12ed11/5
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Prime factorization
22 × 3
Step size
113.75¢
Octave
11\12ed11/5 (1251.25¢)
Twelfth
17\12ed11/5 (1933.76¢)
Consistency limit
3
Distinct consistency limit
2
Special properties
 |
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| ← 11ed11/5 | 12ed11/5 | 13ed11/5 → |
12 equal divisions of 11/5 (abbreviated 12ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 12 equal parts of about 114 ¢ each. Each step represents a frequency ratio of (11/5)1/12, or the 12th root of 11/5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 113.75 | 20/19 |
| 2 | 227.501 | 15/13, 17/15, 22/19, 23/20 |
| 3 | 341.251 | 23/19 |
| 4 | 455.001 | 9/7, 13/10, 17/13, 22/17 |
| 5 | 568.752 | |
| 6 | 682.502 | 3/2, 19/13, 22/15 |
| 7 | 796.252 | |
| 8 | 910.003 | 17/10, 22/13 |
| 9 | 1023.753 | |
| 10 | 1137.504 | 19/10 |
| 11 | 1251.254 | |
| 12 | 1365.004 | 11/5, 20/9 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +51.3 | +31.8 | -11.2 | -56.3 | -30.7 | +43.7 | +40.0 | -50.1 | -5.1 | -56.3 | +20.6 |
| Relative (%) | +45.1 | +28.0 | -9.9 | -49.5 | -27.0 | +38.4 | +35.2 | -44.1 | -4.4 | -49.5 | +18.1 | |
| Steps (reduced) |
11 (11) |
17 (5) |
21 (9) |
24 (0) |
27 (3) |
30 (6) |
32 (8) |
33 (9) |
35 (11) |
36 (0) |
38 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.3 | -18.8 | -24.5 | -22.5 | -13.7 | +1.1 | +21.3 | +46.2 | -38.3 | -5.1 | +31.7 |
| Relative (%) | -3.7 | -16.5 | -21.5 | -19.8 | -12.0 | +1.0 | +18.7 | +40.6 | -33.6 | -4.4 | +27.9 | |
| Steps (reduced) |
39 (3) |
40 (4) |
41 (5) |
42 (6) |
43 (7) |
44 (8) |
45 (9) |
46 (10) |
46 (10) |
47 (11) |
48 (0) | |