7ed9/7
| ← 6ed9/7 | 7ed9/7 | 8ed9/7 → |
7 equal divisions of 9/7 (abbreviated 7ed9/7) is a nonoctave tuning system that divides the interval of 9/7 into 7 equal parts of about 62.2 ¢ each. Each step represents a frequency ratio of (9/7)1/7, or the 7th root of 9/7. It is a very flat version of 19edo.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -17.1 | +28.0 | +28.0 | +15.2 | +10.8 | -7.0 | +10.8 | -6.3 | -2.0 | +19.8 | -6.3 |
| Relative (%) | -27.5 | +44.9 | +44.9 | +24.4 | +17.4 | -11.3 | +17.4 | -10.1 | -3.1 | +31.8 | -10.1 | |
| Steps (reduced) |
19 (3) |
31 (7) |
39 (7) |
45 (5) |
50 (2) |
54 (6) |
58 (2) |
61 (5) |
64 (0) |
67 (3) |
69 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -20.4 | -24.2 | -19.1 | -6.3 | +13.2 | -23.5 | +7.4 | -19.1 | +20.9 | +2.7 | -12.0 |
| Relative (%) | -32.7 | -38.8 | -30.7 | -10.1 | +21.3 | -37.7 | +12.0 | -30.7 | +33.6 | +4.3 | -19.3 | |
| Steps (reduced) |
71 (7) |
73 (1) |
75 (3) |
77 (5) |
79 (7) |
80 (0) |
82 (2) |
83 (3) |
85 (5) |
86 (6) |
87 (7) | |
Due to near-cancellation of the errors in harmonics 3 and 4, 7ed9/7 is similar to 8ed4/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 62.2 | 19/18, 20/19 |
| 2 | 124.3 | 12/11, 13/12, 14/13, 18/17, 21/20 |
| 3 | 186.5 | 8/7, 11/10, 17/15, 19/17, 21/19 |
| 4 | 248.6 | 7/6, 13/11, 20/17 |
| 5 | 310.8 | 6/5, 11/9, 16/13 |
| 6 | 372.9 | 14/11, 17/14, 19/15, 21/17 |
| 7 | 435.1 | 5/4, 13/10 |