14ed5/2
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| ← 13ed5/2 | 14ed5/2 | 15ed5/2 → |
14 equal divisions of 5/2 (abbreviated 14ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 14 equal parts of about 113 ¢ each. Each step represents a frequency ratio of (5/2)1/14, or the 14th root of 5/2.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 113.3 | 15/14 |
| 2 | 226.6 | |
| 3 | 339.9 | 11/9, 23/19 |
| 4 | 453.2 | 9/7, 17/13 |
| 5 | 566.5 | 7/5 |
| 6 | 679.8 | 3/2, 19/13, 22/15 |
| 7 | 793.2 | 11/7 |
| 8 | 906.5 | 5/3 |
| 9 | 1019.8 | 9/5 |
| 10 | 1133.1 | 21/11 |
| 11 | 1246.4 | |
| 12 | 1359.7 | 11/5 |
| 13 | 1473 | 7/3 |
| 14 | 1586.3 | 5/2 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +46.4 | +24.3 | -20.5 | +46.4 | -42.6 | +30.4 | +25.9 | +48.6 | -20.5 | +41.1 | +3.8 |
| Relative (%) | +40.9 | +21.4 | -18.1 | +40.9 | -37.6 | +26.8 | +22.8 | +42.9 | -18.1 | +36.3 | +3.3 | |
| Steps (reduced) |
11 (11) |
17 (3) |
21 (7) |
25 (11) |
27 (13) |
30 (2) |
32 (4) |
34 (6) |
35 (7) |
37 (9) |
38 (10) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -21.5 | -36.5 | -42.6 | -41.1 | -32.7 | -18.4 | +1.4 | +25.9 | +54.7 | -25.8 | +10.5 |
| Relative (%) | -19.0 | -32.2 | -37.6 | -36.2 | -28.9 | -16.2 | +1.2 | +22.8 | +48.3 | -22.8 | +9.3 | |
| Steps (reduced) |
39 (11) |
40 (12) |
41 (13) |
42 (0) |
43 (1) |
44 (2) |
45 (3) |
46 (4) |
47 (5) |
47 (5) |
48 (6) | |
Regular temperaments
14ed5/2 can be thought of as a generator of the misneb temperament (53 & 180), which tempers out 131625/131072 and 140625/140608 in the 2.3.5.13 subgroup. This temperament can be extended to the 2.3.5.13.19 subgroup by tempering out 513/512, 3250/3249 or 28561/28500.