4:5:6:7

Chord information

Harmonics	4:5:6:7
Subharmonics	1/(105:84:70:60)
Intervals from root	1/1–5/4–3/2–7/4
Cents from root	0¢–386¢–702¢–969¢
Step intervals	5/4, 6/5, 7/6
Step cents	386¢, 316¢, 267¢
Color names	yo zo-7 or y,z7 har-7 or h7
Prime limit	7
Genus	3⋅5⋅7 (105)
Intervallic odd limit	7
Otonal odd limit	7
Utonal odd limit	105
Consistent edos (d ≥ 2)	31edo*, 41edo*, 68edo*, 72edo*
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

English Wikipedia has an article on:

Harmonic seventh chord

4:5:6:7, the harmonic seventh chord, is the simplest tetrad in 7-limit harmony. It is often used as a tuning target for the dominant seventh chord in barbershop music (→ Wikipedia: Harmonic seventh chord #Barbershop seventh ), and also for the German augmented sixth chord in septimal meantone.

It is a dyadic chord in the 7-odd-limit, with its most complex interval a 7/5 tritone. It is the octave-reduced version of the first four odd harmonics, 1:3:5:7, or the first eight harmonics, 1::8. It is the fundamental otonal consonance of the 7-odd-limit. The utonal minor version of this chord is 1-6/5-3/2-12/7, sometimes called the subharmonic sixth chord. The harmonic seventh chord can be modified by inflecting the 5/4 down by 25/24 and 7/4 down by 49/48 to get the subharmonic sixth chord.

Rotations around the octave

4:5:6:7 "Root position"

5:6:7:8 "1st inversion"

6:7:8:10 "2nd inversion"

7:8:10:12 "3rd inversion"

Related chords

Chords related to this triad (5-limit except where noted):

• 2:3:5:7 - open voicing
• 60:70:84:105 - chord inversion
• 4:5:6:7:9 - adds 9/4 (two octave spanning pentad)
• 12:14:18:21 - substitutes 5/4 with 7/6