10ed7
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Prime factorization
2 × 5
Step size
336.883¢
Octave
4\10ed7 (1347.53¢) (→2\5ed7)
Twelfth
6\10ed7 (2021.3¢) (→3\5ed7)
Consistency limit
3
Distinct consistency limit
2
| ← 9ed7 | 10ed7 | 11ed7 → |
10 equal divisions of the 7th harmonic (abbreviated 10ed7) is a nonoctave tuning system that divides the interval of 7/1 into 10 equal parts of about 337 ¢ each. Each step represents a frequency ratio of 71/10, or the 10th root of 7. It is contorted in the 11-prime-limit.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 336.9 | 17/14, 21/17 |
| 2 | 673.8 | 3/2, 19/13, 22/15 |
| 3 | 1010.6 | |
| 4 | 1347.5 | 11/5, 15/7 |
| 5 | 1684.4 | 13/5 |
| 6 | 2021.3 | |
| 7 | 2358.2 | |
| 8 | 2695.1 | 14/3 |
| 9 | 3031.9 | 17/3 |
| 10 | 3368.8 | 7/1 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +148 | +119 | -91 | +0 | -109 | -61 | +148 | -44 | -38 | -103 | +119 |
| Relative (%) | +43.8 | +35.4 | -27.1 | +0.0 | -32.3 | -18.1 | +44.0 | -13.1 | -11.3 | -30.4 | +35.3 | |
| Steps (reduced) |
4 (4) |
6 (6) |
8 (8) |
10 (0) |
12 (2) |
13 (3) |
15 (5) |
15 (5) |
16 (6) |
17 (7) |
18 (8) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +149 | -28 | -111 | +72 | -136 | +15 | -42 | +132 | +32 | -16 | -153 |
| Relative (%) | +44.4 | -8.4 | -32.9 | +21.4 | -40.3 | +4.6 | -12.6 | +39.2 | +9.4 | -4.9 | -45.5 | |
| Steps (reduced) |
19 (9) |
19 (9) |
19 (9) |
20 (0) |
20 (0) |
21 (1) |
21 (1) |
22 (2) |
22 (2) |
22 (2) |
22 (2) | |
|
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