9ed11/5
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Prime factorization
32
Step size
151.667¢
Octave
8\9ed11/5 (1213.34¢)
(semiconvergent)
Twelfth
13\9ed11/5 (1971.67¢)
Consistency limit
4
Distinct consistency limit
2
 |
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| ← 8ed11/5 | 9ed11/5 | 10ed11/5 → |
(semiconvergent)
9 equal divisions of 11/5 (abbreviated 9ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 9 equal parts of about 152 ¢ each. Each step represents a frequency ratio of (11/5)1/9, or the 9th root of 11/5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 151.667 | 11/10, 14/13, 15/14, 21/19 |
| 2 | 303.334 | 13/11, 17/14, 19/16, 20/17 |
| 3 | 455.001 | 13/10, 14/11, 17/13, 21/16, 22/17 |
| 4 | 606.669 | 7/5, 10/7 |
| 5 | 758.336 | 11/7, 17/11, 19/12, 20/13 |
| 6 | 910.003 | 17/10, 22/13 |
| 7 | 1061.67 | 13/7, 15/8, 20/11 |
| 8 | 1213.337 | 2/1 |
| 9 | 1365.004 | 11/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +13.3 | +69.7 | +26.7 | -56.3 | -68.6 | -32.1 | +40.0 | -12.2 | -43.0 | -56.3 | -55.3 |
| Relative (%) | +8.8 | +46.0 | +17.6 | -37.1 | -45.2 | -21.2 | +26.4 | -8.1 | -28.3 | -37.1 | -36.4 | |
| Steps (reduced) |
8 (8) |
13 (4) |
16 (7) |
18 (0) |
20 (2) |
22 (4) |
24 (6) |
25 (7) |
26 (8) |
27 (0) |
28 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -42.2 | -18.8 | +13.4 | +53.3 | -51.6 | +1.1 | +59.2 | -29.6 | +37.6 | -43.0 | +31.7 |
| Relative (%) | -27.8 | -12.4 | +8.8 | +35.2 | -34.0 | +0.7 | +39.0 | -19.5 | +24.8 | -28.3 | +20.9 | |
| Steps (reduced) |
29 (2) |
30 (3) |
31 (4) |
32 (5) |
32 (5) |
33 (6) |
34 (7) |
34 (7) |
35 (8) |
35 (8) |
36 (0) | |