11ed9/4
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Prime factorization
11 (prime)
Step size
127.628¢
Octave
9\11ed9/4 (1148.65¢)
Twelfth
15\11ed9/4 (1914.42¢)
(semiconvergent)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 9ed9/4 | 11ed9/4 | 13ed9/4 → |
(semiconvergent)
11 equal divisions of 9/4 (abbreviated 11ed9/4) is a nonoctave tuning system that divides the interval of 9/4 into 11 equal parts of about 128 ¢ each. Each step represents a frequency ratio of (9/4)1/11, or the 11th root of 9/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 127.6 | 18/17 |
| 2 | 255.3 | 7/6, 15/13, 20/17, 22/19 |
| 3 | 382.9 | 19/15, 21/17 |
| 4 | 510.5 | 15/11 |
| 5 | 638.1 | 10/7, 13/9, 19/13, 22/15 |
| 6 | 765.8 | |
| 7 | 893.4 | 5/3, 17/10, 22/13 |
| 8 | 1021 | 9/5 |
| 9 | 1148.7 | |
| 10 | 1276.3 | 19/9, 21/10 |
| 11 | 1403.9 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -51.3 | +12.5 | +24.9 | +21.5 | -38.9 | -50.5 | -26.4 | +24.9 | -29.8 | +60.4 | +37.4 |
| Relative (%) | -40.2 | +9.8 | +19.5 | +16.9 | -30.5 | -39.6 | -20.7 | +19.5 | -23.4 | +47.3 | +29.3 | |
| Steps (reduced) |
9 (9) |
15 (4) |
19 (8) |
22 (0) |
24 (2) |
26 (4) |
28 (6) |
30 (8) |
31 (9) |
33 (0) |
34 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +26.5 | +25.8 | +34.0 | +49.9 | -55.1 | -26.4 | +7.6 | +46.4 | -38.0 | +9.1 | +59.7 |
| Relative (%) | +20.7 | +20.2 | +26.6 | +39.1 | -43.2 | -20.7 | +6.0 | +36.4 | -29.8 | +7.1 | +46.8 | |
| Steps (reduced) |
35 (2) |
36 (3) |
37 (4) |
38 (5) |
38 (5) |
39 (6) |
40 (7) |
41 (8) |
41 (8) |
42 (9) |
43 (10) | |