4:5:6:7: Difference between revisions
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'''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]]. | '''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 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| | 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]]. | ||
== Audio of close voicings == | == Audio of close voicings == | ||
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== Notable voicings == | == Notable voicings == | ||
Sorted by [[Wilson norm | Sorted by [[Wilson norm]]. AOV and CAOV stand for [[Odd limit #Proposed extensions|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. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
!Voices | ! Voices | ||
![[EFR]] | ! [[EFR]] | ||
![[Kite's thoughts on hi-lo notation|Hi-lo name]] | ! [[Kite's thoughts on hi-lo notation|Hi-lo name]] | ||
!Special properties | ! Special properties | ||
|- | |- | ||
| rowspan="5" |4 voices | | rowspan="5" |4 voices | ||
|1:3:5:7 | | 1:3:5:7 | ||
|hi37loR | | hi37loR | ||
|AOV, [[Isodifferential chord|isodifferential]] | | AOV, [[Isodifferential chord|isodifferential]] | ||
|- | |- | ||
|2:3:5:7 | | 2:3:5:7 | ||
|hi37 | | hi37 | ||
|CAOV | | CAOV | ||
|- | |- | ||
|3:4:5:7 | | 3:4:5:7 | ||
|lo5 | | lo5 | ||
| | | | ||
|- | |- | ||
|4:5:6:7 | | 4:5:6:7 | ||
| | | Basic | ||
| | | Isodifferential | ||
|- | |- | ||
|4:6:7:10 | | 4:6:7:10 | ||
|hi3 | | hi3 | ||
| | | | ||
|} | |} | ||
== Related chords == | == Related chords == | ||
Melodic inversion: 7:6:5:4 = [[60:70:84:105]] = | 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 [[ | Plausible [[chord homonym|homonyns]]: none. | ||
Notable extensions (7-limit): | Notable extensions (7-limit): | ||
* [[4:5:6:7:9]] – adds 9/4 | * [[4:5:6:7:9]] – adds 9/4 | ||
* [[12:15:18:21:28]] – adds 7/3 to make the 7-limit Hendrix chord | * [[12:15:18:21:28]] – adds 7/3 to make the 7-limit Hendrix chord | ||
Notable restrictions: | Notable restrictions: | ||
* [[4:5:6]] | * [[4:5:6]] | ||
* [[4:5:7]] | * [[4:5:7]] | ||
Revision as of 09:38, 24 November 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.
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 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: