4:5:6:7
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.
| Chord information |
har-7 or h7
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
Notable voicings
AOV and CAOV stand for all-odd voicing and condensed AOV respectively.
| Voices | Voicing | 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: 7:6:5:4 = 60:70:84:105 = 1/1 - 7/6 - 7/5 - 7/4, and its homonym 12:10:8:7 = 70:84:105:120 = 1/1 - 6/5 - 3/2 - 12/7.
Plausible homonyns: 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: