3ed5
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Prime factorization
3 (prime)
Step size
928.771¢
Octave
1\3ed5 (928.771¢)
(semiconvergent)
Twelfth
2\3ed5 (1857.54¢)
(convergent)
Consistency limit
3
Distinct consistency limit
2
| ← 2ed5 | 3ed5 | 4ed5 → |
(semiconvergent)
(convergent)
3 equal divisions of the 5th harmonic (abbreviated 3ed5) is a nonoctave tuning system that divides the interval of 5/1 into 3 equal parts of about 929 ¢ each. Each step represents a frequency ratio of 51/3, or the 3rd root of 5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1, 14/13, 15/14, 18/17, 19/18, 20/19 |
| 1 | 928.771 | 5/3, 9/5, 11/6, 17/10, 18/11, 19/11, 19/12, 20/11 |
| 2 | 1857.542 | 3/1, 11/4, 14/5, 17/6 |
| 3 | 2786.314 | 5/1, 14/3, 19/4 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -271 | -44 | +386 | +0 | -316 | +346 | +115 | -89 | -271 | -436 | +342 |
| Relative (%) | -29.2 | -4.8 | +41.6 | +0.0 | -34.0 | +37.3 | +12.4 | -9.6 | -29.2 | -47.0 | +36.8 | |
| Steps (reduced) |
1 (1) |
2 (2) |
3 (0) |
3 (0) |
3 (0) |
4 (1) |
4 (1) |
4 (1) |
4 (1) |
4 (1) |
5 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +203 | +75 | -44 | -156 | -261 | -360 | -454 | +386 | +302 | +221 | +144 |
| Relative (%) | +21.9 | +8.1 | -4.8 | -16.8 | -28.1 | -38.8 | -48.8 | +41.6 | +32.5 | +23.8 | +15.5 | |
| Steps (reduced) |
5 (2) |
5 (2) |
5 (2) |
5 (2) |
5 (2) |
5 (2) |
5 (2) |
6 (0) |
6 (0) |
6 (0) |
6 (0) | |