50edt
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Prime factorization
2 × 52
Step size
38.0391¢
Octave
32\50edt (1217.25¢) (→16\25edt)
Consistency limit
2
Distinct consistency limit
2
| ← 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.
Notation
This tuning can use 25-tone notation with quartertones. There would be 9 letter names, A to I. The perfect 5th would be notated as D (from an A root), a P4 interval. The septimal minor 3rd would be A-Bt, or a sM2.
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 (¢) | +17.3 | +0.0 | -3.5 | -9.5 | +17.3 | +16.7 | +13.7 | +0.0 | +7.8 | -5.1 | -3.5 |
| Relative (%) | +45.4 | +0.0 | -9.3 | -24.9 | +45.4 | +43.8 | +36.1 | +0.0 | +20.5 | -13.3 | -9.3 | |
| Steps (reduced) |
32 (32) |
50 (0) |
63 (13) |
73 (23) |
82 (32) |
89 (39) |
95 (45) |
100 (0) |
105 (5) |
109 (9) |
113 (13) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.0 | -4.1 | -9.5 | -7.1 | +2.1 | +17.3 | -0.3 | -13.0 | +16.7 | +12.2 | +11.3 |
| Relative (%) | +26.4 | -10.9 | -24.9 | -18.6 | +5.5 | +45.4 | -0.7 | -34.2 | +43.8 | +32.1 | +29.8 | |
| Steps (reduced) |
117 (17) |
120 (20) |
123 (23) |
126 (26) |
129 (29) |
132 (32) |
134 (34) |
136 (36) |
139 (39) |
141 (41) |
143 (43) | |