15ed5/4
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Prime factorization
3 × 5
Step size
25.7542¢
Octave
47\15ed5/4 (1210.45¢)
Twelfth
74\15ed5/4 (1905.81¢)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 14ed5/4 | 15ed5/4 | 16ed5/4 → |
15 equal divisions of 5/4 (abbreviated 15ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 15 equal parts of about 25.8 ¢ each. Each step represents a frequency ratio of (5/4)1/15, or the 15th root of 5/4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 25.754 | |
| 2 | 51.508 | |
| 3 | 77.263 | 19/18, 21/20, 22/21, 23/22 |
| 4 | 103.017 | 15/14, 20/19 |
| 5 | 128.771 | |
| 6 | 154.525 | 11/10, 23/21 |
| 7 | 180.28 | 10/9, 21/19 |
| 8 | 206.034 | 17/15, 19/17 |
| 9 | 231.788 | 23/20 |
| 10 | 257.542 | 7/6, 15/13, 22/19 |
| 11 | 283.297 | 13/11 |
| 12 | 309.051 | |
| 13 | 334.805 | 6/5, 11/9, 23/19 |
| 14 | 360.559 | |
| 15 | 386.314 | 21/17 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.4 | +3.9 | -4.9 | -4.9 | -11.4 | +5.0 | +5.6 | +7.7 | +5.6 | -4.9 | -1.0 |
| Relative (%) | +40.6 | +15.0 | -18.9 | -18.9 | -44.4 | +19.3 | +21.7 | +30.0 | +21.7 | -19.0 | -3.9 | |
| Steps (reduced) |
47 (2) |
74 (14) |
93 (3) |
108 (3) |
120 (0) |
131 (11) |
140 (5) |
148 (13) |
155 (5) |
161 (11) |
167 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -10.8 | -10.3 | -1.0 | -9.7 | -11.6 | -7.6 | +1.8 | -9.7 | +8.8 | +5.6 | +5.9 |
| Relative (%) | -41.9 | -40.1 | -3.9 | -37.7 | -45.2 | -29.5 | +7.1 | -37.7 | +34.3 | +21.6 | +22.8 | |
| Steps (reduced) |
172 (7) |
177 (12) |
182 (2) |
186 (6) |
190 (10) |
194 (14) |
198 (3) |
201 (6) |
205 (10) |
208 (13) |
211 (1) | |