15ed5/2
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Prime factorization
3 × 5
Step size
105.754¢
Octave
11\15ed5/2 (1163.3¢)
Twelfth
18\15ed5/2 (1903.58¢) (→6\5ed5/2)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 14ed5/2 | 15ed5/2 | 16ed5/2 → |
15 equal divisions of 5/2 (abbreviated 15ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 15 equal parts of about 106 ¢ each. Each step represents a frequency ratio of (5/2)1/15, or the 15th root of 5/2.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 105.754 | 15/14, 18/17, 19/18 |
| 2 | 211.508 | 17/15, 19/17 |
| 3 | 317.263 | 6/5, 17/14, 23/19 |
| 4 | 423.017 | 9/7, 14/11, 19/15, 23/18 |
| 5 | 528.771 | 15/11, 19/14, 23/17 |
| 6 | 634.525 | 13/9 |
| 7 | 740.28 | 17/11, 23/15 |
| 8 | 846.034 | 18/11, 21/13, 23/14 |
| 9 | 951.788 | 19/11 |
| 10 | 1057.542 | 11/6, 13/7 |
| 11 | 1163.297 | |
| 12 | 1269.051 | 23/11 |
| 13 | 1374.805 | 11/5 |
| 14 | 1480.559 | 7/3 |
| 15 | 1586.314 | 5/2 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -36.7 | +1.6 | +32.3 | -36.7 | -35.1 | +15.3 | -4.4 | +3.2 | +32.3 | -26.9 | +34.0 |
| Relative (%) | -34.7 | +1.5 | +30.6 | -34.7 | -33.2 | +14.5 | -4.1 | +3.1 | +30.6 | -25.4 | +32.1 | |
| Steps (reduced) |
11 (11) |
18 (3) |
23 (8) |
26 (11) |
29 (14) |
32 (2) |
34 (4) |
36 (6) |
38 (8) |
39 (9) |
41 (11) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.2 | -21.4 | -35.1 | -41.1 | -40.3 | -33.5 | -21.3 | -4.4 | +16.9 | +42.1 | -34.8 |
| Relative (%) | +1.1 | -20.2 | -33.2 | -38.8 | -38.1 | -31.6 | -20.1 | -4.1 | +16.0 | +39.9 | -32.9 | |
| Steps (reduced) |
42 (12) |
43 (13) |
44 (14) |
45 (0) |
46 (1) |
47 (2) |
48 (3) |
49 (4) |
50 (5) |
51 (6) |
51 (6) | |