4:6:7: Difference between revisions

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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]].  
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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 ==
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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]]