8ed8/3
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(convergent)
8 equal divisions of 8/3 (abbreviated 8ed8/3) is a nonoctave tuning system that divides the interval of 8/3 into 8 equal parts of about 212 ¢ each. Each step represents a frequency ratio of (8/3)1/8, or the 8th root of 8/3.
Interval table
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 212.3 | 10/9, 15/13, 17/15, 19/17, 21/19 |
| 2 | 424.5 | 9/7, 13/10, 14/11, 17/13, 19/15 |
| 3 | 636.8 | 10/7, 13/9, 19/13 |
| 4 | 849 | 5/3, 18/11, 21/13 |
| 5 | 1061.3 | 9/5, 11/6, 13/7, 17/9, 20/11 |
| 6 | 1273.5 | 19/9, 21/10 |
| 7 | 1485.8 | 7/3 |
| 8 | 1698 | 13/5, 19/7 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +73.5 | +8.3 | -65.2 | -27.0 | +81.9 | +27.3 | +8.3 | +16.7 | +46.5 | +93.8 | -56.8 |
| Relative (%) | +34.6 | +3.9 | -30.7 | -12.7 | +38.6 | +12.8 | +3.9 | +7.9 | +21.9 | +44.2 | -26.8 | |
| Steps (reduced) |
6 (6) |
9 (1) |
11 (3) |
13 (5) |
15 (7) |
16 (0) |
17 (1) |
18 (2) |
19 (3) |
20 (4) |
20 (4) | |