6:7:8

Chord information

Harmonics	6:7:8
Subharmonics	1/(28:24:21)
Intervals from root	1/1–7/6–4/3
Cents from root	0¢–267¢–498¢
Step intervals	7/6, 8/7
Step cents	267¢, 231¢
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; …

6:7:8 is a 7-limit triad consisting of the intervals 7/6 and 8/7 stacked on top of each other. This chord deviates from traditional harmony in that the intervals divide the perfect fourth rather than the perfect fifth. The 7/6 and 8/7 intervals 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. The 6:7:8 chord may be better voiced as 4:7:12 in order to place the root on the bottom and avoid clashes. It's rotation 4:6:7 is a subchord of 4:5:6:7, the harmonic seventh chord.