6:7:9
| Chord information |
6:7:9, the subminor triad or septimal minor triad, is a triad in the 7-limit sometimes used in place of a minor triad. It appears as a minor triad in the diatonic scale of superpyth, as 64/63 being tempered out means 32/27 is equated with 7/6. This is in contrast to meantone, where 32/27 is equated with 6/5, and thus the minor triad becomes 10:12:15.
6:7:9 is the second-simplest otonal tertian triad, past 4:5:6, and is thus very consonant. The inverse of 6:7:9 is 14:18:21, the supermajor triad. These triads can be used in the same way as the 5-limit ones, leading to a septimal version of tertian harmony. However, this has a number of issues. First of all, 14:18:21 may sound unstable due to its relatively high otonal complexity. In addition, the 7/6 and 9/7 intervals differ by 54/49, an interval of 168 cents, unlike 5/4 and 6/5, which differ by 25/24, an interval only about 71 cents in size. This means the 6:7:9 and 14:18:21 chords don't contrast as well as the 5-limit 4:5:6 and 10:12:15 chords. Another important fact is that the 6:7:9 chord doesn't contain the root, though it is a subchord of 4:5:6:7:9 which does.
The 6:7:9 triad and its inverse 14:18:21 are nonetheless useful in tertian harmony, bringing new flavors not found in the 5-limit.
| Edo | Steps | Cents (¢) | Absolute errors (¢) | RMS (¢) | RMS (%) | |
|---|---|---|---|---|---|---|
| ▶ | 8 | 0 2 5 |
0.00 300.00 750.00 |
0.00 +33.13 +48.04 |
20.08 | 13.39 |
| ▶ | 9 | 0 2 5 |
0.00 266.67 666.67 |
0.00 -0.20 -35.29 |
16.59 | 12.44 |
| ▶ | 14 | 0 3 8 |
0.00 257.14 685.71 |
0.00 -9.73 -16.24 |
6.67 | 7.79 |
| ▶ | 17 | 0 4 10 |
0.00 282.35 705.88 |
0.00 +15.48 +3.93 |
6.57 | 9.31 |
| ▶ | 19 | 0 4 11 |
0.00 252.63 694.74 |
0.00 -14.24 -7.22 |
5.81 | 9.20 |
| ▶ | 22 | 0 5 13 |
0.00 272.73 709.09 |
0.00 +5.86 +7.14 |
3.11 | 5.70 |
| ▶ | 27 | 0 6 16 |
0.00 266.67 711.11 |
0.00 -0.20 +9.16 |
4.37 | 9.82 |
| ▶ | 31 | 0 7 18 |
0.00 270.97 696.77 |
0.00 +4.10 -5.18 |
3.80 | 9.81 |
| ▶ | 36 | 0 8 21 |
0.00 266.67 700.00 |
0.00 -0.20 -1.96 |
0.88 | 2.63 |
| ▶ | 39 | 0 9 23 |
0.00 276.92 707.69 |
0.00 +10.05 +5.74 |
4.12 | 13.38 |
| ▶ | 41 | 0 9 24 |
0.00 263.41 702.44 |
0.00 -3.46 +0.48 |
1.75 | 5.99 |
| ▶ | 44 | 0 10 26 |
0.00 272.73 709.09 |
0.00 +5.86 +7.14 |
3.11 | 11.39 |
| ▶ | 46 | 0 10 27 |
0.00 260.87 704.35 |
0.00 -6.00 +2.39 |
3.53 | 13.54 |
| ▶ | 49 | 0 11 29 |
0.00 269.39 710.20 |
0.00 +2.52 +8.25 |
3.45 | 14.10 |
| ▶ | 50 | 0 11 29 |
0.00 264.00 696.00 |
0.00 -2.87 -5.96 |
2.43 | 10.13 |
| ▶ | 53 | 0 12 31 |
0.00 271.70 701.89 |
0.00 +4.83 -0.07 |
2.29 | 10.12 |
| ▶ | 55 | 0 12 32 |
0.00 261.82 698.18 |
0.00 -5.05 -3.77 |
2.14 | 9.83 |
| ▶ | 58 | 0 13 34 |
0.00 268.97 703.45 |
0.00 +2.09 +1.49 |
0.88 | 4.26 |
| ▶ | 60 | 0 13 35 |
0.00 260.00 700.00 |
0.00 -6.87 -1.96 |
2.89 | 14.45 |
See also
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Todo: add sound example, research
This chord may be closely connected to 7-limit interpretations of the Blues scale. |