6ed7
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Prime factorization
2 × 3
Step size
561.471¢
Octave
2\6ed7 (1122.94¢) (→1\3ed7)
Twelfth
3\6ed7 (1684.41¢) (→1\2ed7)
Consistency limit
5
Distinct consistency limit
2
Special properties
| ← 5ed7 | 6ed7 | 7ed7 → |
6 equal divisions of the 7th harmonic (abbreviated 6ed7) is a nonoctave tuning system that divides the interval of 7/1 into 6 equal parts of about 561 ¢ each. Each step represents a frequency ratio of 71/6, or the 6th root of 7.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 561.5 | 7/5, 10/7, 11/8, 15/11, 19/14 |
| 2 | 1122.9 | 13/7, 15/8, 19/10, 21/11 |
| 3 | 1684.4 | 8/3, 13/5, 19/7, 21/8 |
| 4 | 2245.9 | 11/3, 15/4 |
| 5 | 2807.4 | 5/1 |
| 6 | 3368.8 | 7/1 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -77 | -218 | +21 | +0 | -221 | +51 | +148 | -44 | +186 | -215 | +231 |
| Relative (%) | -13.7 | -38.7 | +3.7 | +0.0 | -39.4 | +9.1 | +26.4 | -7.9 | +33.2 | -38.3 | +41.2 | |
| Steps (reduced) |
2 (2) |
3 (3) |
5 (5) |
6 (0) |
7 (1) |
8 (2) |
9 (3) |
9 (3) |
10 (4) |
10 (4) |
11 (5) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -75 | -253 | +226 | +72 | -136 | +240 | +182 | +20 | -81 | -129 | -265 |
| Relative (%) | -13.4 | -45.0 | +40.3 | +12.8 | -24.2 | +42.7 | +32.5 | +3.5 | -14.4 | -22.9 | -47.3 | |
| Steps (reduced) |
11 (5) |
11 (5) |
12 (0) |
12 (0) |
12 (0) |
13 (1) |
13 (1) |
13 (1) |
13 (1) |
13 (1) |
13 (1) | |
|
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