150edt
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150 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 150edt or 150ed3), is a nonoctave tuning system that divides the interval of 3/1 into 150 equal parts of about 12.7 ¢ each. Each step represents a frequency ratio of 31/150, or the 150th root of 3.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 12.7 | 8.7 | |
| 2 | 25.4 | 17.3 | |
| 3 | 38 | 26 | 45/44, 46/45, 47/46 |
| 4 | 50.7 | 34.7 | 35/34 |
| 5 | 63.4 | 43.3 | |
| 6 | 76.1 | 52 | 23/22, 47/45 |
| 7 | 88.8 | 60.7 | |
| 8 | 101.4 | 69.3 | 52/49 |
| 9 | 114.1 | 78 | 31/29, 47/44 |
| 10 | 126.8 | 86.7 | |
| 11 | 139.5 | 95.3 | |
| 12 | 152.2 | 104 | |
| 13 | 164.8 | 112.7 | |
| 14 | 177.5 | 121.3 | 41/37, 51/46 |
| 15 | 190.2 | 130 | 29/26 |
| 16 | 202.9 | 138.7 | |
| 17 | 215.6 | 147.3 | 17/15 |
| 18 | 228.2 | 156 | |
| 19 | 240.9 | 164.7 | 54/47 |
| 20 | 253.6 | 173.3 | 22/19 |
| 21 | 266.3 | 182 | 7/6 |
| 22 | 279 | 190.7 | 27/23 |
| 23 | 291.6 | 199.3 | 45/38 |
| 24 | 304.3 | 208 | 31/26 |
| 25 | 317 | 216.7 | 6/5 |
| 26 | 329.7 | 225.3 | 23/19, 52/43 |
| 27 | 342.4 | 234 | |
| 28 | 355 | 242.7 | 27/22, 43/35 |
| 29 | 367.7 | 251.3 | 47/38 |
| 30 | 380.4 | 260 | |
| 31 | 393.1 | 268.7 | 54/43 |
| 32 | 405.8 | 277.3 | 43/34 |
| 33 | 418.4 | 286 | |
| 34 | 431.1 | 294.7 | |
| 35 | 443.8 | 303.3 | |
| 36 | 456.5 | 312 | |
| 37 | 469.1 | 320.7 | 38/29 |
| 38 | 481.8 | 329.3 | |
| 39 | 494.5 | 338 | |
| 40 | 507.2 | 346.7 | 55/41 |
| 41 | 519.9 | 355.3 | |
| 42 | 532.5 | 364 | 34/25, 49/36 |
| 43 | 545.2 | 372.7 | 37/27 |
| 44 | 557.9 | 381.3 | 29/21 |
| 45 | 570.6 | 390 | 57/41 |
| 46 | 583.3 | 398.7 | 7/5 |
| 47 | 595.9 | 407.3 | 55/39 |
| 48 | 608.6 | 416 | 27/19 |
| 49 | 621.3 | 424.7 | |
| 50 | 634 | 433.3 | 49/34 |
| 51 | 646.7 | 442 | 45/31 |
| 52 | 659.3 | 450.7 | |
| 53 | 672 | 459.3 | |
| 54 | 684.7 | 468 | 46/31, 52/35 |
| 55 | 697.4 | 476.7 | |
| 56 | 710.1 | 485.3 | |
| 57 | 722.7 | 494 | 41/27, 44/29 |
| 58 | 735.4 | 502.7 | 26/17 |
| 59 | 748.1 | 511.3 | 57/37 |
| 60 | 760.8 | 520 | 45/29 |
| 61 | 773.5 | 528.7 | |
| 62 | 786.1 | 537.3 | |
| 63 | 798.8 | 546 | 46/29 |
| 64 | 811.5 | 554.7 | |
| 65 | 824.2 | 563.3 | 29/18, 37/23 |
| 66 | 836.9 | 572 | 47/29 |
| 67 | 849.5 | 580.7 | 49/30 |
| 68 | 862.2 | 589.3 | 51/31 |
| 69 | 874.9 | 598 | |
| 70 | 887.6 | 606.7 | |
| 71 | 900.3 | 615.3 | 37/22 |
| 72 | 912.9 | 624 | 39/23 |
| 73 | 925.6 | 632.7 | 29/17 |
| 74 | 938.3 | 641.3 | 43/25 |
| 75 | 951 | 650 | 26/15, 45/26 |
| 76 | 963.7 | 658.7 | |
| 77 | 976.3 | 667.3 | 51/29 |
| 78 | 989 | 676 | 23/13 |
| 79 | 1001.7 | 684.7 | 41/23 |
| 80 | 1014.4 | 693.3 | |
| 81 | 1027.1 | 702 | 38/21 |
| 82 | 1039.7 | 710.7 | 31/17 |
| 83 | 1052.4 | 719.3 | |
| 84 | 1065.1 | 728 | |
| 85 | 1077.8 | 736.7 | 41/22, 54/29 |
| 86 | 1090.5 | 745.3 | |
| 87 | 1103.1 | 754 | |
| 88 | 1115.8 | 762.7 | |
| 89 | 1128.5 | 771.3 | |
| 90 | 1141.2 | 780 | 29/15 |
| 91 | 1153.9 | 788.7 | 37/19 |
| 92 | 1166.5 | 797.3 | 49/25, 51/26 |
| 93 | 1179.2 | 806 | |
| 94 | 1191.9 | 814.7 | |
| 95 | 1204.6 | 823.3 | |
| 96 | 1217.3 | 832 | |
| 97 | 1229.9 | 840.7 | |
| 98 | 1242.6 | 849.3 | |
| 99 | 1255.3 | 858 | 31/15 |
| 100 | 1268 | 866.7 | 52/25 |
| 101 | 1280.6 | 875.3 | 44/21 |
| 102 | 1293.3 | 884 | 19/9 |
| 103 | 1306 | 892.7 | |
| 104 | 1318.7 | 901.3 | 15/7 |
| 105 | 1331.4 | 910 | 41/19 |
| 106 | 1344 | 918.7 | |
| 107 | 1356.7 | 927.3 | 46/21 |
| 108 | 1369.4 | 936 | |
| 109 | 1382.1 | 944.7 | |
| 110 | 1394.8 | 953.3 | 47/21 |
| 111 | 1407.4 | 962 | |
| 112 | 1420.1 | 970.7 | |
| 113 | 1432.8 | 979.3 | |
| 114 | 1445.5 | 988 | |
| 115 | 1458.2 | 996.7 | |
| 116 | 1470.8 | 1005.3 | |
| 117 | 1483.5 | 1014 | |
| 118 | 1496.2 | 1022.7 | |
| 119 | 1508.9 | 1031.3 | 43/18, 55/23 |
| 120 | 1521.6 | 1040 | |
| 121 | 1534.2 | 1048.7 | |
| 122 | 1546.9 | 1057.3 | 22/9 |
| 123 | 1559.6 | 1066 | |
| 124 | 1572.3 | 1074.7 | 57/23 |
| 125 | 1585 | 1083.3 | 5/2 |
| 126 | 1597.6 | 1092 | |
| 127 | 1610.3 | 1100.7 | 38/15 |
| 128 | 1623 | 1109.3 | 23/9 |
| 129 | 1635.7 | 1118 | 18/7 |
| 130 | 1648.4 | 1126.7 | 57/22 |
| 131 | 1661 | 1135.3 | 47/18 |
| 132 | 1673.7 | 1144 | |
| 133 | 1686.4 | 1152.7 | 45/17 |
| 134 | 1699.1 | 1161.3 | |
| 135 | 1711.8 | 1170 | |
| 136 | 1724.4 | 1178.7 | 46/17 |
| 137 | 1737.1 | 1187.3 | |
| 138 | 1749.8 | 1196 | |
| 139 | 1762.5 | 1204.7 | |
| 140 | 1775.2 | 1213.3 | |
| 141 | 1787.8 | 1222 | |
| 142 | 1800.5 | 1230.7 | |
| 143 | 1813.2 | 1239.3 | |
| 144 | 1825.9 | 1248 | |
| 145 | 1838.6 | 1256.7 | |
| 146 | 1851.2 | 1265.3 | |
| 147 | 1863.9 | 1274 | 44/15 |
| 148 | 1876.6 | 1282.7 | |
| 149 | 1889.3 | 1291.3 | |
| 150 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.57 | +0.00 | -3.54 | +3.22 | +4.57 | +3.97 | +1.03 | +0.00 | -4.89 | -5.06 | -3.54 |
| Relative (%) | +36.1 | +0.0 | -27.9 | +25.4 | +36.1 | +31.3 | +8.2 | +0.0 | -38.5 | -39.9 | -27.9 | |
| Steps (reduced) |
95 (95) |
150 (0) |
189 (39) |
220 (70) |
245 (95) |
266 (116) |
284 (134) |
300 (0) |
314 (14) |
327 (27) |
339 (39) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | -4.13 | +3.22 | +5.61 | +2.09 | +4.57 | -0.27 | -0.32 | +3.97 | -0.48 | -1.36 |
| Relative (%) | -20.8 | -32.6 | +25.4 | +44.2 | +16.5 | +36.1 | -2.2 | -2.5 | +31.3 | -3.8 | -10.7 | |
| Steps (reduced) |
350 (50) |
360 (60) |
370 (70) |
379 (79) |
387 (87) |
395 (95) |
402 (102) |
409 (109) |
416 (116) |
422 (122) |
428 (128) | |