12ed8/3
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| ← 11ed8/3 | 12ed8/3 | 13ed8/3 → |
12 equal divisions of 8/3 (abbreviated 12ed8/3) is a nonoctave tuning system that divides the interval of 8/3 into 12 equal parts of about 142 ¢ each. Each step represents a frequency ratio of (8/3)1/12, or the 12th root of 8/3.
Interval table
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 141.5 | 11/10, 14/13, 15/14, 23/21 |
| 2 | 283 | 13/11 |
| 3 | 424.5 | 14/11, 19/15 |
| 4 | 566 | 7/5 |
| 5 | 707.5 | 3/2 |
| 6 | 849 | 21/13, 23/14 |
| 7 | 990.5 | 23/13 |
| 8 | 1132 | 19/10, 21/11 |
| 9 | 1273.5 | 21/10, 23/11 |
| 10 | 1415 | 9/4, 23/10 |
| 11 | 1556.5 | 17/7, 22/9 |
| 12 | 1698 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -68.0 | -62.4 | +5.6 | +43.8 | +11.1 | +27.3 | -62.4 | +16.7 | -24.2 | -47.7 | -56.8 |
| Relative (%) | -48.0 | -44.1 | +3.9 | +30.9 | +7.9 | +19.3 | -44.1 | +11.8 | -17.1 | -33.7 | -40.2 | |
| Steps (reduced) |
8 (8) |
13 (1) |
17 (5) |
20 (8) |
22 (10) |
24 (0) |
25 (1) |
27 (3) |
28 (4) |
29 (5) |
30 (6) | |