14ed7/3
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Prime factorization
2 × 7
Step size
104.776¢
Octave
11\14ed7/3 (1152.54¢)
Twelfth
18\14ed7/3 (1885.98¢) (→9\7ed7/3)
Consistency limit
3
Distinct consistency limit
2
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| ← 13ed7/3 | 14ed7/3 | 15ed7/3 → |
14 equal divisions of 7/3 (abbreviated 14ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 14 equal parts of about 105 ¢ each. Each step represents a frequency ratio of (7/3)1/14, or the 14th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 104.776 | 14/13, 21/20 |
| 2 | 209.553 | 17/15, 19/17 |
| 3 | 314.329 | 23/19 |
| 4 | 419.106 | 9/7, 19/15 |
| 5 | 523.882 | 15/11, 23/17 |
| 6 | 628.659 | 10/7, 13/9 |
| 7 | 733.435 | 17/11, 20/13, 23/15 |
| 8 | 838.212 | 21/13 |
| 9 | 942.988 | 19/11 |
| 10 | 1047.765 | |
| 11 | 1152.541 | |
| 12 | 1257.318 | 23/11 |
| 13 | 1362.094 | 11/5, 13/6, 20/9 |
| 14 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -47.5 | -16.0 | +9.9 | +42.7 | +41.3 | -16.0 | -37.6 | -32.0 | -4.8 | +39.7 | -6.1 |
| Relative (%) | -45.3 | -15.2 | +9.4 | +40.7 | +39.5 | -15.2 | -35.9 | -30.5 | -4.6 | +37.9 | -5.8 | |
| Steps (reduced) |
11 (11) |
18 (4) |
23 (9) |
27 (13) |
30 (2) |
32 (4) |
34 (6) |
36 (8) |
38 (10) |
40 (12) |
41 (13) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -39.9 | +41.3 | +26.7 | +19.7 | +19.5 | +25.4 | +36.5 | -52.3 | -32.0 | -7.7 | +20.1 |
| Relative (%) | -38.1 | +39.5 | +25.5 | +18.8 | +18.6 | +24.2 | +34.9 | -49.9 | -30.5 | -7.4 | +19.2 | |
| Steps (reduced) |
42 (0) |
44 (2) |
45 (3) |
46 (4) |
47 (5) |
48 (6) |
49 (7) |
49 (7) |
50 (8) |
51 (9) |
52 (10) | |