11ed5/2
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Prime factorization
11 (prime)
Step size
144.21¢
Octave
8\11ed5/2 (1153.68¢)
Twelfth
13\11ed5/2 (1874.73¢)
(semiconvergent)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 10ed5/2 | 11ed5/2 | 12ed5/2 → |
(semiconvergent)
11 equal divisions of 5/2 (abbreviated 11ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 11 equal parts of about 144 ¢ each. Each step represents a frequency ratio of (5/2)1/11, or the 11th root of 5/2.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 144.2 | 15/14, 21/19 |
| 2 | 288.4 | 6/5, 7/6, 13/11 |
| 3 | 432.6 | 9/7, 19/15, 22/17 |
| 4 | 576.8 | 7/5 |
| 5 | 721.1 | 3/2 |
| 6 | 865.3 | 5/3 |
| 7 | 1009.5 | 9/5 |
| 8 | 1153.7 | |
| 9 | 1297.9 | 15/7, 19/9, 21/10 |
| 10 | 1442.1 | 7/3 |
| 11 | 1586.3 | 5/2 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -46.3 | -27.2 | +51.6 | -46.3 | +70.7 | -52.0 | +5.3 | -54.4 | +51.6 | +30.8 | +24.4 |
| Relative (%) | -32.1 | -18.9 | +35.8 | -32.1 | +49.0 | -36.1 | +3.6 | -37.8 | +35.8 | +21.3 | +16.9 | |
| Steps (reduced) |
8 (8) |
13 (2) |
17 (6) |
19 (8) |
22 (0) |
23 (1) |
25 (3) |
26 (4) |
28 (6) |
29 (7) |
30 (8) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +30.0 | +45.9 | +70.7 | -41.1 | -1.8 | +43.5 | -50.2 | +5.3 | +65.0 | -15.5 | +51.7 |
| Relative (%) | +20.8 | +31.8 | +49.0 | -28.5 | -1.3 | +30.1 | -34.8 | +3.6 | +45.1 | -10.8 | +35.9 | |
| Steps (reduced) |
31 (9) |
32 (10) |
33 (0) |
33 (0) |
34 (1) |
35 (2) |
35 (2) |
36 (3) |
37 (4) |
37 (4) |
38 (5) | |