8ed5
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Prime factorization
23
Step size
348.289¢
Octave
3\8ed5 (1044.87¢)
Twelfth
5\8ed5 (1741.45¢)
Consistency limit
3
Distinct consistency limit
2
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| ← 7ed5 | 8ed5 | 9ed5 → |
8 equal divisions of the 5th harmonic (abbreviated 8ed5) is a nonoctave tuning system that divides the interval of 5/1 into 8 equal parts of about 348 ¢ each. Each step represents a frequency ratio of 51/8, or the 8th root of 5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 348.289 | 17/14, 21/17 |
| 2 | 696.578 | 3/2, 19/13, 22/15 |
| 3 | 1044.868 | 13/7 |
| 4 | 1393.157 | 9/4, 11/5, 20/9 |
| 5 | 1741.446 | 14/5, 19/7 |
| 6 | 2089.735 | 10/3, 17/5 |
| 7 | 2438.024 | |
| 8 | 2786.314 | 5/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -155 | -161 | +38 | +0 | +33 | +114 | -117 | +27 | -155 | +28 | -122 |
| Relative (%) | -44.5 | -46.1 | +10.9 | +0.0 | +9.4 | +32.8 | -33.6 | +7.8 | -44.5 | +8.1 | -35.2 | |
| Steps (reduced) |
3 (3) |
5 (5) |
7 (7) |
8 (0) |
9 (1) |
10 (2) |
10 (2) |
11 (3) |
11 (3) |
12 (4) |
12 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +87 | -41 | -161 | +76 | -29 | -128 | +127 | +38 | -46 | -127 | +144 |
| Relative (%) | +25.0 | -11.8 | -46.1 | +21.8 | -8.3 | -36.7 | +36.4 | +10.9 | -13.3 | -36.5 | +41.4 | |
| Steps (reduced) |
13 (5) |
13 (5) |
13 (5) |
14 (6) |
14 (6) |
14 (6) |
15 (7) |
15 (7) |
15 (7) |
15 (7) |
16 (0) | |