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 the subharmonic sixth chord. | 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 the subharmonic sixth chord. The intervals [[25/24]] and [[49/48]] thus serve as chromas, and they are equated when [[50/49]] is tempered out, such as in [[pajara]]. | ||
== Rotations around the octave == | == Rotations around the octave == | ||
Revision as of 05:51, 13 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 the subharmonic sixth chord. The intervals 25/24 and 49/48 thus serve as chromas, and they are equated when 50/49 is tempered out, such as in pajara.
Rotations around the octave
Voicings and rotations around two octaves
Voicing Rotation
|
Root | '3 | '5 | '7 | '3'5 | '3'7 | '5'7 | '3'5'7 |
|---|---|---|---|---|---|---|---|---|
| On 1 | 4:5:6:7 | 4:5:7:12 | 4:6:7:10 | 4:5:6:14 | 4:7:10:12 | 4:5:12:14 | 2:3:5:7 | 2:5:6:7 |
| On 3 | 6:7:16:20 | 3:4:5:7 | 6:7:10:16 | 3:7:8:10 | 3:4:7:10 | 6:7:8:10 | 3:5:7:8 | 6:7:8:20 |
| On 5 | 5:6:7:16 | 5:7:12:16 | 5:8:12:14 | 5:6:14:16 | 5:6:8:14 | 5:12:14:16 | 5:7:8:12 | 5:6:7:8 |
| On 7 | 7:16:20:24 | 7:12:16:20 | 7:10:16:24 | 7:8:10:12 | 7:10:12:16 | 7:8:10:24 | 7:8:12:20 | 7:8:20:24 |
Enumerations in italics map to an existing octave-reduced rotation.
Related chords
Chords related to this triad (7-limit except where noted):
- 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