9ed8/3
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| ← 8ed8/3 | 9ed8/3 | 10ed8/3 → |
(semiconvergent)
9 equal divisions of 8/3 (abbreviated 9ed8/3) is a nonoctave tuning system that divides the interval of 8/3 into 9 equal parts of about 189 ¢ each. Each step represents a frequency ratio of (8/3)1/9, or the 9th root of 8/3.
Interval table
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 188.7 | 10/9, 11/10, 17/15, 19/17, 21/19 |
| 2 | 377.3 | 11/9, 19/15, 21/17 |
| 3 | 566 | 7/5, 15/11, 19/14 |
| 4 | 754.7 | 11/7, 14/9, 17/11 |
| 5 | 943.4 | 17/10, 19/11 |
| 6 | 1132 | 17/9, 19/10, 21/11 |
| 7 | 1320.7 | 15/7, 19/9, 21/10 |
| 8 | 1509.4 | 17/7, 22/9 |
| 9 | 1698 | 19/7 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -68.0 | -15.2 | +52.7 | +43.8 | -83.2 | +27.3 | -15.2 | -30.5 | -24.2 | -0.5 | +37.5 |
| Relative (%) | -36.0 | -8.1 | +27.9 | +23.2 | -44.1 | +14.5 | -8.1 | -16.2 | -12.8 | -0.3 | +19.9 | |
| Steps (reduced) |
6 (6) |
10 (1) |
13 (4) |
15 (6) |
16 (7) |
18 (0) |
19 (1) |
20 (2) |
21 (3) |
22 (4) |
23 (5) | |