7ed4
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Prime factorization
7 (prime)
Step size
342.857¢
Octave
4\7ed4 (1371.43¢)
Twelfth
6\7ed4 (2057.14¢)
Consistency limit
1
Distinct consistency limit
1
| ← 5ed4 | 7ed4 | 9ed4 → |
7 equal divisions of the 4th harmonic (abbreviated 7ed4) is a nonoctave tuning system that divides the interval of 4/1 into 7 equal parts of about 343 ¢ each. Each step represents a frequency ratio of 41/7, or the 7th root of 4.
Intervals
| Step | Interval (¢) | JI approximated | Simplified ratio |
|---|---|---|---|
| 1 | 342.86 | 78/64 | 39/32 |
| 2 | 685.71 | 6/4 | 3/2 |
| 3 | 1393.16 | 29/16 | |
| 4 | 1857.54 | 64/29 | |
| 5 | 2321.93 | 16/6, 35/13 | 8/3 |
| 6 | 2786.31 | 13/4 | |
| 7 | 2786.31 | 4/1 |
The subgroup interpretation used is 4.6.13.29.35. Other interpretations are possible.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +171 | +155 | +0 | -43 | -16 | +60 | +171 | -32 | +128 | -37 | +155 |
| Relative (%) | +50.0 | +45.3 | +0.0 | -12.7 | -4.7 | +17.4 | +50.0 | -9.5 | +37.3 | -10.8 | +45.3 | |
| Steps (reduced) |
4 (4) |
6 (6) |
7 (0) |
8 (1) |
9 (2) |
10 (3) |
11 (4) |
11 (4) |
12 (5) |
12 (5) |
13 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +17 | -112 | +112 | +0 | -105 | +139 | +45 | -43 | -128 | +134 | +57 |
| Relative (%) | +4.8 | -32.6 | +32.6 | +0.0 | -30.6 | +40.5 | +13.2 | -12.7 | -37.3 | +39.2 | +16.8 | |
| Steps (reduced) |
13 (6) |
13 (6) |
14 (0) |
14 (0) |
14 (0) |
15 (1) |
15 (1) |
15 (1) |
15 (1) |
16 (2) |
16 (2) | |
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