4ed5/3
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Prime factorization
22
Step size
221.09¢
Octave
5\4ed5/3 (1105.45¢)
Twelfth
9\4ed5/3 (1989.81¢)
Consistency limit
2
Distinct consistency limit
2
Special properties
 |
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| ← 3ed5/3 | 4ed5/3 | 5ed5/3 → |
4 equal divisions of 5/3 (abbreviated 4ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 4 equal parts of about 221 ¢ each. Each step represents a frequency ratio of (5/3)1/4, or the 4th root of 5/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1, 19/18, 20/19 |
| 1 | 221.1 | 6/5, 7/6, 11/10, 13/11, 13/12, 19/17, 20/17, 21/19 |
| 2 | 442.2 | 13/10, 17/13, 21/17 |
| 3 | 663.3 | 10/7, 17/11, 17/12, 19/13, 20/13 |
| 4 | 884.4 | 5/3, 12/7, 17/10, 18/11, 19/11, 19/12, 21/13 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -94.6 | +87.9 | +32.0 | +87.9 | -6.7 | -52.5 | -62.6 | -45.4 | -6.7 | +49.4 | -101.3 |
| Relative (%) | -42.8 | +39.7 | +14.5 | +39.7 | -3.0 | -23.7 | -28.3 | -20.5 | -3.0 | +22.3 | -45.8 | |
| Steps (reduced) |
5 (1) |
9 (1) |
11 (3) |
13 (1) |
14 (2) |
15 (3) |
16 (0) |
17 (1) |
18 (2) |
19 (3) |
19 (3) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -18.7 | +74.1 | -45.4 | +64.0 | -41.0 | +81.2 | -12.5 | -101.3 | +35.4 | -45.2 | +99.0 |
| Relative (%) | -8.5 | +33.5 | -20.5 | +28.9 | -18.5 | +36.7 | -5.6 | -45.8 | +16.0 | -20.4 | +44.8 | |
| Steps (reduced) |
20 (0) |
21 (1) |
21 (1) |
22 (2) |
22 (2) |
23 (3) |
23 (3) |
23 (3) |
24 (0) |
24 (0) |
25 (1) | |