8ed7/4
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Prime factorization
23
Step size
121.103¢
Octave
10\8ed7/4 (1211.03¢) (→5\4ed7/4)
Twelfth
16\8ed7/4 (1937.65¢) (→2\1ed7/4)
Consistency limit
8
Distinct consistency limit
2
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| ← 7ed7/4 | 8ed7/4 | 9ed7/4 → |
8 equal divisions of 7/4 (abbreviated 8ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 8 equal parts of about 121 ¢ each. Each step represents a frequency ratio of (7/4)1/8, or the 8th root of 7/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 121.103 | 11/10, 13/12, 14/13, 15/14, 16/15, 17/16, 18/17, 20/19, 21/20 |
| 2 | 242.206 | 7/6, 8/7, 9/8, 15/13, 17/15, 20/17, 22/19 |
| 3 | 363.31 | 5/4, 16/13, 17/14, 21/17 |
| 4 | 484.413 | 4/3, 13/10, 17/13, 19/14, 21/16 |
| 5 | 605.516 | 7/5, 10/7, 13/9, 17/12, 18/13 |
| 6 | 726.619 | 3/2, 14/9, 20/13 |
| 7 | 847.723 | 5/3, 8/5, 13/8, 21/13 |
| 8 | 968.826 | 7/4, 12/7, 16/9, 19/11 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +11.0 | +35.7 | +22.1 | -0.9 | +46.7 | +22.1 | +33.1 | -49.7 | +10.1 | -33.8 | +57.8 |
| Relative (%) | +9.1 | +29.5 | +18.2 | -0.8 | +38.6 | +18.2 | +27.3 | -41.0 | +8.3 | -27.9 | +47.7 | |
| Steps (reduced) |
10 (2) |
16 (0) |
20 (4) |
23 (7) |
26 (2) |
28 (4) |
30 (6) |
31 (7) |
33 (1) |
34 (2) |
36 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +40.3 | +33.1 | +34.8 | +44.1 | +60.3 | -38.7 | -11.2 | +21.1 | +57.8 | -22.8 | +21.4 |
| Relative (%) | +33.3 | +27.3 | +28.7 | +36.4 | +49.8 | -31.9 | -9.2 | +17.4 | +47.7 | -18.8 | +17.6 | |
| Steps (reduced) |
37 (5) |
38 (6) |
39 (7) |
40 (0) |
41 (1) |
41 (1) |
42 (2) |
43 (3) |
44 (4) |
44 (4) |
45 (5) | |