4:6:7: Difference between revisions
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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 | 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 == | ||
Revision as of 16:50, 20 January 2026
| Chord information |
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.
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 perfect fourth rather than the 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 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 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
Related chords
Chords related to this triad:
- 4:7:12 – open voicing
- 6:7:8 – first rotation
- 3:4:7 – first rotation, open voicing
- 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