9ed9/5
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Prime factorization
32
Step size
113.066¢
Octave
11\9ed9/5 (1243.73¢)
Twelfth
17\9ed9/5 (1922.13¢)
Consistency limit
3
Distinct consistency limit
3
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| ← 8ed9/5 | 9ed9/5 | 10ed9/5 → |
9 equal divisions of 9/5 (abbreviated 9ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 9 equal parts of about 113 ¢ each. Each step represents a frequency ratio of (9/5)1/9, or the 9th root of 9/5.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 113.066 | 15/14, 22/21 |
| 2 | 226.133 | 19/17 |
| 3 | 339.199 | 6/5, 11/9 |
| 4 | 452.265 | 9/7, 14/11, 17/13 |
| 5 | 565.331 | 7/5, 15/11 |
| 6 | 678.398 | 3/2, 19/13, 22/15 |
| 7 | 791.464 | 11/7, 14/9 |
| 8 | 904.53 | 5/3 |
| 9 | 1017.596 | 9/5, 11/6 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +43.7 | +20.2 | -25.6 | +40.3 | -49.2 | +23.2 | +18.1 | +40.3 | -29.0 | +32.1 | -5.4 |
| Relative (%) | +38.7 | +17.8 | -22.6 | +35.7 | -43.5 | +20.5 | +16.0 | +35.7 | -25.6 | +28.4 | -4.8 | |
| Steps (reduced) |
11 (2) |
17 (8) |
21 (3) |
25 (7) |
27 (0) |
30 (3) |
32 (5) |
34 (7) |
35 (8) |
37 (1) |
38 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -30.9 | -46.2 | -52.6 | -51.2 | -43.1 | -29.0 | -9.5 | +14.7 | +43.3 | -37.2 | -1.1 |
| Relative (%) | -27.4 | -40.8 | -46.5 | -45.3 | -38.1 | -25.6 | -8.4 | +13.0 | +38.3 | -32.9 | -1.0 | |
| Steps (reduced) |
39 (3) |
40 (4) |
41 (5) |
42 (6) |
43 (7) |
44 (8) |
45 (0) |
46 (1) |
47 (2) |
47 (2) |
48 (3) | |