50ed12
50 equal divisions of the 12th harmonic (abbreviated 50ed12) is a nonoctave tuning system that divides the interval of 12/1 into 50 equal parts of about 86 ¢ each. Each step represents a frequency ratio of 121/50, or the 50th root of 12.
Interval table
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 86 | 20/19, 21/20, 22/21 |
| 2 | 172.1 | 21/19, 31/28, 32/29 |
| 3 | 258.1 | 22/19 |
| 4 | 344.2 | 11/9, 28/23 |
| 5 | 430.2 | 9/7 |
| 6 | 516.2 | 27/20, 31/23 |
| 7 | 602.3 | 17/12, 24/17 |
| 8 | 688.3 | |
| 9 | 774.4 | |
| 10 | 860.4 | 23/14, 28/17 |
| 11 | 946.4 | 19/11, 31/18 |
| 12 | 1032.5 | 20/11, 29/16 |
| 13 | 1118.5 | 21/11 |
| 14 | 1204.5 | 2/1 |
| 15 | 1290.6 | 19/9 |
| 16 | 1376.6 | 31/14 |
| 17 | 1462.7 | 7/3 |
| 18 | 1548.7 | 22/9 |
| 19 | 1634.7 | 18/7 |
| 20 | 1720.8 | 27/10 |
| 21 | 1806.8 | 17/6 |
| 22 | 1892.9 | |
| 23 | 1978.9 | 22/7 |
| 24 | 2064.9 | 23/7 |
| 25 | 2151 | |
| 26 | 2237 | |
| 27 | 2323.1 | 23/6 |
| 28 | 2409.1 | |
| 29 | 2495.1 | |
| 30 | 2581.2 | 31/7 |
| 31 | 2667.2 | 14/3 |
| 32 | 2753.3 | |
| 33 | 2839.3 | 31/6 |
| 34 | 2925.3 | |
| 35 | 3011.4 | |
| 36 | 3097.4 | 6/1 |
| 37 | 3183.4 | |
| 38 | 3269.5 | |
| 39 | 3355.5 | |
| 40 | 3441.6 | |
| 41 | 3527.6 | 23/3 |
| 42 | 3613.6 | |
| 43 | 3699.7 | 17/2 |
| 44 | 3785.7 | |
| 45 | 3871.8 | 28/3 |
| 46 | 3957.8 | |
| 47 | 4043.8 | 31/3 |
| 48 | 4129.9 | |
| 49 | 4215.9 | |
| 50 | 4302 | 12/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.5 | -9.1 | +9.1 | -33.1 | -4.5 | -13.3 | +13.6 | -18.2 | -28.5 | -21.4 | +0.0 |
| Relative (%) | +5.3 | -10.6 | +10.6 | -38.4 | -5.3 | -15.5 | +15.9 | -21.1 | -33.1 | -24.9 | +0.0 | |
| Steps (reduced) |
14 (14) |
22 (22) |
28 (28) |
32 (32) |
36 (36) |
39 (39) |
42 (42) |
44 (44) |
46 (46) |
48 (48) |
50 (0) | |