4:5:6:7: Difference between revisions
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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 [[16/15|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. | |||
{{chord edo approximation}} | |||
== Audio of close voicings == | == Audio of close voicings == | ||
[[File:SculpEufaDem4-5-6-7-onD.mp3|none|thumb|4:5:6:7, Root position]] | [[File:SculpEufaDem4-5-6-7-onD.mp3|none|thumb|4:5:6:7, Root position]] | ||
[[File:SculpEufaDem5-6-7-8-onD.mp3|none|thumb|5:6:7:8, 1st inversion]] | [[File:SculpEufaDem5-6-7-8-onD.mp3|none|thumb|5:6:7:8, 1st inversion]] | ||
[[File:SculpEufaDem6-7-8-10-onD.mp3|none|thumb|6:7:8:10, 2nd inversion]] | [[File:SculpEufaDem6-7-8-10-onD.mp3|none|thumb|6:7:8:10, 2nd inversion]] | ||
[[File:SculpEufaDem7-8-10-12-onD.mp3|none|thumb|7:8:10:12, 3rd inversion]] | [[File:SculpEufaDem7-8-10-12-onD.mp3|none|thumb|7:8:10:12, 3rd inversion]] | ||
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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. | 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 [[chord homonym| | Plausible [[chord homonym|homonyms]]: none. | ||
Notable extensions (7-limit): | Notable extensions (7-limit): | ||
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* [[5:6:7]] | * [[5:6:7]] | ||
[[Category:Dominant seventh chords|#]] | |||
[[Category:German sixth chords|#]] <!-- 1-digit first number --> | [[Category:German sixth chords|#]] <!-- 1-digit first number --> | ||
Latest revision as of 04:29, 26 May 2026
| 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.
| Edo | Steps | Cents (¢) | Absolute errors (¢) | RMS (¢) | RMS (%) | |
|---|---|---|---|---|---|---|
| ▶ | 10 | 0 3 6 8 |
0.00 360.00 720.00 960.00 |
0.00 -26.31 +18.04 -8.83 |
15.99 | 13.33 |
| ▶ | 12 | 0 4 7 10 |
0.00 400.00 700.00 1000.00 |
0.00 +13.69 -1.96 +31.17 |
13.25 | 13.25 |
| ▶ | 15 | 0 5 9 12 |
0.00 400.00 720.00 960.00 |
0.00 +13.69 +18.04 -8.83 |
10.72 | 13.40 |
| ▶ | 19 | 0 6 11 15 |
0.00 378.95 694.74 947.37 |
0.00 -7.37 -7.22 -21.46 |
7.78 | 12.32 |
| ▶ | 22 | 0 7 13 18 |
0.00 381.82 709.09 981.82 |
0.00 -4.50 +7.14 +12.99 |
6.69 | 12.26 |
| ▶ | 27 | 0 9 16 22 |
0.00 400.00 711.11 977.78 |
0.00 +13.69 +9.16 +8.95 |
4.96 | 11.17 |
| ▶ | 31 | 0 10 18 25 |
0.00 387.10 696.77 967.74 |
0.00 +0.78 -5.18 -1.08 |
2.30 | 5.94 |
| ▶ | 37 | 0 12 22 30 |
0.00 389.19 713.51 972.97 |
0.00 +2.88 +11.56 +4.15 |
4.26 | 13.15 |
| ▶ | 41 | 0 13 24 33 |
0.00 380.49 702.44 965.85 |
0.00 -5.83 +0.48 -2.97 |
2.54 | 8.67 |
| ▶ | 46 | 0 15 27 37 |
0.00 391.30 704.35 965.22 |
0.00 +4.99 +2.39 -3.61 |
3.17 | 12.14 |
| ▶ | 50 | 0 16 29 40 |
0.00 384.00 696.00 960.00 |
0.00 -2.31 -5.96 -8.83 |
3.38 | 14.08 |
| ▶ | 53 | 0 17 31 43 |
0.00 384.91 701.89 973.58 |
0.00 -1.41 -0.07 +4.76 |
2.34 | 10.34 |
| ▶ | 58 | 0 19 34 47 |
0.00 393.10 703.45 972.41 |
0.00 +6.79 +1.49 +3.59 |
2.55 | 12.32 |
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: