11ed9/5
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Prime factorization
11 (prime)
Step size
92.5088¢
Octave
13\11ed9/5 (1202.61¢)
(convergent)
Twelfth
21\11ed9/5 (1942.68¢)
Consistency limit
4
Distinct consistency limit
4
 |
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| ← 10ed9/5 | 11ed9/5 | 12ed9/5 → |
(convergent)
11 equal divisions of 9/5 (abbreviated 11ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 11 equal parts of about 92.5 ¢ each. Each step represents a frequency ratio of (9/5)1/11, or the 11th root of 9/5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 92.509 | 16/15, 17/16, 20/19, 21/20, 22/21 |
| 2 | 185.018 | 11/10, 19/17, 21/19 |
| 3 | 277.526 | 13/11, 15/13, 19/16, 20/17, 22/19 |
| 4 | 370.035 | 5/4, 16/13, 21/17 |
| 5 | 462.544 | 13/10, 17/13, 21/16, 22/17 |
| 6 | 555.053 | 7/5, 11/8, 15/11, 19/14 |
| 7 | 647.561 | 10/7, 16/11, 19/13, 22/15 |
| 8 | 740.07 | 17/11, 20/13 |
| 9 | 832.579 | 8/5, 13/8, 21/13 |
| 10 | 925.088 | 17/10, 19/11, 22/13 |
| 11 | 1017.596 | 20/11 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.6 | +40.7 | +5.2 | -11.1 | +43.3 | -38.5 | +7.8 | -11.1 | -8.4 | +11.6 | +46.0 |
| Relative (%) | +2.8 | +44.0 | +5.7 | -11.9 | +46.9 | -41.6 | +8.5 | -11.9 | -9.1 | +12.5 | +49.7 | |
| Steps (reduced) |
13 (2) |
21 (10) |
26 (4) |
30 (8) |
34 (1) |
36 (3) |
39 (6) |
41 (8) |
43 (10) |
45 (1) |
47 (3) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.1 | -35.9 | +29.7 | +10.5 | -2.0 | -8.4 | -9.5 | -5.8 | +2.2 | +14.2 | +29.7 |
| Relative (%) | -0.1 | -38.8 | +32.1 | +11.3 | -2.2 | -9.1 | -10.3 | -6.3 | +2.4 | +15.3 | +32.2 | |
| Steps (reduced) |
48 (4) |
49 (5) |
51 (7) |
52 (8) |
53 (9) |
54 (10) |
55 (0) |
56 (1) |
57 (2) |
58 (3) |
59 (4) | |