154edt
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154 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 154edt or 154ed3), is a nonoctave tuning system that divides the interval of 3/1 into 154 equal parts of about 12.4 ¢ each. Each step represents a frequency ratio of 31/154, or the 154th root of 3.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 12.4 | 8.4 | |
| 2 | 24.7 | 16.9 | |
| 3 | 37.1 | 25.3 | 46/45, 47/46 |
| 4 | 49.4 | 33.8 | |
| 5 | 61.8 | 42.2 | 28/27, 29/28, 57/55 |
| 6 | 74.1 | 50.6 | 47/45 |
| 7 | 86.5 | 59.1 | 41/39 |
| 8 | 98.8 | 67.5 | 18/17 |
| 9 | 111.2 | 76 | |
| 10 | 123.5 | 84.4 | 29/27 |
| 11 | 135.9 | 92.9 | 40/37 |
| 12 | 148.2 | 101.3 | 49/45 |
| 13 | 160.6 | 109.7 | 34/31, 45/41, 56/51 |
| 14 | 172.9 | 118.2 | 21/19 |
| 15 | 185.3 | 126.6 | |
| 16 | 197.6 | 135.1 | 37/33 |
| 17 | 210 | 143.5 | |
| 18 | 222.3 | 151.9 | 33/29, 58/51 |
| 19 | 234.7 | 160.4 | |
| 20 | 247 | 168.8 | 15/13 |
| 21 | 259.4 | 177.3 | 36/31, 43/37 |
| 22 | 271.7 | 185.7 | 55/47 |
| 23 | 284.1 | 194.2 | 33/28 |
| 24 | 296.4 | 202.6 | 51/43 |
| 25 | 308.8 | 211 | 43/36, 49/41, 55/46 |
| 26 | 321.1 | 219.5 | |
| 27 | 333.5 | 227.9 | 40/33, 57/47 |
| 28 | 345.8 | 236.4 | |
| 29 | 358.2 | 244.8 | |
| 30 | 370.5 | 253.2 | 26/21, 57/46 |
| 31 | 382.9 | 261.7 | |
| 32 | 395.2 | 270.1 | 49/39, 54/43 |
| 33 | 407.6 | 278.6 | 43/34 |
| 34 | 419.9 | 287 | 51/40 |
| 35 | 432.3 | 295.5 | |
| 36 | 444.6 | 303.9 | |
| 37 | 457 | 312.3 | 43/33, 56/43 |
| 38 | 469.3 | 320.8 | 38/29 |
| 39 | 481.7 | 329.2 | 37/28 |
| 40 | 494 | 337.7 | |
| 41 | 506.4 | 346.1 | |
| 42 | 518.7 | 354.5 | 27/20, 58/43 |
| 43 | 531.1 | 363 | |
| 44 | 543.4 | 371.4 | 26/19 |
| 45 | 555.8 | 379.9 | 40/29, 51/37 |
| 46 | 568.1 | 388.3 | |
| 47 | 580.5 | 396.8 | |
| 48 | 592.8 | 405.2 | 31/22, 38/27 |
| 49 | 605.2 | 413.6 | 44/31 |
| 50 | 617.5 | 422.1 | 10/7 |
| 51 | 629.9 | 430.5 | |
| 52 | 642.2 | 439 | 29/20, 42/29 |
| 53 | 654.6 | 447.4 | 54/37 |
| 54 | 666.9 | 455.8 | |
| 55 | 679.3 | 464.3 | 40/27 |
| 56 | 691.6 | 472.7 | |
| 57 | 704 | 481.2 | |
| 58 | 716.3 | 489.6 | 56/37 |
| 59 | 728.7 | 498.1 | |
| 60 | 741 | 506.5 | 23/15 |
| 61 | 753.4 | 514.9 | 17/11 |
| 62 | 765.7 | 523.4 | 14/9 |
| 63 | 778.1 | 531.8 | 47/30, 58/37 |
| 64 | 790.4 | 540.3 | 30/19 |
| 65 | 802.8 | 548.7 | |
| 66 | 815.1 | 557.1 | |
| 67 | 827.5 | 565.6 | |
| 68 | 839.8 | 574 | |
| 69 | 852.2 | 582.5 | 18/11 |
| 70 | 864.5 | 590.9 | 28/17 |
| 71 | 876.9 | 599.4 | |
| 72 | 889.2 | 607.8 | |
| 73 | 901.6 | 616.2 | |
| 74 | 913.9 | 624.7 | 39/23 |
| 75 | 926.3 | 633.1 | |
| 76 | 938.6 | 641.6 | |
| 77 | 951 | 650 | 26/15, 45/26 |
| 78 | 963.3 | 658.4 | |
| 79 | 975.7 | 666.9 | 58/33 |
| 80 | 988 | 675.3 | 23/13 |
| 81 | 1000.4 | 683.8 | 41/23 |
| 82 | 1012.7 | 692.2 | |
| 83 | 1025.1 | 700.6 | 47/26, 56/31 |
| 84 | 1037.4 | 709.1 | 51/28 |
| 85 | 1049.8 | 717.5 | 11/6 |
| 86 | 1062.1 | 726 | |
| 87 | 1074.5 | 734.4 | |
| 88 | 1086.8 | 742.9 | |
| 89 | 1099.2 | 751.3 | |
| 90 | 1111.5 | 759.7 | 19/10 |
| 91 | 1123.9 | 768.2 | |
| 92 | 1136.2 | 776.6 | 27/14 |
| 93 | 1148.6 | 785.1 | 33/17 |
| 94 | 1160.9 | 793.5 | 43/22, 45/23 |
| 95 | 1173.3 | 801.9 | |
| 96 | 1185.6 | 810.4 | |
| 97 | 1198 | 818.8 | |
| 98 | 1210.3 | 827.3 | |
| 99 | 1222.7 | 835.7 | |
| 100 | 1235 | 844.2 | |
| 101 | 1247.4 | 852.6 | 37/18 |
| 102 | 1259.7 | 861 | 29/14 |
| 103 | 1272.1 | 869.5 | |
| 104 | 1284.4 | 877.9 | 21/10 |
| 105 | 1296.8 | 886.4 | 55/26 |
| 106 | 1309.1 | 894.8 | 49/23 |
| 107 | 1321.5 | 903.2 | |
| 108 | 1333.8 | 911.7 | |
| 109 | 1346.2 | 920.1 | 37/17 |
| 110 | 1358.5 | 928.6 | 46/21, 57/26 |
| 111 | 1370.9 | 937 | |
| 112 | 1383.2 | 945.5 | 20/9 |
| 113 | 1395.6 | 953.9 | 47/21 |
| 114 | 1407.9 | 962.3 | |
| 115 | 1420.3 | 970.8 | |
| 116 | 1432.6 | 979.2 | |
| 117 | 1445 | 987.7 | |
| 118 | 1457.3 | 996.1 | |
| 119 | 1469.7 | 1004.5 | |
| 120 | 1482 | 1013 | 40/17 |
| 121 | 1494.4 | 1021.4 | |
| 122 | 1506.7 | 1029.9 | 43/18 |
| 123 | 1519.1 | 1038.3 | |
| 124 | 1531.4 | 1046.8 | 46/19 |
| 125 | 1543.8 | 1055.2 | |
| 126 | 1556.1 | 1063.6 | |
| 127 | 1568.5 | 1072.1 | 47/19, 52/21 |
| 128 | 1580.8 | 1080.5 | |
| 129 | 1593.2 | 1089 | |
| 130 | 1605.5 | 1097.4 | 43/17 |
| 131 | 1617.9 | 1105.8 | 28/11 |
| 132 | 1630.2 | 1114.3 | |
| 133 | 1642.6 | 1122.7 | 31/12 |
| 134 | 1654.9 | 1131.2 | 13/5 |
| 135 | 1667.3 | 1139.6 | 55/21 |
| 136 | 1679.6 | 1148.1 | 29/11 |
| 137 | 1692 | 1156.5 | |
| 138 | 1704.3 | 1164.9 | |
| 139 | 1716.7 | 1173.4 | |
| 140 | 1729.1 | 1181.8 | 19/7 |
| 141 | 1741.4 | 1190.3 | 41/15 |
| 142 | 1753.8 | 1198.7 | |
| 143 | 1766.1 | 1207.1 | |
| 144 | 1778.5 | 1215.6 | |
| 145 | 1790.8 | 1224 | |
| 146 | 1803.2 | 1232.5 | 17/6 |
| 147 | 1815.5 | 1240.9 | |
| 148 | 1827.9 | 1249.4 | |
| 149 | 1840.2 | 1257.8 | 55/19 |
| 150 | 1852.6 | 1266.2 | |
| 151 | 1864.9 | 1274.7 | |
| 152 | 1877.3 | 1283.1 | |
| 153 | 1889.6 | 1291.6 | |
| 154 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.02 | +0.00 | -4.03 | +4.87 | -2.02 | +2.82 | -6.05 | +0.00 | +2.85 | -1.60 | -4.03 |
| Relative (%) | -16.3 | +0.0 | -32.6 | +39.4 | -16.3 | +22.8 | -49.0 | +0.0 | +23.1 | -12.9 | -32.6 | |
| Steps (reduced) |
97 (97) |
154 (0) |
194 (40) |
226 (72) |
251 (97) |
273 (119) |
291 (137) |
308 (0) |
323 (15) |
336 (28) |
348 (40) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.60 | +0.81 | +4.87 | +4.29 | -1.86 | -2.02 | +3.18 | +0.84 | +2.82 | -3.61 | +5.88 |
| Relative (%) | +45.4 | +6.5 | +39.4 | +34.7 | -15.1 | -16.3 | +25.8 | +6.8 | +22.8 | -29.3 | +47.6 | |
| Steps (reduced) |
360 (52) |
370 (62) |
380 (72) |
389 (81) |
397 (89) |
405 (97) |
413 (105) |
420 (112) |
427 (119) |
433 (125) |
440 (132) | |