10ed5/3
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10 equal divisions of 5/3 (abbreviated 10ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 10 equal parts of about 88.4 ¢ each. Each step represents a frequency ratio of (5/3)1/10, or the 10th root of 5/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 88.4 | 22/21 |
| 2 | 176.9 | 9/8, 10/9, 21/19 |
| 3 | 265.3 | 13/11, 22/19 |
| 4 | 353.7 | 5/4 |
| 5 | 442.2 | 14/11, 17/13 |
| 6 | 530.6 | 4/3, 19/14 |
| 7 | 619.1 | |
| 8 | 707.5 | 3/2 |
| 9 | 795.9 | 11/7 |
| 10 | 884.4 | 5/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +38.1 | +43.6 | -12.2 | +43.6 | -6.7 | -8.3 | +25.9 | -1.2 | -6.7 | +5.2 | +31.4 |
| Relative (%) | +43.1 | +49.3 | -13.8 | +49.3 | -7.6 | -9.3 | +29.3 | -1.3 | -7.6 | +5.8 | +35.5 | |
| Steps (reduced) |
14 (4) |
22 (2) |
27 (7) |
32 (2) |
35 (5) |
38 (8) |
41 (1) |
43 (3) |
45 (5) |
47 (7) |
49 (9) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -18.7 | +29.8 | -1.2 | -24.5 | -41.0 | +36.9 | +31.8 | +31.4 | +35.4 | +43.3 | -33.7 |
| Relative (%) | -21.2 | +33.7 | -1.3 | -27.7 | -46.3 | +41.8 | +35.9 | +35.5 | +40.0 | +48.9 | -38.1 | |
| Steps (reduced) |
50 (0) |
52 (2) |
53 (3) |
54 (4) |
55 (5) |
57 (7) |
58 (8) |
59 (9) |
60 (0) |
61 (1) |
61 (1) | |