4ed4/3
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Prime factorization
22
Step size
124.511¢
Octave
10\4ed4/3 (1245.11¢) (→5\2ed4/3)
Twelfth
15\4ed4/3 (1867.67¢)
(semiconvergent)
Consistency limit
2
Distinct consistency limit
1
Special properties
|
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| ← 3ed4/3 | 4ed4/3 | 5ed4/3 → |
(semiconvergent)
4 equal divisions of 4/3 (abbreviated 4ed4/3) is a nonoctave tuning system that divides the interval of 4/3 into 4 equal parts of about 125 ¢ each. Each step represents a frequency ratio of (4/3)1/4, or the 4th root of 4/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1, 21/20 |
| 1 | 124.5 | 11/10, 13/12, 14/13, 18/17, 19/18, 20/19, 21/19 |
| 2 | 249 | 7/6, 10/9, 17/14, 17/15, 19/17 |
| 3 | 373.5 | 6/5, 9/7, 11/9, 13/11, 17/13, 20/17, 21/17 |
| 4 | 498 | 13/10, 14/11, 15/11, 18/13, 19/14, 19/15 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +45.1 | -34.3 | -34.3 | -47.1 | +10.8 | -7.0 | +10.8 | +55.9 | -2.0 | -42.4 | +55.9 |
| Relative (%) | +36.2 | -27.5 | -27.5 | -37.8 | +8.7 | -5.6 | +8.7 | +44.9 | -1.6 | -34.1 | +44.9 | |
| Steps (reduced) |
10 (2) |
15 (3) |
19 (3) |
22 (2) |
25 (1) |
27 (3) |
29 (1) |
31 (3) |
32 (0) |
33 (1) |
35 (3) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +41.9 | +38.1 | +43.2 | +55.9 | -49.0 | -23.5 | +7.4 | +43.2 | -41.3 | +2.7 | +50.2 |
| Relative (%) | +33.6 | +30.6 | +34.7 | +44.9 | -39.4 | -18.8 | +6.0 | +34.7 | -33.2 | +2.1 | +40.3 | |
| Steps (reduced) |
36 (0) |
37 (1) |
38 (2) |
39 (3) |
39 (3) |
40 (0) |
41 (1) |
42 (2) |
42 (2) |
43 (3) |
44 (0) | |