9ed9/4
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Prime factorization
32
Step size
155.99¢
Octave
8\9ed9/4 (1247.92¢)
Twelfth
12\9ed9/4 (1871.88¢) (→4\3ed9/4)
Consistency limit
2
Distinct consistency limit
2
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| ← 7ed9/4 | 9ed9/4 | 11ed9/4 → |
9 equal divisions of 9/4 (abbreviated 9ed9/4) is a nonoctave tuning system that divides the interval of 9/4 into 9 equal parts of about 156 ¢ each. Each step represents a frequency ratio of (9/4)1/9, or the 9th root of 9/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 156 | 11/10, 12/11, 21/19 |
| 2 | 312 | 6/5 |
| 3 | 468 | 17/13 |
| 4 | 624 | 10/7, 13/9 |
| 5 | 780 | 11/7, 19/12 |
| 6 | 935.9 | 7/4, 12/7, 19/11 |
| 7 | 1091.9 | 17/9, 19/10, 21/11 |
| 8 | 1247.9 | 21/10 |
| 9 | 1403.9 | 11/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +47.9 | -30.1 | -60.1 | +21.5 | +17.8 | +63.0 | -12.2 | -60.1 | +69.4 | +60.4 | +65.8 |
| Relative (%) | +30.7 | -19.3 | -38.6 | +13.8 | +11.4 | +40.4 | -7.8 | -38.6 | +44.5 | +38.7 | +42.2 | |
| Steps (reduced) |
8 (8) |
12 (3) |
15 (6) |
18 (0) |
20 (2) |
22 (4) |
23 (5) |
24 (6) |
26 (8) |
27 (0) |
28 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -72.8 | -45.1 | -8.6 | +35.7 | -69.3 | -12.2 | +50.2 | -38.6 | +32.9 | -47.7 | +31.4 |
| Relative (%) | -46.7 | -28.9 | -5.5 | +22.9 | -44.4 | -7.8 | +32.2 | -24.8 | +21.1 | -30.6 | +20.1 | |
| Steps (reduced) |
28 (1) |
29 (2) |
30 (3) |
31 (4) |
31 (4) |
32 (5) |
33 (6) |
33 (6) |
34 (7) |
34 (7) |
35 (8) | |