '3~~'7
	~~! style="width:120px;"~~ \| ~~'''<nowiki/>'5'7'''~~
	! ~~style="width:120px;" \| '3'5'7~~
	\|-		\|-
	~~! style="width:120px;" \| On 1~~		\| rowspan="5" \|4 voices
	\| ~~data-sort-value~~="~~004-005-006-007" \| ''4:~~5~~:6:7''~~		\|1:3:5:7
	~~\| data-sort-value="004-005-007-012~~" \| 4~~:5:7:12~~		\|hi37loR
	\| ~~data-sort-value="004-006-007-010" \| 4~~:~~6:7:10~~		\|AOV, [[Isodifferential chord\|isodifferential]]
	~~\| data-sort-value="004-005-006-014" \| 4~~:5~~:6:14~~
	~~\| data-sort-value="004-007-010-012" \| 4~~:7~~:10:12~~
	~~\| data-sort-value="004-005-012-014" \| 4:5:12:14~~
	\| ~~data-sort-value="002-003-005-007" \| 2:3:5:7~~
	\| ~~data-sort-value="002-005-006-007"~~ \| ~~2:5:6:7~~
	\|-		\|-
	~~! style="width:120px;" \| On 3~~		\|2:3:5:7
	\| ~~data-sort-value="006-007-016-020" \| 6:7:16~~:20		\|hi37
	~~\| data-sort-value="003-004-005-007" \|~~ 3:4:5:7		\|CAOV
	\| ~~data-sort-value="006-007-010-016" \| 6:7:10:16~~
	~~\| data-sort-value="003-007-008-010" \| 3:7:8:10~~
	~~\| data-sort-value="003-004-007-010" \| 3:4:7:10~~
	~~\| data-sort-value="006-007-008-010" \| ''6:7:8:10''~~
	\| ~~data-sort-value="003-005-007-008" \| 3:5:7:8~~
	~~\| data-sort-value="006-007-008-020" \| 6:7:8:20~~
	\|-		\|-
	~~! style="width:120px;" \| On 5~~		\|3:4:5:7
	\| ~~data-sort-value="005-006-007-016" \| 5:6~~:7:16		\|lo5
	~~\| data-sort-value="005-007-012-016" \|~~ 5:7~~:12:16~~		\|
	\| ~~data-sort-value="005-008-012-014" \| 5:8:12:14~~
	\| ~~data-sort-value="005-006-014-016" \| 5:6:14:16~~
	~~\| data-sort-value="005-006-008-014" \| 5:6:8:14~~
	~~\| data-sort-value="005-012-014-016" \| 5:12:14:16~~
	~~\| data-sort-value="005-007-008-012" \| 5:7:8:12~~
	~~\| data-sort-value="005-006-007-008" \| ''5:6:7:8''~~
	\|-		\|-
	~~! style="width:120px;" \| On 7~~		\|4:5:6:7
	\| ~~data-sort-value="007-016-020-024" \| 7~~:16:20:24		\|basic
	\| ~~data-sort-value="007-012-016-020" \| 7:12:16:20~~		\|isodifferential
	\| ~~data-sort-value="007-010-016-024" \| 7:10:16:24~~		\|-
	\| ~~data-sort-value="007-008-010~~-~~012" \| ''7:8:10:12''~~		\|4:6:7:10
	\| ~~data-sort-value="007-010-012-016" \| 7~~:10:~~12:16~~		\|hi3
	~~\| data-sort-value="007-008-010-024" \|~~ 7:8:10~~:24~~		\|
	\| ~~data-sort-value="007-008-012-020" \| 7:8:12:20~~
	\| ~~data-sort-value="007-008-020-024" \| 7:8:20:24~~
	\|}		\|}

	~~Enumerations in italics map to an existing octave~~-~~reduced rotation~~.		== Related chords ==
			Melodic inversion: 7:6:5:4 = [[60:70:84:105]] = 1/1 - 7/6 - 7/5 - 7/4, and its homonym 12:10:8:7 = [[70:84:105:120]] = 1/1 - 6/5 - 3/2 - 12/7.

	~~== Related chords ==~~		Plausible [[Chord homonym\|homonyns]]: none.
	~~Chords related to this triad~~ (7-limit ~~except where noted~~):
	* [[60:70:84:105]] – chord inversion		Notable extensions (7-limit):
	* [[4:5:6:7:9]] – adds 9/4 ~~(two octave spanning pentad)~~		* [[4:5:6:7:9]] – adds 9/4
	* [[12:14:18:21]] – ~~substitutes~~ 5/4 ~~with~~ 7/6		* [[12:15:18:21:28]] – adds 7/3 to make the 7-limit Hendrix chord
			Notable restrictions:

			* [[4:5:6]]
			* [[4:5:7]]
			* [[4:6:7]]
			* [[5:6:7]]

	[[Category:German sixth chords\|#]] <!-- 1-digit first number -->		[[Category:German sixth chords\|#]] <!-- 1-digit first number -->