User:MisterShafXen/6ed9/7
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6 equal divisions of 9/7 (abbreviated 6ed9/7) is a nonoctave tuning system that divides the interval of 9/7 into 6 equal parts of about 72.5 ¢ each. Each step represents a frequency ratio of (9/7)1/6, or the 6th root of 9/7.
Theory
This tuning tempers out 21/20 in the 7-limit, 55/54 in the 11-limit, 27/26, 55/52, and 16/13 in the 13-limit, 17/16 and 17/13 in the 17-limit, and 38/33 in the 19-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +32.7 | -16.6 | -7.0 | -30.8 | +16.1 | -33.2 | +25.7 | -33.2 | +2.0 | -18.0 | -23.6 | -17.2 | -0.4 | +25.1 | -14.1 | +26.0 | -0.4 | -21.5 | +34.7 | +22.7 |
| Relative (%) | +45.1 | -22.9 | -9.7 | -42.4 | +22.3 | -45.8 | +35.4 | -45.8 | +2.7 | -24.8 | -32.6 | -23.7 | -0.6 | +34.7 | -19.4 | +35.9 | -0.6 | -29.7 | +47.8 | +31.4 | |
| Steps (reduced) |
17 (5) |
26 (2) |
33 (3) |
38 (2) |
43 (1) |
46 (4) |
50 (2) |
52 (4) |
55 (1) |
57 (3) |
59 (5) |
61 (1) |
63 (3) |
65 (5) |
66 (0) |
68 (2) |
69 (3) |
70 (4) |
72 (0) |
73 (1) | |