7ed7
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Prime factorization
7 (prime)
Step size
481.261¢
Octave
2\7ed7 (962.522¢)
Twelfth
4\7ed7 (1925.04¢)
(convergent)
Consistency limit
2
Distinct consistency limit
2
| ← 6ed7 | 7ed7 | 8ed7 → |
(convergent)
7 equal divisions of the 7th harmonic (abbreviated 7ed7) is a nonoctave tuning system that divides the interval of 7/1 into 7 equal parts of about 481 ¢ each. Each step represents a frequency ratio of 71/7, or the 7th root of 7.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 481.3 | 9/7, 13/10, 17/13 |
| 2 | 962.5 | 17/10, 19/11 |
| 3 | 1443.8 | 7/3 |
| 4 | 1925 | 3/1 |
| 5 | 2406.3 | |
| 6 | 2887.6 | |
| 7 | 3368.8 | 7/1 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -237 | +23 | +101 | +0 | +180 | -109 | -92 | +196 | -134 | -54 | -170 |
| Relative (%) | -49.3 | +4.8 | +21.0 | +0.0 | +37.4 | -22.7 | -19.2 | +40.8 | -27.9 | -11.3 | -35.3 | |
| Steps (reduced) |
2 (2) |
4 (4) |
6 (6) |
7 (0) |
9 (2) |
9 (2) |
10 (3) |
11 (4) |
11 (4) |
12 (5) |
12 (5) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5 | -173 | +226 | +72 | -136 | +160 | +102 | -60 | -161 | -209 | +136 |
| Relative (%) | +1.0 | -35.9 | +47.0 | +15.0 | -28.2 | +33.2 | +21.2 | -12.5 | -33.4 | -43.4 | +28.2 | |
| Steps (reduced) |
13 (6) |
13 (6) |
14 (0) |
14 (0) |
14 (0) |
15 (1) |
15 (1) |
15 (1) |
15 (1) |
15 (1) |
16 (2) | |
|
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