14ed5/4
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Prime factorization
2 × 7
Step size
27.5938¢
Octave
43\14ed5/4 (1186.53¢)
Twelfth
69\14ed5/4 (1903.97¢)
(semiconvergent)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 13ed5/4 | 14ed5/4 | 15ed5/4 → |
(semiconvergent)
14 equal divisions of 5/4 (abbreviated 14ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 14 equal parts of about 27.6 ¢ each. Each step represents a frequency ratio of (5/4)1/14, or the 14th root of 5/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 27.6 | |
| 2 | 55.2 | |
| 3 | 82.8 | 18/17 |
| 4 | 110.4 | 14/13, 19/18 |
| 5 | 138 | 12/11, 15/14 |
| 6 | 165.6 | 10/9, 11/10, 21/19, 23/21 |
| 7 | 193.2 | 19/17 |
| 8 | 220.8 | 17/15 |
| 9 | 248.3 | 15/13 |
| 10 | 275.9 | 7/6 |
| 11 | 303.5 | 6/5, 13/11 |
| 12 | 331.1 | 11/9, 23/19 |
| 13 | 358.7 | 17/14, 21/17 |
| 14 | 386.3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -13.5 | +2.0 | +0.7 | +0.7 | -11.4 | -2.4 | -12.8 | +4.0 | -12.8 | -12.2 | +2.7 |
| Relative (%) | -48.8 | +7.3 | +2.4 | +2.4 | -41.5 | -8.6 | -46.4 | +14.6 | -46.4 | -44.4 | +9.7 | |
| Steps (reduced) |
43 (1) |
69 (13) |
87 (3) |
101 (3) |
112 (0) |
122 (10) |
130 (4) |
138 (12) |
144 (4) |
150 (10) |
156 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.1 | +11.8 | +2.7 | +1.3 | +6.7 | -9.4 | +7.3 | +1.3 | -0.4 | +1.9 | +7.7 |
| Relative (%) | +7.5 | +42.6 | +9.7 | +4.8 | +24.5 | -34.2 | +26.6 | +4.8 | -1.3 | +6.8 | +27.9 | |
| Steps (reduced) |
161 (7) |
166 (12) |
170 (2) |
174 (6) |
178 (10) |
181 (13) |
185 (3) |
188 (6) |
191 (9) |
194 (12) |
197 (1) | |