11ed11/5
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Prime factorization
11 (prime)
Step size
124.091¢
Octave
10\11ed11/5 (1240.91¢)
Twelfth
15\11ed11/5 (1861.37¢)
Consistency limit
2
Distinct consistency limit
2
| ← 10ed11/5 | 11ed11/5 | 12ed11/5 → |
11 equal divisions of 11/5 (abbreviated 11ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 11 equal parts of about 124 ¢ each. Each step represents a frequency ratio of (11/5)1/11, or the 11th root of 11/5.
Intervals
| Step | Interval (¢) | JI approximated | Simplified ratios |
|---|---|---|---|
| 1 | 124.09 | 29/27 | |
| 2 | 248.18 | 22/19 | |
| 3 | 372.27 | 31/25 | |
| 4 | 496.37 | 8/6, 29/22 | 4/3 |
| 5 | 620.46 | 52/36 | 13/9 |
| 6 | 744.55 | 80/52 | 20/13 |
| 7 | 868.46 | 10/6, 36/22 | 5/3, 18/11 |
| 8 | 992.73 | 39/22, 55/31, 64/36 | 16/9 |
| 9 | 1116.82 | 19/10 | |
| 10 | 1240.91 | 39/19 | |
| 11 | 1365.00 | 11/5 |
The subgroup interpretation used is 11/5.6.8.10.19.25.27.29.31.39.45.52. Other interpretations are possible. Don't forget that fractions can multiply, e.g. 10*11/5=22, 25*11/5=55.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +40.9 | -40.6 | -42.3 | -56.3 | +0.3 | -18.4 | -1.4 | +42.9 | -15.4 | -56.3 | +41.2 |
| Relative (%) | +33.0 | -32.7 | -34.1 | -45.4 | +0.3 | -14.8 | -1.1 | +34.6 | -12.4 | -45.4 | +33.2 | |
| Steps (reduced) |
10 (10) |
15 (4) |
19 (8) |
22 (0) |
25 (3) |
27 (5) |
29 (7) |
31 (9) |
32 (10) |
33 (0) |
35 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +26.8 | +22.6 | +27.2 | +39.6 | +58.7 | -40.3 | -9.8 | +25.5 | -58.9 | -15.4 | +31.7 |
| Relative (%) | +21.6 | +18.2 | +21.9 | +31.9 | +47.3 | -32.4 | -7.9 | +20.6 | -47.5 | -12.4 | +25.6 | |
| Steps (reduced) |
36 (3) |
37 (4) |
38 (5) |
39 (6) |
40 (7) |
40 (7) |
41 (8) |
42 (9) |
42 (9) |
43 (10) |
44 (0) | |
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