14:21:24
| Chord information |
14:21:24 is a 7-limit chord found as a subset of the subharmonic sixth chord, 70:84:105:120, or of the septimal major sixth chord, 14:18:21:24. Due to having no fives, it is the first utonal 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, 21:24:28, is significant because it consists of the intervals 8/7 and 7/6 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 6/5 and 5/4 contrast by 25/24 in 10:12:15. By swapping the order of 8/7 and 7/6, we get the otonal inverse of 21:24:28, that being 6:7:8.
Another notable setting is the open voicing 7:12:21, which shares the property with 21:24:28 that its intervals, 12/7 and 7/4, contrast by 49/48, but they divide the perfect twelfth instead. Its otonal version is 4:7:12, an open voicing of 4:6:7.
Its second rotation, 12:14:21, is also significant because it functions as the fifthless version of the septimal minor seventh chord, 12:14:18:21.
| Edo | Steps | Cents (¢) | Absolute errors (¢) | RMS (¢) | RMS (%) | |
|---|---|---|---|---|---|---|
| ▶ | 9 | 0 5 7 |
0.00 666.67 933.33 |
0.00 -35.29 +0.20 |
16.68 | 12.51 |
| ▶ | 10 | 0 6 8 |
0.00 720.00 960.00 |
0.00 +18.04 +26.87 |
11.18 | 9.32 |
| ▶ | 14 | 0 8 11 |
0.00 685.71 942.86 |
0.00 -16.24 +9.73 |
10.71 | 12.50 |
| ▶ | 15 | 0 9 12 |
0.00 720.00 960.00 |
0.00 +18.04 +26.87 |
11.18 | 13.98 |
| ▶ | 17 | 0 10 13 |
0.00 705.88 917.65 |
0.00 +3.93 -15.48 |
8.38 | 11.87 |
| ▶ | 19 | 0 11 15 |
0.00 694.74 947.37 |
0.00 -7.22 +14.24 |
8.91 | 14.12 |
| ▶ | 21 | 0 12 16 |
0.00 685.71 914.29 |
0.00 -16.24 -18.84 |
8.34 | 14.59 |
| ▶ | 22 | 0 13 17 |
0.00 709.09 927.27 |
0.00 +7.14 -5.86 |
5.31 | 9.74 |
| ▶ | 26 | 0 15 20 |
0.00 692.31 923.08 |
0.00 -9.65 -10.05 |
4.65 | 10.07 |
| ▶ | 27 | 0 16 21 |
0.00 711.11 933.33 |
0.00 +9.16 +0.20 |
4.27 | 9.61 |
| ▶ | 31 | 0 18 24 |
0.00 696.77 929.03 |
0.00 -5.18 -4.10 |
2.23 | 5.76 |
| ▶ | 32 | 0 19 25 |
0.00 712.50 937.50 |
0.00 +10.54 +4.37 |
4.33 | 11.54 |
| ▶ | 36 | 0 21 28 |
0.00 700.00 933.33 |
0.00 -1.96 +0.20 |
0.97 | 2.92 |
| ▶ | 37 | 0 22 29 |
0.00 713.51 940.54 |
0.00 +11.56 +7.41 |
4.78 | 14.74 |
| ▶ | 41 | 0 24 32 |
0.00 702.44 936.59 |
0.00 +0.48 +3.46 |
1.53 | 5.22 |
| ▶ | 46 | 0 27 36 |
0.00 704.35 939.13 |
0.00 +2.39 +6.00 |
2.47 | 9.46 |
| ▶ | 48 | 0 28 37 |
0.00 700.00 925.00 |
0.00 -1.96 -8.13 |
3.46 | 13.86 |
| ▶ | 51 | 0 30 40 |
0.00 705.88 941.18 |
0.00 +3.93 +8.05 |
3.29 | 13.96 |
| ▶ | 53 | 0 31 41 |
0.00 701.89 928.30 |
0.00 -0.07 -4.83 |
2.26 | 9.98 |
| ▶ | 58 | 0 34 45 |
0.00 703.45 931.03 |
0.00 +1.49 -2.09 |
1.47 | 7.11 |