50edt
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 49edt | 50edt | 51edt → |
50 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 50edt or 50ed3), is a nonoctave tuning system that divides the interval of 3/1 into 50 equal parts of about 38 ¢ each. Each step represents a frequency ratio of 31/50, or the 50th root of 3.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 38 | 26 | |
| 2 | 76.1 | 52 | 22/21, 23/22 |
| 3 | 114.1 | 78 | 31/29 |
| 4 | 152.2 | 104 | 23/21 |
| 5 | 190.2 | 130 | 19/17 |
| 6 | 228.2 | 156 | |
| 7 | 266.3 | 182 | 7/6 |
| 8 | 304.3 | 208 | |
| 9 | 342.4 | 234 | 11/9 |
| 10 | 380.4 | 260 | |
| 11 | 418.4 | 286 | |
| 12 | 456.5 | 312 | 13/10, 30/23 |
| 13 | 494.5 | 338 | |
| 14 | 532.5 | 364 | 15/11 |
| 15 | 570.6 | 390 | |
| 16 | 608.6 | 416 | 27/19 |
| 17 | 646.7 | 442 | |
| 18 | 684.7 | 468 | |
| 19 | 722.7 | 494 | |
| 20 | 760.8 | 520 | |
| 21 | 798.8 | 546 | 27/17 |
| 22 | 836.9 | 572 | |
| 23 | 874.9 | 598 | |
| 24 | 912.9 | 624 | 22/13 |
| 25 | 951 | 650 | 19/11 |
| 26 | 989 | 676 | 23/13 |
| 27 | 1027.1 | 702 | |
| 28 | 1065.1 | 728 | |
| 29 | 1103.1 | 754 | 17/9 |
| 30 | 1141.2 | 780 | 29/15 |
| 31 | 1179.2 | 806 | |
| 32 | 1217.3 | 832 | |
| 33 | 1255.3 | 858 | 31/15 |
| 34 | 1293.3 | 884 | 19/9 |
| 35 | 1331.4 | 910 | |
| 36 | 1369.4 | 936 | 11/5 |
| 37 | 1407.4 | 962 | |
| 38 | 1445.5 | 988 | 23/10, 30/13 |
| 39 | 1483.5 | 1014 | |
| 40 | 1521.6 | 1040 | |
| 41 | 1559.6 | 1066 | 27/11 |
| 42 | 1597.6 | 1092 | |
| 43 | 1635.7 | 1118 | 18/7 |
| 44 | 1673.7 | 1144 | 29/11 |
| 45 | 1711.8 | 1170 | |
| 46 | 1749.8 | 1196 | |
| 47 | 1787.8 | 1222 | |
| 48 | 1825.9 | 1248 | |
| 49 | 1863.9 | 1274 | |
| 50 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.47 | +0.00 | -4.95 | +3.22 | -2.47 | -1.66 | +6.67 | +0.00 | +0.75 | +4.81 | -4.95 |
| Relative (%) | -17.6 | +0.0 | -35.1 | +22.9 | -17.6 | -11.8 | +47.3 | +0.0 | +5.3 | +34.1 | -35.1 | |
| Steps (reduced) |
85 (85) |
135 (0) |
170 (35) |
198 (63) |
220 (85) |
239 (104) |
256 (121) |
270 (0) |
283 (13) |
295 (25) |
305 (35) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | -4.13 | +3.22 | +4.20 | -2.14 | -2.47 | +2.54 | -1.73 | -1.66 | +2.33 | -4.18 |
| Relative (%) | -18.7 | -29.3 | +22.9 | +29.8 | -15.2 | -17.6 | +18.1 | -12.2 | -11.8 | +16.6 | -29.7 | |
| Steps (reduced) |
315 (45) |
324 (54) |
333 (63) |
341 (71) |
348 (78) |
355 (85) |
362 (92) |
368 (98) |
374 (104) |
380 (110) |
385 (115) | |