10ed5/2
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Prime factorization
2 × 5
Step size
158.631¢
Octave
8\10ed5/2 (1269.05¢) (→4\5ed5/2)
Twelfth
12\10ed5/2 (1903.58¢) (→6\5ed5/2)
Consistency limit
3
Distinct consistency limit
2
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| ← 9ed5/2 | 10ed5/2 | 11ed5/2 → |
10 equal divisions of 5/2 (abbreviated 10ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 10 equal parts of about 159 ¢ each. Each step represents a frequency ratio of (5/2)1/10, or the 10th root of 5/2.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 158.631 | 14/13, 19/17, 21/19 |
| 2 | 317.263 | 6/5, 11/9, 13/11, 17/14 |
| 3 | 475.894 | 17/13, 22/17 |
| 4 | 634.525 | 13/9, 19/13, 22/15 |
| 5 | 793.157 | 11/7, 14/9 |
| 6 | 951.788 | 19/11 |
| 7 | 1110.42 | 17/9, 21/11 |
| 8 | 1269.051 | 19/9 |
| 9 | 1427.682 | |
| 10 | 1586.314 | 5/2 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +69.1 | +1.6 | -20.5 | +69.1 | +70.7 | -37.6 | +48.5 | +3.2 | -20.5 | -26.9 | -18.9 |
| Relative (%) | +43.5 | +1.0 | -12.9 | +43.5 | +44.6 | -23.7 | +30.6 | +2.0 | -12.9 | -17.0 | -11.9 | |
| Steps (reduced) |
8 (8) |
12 (2) |
15 (5) |
18 (8) |
20 (0) |
21 (1) |
23 (3) |
24 (4) |
25 (5) |
26 (6) |
27 (7) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.2 | +31.5 | +70.7 | -41.1 | +12.6 | +72.3 | -21.3 | +48.5 | -35.9 | +42.1 | -34.8 |
| Relative (%) | +0.7 | +19.8 | +44.6 | -25.9 | +8.0 | +45.6 | -13.4 | +30.6 | -22.7 | +26.6 | -21.9 | |
| Steps (reduced) |
28 (8) |
29 (9) |
30 (0) |
30 (0) |
31 (1) |
32 (2) |
32 (2) |
33 (3) |
33 (3) |
34 (4) |
34 (4) | |