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.
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 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -19.1 | +24.8 | +10.7 | -12.5 | +13.1 | -27.5 | +5.3 | -0.8 | -20.8 | +13.0 | +21.8 | +26.3 |
| Relative (%) | -30.7 | +40.0 | +17.1 | -20.1 | +21.0 | -44.3 | +8.5 | -1.3 | -33.5 | +20.9 | +35.1 | +42.3 | |
| Steps (reduced) |
19 (5) |
31 (3) |
45 (3) |
54 (5) |
67 (4) |
71 (1) |
79 (2) |
82 (5) |
87 (3) |
94 (3) |
96 (5) |
101 (3) | |