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.

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 ==

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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.
-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)&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]].
+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 ==