6ed5
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Prime factorization
2 × 3
Step size
464.386¢
Octave
3\6ed5 (1393.16¢) (→1\2ed5)
Twelfth
4\6ed5 (1857.54¢) (→2\3ed5)
Consistency limit
2
Distinct consistency limit
1
Special properties
| ← 5ed5 | 6ed5 | 7ed5 → |
6 equal divisions of the 5th harmonic (abbreviated 6ed5) is a nonoctave tuning system that divides the interval of 5/1 into 6 equal parts of about 464 ¢ each. Each step represents a frequency ratio of 51/6, or the 6th root of 5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 464.386 | 9/7, 13/10, 14/11, 17/13, 19/15 |
| 2 | 928.771 | 5/3, 17/10, 19/11 |
| 3 | 1393.157 | 11/5, 13/6 |
| 4 | 1857.542 | 3/1, 17/6 |
| 5 | 2321.928 | 19/5 |
| 6 | 2786.314 | 5/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +193 | -44 | -78 | +0 | +149 | -118 | +115 | -89 | +193 | +28 | -122 |
| Relative (%) | +41.6 | -9.6 | -16.8 | +0.0 | +32.0 | -25.4 | +24.8 | -19.1 | +41.6 | +6.1 | -26.4 | |
| Steps (reduced) |
3 (3) |
4 (4) |
5 (5) |
6 (0) |
7 (1) |
7 (1) |
8 (2) |
8 (2) |
9 (3) |
9 (3) |
9 (3) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +203 | +75 | -44 | -156 | +203 | +104 | +11 | -78 | -163 | +221 | +144 |
| Relative (%) | +43.8 | +16.2 | -9.6 | -33.6 | +43.8 | +22.5 | +2.3 | -16.8 | -35.0 | +47.7 | +31.1 | |
| Steps (reduced) |
10 (4) |
10 (4) |
10 (4) |
10 (4) |
11 (5) |
11 (5) |
11 (5) |
11 (5) |
11 (5) |
12 (0) |
12 (0) | |