9ed5/2
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Prime factorization
32
Step size
176.257¢
Octave
7\9ed5/2 (1233.8¢)
(semiconvergent)
Twelfth
11\9ed5/2 (1938.83¢)
Consistency limit
6
Distinct consistency limit
2
| ← 8ed5/2 | 9ed5/2 | 10ed5/2 → |
(semiconvergent)
9 equal divisions of 5/2 (abbreviated 9ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 9 equal parts of about 176 ¢ each. Each step represents a frequency ratio of (5/2)1/9, or the 9th root of 5/2.
Intervals
| Step | Interval (¢) | JI approximated | Simplified ratios |
|---|---|---|---|
| 1 | 176.26 | 21/19 | |
| 2 | 352.51 | 32/26 | 16/13 |
| 3 | 528.77 | 19/14 | |
| 4 | 705.03 | 21/14 | 3/2 |
| 5 | 881.29 | 35/21, 43/26, 48/29 | 5/3 |
| 6 | 1057.54 | 26/14, 35/19, 48/26 | 13/7, 24/13 |
| 7 | 1233.80 | 39/19, 43/21 | |
| 8 | 1410.06 | 43/19 | |
| 9 | 1586.31 | 5/2 |
The subgroup interpretation used is 5/2.14.19.21.26.29.32.35.39.43.48. Other interpretations are possible. Don't forget that fractions can multiply.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +33.8 | +36.9 | +67.6 | +33.8 | +70.7 | -19.9 | -74.9 | +73.7 | +67.6 | +78.9 | -71.8 |
| Relative (%) | +19.2 | +20.9 | +38.4 | +19.2 | +40.1 | -11.3 | -42.5 | +41.8 | +38.4 | +44.7 | -40.7 | |
| Steps (reduced) |
7 (7) |
11 (2) |
14 (5) |
16 (7) |
18 (0) |
19 (1) |
20 (2) |
22 (4) |
23 (5) |
24 (6) |
24 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -34.1 | +13.9 | +70.7 | -41.1 | +30.2 | -68.7 | +13.9 | -74.9 | +16.9 | -63.6 | +35.7 |
| Relative (%) | -19.3 | +7.9 | +40.1 | -23.3 | +17.2 | -39.0 | +7.9 | -42.5 | +9.6 | -36.1 | +20.3 | |
| Steps (reduced) |
25 (7) |
26 (8) |
27 (0) |
27 (0) |
28 (1) |
28 (1) |
29 (2) |
29 (2) |
30 (3) |
30 (3) |
31 (4) | |
 |
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