4:6:7 - Revision history

Pailiaq at 04:28, 26 May 2026

2026-05-26T04:28:14Z

← Older revision		Revision as of 04:28, 26 May 2026
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	[[File:SculpEufaDem6-7-8-onD.mp3\|none\|thumb\|6:7:8 "1st inversion"]]		[[File:SculpEufaDem6-7-8-onD.mp3\|none\|thumb\|6:7:8 "1st inversion"]]
	[[File:SculpEufaDem7-8-12-onD.mp3\|none\|thumb\|7:8:12 "2nd inversion"]]		[[File:SculpEufaDem7-8-12-onD.mp3\|none\|thumb\|7:8:12 "2nd inversion"]]

			{{chord edo approximation}}

	== Related chords ==		== Related chords ==

FloraC: De-bold non-target

2026-01-20T16:50:22Z

De-bold non-target

← Older revision		Revision as of 16:50, 20 January 2026
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	Its first rotation, '''6:7:8''', is significant because it consists of the intervals [[7/6]] and [[8/7]] stacked on top of each other. The intervals in this chord divide the [[4/3\|perfect fourth]] rather than the [[3/2\|perfect fifth]], and contrast by [[49/48]], similarly to how [[5/4]] and [[6/5]] contrast by [[25/24]] in [[4:5:6]]. By swapping the order of 7/6 and 8/7, we get the utonal inverse of 6:7:8, that being [[21:24:28\|1/(8:7:6) = 21:24:28]].		Its first rotation, '''6:7:8''', is significant because it consists of the intervals [[7/6]] and [[8/7]] stacked on top of each other. The intervals in this chord divide the [[4/3\|perfect fourth]] rather than the [[3/2\|perfect fifth]], and contrast by [[49/48]], similarly to how [[5/4]] and [[6/5]] contrast by [[25/24]] in [[4:5:6]]. By swapping the order of 7/6 and 8/7, we get the utonal inverse of 6:7:8, that being [[21:24:28\|1/(8:7:6) = 21:24:28]].

	Another notable setting is the open voicing ~~'''~~4:7:12~~'''~~, which shares the property with 6:7:8 that its intervals, 7/4 and [[12/7]], contrast by 49/48, but they divide the [[3/1\|perfect twelfth]] instead. This also has the advantage of avoiding the unresolvedness of a dominant seventh chord that occurs in the 6:7:8 and 4:6:7 voicings. Its utonal version is 7:12:21, an open voicing of [[14:21:24]].		Another notable setting is the open voicing 4:7:12, which shares the property with 6:7:8 that its intervals, 7/4 and [[12/7]], contrast by 49/48, but they divide the [[3/1\|perfect twelfth]] instead. This also has the advantage of avoiding the unresolvedness of a dominant seventh chord that occurs in the 6:7:8 and 4:6:7 voicings. Its utonal version is 7:12:21, an open voicing of [[14:21:24]].

	== Rotations around the octave ==		== Rotations around the octave ==

Overthink: /* Related chords */ add 28:36:42:49

2025-12-30T09:24:32Z

Related chords: add 28:36:42:49

← Older revision		Revision as of 09:24, 30 December 2025
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	* 6:7:8 – first rotation		* 6:7:8 – first rotation
	* 3:4:7 – first rotation, open voicing		* 3:4:7 – first rotation, open voicing
	* [[12:14:21]] - melodic inversion		* [[12:14:21]] – melodic inversion
	* [[4:5:7]] – no threes version		* [[4:5:7]] – no threes version
	* [[4:5:6:7]] – full tetrad		* [[4:5:6:7]] – full tetrad
	* [[12:14:18:21]] - adds [[7/6]]		* [[12:14:18:21]] – adds [[7/6]]
			* [[28:36:42:49]] – adds [[9/7]], a type of [[dominant seventh chord]]

Overthink: no-break spaces and bold

2025-12-25T08:37:19Z

no-break spaces and bold

← Older revision		Revision as of 08:37, 25 December 2025
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	'''4:6:7''' is a [[7-limit]] [[chord]] found as a subset of the harmonic seventh chord, [[4:5:6:7]]. Due to having no fives, it is the first otonal chord that deviates from traditional harmony. As such, it is a candidate for [[metallic harmony]], a form of [[extraclassical tonality]] that employs 7 instead of 5 as its other prime.		'''4:6:7''' is a [[7-limit]] [[chord]] found as a subset of the harmonic seventh chord, [[4:5:6:7]]. Due to having no fives, it is the first otonal chord that deviates from traditional harmony. As such, it is a candidate for [[metallic harmony]], a form of [[extraclassical tonality]] that employs 7 instead of 5 as its other prime.

	Its first rotation, '''6:7:8''', is significant because it consists of the intervals [[7/6]] and [[8/7]] stacked on top of each other. The intervals in this chord divide the [[4/3\|perfect fourth]] rather than the [[3/2\|perfect fifth]], and contrast by [[49/48]], similarly to how [[5/4]] and [[6/5]] contrast by [[25/24]] in [[4:5:6]]. By swapping the order of 7/6 and 8/7, we get the utonal inverse of 6:7:8, that being [[21:24:28\|1/(8:7:6) = 21:24:28]].		Its first rotation, '''6:7:8''', is significant because it consists of the intervals [[7/6]] and [[8/7]] stacked on top of each other. The intervals in this chord divide the [[4/3\|perfect fourth]] rather than the [[3/2\|perfect fifth]], and contrast by [[49/48]], similarly to how [[5/4]] and [[6/5]] contrast by [[25/24]] in [[4:5:6]]. By swapping the order of 7/6 and 8/7, we get the utonal inverse of 6:7:8, that being [[21:24:28\|1/(8:7:6) = 21:24:28]].

	Another notable setting is the open voicing 4:7:12, which shares the property with 6:7:8 that its intervals, 7/4 and [[12/7]], contrast by 49/48, but they divide the [[3/1\|perfect twelfth]] instead. This also has the advantage of avoiding the unresolvedness of a dominant seventh chord that occurs in the 6:7:8 and 4:6:7 voicings. Its utonal version is 7:12:21, an open voicing of [[14:21:24]].		Another notable setting is the open voicing '''4:7:12''', which shares the property with 6:7:8 that its intervals, 7/4 and [[12/7]], contrast by 49/48, but they divide the [[3/1\|perfect twelfth]] instead. This also has the advantage of avoiding the unresolvedness of a dominant seventh chord that occurs in the 6:7:8 and 4:6:7 voicings. Its utonal version is 7:12:21, an open voicing of [[14:21:24]].

	== Rotations around the octave ==		== Rotations around the octave ==

Overthink: note dominant seventh unresolvedness

2025-12-25T08:35:00Z

note dominant seventh unresolvedness

← Older revision		Revision as of 08:35, 25 December 2025
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	Its first rotation, '''6:7:8''', is significant because it consists of the intervals [[7/6]] and [[8/7]] stacked on top of each other. The intervals in this chord divide the [[4/3\|perfect fourth]] rather than the [[3/2\|perfect fifth]], and contrast by [[49/48]], similarly to how [[5/4]] and [[6/5]] contrast by [[25/24]] in [[4:5:6]]. By swapping the order of 7/6 and 8/7, we get the utonal inverse of 6:7:8, that being [[21:24:28\|1/(8:7:6) = 21:24:28]].		Its first rotation, '''6:7:8''', is significant because it consists of the intervals [[7/6]] and [[8/7]] stacked on top of each other. The intervals in this chord divide the [[4/3\|perfect fourth]] rather than the [[3/2\|perfect fifth]], and contrast by [[49/48]], similarly to how [[5/4]] and [[6/5]] contrast by [[25/24]] in [[4:5:6]]. By swapping the order of 7/6 and 8/7, we get the utonal inverse of 6:7:8, that being [[21:24:28\|1/(8:7:6) = 21:24:28]].

	Another notable setting is the open voicing 4:7:12, which shares the property with 6:7:8 that its intervals, 7/4 and [[12/7]], contrast by 49/48, but they divide the [[3/1\|perfect twelfth]] instead. Its utonal version is 7:12:21, an open voicing of [[14:21:24]].		Another notable setting is the open voicing 4:7:12, which shares the property with 6:7:8 that its intervals, 7/4 and [[12/7]], contrast by 49/48, but they divide the [[3/1\|perfect twelfth]] instead. This also has the advantage of avoiding the unresolvedness of a dominant seventh chord that occurs in the 6:7:8 and 4:6:7 voicings. Its utonal version is 7:12:21, an open voicing of [[14:21:24]].

	== Rotations around the octave ==		== Rotations around the octave ==

FloraC: Absorb contents from 6:7:8 and expand on 4:7:12

2025-12-18T11:44:39Z

Absorb contents from 6:7:8 and expand on 4:7:12

← Older revision		Revision as of 11:44, 18 December 2025
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	{{Infobox Chord\|ColorName=yo zo-7 no-5 or y,z7no5, har-7 no-5 or h7no5}}		{{Infobox Chord\|ColorName=yo zo-7 no-5 or y,z7no5, har-7 no-5 or h7no5}}
	'''4:6:7''' is a [[7-limit]] [[chord]] found as a subset of the harmonic seventh chord, [[4:5:6:7]]. Due to having no fives, it is the first otonal chord that deviates from ~~tonal music theory~~. As such, it is a candidate for [[metallic harmony]], a form of [[extraclassical tonality]] that employs 7 instead of 5 as its other prime.		'''4:6:7''' is a [[7-limit]] [[chord]] found as a subset of the harmonic seventh chord, [[4:5:6:7]]. Due to having no fives, it is the first otonal chord that deviates from traditional harmony. As such, it is a candidate for [[metallic harmony]], a form of [[extraclassical tonality]] that employs 7 instead of 5 as its other prime.

			Its first rotation, '''6:7:8''', is significant because it consists of the intervals [[7/6]] and [[8/7]] stacked on top of each other. The intervals in this chord divide the [[4/3\|perfect fourth]] rather than the [[3/2\|perfect fifth]], and contrast by [[49/48]], similarly to how [[5/4]] and [[6/5]] contrast by [[25/24]] in [[4:5:6]]. By swapping the order of 7/6 and 8/7, we get the utonal inverse of 6:7:8, that being [[21:24:28\|1/(8:7:6) = 21:24:28]].

			Another notable setting is the open voicing 4:7:12, which shares the property with 6:7:8 that its intervals, 7/4 and [[12/7]], contrast by 49/48, but they divide the [[3/1\|perfect twelfth]] instead. Its utonal version is 7:12:21, an open voicing of [[14:21:24]].

	== Rotations around the octave ==		== Rotations around the octave ==

Overthink: /* Related chords */ added more

2025-11-22T00:33:53Z

Related chords: added more

← Older revision		Revision as of 00:33, 22 November 2025
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	* 6:7:8 – first rotation		* 6:7:8 – first rotation
	* 3:4:7 – first rotation, open voicing		* 3:4:7 – first rotation, open voicing
			* [[12:14:21]] - melodic inversion
	* [[4:5:7]] – no threes version		* [[4:5:7]] – no threes version
	* [[4:5:6:7]] – full tetrad		* [[4:5:6:7]] – full tetrad
			* [[12:14:18:21]] - adds [[7/6]]

FloraC: Open voicing shouldn't change its bass note

2025-11-10T10:10:15Z

Open voicing shouldn't change its bass note

← Older revision		Revision as of 10:10, 10 November 2025
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	{{Infobox Chord\|ColorName=yo zo-7 no-5 or y,z7no5, har-7 no-5 or h7no5}}'''4:6:7''' is a [[7-limit]] [[chord]] found as a subset of the harmonic seventh chord, [[4:5:6:7]]. Due to having no fives, it is the first otonal chord that deviates from tonal music theory. As such, it is a candidate for [[metallic harmony]], a form of [[extraclassical tonality]] that employs 7 instead of 5 as its other prime.		{{Infobox Chord\|ColorName=yo zo-7 no-5 or y,z7no5, har-7 no-5 or h7no5}}
			'''4:6:7''' is a [[7-limit]] [[chord]] found as a subset of the harmonic seventh chord, [[4:5:6:7]]. Due to having no fives, it is the first otonal chord that deviates from tonal music theory. As such, it is a candidate for [[metallic harmony]], a form of [[extraclassical tonality]] that employs 7 instead of 5 as its other prime.

	== Rotations around the octave ==		== Rotations around the octave ==
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	== Related chords ==		== Related chords ==
	Chords related to this triad:		Chords related to this triad:
			* 4:7:12 – open voicing
	* 3:4:7 – open voicing		* 6:7:8 – first rotation
			* 3:4:7 – first rotation, open voicing
	* [[4:5:7]] – no threes version		* [[4:5:7]] – no threes version
	* [[4:5:6:7]] – full tetrad		* [[4:5:6:7]] – full tetrad

FloraC: Utonal -> otonal. + links

2025-11-10T10:05:31Z

Utonal -> otonal. + links

← Older revision		Revision as of 10:05, 10 November 2025
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	{{Infobox Chord\|ColorName=yo zo-7 no-5 or y,z7no5, har-7 no-5 or h7no5}}'''4:6:7''' is a 7-limit chord found as a subset of the harmonic seventh chord, [[4:5:6:7]]. Due to having no fives, it is the first ~~utonal~~ chord that deviates from tonal music theory. As such, it is a candidate for [[metallic harmony]], a form of [[extraclassical tonality]] that employs 7 instead of 5 as its other prime.		{{Infobox Chord\|ColorName=yo zo-7 no-5 or y,z7no5, har-7 no-5 or h7no5}}'''4:6:7''' is a [[7-limit]] [[chord]] found as a subset of the harmonic seventh chord, [[4:5:6:7]]. Due to having no fives, it is the first otonal chord that deviates from tonal music theory. As such, it is a candidate for [[metallic harmony]], a form of [[extraclassical tonality]] that employs 7 instead of 5 as its other prime.

	== ~~<span data-darkreader-inline-color="">~~Rotations around the octave~~</span>~~ ==		== Rotations around the octave ==
	[[File:SculpEufaDem4-6-7-onD.mp3\|none\|thumb\|4:6:7 "Root position"]]		[[File:SculpEufaDem4-6-7-onD.mp3\|none\|thumb\|4:6:7 "Root position"]]
	[[File:SculpEufaDem6-7-8-onD.mp3\|none\|thumb\|6:7:8 "1st inversion"]]		[[File:SculpEufaDem6-7-8-onD.mp3\|none\|thumb\|6:7:8 "1st inversion"]]
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	Chords related to this triad:		Chords related to this triad:

	* 3:4:7 - open voicing		* 3:4:7 – open voicing
	* [[4:5:7]] - no threes version		* [[4:5:7]] – no threes version
	* [[4:5:6:7]] - full tetrad		* [[4:5:6:7]] – full tetrad

Eufalesio: Birth

2025-11-09T15:25:59Z

Birth

New page

{{Infobox Chord|ColorName=yo zo-7 no-5 or y,z7no5, har-7 no-5 or h7no5}}'''4:6:7''' is a 7-limit chord found as a subset of the harmonic seventh chord, [[4:5:6:7]]. Due to having no fives, it is the first utonal chord that deviates from tonal music theory. As such, it is a candidate for [[metallic harmony]], a form of [[extraclassical tonality]] that employs 7 instead of 5 as its other prime.

== <span data-darkreader-inline-color="">Rotations around the octave</span> ==
[[File:SculpEufaDem4-6-7-onD.mp3|none|thumb|4:6:7 "Root position"]]
[[File:SculpEufaDem6-7-8-onD.mp3|none|thumb|6:7:8 "1st inversion"]]
[[File:SculpEufaDem7-8-12-onD.mp3|none|thumb|7:8:12 "2nd inversion"]]

== Related chords ==
Chords related to this triad:

* 3:4:7 - open voicing
* [[4:5:7]] - no threes version
* [[4:5:6:7]] - full tetrad