15ed5/3
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Prime factorization
3 × 5
Step size
58.9572¢
Octave
20\15ed5/3 (1179.14¢) (→4\3ed5/3)
Twelfth
32\15ed5/3 (1886.63¢)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 14ed5/3 | 15ed5/3 | 16ed5/3 → |
15 equal divisions of 5/3 (abbreviated 15ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 15 equal parts of about 59 ¢ each. Each step represents a frequency ratio of (5/3)1/15, or the 15th root of 5/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 58.957 | 22/21 |
| 2 | 117.914 | 14/13, 15/14 |
| 3 | 176.872 | 10/9, 11/10, 19/17, 21/19, 23/21 |
| 4 | 235.829 | 15/13, 17/15, 22/19 |
| 5 | 294.786 | 6/5, 13/11 |
| 6 | 353.743 | 11/9, 17/14, 21/17 |
| 7 | 412.701 | 14/11, 19/15 |
| 8 | 471.658 | 13/10, 17/13 |
| 9 | 530.615 | 15/11, 19/14, 23/17 |
| 10 | 589.572 | 7/5 |
| 11 | 648.53 | 13/9, 19/13, 22/15 |
| 12 | 707.487 | 3/2 |
| 13 | 766.444 | 11/7, 14/9, 17/11 |
| 14 | 825.401 | 21/13 |
| 15 | 884.359 | 5/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -20.9 | -15.3 | +17.2 | -15.3 | +22.8 | -8.3 | -3.6 | +28.3 | +22.8 | -24.3 | +1.9 |
| Relative (%) | -35.4 | -26.0 | +29.3 | -26.0 | +38.6 | -14.0 | -6.1 | +48.0 | +38.6 | -41.2 | +3.3 | |
| Steps (reduced) |
20 (5) |
32 (2) |
41 (11) |
47 (2) |
53 (8) |
57 (12) |
61 (1) |
65 (5) |
68 (8) |
70 (10) |
73 (13) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -18.7 | -29.1 | +28.3 | -24.5 | -11.5 | +7.5 | -27.2 | +1.9 | -23.6 | +13.8 | -4.2 |
| Relative (%) | -31.8 | -49.4 | +48.0 | -41.5 | -19.5 | +12.6 | -46.1 | +3.3 | -40.0 | +23.4 | -7.1 | |
| Steps (reduced) |
75 (0) |
77 (2) |
80 (5) |
81 (6) |
83 (8) |
85 (10) |
86 (11) |
88 (13) |
89 (14) |
91 (1) |
92 (2) | |