4:6:7
| Chord information |
har-7 no-5 or h7no5
4:6:7 is a 7-limit chord found as a subset of the harmonic seventh chord, 4:5:6:7. Due to having no fives, it is the first otonal chord that deviates from traditional harmony. As such, it is a candidate for metallic harmony, a form of extraclassical tonality that employs 7 instead of 5 as its other prime.
Its first rotation, 6:7:8, is significant because it consists of the intervals 7/6 and 8/7 stacked on top of each other. The intervals in this chord divide the perfect fourth rather than the perfect fifth, and contrast by 49/48, similarly to how 5/4 and 6/5 contrast by 25/24 in 4:5:6. By swapping the order of 7/6 and 8/7, we get the utonal inverse of 6:7:8, that being 1/(8:7:6) = 21:24:28.
Another notable setting is the open voicing 4:7:12, which shares the property with 6:7:8 that its intervals, 7/4 and 12/7, contrast by 49/48, but they divide the perfect twelfth instead. This also has the advantage of avoiding the unresolvedness of a dominant seventh chord that occurs in the 6:7:8 and 4:6:7 voicings. Its utonal version is 7:12:21, an open voicing of 14:21:24.
Rotations around the octave
| Edo | Steps | Cents (¢) | Absolute errors (¢) | RMS (¢) | RMS (%) | |
|---|---|---|---|---|---|---|
| ▶ | 9 | 0 5 7 |
0.00 666.67 933.33 |
0.00 -35.29 -35.49 |
16.68 | 12.51 |
| ▶ | 10 | 0 6 8 |
0.00 720.00 960.00 |
0.00 +18.04 -8.83 |
11.18 | 9.32 |
| ▶ | 14 | 0 8 11 |
0.00 685.71 942.86 |
0.00 -16.24 -25.97 |
10.71 | 12.50 |
| ▶ | 15 | 0 9 12 |
0.00 720.00 960.00 |
0.00 +18.04 -8.83 |
11.18 | 13.98 |
| ▶ | 17 | 0 10 14 |
0.00 705.88 988.24 |
0.00 +3.93 +19.41 |
8.38 | 11.87 |
| ▶ | 19 | 0 11 15 |
0.00 694.74 947.37 |
0.00 -7.22 -21.46 |
8.91 | 14.12 |
| ▶ | 21 | 0 12 17 |
0.00 685.71 971.43 |
0.00 -16.24 +2.60 |
8.34 | 14.59 |
| ▶ | 22 | 0 13 18 |
0.00 709.09 981.82 |
0.00 +7.14 +12.99 |
5.31 | 9.74 |
| ▶ | 26 | 0 15 21 |
0.00 692.31 969.23 |
0.00 -9.65 +0.40 |
4.65 | 10.07 |
| ▶ | 27 | 0 16 22 |
0.00 711.11 977.78 |
0.00 +9.16 +8.95 |
4.27 | 9.61 |
| ▶ | 31 | 0 18 25 |
0.00 696.77 967.74 |
0.00 -5.18 -1.08 |
2.23 | 5.76 |
| ▶ | 32 | 0 19 26 |
0.00 712.50 975.00 |
0.00 +10.54 +6.17 |
4.33 | 11.54 |
| ▶ | 36 | 0 21 29 |
0.00 700.00 966.67 |
0.00 -1.96 -2.16 |
0.97 | 2.92 |
| ▶ | 37 | 0 22 30 |
0.00 713.51 972.97 |
0.00 +11.56 +4.15 |
4.78 | 14.74 |
| ▶ | 41 | 0 24 33 |
0.00 702.44 965.85 |
0.00 +0.48 -2.97 |
1.53 | 5.22 |
| ▶ | 46 | 0 27 37 |
0.00 704.35 965.22 |
0.00 +2.39 -3.61 |
2.47 | 9.46 |
| ▶ | 48 | 0 28 39 |
0.00 700.00 975.00 |
0.00 -1.96 +6.17 |
3.46 | 13.86 |
| ▶ | 51 | 0 30 41 |
0.00 705.88 964.71 |
0.00 +3.93 -4.12 |
3.29 | 13.96 |
| ▶ | 53 | 0 31 43 |
0.00 701.89 973.58 |
0.00 -0.07 +4.76 |
2.26 | 9.98 |
| ▶ | 58 | 0 34 47 |
0.00 703.45 972.41 |
0.00 +1.49 +3.59 |
1.47 | 7.11 |
Related chords
Chords related to this triad:
- 4:7:12 – open voicing
- 6:7:8 – first rotation
- 3:4:7 – first rotation, open voicing
- 12:14:21 – melodic inversion
- 4:5:7 – no threes version
- 4:5:6:7 – full tetrad
- 12:14:18:21 – adds 7/6
- 28:36:42:49 – adds 9/7, a type of dominant seventh chord