158edt
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 157edt | 158edt | 159edt → |
158 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 158edt or 158ed3), is a nonoctave tuning system that divides the interval of 3/1 into 158 equal parts of about 12 ¢ each. Each step represents a frequency ratio of 31/158, or the 158th root of 3.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 12 | 8.2 | |
| 2 | 24.1 | 16.5 | |
| 3 | 36.1 | 24.7 | 47/46 |
| 4 | 48.2 | 32.9 | |
| 5 | 60.2 | 41.1 | |
| 6 | 72.2 | 49.4 | 49/47 |
| 7 | 84.3 | 57.6 | 21/20 |
| 8 | 96.3 | 65.8 | 37/35 |
| 9 | 108.3 | 74.1 | 33/31, 49/46 |
| 10 | 120.4 | 82.3 | |
| 11 | 132.4 | 90.5 | 41/38 |
| 12 | 144.5 | 98.7 | |
| 13 | 156.5 | 107 | 23/21 |
| 14 | 168.5 | 115.2 | 43/39, 54/49 |
| 15 | 180.6 | 123.4 | |
| 16 | 192.6 | 131.6 | 19/17 |
| 17 | 204.6 | 139.9 | |
| 18 | 216.7 | 148.1 | 17/15 |
| 19 | 228.7 | 156.3 | |
| 20 | 240.8 | 164.6 | 23/20, 54/47 |
| 21 | 252.8 | 172.8 | |
| 22 | 264.8 | 181 | |
| 23 | 276.9 | 189.2 | 27/23 |
| 24 | 288.9 | 197.5 | 13/11 |
| 25 | 300.9 | 205.7 | |
| 26 | 313 | 213.9 | |
| 27 | 325 | 222.2 | 35/29, 41/34 |
| 28 | 337.1 | 230.4 | |
| 29 | 349.1 | 238.6 | |
| 30 | 361.1 | 246.8 | |
| 31 | 373.2 | 255.1 | |
| 32 | 385.2 | 263.3 | |
| 33 | 397.2 | 271.5 | 39/31 |
| 34 | 409.3 | 279.7 | 19/15 |
| 35 | 421.3 | 288 | 37/29 |
| 36 | 433.4 | 296.2 | |
| 37 | 445.4 | 304.4 | |
| 38 | 457.4 | 312.7 | 43/33 |
| 39 | 469.5 | 320.9 | |
| 40 | 481.5 | 329.1 | |
| 41 | 493.5 | 337.3 | |
| 42 | 505.6 | 345.6 | |
| 43 | 517.6 | 353.8 | 31/23, 58/43 |
| 44 | 529.7 | 362 | |
| 45 | 541.7 | 370.3 | 41/30 |
| 46 | 553.7 | 378.5 | |
| 47 | 565.8 | 386.7 | 43/31 |
| 48 | 577.8 | 394.9 | |
| 49 | 589.8 | 403.2 | |
| 50 | 601.9 | 411.4 | 58/41 |
| 51 | 613.9 | 419.6 | |
| 52 | 626 | 427.8 | 33/23 |
| 53 | 638 | 436.1 | 13/9 |
| 54 | 650 | 444.3 | |
| 55 | 662.1 | 452.5 | |
| 56 | 674.1 | 460.8 | 31/21 |
| 57 | 686.1 | 469 | 55/37, 58/39 |
| 58 | 698.2 | 477.2 | |
| 59 | 710.2 | 485.4 | |
| 60 | 722.3 | 493.7 | 41/27 |
| 61 | 734.3 | 501.9 | |
| 62 | 746.3 | 510.1 | 20/13 |
| 63 | 758.4 | 518.4 | 31/20 |
| 64 | 770.4 | 526.6 | |
| 65 | 782.4 | 534.8 | 11/7 |
| 66 | 794.5 | 543 | |
| 67 | 806.5 | 551.3 | 43/27 |
| 68 | 818.6 | 559.5 | |
| 69 | 830.6 | 567.7 | 21/13 |
| 70 | 842.6 | 575.9 | |
| 71 | 854.7 | 584.2 | |
| 72 | 866.7 | 592.4 | 33/20 |
| 73 | 878.8 | 600.6 | |
| 74 | 890.8 | 608.9 | |
| 75 | 902.8 | 617.1 | |
| 76 | 914.9 | 625.3 | 39/23 |
| 77 | 926.9 | 633.5 | |
| 78 | 938.9 | 641.8 | |
| 79 | 951 | 650 | |
| 80 | 963 | 658.2 | |
| 81 | 975.1 | 666.5 | 58/33 |
| 82 | 987.1 | 674.7 | 23/13 |
| 83 | 999.1 | 682.9 | |
| 84 | 1011.2 | 691.1 | |
| 85 | 1023.2 | 699.4 | |
| 86 | 1035.2 | 707.6 | 20/11 |
| 87 | 1047.3 | 715.8 | |
| 88 | 1059.3 | 724.1 | |
| 89 | 1071.4 | 732.3 | 13/7 |
| 90 | 1083.4 | 740.5 | 43/23, 58/31 |
| 91 | 1095.4 | 748.7 | |
| 92 | 1107.5 | 757 | 55/29 |
| 93 | 1119.5 | 765.2 | 21/11 |
| 94 | 1131.5 | 773.4 | |
| 95 | 1143.6 | 781.6 | |
| 96 | 1155.6 | 789.9 | 39/20 |
| 97 | 1167.7 | 798.1 | |
| 98 | 1179.7 | 806.3 | |
| 99 | 1191.7 | 814.6 | |
| 100 | 1203.8 | 822.8 | |
| 101 | 1215.8 | 831 | |
| 102 | 1227.8 | 839.2 | |
| 103 | 1239.9 | 847.5 | 43/21 |
| 104 | 1251.9 | 855.7 | |
| 105 | 1264 | 863.9 | 27/13 |
| 106 | 1276 | 872.2 | 23/11 |
| 107 | 1288 | 880.4 | |
| 108 | 1300.1 | 888.6 | |
| 109 | 1312.1 | 896.8 | |
| 110 | 1324.1 | 905.1 | 43/20, 58/27 |
| 111 | 1336.2 | 913.3 | |
| 112 | 1348.2 | 921.5 | |
| 113 | 1360.3 | 929.7 | |
| 114 | 1372.3 | 938 | |
| 115 | 1384.3 | 946.2 | |
| 116 | 1396.4 | 954.4 | |
| 117 | 1408.4 | 962.7 | |
| 118 | 1420.4 | 970.9 | |
| 119 | 1432.5 | 979.1 | |
| 120 | 1444.5 | 987.3 | |
| 121 | 1456.6 | 995.6 | |
| 122 | 1468.6 | 1003.8 | |
| 123 | 1480.6 | 1012 | 47/20 |
| 124 | 1492.7 | 1020.3 | 45/19 |
| 125 | 1504.7 | 1028.5 | 31/13 |
| 126 | 1516.7 | 1036.7 | |
| 127 | 1528.8 | 1044.9 | |
| 128 | 1540.8 | 1053.2 | |
| 129 | 1552.9 | 1061.4 | |
| 130 | 1564.9 | 1069.6 | |
| 131 | 1576.9 | 1077.8 | |
| 132 | 1589 | 1086.1 | |
| 133 | 1601 | 1094.3 | 58/23 |
| 134 | 1613.1 | 1102.5 | 33/13 |
| 135 | 1625.1 | 1110.8 | 23/9 |
| 136 | 1637.1 | 1119 | |
| 137 | 1649.2 | 1127.2 | |
| 138 | 1661.2 | 1135.4 | 47/18 |
| 139 | 1673.2 | 1143.7 | |
| 140 | 1685.3 | 1151.9 | 45/17 |
| 141 | 1697.3 | 1160.1 | |
| 142 | 1709.4 | 1168.4 | 51/19 |
| 143 | 1721.4 | 1176.6 | |
| 144 | 1733.4 | 1184.8 | 49/18 |
| 145 | 1745.5 | 1193 | |
| 146 | 1757.5 | 1201.3 | 58/21 |
| 147 | 1769.5 | 1209.5 | |
| 148 | 1781.6 | 1217.7 | |
| 149 | 1793.6 | 1225.9 | 31/11 |
| 150 | 1805.7 | 1234.2 | |
| 151 | 1817.7 | 1242.4 | 20/7 |
| 152 | 1829.7 | 1250.6 | |
| 153 | 1841.8 | 1258.9 | |
| 154 | 1853.8 | 1267.1 | |
| 155 | 1865.8 | 1275.3 | |
| 156 | 1877.9 | 1283.5 | |
| 157 | 1889.9 | 1291.8 | |
| 158 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.77 | +0.00 | -4.50 | -5.61 | +3.77 | +1.73 | -0.73 | +0.00 | -1.84 | +1.69 | -4.50 |
| Relative (%) | +31.3 | +0.0 | -37.4 | -46.6 | +31.3 | +14.3 | -6.1 | +0.0 | -15.3 | +14.0 | -37.4 | |
| Steps (reduced) |
100 (100) |
158 (0) |
199 (41) |
231 (73) |
258 (100) |
280 (122) |
299 (141) |
316 (0) |
331 (15) |
345 (29) |
357 (41) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.38 | +5.50 | -5.61 | +3.04 | -5.62 | +3.77 | -5.57 | +1.93 | +1.73 | +5.45 | +0.72 |
| Relative (%) | +11.5 | +45.7 | -46.6 | +25.2 | -46.7 | +31.3 | -46.3 | +16.0 | +14.3 | +45.3 | +6.0 | |
| Steps (reduced) |
369 (53) |
380 (64) |
389 (73) |
399 (83) |
407 (91) |
416 (100) |
423 (107) |
431 (115) |
438 (122) |
445 (129) |
451 (135) | |