11ed4
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11 equal divisions of the 4th harmonic (abbreviated 11ed4) is a nonoctave tuning system that divides the interval of 4/1 into 11 equal parts of about 218 ¢ each. Each step represents a frequency ratio of 41/11, or the 11th root of 4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 218.2 | 19/17 |
| 2 | 436.4 | 14/11, 17/13 |
| 3 | 654.5 | 19/13, 22/15 |
| 4 | 872.7 | 5/3 |
| 5 | 1090.9 | 13/7, 21/11 |
| 6 | 1309.1 | |
| 7 | 1527.3 | 17/7, 22/9 |
| 8 | 1745.5 | 19/7 |
| 9 | 1963.6 | |
| 10 | 2181.8 | |
| 11 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +109.1 | +61.7 | +0.0 | +50.0 | -47.4 | -96.1 | +109.1 | -94.8 | -59.0 | -5.9 | +61.7 |
| Relative (%) | +50.0 | +28.3 | +0.0 | +22.9 | -21.7 | -44.0 | +50.0 | -43.5 | -27.1 | -2.7 | +28.3 | |
| Steps (reduced) |
6 (6) |
9 (9) |
11 (0) |
13 (2) |
14 (3) |
15 (4) |
17 (6) |
17 (6) |
18 (7) |
19 (8) |
20 (9) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -76.9 | +13.0 | -106.5 | +0.0 | -105.0 | +14.3 | -79.3 | +50.0 | -34.4 | +103.2 | +26.3 |
| Relative (%) | -35.2 | +6.0 | -48.8 | +0.0 | -48.1 | +6.5 | -36.4 | +22.9 | -15.8 | +47.3 | +12.0 | |
| Steps (reduced) |
20 (9) |
21 (10) |
21 (10) |
22 (0) |
22 (0) |
23 (1) |
23 (1) |
24 (2) |
24 (2) |
25 (3) |
25 (3) | |