15ed11/5
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Prime factorization
3 × 5
Step size
91.0003¢
Octave
13\15ed11/5 (1183¢)
Twelfth
21\15ed11/5 (1911.01¢) (→7\5ed11/5)
Consistency limit
4
Distinct consistency limit
4
 |
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| ← 14ed11/5 | 15ed11/5 | 16ed11/5 → |
15 equal divisions of 11/5 (abbreviated 15ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 15 equal parts of about 91 ¢ each. Each step represents a frequency ratio of (11/5)1/15, or the 15th root of 11/5.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 91 | 18/17, 19/18, 20/19, 21/20, 22/21, 23/22 |
| 2 | 182 | 10/9, 11/10, 19/17, 21/19 |
| 3 | 273 | 7/6, 13/11, 20/17, 22/19 |
| 4 | 364 | 11/9, 21/17 |
| 5 | 455 | 9/7, 13/10, 17/13, 22/17 |
| 6 | 546 | 15/11, 18/13, 19/14 |
| 7 | 637 | 10/7, 13/9, 19/13 |
| 8 | 728 | 20/13, 23/15 |
| 9 | 819 | 21/13 |
| 10 | 910 | 17/10, 22/13 |
| 11 | 1001 | 9/5, 23/13 |
| 12 | 1092 | 13/7, 17/9, 19/10 |
| 13 | 1183 | 2/1 |
| 14 | 1274 | 19/9, 21/10, 23/11 |
| 15 | 1365 | 11/5, 20/9 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -17.0 | +9.1 | -34.0 | +34.7 | -7.9 | -1.8 | +40.0 | +18.1 | +17.7 | +34.7 | -24.9 |
| Relative (%) | -18.7 | +9.9 | -37.4 | +38.1 | -8.7 | -2.0 | +44.0 | +19.9 | +19.4 | +38.1 | -27.4 | |
| Steps (reduced) |
13 (13) |
21 (6) |
26 (11) |
31 (1) |
34 (4) |
37 (7) |
40 (10) |
42 (12) |
44 (14) |
46 (1) |
47 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +18.5 | -18.8 | +43.7 | +23.0 | +9.1 | +1.1 | -1.5 | +0.7 | +7.2 | +17.7 | +31.7 |
| Relative (%) | +20.3 | -20.7 | +48.1 | +25.3 | +10.0 | +1.2 | -1.6 | +0.8 | +8.0 | +19.4 | +34.9 | |
| Steps (reduced) |
49 (4) |
50 (5) |
52 (7) |
53 (8) |
54 (9) |
55 (10) |
56 (11) |
57 (12) |
58 (13) |
59 (14) |
60 (0) | |