5ed5
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Prime factorization
5 (prime)
Step size
557.263¢
Octave
2\5ed5 (1114.53¢)
(semiconvergent)
Twelfth
3\5ed5 (1671.79¢)
Consistency limit
4
Distinct consistency limit
2
| ← 4ed5 | 5ed5 | 6ed5 → |
(semiconvergent)
5 equal divisions of the 5th harmonic (abbreviated 5ed5) is a nonoctave tuning system that divides the interval of 5/1 into 5 equal parts of about 557 ¢ each. Each step represents a frequency ratio of 51/5, or the 5th root of 5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 557.263 | 4/3, 7/5, 10/7, 11/8, 15/11, 19/14 |
| 2 | 1114.525 | 11/6, 13/7, 15/8, 19/10, 21/11 |
| 3 | 1671.788 | 8/3, 13/5, 19/7, 21/8 |
| 4 | 2229.051 | 7/2, 11/3, 15/4 |
| 5 | 2786.314 | 5/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -85 | -230 | -171 | +0 | +242 | -25 | -256 | +97 | -85 | -250 | +156 |
| Relative (%) | -15.3 | -41.3 | -30.7 | +0.0 | +43.4 | -4.5 | -46.0 | +17.4 | -15.3 | -44.9 | +28.0 | |
| Steps (reduced) |
2 (2) |
3 (3) |
4 (4) |
5 (0) |
6 (1) |
6 (1) |
6 (1) |
7 (2) |
7 (2) |
7 (2) |
8 (3) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +18 | -111 | -230 | +215 | +110 | +11 | -82 | -171 | -255 | +221 | +144 |
| Relative (%) | +3.2 | -19.9 | -41.3 | +38.6 | +19.8 | +2.1 | -14.7 | -30.7 | -45.8 | +39.7 | +25.9 | |
| Steps (reduced) |
8 (3) |
8 (3) |
8 (3) |
9 (4) |
9 (4) |
9 (4) |
9 (4) |
9 (4) |
9 (4) |
10 (0) |
10 (0) | |