3ed4
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Prime factorization
3 (prime)
Step size
800¢
Octave
2\3ed4 (1600¢)
Twelfth
2\3ed4 (1600¢)
(semiconvergent)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 1ed4 | 3ed4 | 5ed4 → |
(semiconvergent)
3 equal divisions of the 4th harmonic (abbreviated 3ed4) is a nonoctave tuning system that divides the interval of 4/1 into 3 equal parts of exactly 800 ¢ each. Each step represents a frequency ratio of 41/3, or the 3rd root of 4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1, 14/13, 18/17, 19/18 |
| 1 | 800 | 5/3, 11/7, 17/10, 17/11, 18/11, 20/13 |
| 2 | 1600 | 7/3, 17/7, 18/7, 19/7 |
| 3 | 2400 | 19/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +400 | -302 | +0 | -386 | +98 | -169 | +400 | +196 | +14 | -151 | -302 |
| Relative (%) | +50.0 | -37.7 | +0.0 | -48.3 | +12.3 | -21.1 | +50.0 | +24.5 | +1.7 | -18.9 | -37.7 | |
| Steps (reduced) |
2 (2) |
2 (2) |
3 (0) |
3 (0) |
4 (1) |
4 (1) |
5 (2) |
5 (2) |
5 (2) |
5 (2) |
5 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +359 | +231 | +112 | +0 | -105 | -204 | -298 | -386 | +329 | +249 | +172 |
| Relative (%) | +44.9 | +28.9 | +14.0 | +0.0 | -13.1 | -25.5 | -37.2 | -48.3 | +41.2 | +31.1 | +21.5 | |
| Steps (reduced) |
6 (0) |
6 (0) |
6 (0) |
6 (0) |
6 (0) |
6 (0) |
6 (0) |
6 (0) |
7 (1) |
7 (1) |
7 (1) | |