4:6:7: Difference between revisions

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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 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.

== ~~<span data-darkreader-inline-color~~=~~"">~~Rotations around the octave~~</span>~~ ==

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]].

== Rotations around the octave ==

[[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:

* 4:7:12 – open voicing

* 3:4:7 - open voicing

* 6:7:8 – first rotation

* [[4:5:7]] - no threes version

* 3:4:7 – first rotation, open voicing

* [[4:5:6:7]] - full tetrad

* [[12:14:21]] – melodic inversion

* [[4:5:7]] – no threes version

* [[4:5:6:7]] – full tetrad

* [[12:14:18:21]] – adds [[7/6]]

* [[28:36:42:49]] – adds [[9/7]], a type of [[dominant seventh chord]]

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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 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.
-== <span data-darkreader-inline-color="">Rotations around the octave</span> ==
+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)&nbsp;=&nbsp;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]].
+== Rotations around the octave ==
 [[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"]]
+{{chord edo approximation}}
 == Related chords ==
 Chords related to this triad:
+* 4:7:12 – open voicing
-* 3:4:7 - open voicing
+* 6:7:8 – first rotation
-* [[4:5:7]] - no threes version
+* 3:4:7 – first rotation, open voicing
-* [[4:5:6:7]] - full tetrad
+* [[12:14:21]] – melodic inversion
+* [[4:5:7]] – no threes version
+* [[4:5:6:7]] – full tetrad
+* [[12:14:18:21]] – adds [[7/6]]
+* [[28:36:42:49]] – adds [[9/7]], a type of [[dominant seventh chord]]