6ed7/4
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Prime factorization
2 × 3
Step size
161.471¢
Octave
7\6ed7/4 (1130.3¢)
Twelfth
12\6ed7/4 (1937.65¢) (→2\1ed7/4)
Consistency limit
2
Distinct consistency limit
2
Special properties
 |
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| ← 5ed7/4 | 6ed7/4 | 7ed7/4 → |
6 equal divisions of 7/4 (abbreviated 6ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 6 equal parts of about 161 ¢ each. Each step represents a frequency ratio of (7/4)1/6, or the 6th root of 7/4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 161.471 | 15/14, 17/15, 21/19 |
| 2 | 322.942 | 6/5, 7/6, 11/9, 13/11, 17/14 |
| 3 | 484.413 | 9/7, 15/11 |
| 4 | 645.884 | 13/9, 17/12, 19/13 |
| 5 | 807.355 | 11/7, 18/11, 21/13 |
| 6 | 968.826 | 17/10, 19/11 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -69.7 | +35.7 | +22.1 | -41.3 | -34.0 | +22.1 | -47.6 | +71.4 | +50.5 | +46.9 | +57.8 |
| Relative (%) | -43.2 | +22.1 | +13.7 | -25.6 | -21.1 | +13.7 | -29.5 | +44.2 | +31.3 | +29.1 | +35.8 | |
| Steps (reduced) |
7 (1) |
12 (0) |
15 (3) |
17 (5) |
19 (1) |
21 (3) |
22 (4) |
24 (0) |
25 (1) |
26 (2) |
27 (3) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +80.7 | -47.6 | -5.6 | +44.1 | -60.8 | +1.7 | +69.6 | -19.2 | +57.8 | -22.8 | +61.7 |
| Relative (%) | +50.0 | -29.5 | -3.5 | +27.3 | -37.7 | +1.0 | +43.1 | -11.9 | +35.8 | -14.1 | +38.2 | |
| Steps (reduced) |
28 (4) |
28 (4) |
29 (5) |
30 (0) |
30 (0) |
31 (1) |
32 (2) |
32 (2) |
33 (3) |
33 (3) |
34 (4) | |