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It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction|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 [[70:84:105:120|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'' [[70:90:105:126|1–9/7–3/2–9/5]]. | It is a [[dyadic chord]] in the [[7-odd-limit]], with its most complex interval a [[7/5]] tritone. It is the [[octave reduction|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 [[70:84:105:120|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'' [[70:90:105:126|1–9/7–3/2–9/5]]. | ||
Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The [[15/16]] can step up by [[16/15]] to reach [[1/1]], and the [[21/16]] down by [[21/20]] to reach [[5/4]], to | Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being [[3/2]]–[[15/8]]–[[9/4]]–[[21/8]] above the tonic, which is octave-equivalent to [[15/16]]–[[9/8]]–[[21/16]]–[[3/2]]. The [[15/16]] can step up by [[16/15]] to reach [[1/1]], and the [[21/16]] down by [[21/20]] to reach [[5/4]], resolving to the [[4:5:6]] chord on the tonic. | ||
== Audio of close voicings == | == Audio of close voicings == | ||
Revision as of 02:23, 26 December 2025
| Chord information |
har-7 or h7
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.
Despite being harmonically simple, this chord may sound unresolved because it is so similar to the dominant seventh chord. However, this means it can be used as one, with a 4:5:6:7 chord on the dominant being 3/2–15/8–9/4–21/8 above the tonic, which is octave-equivalent to 15/16–9/8–21/16–3/2. The 15/16 can step up by 16/15 to reach 1/1, and the 21/16 down by 21/20 to reach 5/4, resolving to the 4:5:6 chord on the tonic.
Audio of close voicings
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: