4ed7
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Prime factorization
22
Step size
842.206¢
Octave
1\4ed7 (842.206¢)
Twelfth
2\4ed7 (1684.41¢) (→1\2ed7)
Consistency limit
3
Distinct consistency limit
2
Special properties
| ← 3ed7 | 4ed7 | 5ed7 → |
4 equal divisions of the 7th harmonic (abbreviated 4ed7) is a nonoctave tuning system that divides the interval of 7/1 into 4 equal parts of about 842 ¢ each. Each step represents a frequency ratio of 71/4, or the 4th root of 7.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 842.2 | 5/3, 11/7, 14/9, 17/11, 21/13 |
| 2 | 1684.4 | 13/5, 19/7 |
| 3 | 2526.6 | 9/2, 13/3, 21/5 |
| 4 | 3368.8 | 7/1 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -358 | -218 | -260 | +0 | +60 | -229 | +148 | -44 | -375 | +66 | -50 |
| Relative (%) | -42.5 | -25.8 | -30.8 | +0.0 | +7.1 | -27.2 | +17.6 | -5.3 | -44.5 | +7.8 | -5.9 | |
| Steps (reduced) |
1 (1) |
2 (2) |
3 (3) |
4 (0) |
5 (1) |
5 (1) |
6 (2) |
6 (2) |
6 (2) |
7 (3) |
7 (3) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -356 | +309 | +226 | +72 | -136 | -322 | -379 | +301 | +200 | +152 | +15 |
| Relative (%) | -42.3 | +36.6 | +26.9 | +8.6 | -16.1 | -38.2 | -45.0 | +35.7 | +23.8 | +18.1 | +1.8 | |
| Steps (reduced) |
7 (3) |
8 (0) |
8 (0) |
8 (0) |
8 (0) |
8 (0) |
8 (0) |
9 (1) |
9 (1) |
9 (1) |
9 (1) | |
|
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