14ed7/4
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Prime factorization
2 × 7
Step size
69.2019¢
Octave
17\14ed7/4 (1176.43¢)
Twelfth
27\14ed7/4 (1868.45¢)
(semiconvergent)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 13ed7/4 | 14ed7/4 | 15ed7/4 → |
(semiconvergent)
14 equal divisions of 7/4 (abbreviated 14ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 14 equal parts of about 69.2 ¢ each. Each step represents a frequency ratio of (7/4)1/14, or the 14th root of 7/4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 69.202 | 22/21, 23/22 |
| 2 | 138.404 | 14/13, 23/21 |
| 3 | 207.606 | 9/8, 19/17 |
| 4 | 276.807 | 13/11 |
| 5 | 346.009 | 17/14, 21/17 |
| 6 | 415.211 | 14/11 |
| 7 | 484.413 | 4/3, 17/13 |
| 8 | 553.615 | |
| 9 | 622.817 | |
| 10 | 692.019 | 3/2 |
| 11 | 761.22 | 11/7, 17/11, 23/15 |
| 12 | 830.422 | 21/13 |
| 13 | 899.624 | 5/3, 22/13 |
| 14 | 968.826 | 19/11, 23/13 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -23.6 | -33.5 | +22.1 | -18.2 | +12.1 | +22.1 | -1.5 | +2.2 | +27.4 | +0.8 | -11.4 |
| Relative (%) | -34.1 | -48.4 | +31.9 | -26.4 | +17.5 | +31.9 | -2.2 | +3.2 | +39.6 | +1.1 | -16.5 | |
| Steps (reduced) |
17 (3) |
27 (13) |
35 (7) |
40 (12) |
45 (3) |
49 (7) |
52 (10) |
55 (13) |
58 (2) |
60 (4) |
62 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.6 | -1.5 | +17.5 | -25.1 | +8.4 | -21.4 | +23.4 | +3.8 | -11.4 | -22.8 | -30.5 |
| Relative (%) | -16.8 | -2.2 | +25.2 | -36.2 | +12.1 | -30.9 | +33.8 | +5.5 | -16.5 | -32.9 | -44.1 | |
| Steps (reduced) |
64 (8) |
66 (10) |
68 (12) |
69 (13) |
71 (1) |
72 (2) |
74 (4) |
75 (5) |
76 (6) |
77 (7) |
78 (8) | |