19ed5/2
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Prime factorization
19 (prime)
Step size
83.4902¢
Octave
14\19ed5/2 (1168.86¢)
Twelfth
23\19ed5/2 (1920.27¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 18ed5/2 | 19ed5/2 | 20ed5/2 → |
19 equal divisions of 5/2 (abbreviated 19ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 19 equal parts of about 83.5 ¢ each. Each step represents a frequency ratio of (5/2)1/19, or the 19th root of 5/2.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 83.5 | 18/17, 19/18, 22/21, 23/22 |
| 2 | 167 | 21/19, 23/21 |
| 3 | 250.5 | 7/6, 15/13, 22/19 |
| 4 | 334 | 11/9, 23/19 |
| 5 | 417.5 | 19/15, 23/18 |
| 6 | 500.9 | |
| 7 | 584.4 | 7/5 |
| 8 | 667.9 | 19/13, 22/15 |
| 9 | 751.4 | 17/11, 23/15 |
| 10 | 834.9 | 21/13 |
| 11 | 918.4 | 12/7, 22/13 |
| 12 | 1001.9 | 23/13 |
| 13 | 1085.4 | 13/7, 17/9 |
| 14 | 1168.9 | |
| 15 | 1252.4 | |
| 16 | 1335.8 | 13/6, 15/7 |
| 17 | 1419.3 | |
| 18 | 1502.8 | 12/5 |
| 19 | 1586.3 | 5/2 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -31.1 | +18.3 | +21.2 | -31.1 | -12.8 | -29.2 | -9.9 | +36.6 | +21.2 | +23.2 | +39.5 |
| Relative (%) | -37.3 | +21.9 | +25.4 | -37.3 | -15.4 | -35.0 | -11.9 | +43.9 | +25.4 | +27.8 | +47.4 | |
| Steps (reduced) |
14 (14) |
23 (4) |
29 (10) |
33 (14) |
37 (18) |
40 (2) |
43 (5) |
46 (8) |
48 (10) |
50 (12) |
52 (14) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -15.5 | +23.1 | -12.8 | -41.1 | +21.0 | +5.5 | -4.6 | -9.9 | -10.9 | -7.9 | -1.4 |
| Relative (%) | -18.6 | +27.7 | -15.4 | -49.2 | +25.1 | +6.6 | -5.5 | -11.9 | -13.1 | -9.5 | -1.7 | |
| Steps (reduced) |
53 (15) |
55 (17) |
56 (18) |
57 (0) |
59 (2) |
60 (3) |
61 (4) |
62 (5) |
63 (6) |
64 (7) |
65 (8) | |