4:6:7

Chord information

Harmonics	4:6:7
Subharmonics	1/(21:14:12)
Intervals from root	1/1–3/2–7/4
Cents from root	0¢–702¢–969¢
Step intervals	3/2, 7/6
Step cents	702¢, 267¢
Color names	yo zo-7 no-5 or y,z7no5 har-7 no-5 or h7no5
Prime limit	7
Genus	3⋅7 (21)
Intervallic odd limit	7
Otonal odd limit	7
Utonal odd limit	21
Consistent edos (d ≥ 2)	5edo**, 10edo*, 22edo*, 26edo*, …
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

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

4:6:7 "Root position"

6:7:8 "1st inversion"

7:8:12 "2nd inversion"

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