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 this chord, or by inflecting both up by 36/35 to get the subharmonic seventh chord 1–9/7–3/2–9/5.

Audio of close voicings

4:5:6:7, Root position

5:6:7:8, 1st inversion

6:7:8:10, 2nd inversion

7:8:10:12, 3rd inversion

Notable voicings

Sorted by Wilson norm. AOV and CAOV stand for all-odd voicing and condensed AOV respectively. This list is only a brief overview, see Voicings of 4:5:6:7 for a more comprehensive list.

Voices	EFR	Hi-lo name	Special properties
4 voices	1:3:5:7	hi37loR	AOV, isodifferential
	2:3:5:7	hi37	CAOV
	3:4:5:7	lo5
	4:5:6:7	basic	Isodifferential
	4:6:7:10	hi3

Related chords

Melodic inversion: 1/(7:6:5:4) = 60:70:84:105 = 1–7/6–7/5–7/4, and its homonym 1/(12:10:8:7) = 70:84:105:120 = 1–6/5–3/2–12/7.

Plausible homonyms: none.

Notable extensions (7-limit):

• 4:5:6:7:9 – adds 9/4
• 12:15:18:21:28 – adds 7/3 to make the 7-limit Hendrix chord

Notable restrictions:

• 4:5:6
• 4:5:7
• 4:6:7
• 5:6:7