74edt
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74 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 74edt or 74ed3), is a nonoctave tuning system that divides the interval of 3/1 into 74 equal parts of about 25.7 ¢ each. Each step represents a frequency ratio of 31/74, or the 74th root of 3.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 25.7 | 17.6 | |
| 2 | 51.4 | 35.1 | 34/33 |
| 3 | 77.1 | 52.7 | |
| 4 | 102.8 | 70.3 | |
| 5 | 128.5 | 87.8 | 14/13 |
| 6 | 154.2 | 105.4 | 23/21 |
| 7 | 179.9 | 123 | 10/9 |
| 8 | 205.6 | 140.5 | |
| 9 | 231.3 | 158.1 | |
| 10 | 257 | 175.7 | |
| 11 | 282.7 | 193.2 | 20/17, 33/28 |
| 12 | 308.4 | 210.8 | 37/31 |
| 13 | 334.1 | 228.4 | 17/14, 23/19 |
| 14 | 359.8 | 245.9 | 37/30 |
| 15 | 385.5 | 263.5 | |
| 16 | 411.2 | 281.1 | 19/15, 33/26 |
| 17 | 436.9 | 298.6 | 9/7 |
| 18 | 462.6 | 316.2 | 17/13, 30/23 |
| 19 | 488.3 | 333.8 | |
| 20 | 514 | 351.4 | 31/23 |
| 21 | 539.7 | 368.9 | |
| 22 | 565.4 | 386.5 | 18/13 |
| 23 | 591.1 | 404.1 | 38/27 |
| 24 | 616.9 | 421.6 | 10/7 |
| 25 | 642.6 | 439.2 | 29/20 |
| 26 | 668.3 | 456.8 | |
| 27 | 694 | 474.3 | |
| 28 | 719.7 | 491.9 | |
| 29 | 745.4 | 509.5 | 20/13 |
| 30 | 771.1 | 527 | |
| 31 | 796.8 | 544.6 | |
| 32 | 822.5 | 562.2 | 29/18, 37/23 |
| 33 | 848.2 | 579.7 | 31/19 |
| 34 | 873.9 | 597.3 | |
| 35 | 899.6 | 614.9 | |
| 36 | 925.3 | 632.4 | 29/17 |
| 37 | 951 | 650 | |
| 38 | 976.7 | 667.6 | |
| 39 | 1002.4 | 685.1 | |
| 40 | 1028.1 | 702.7 | 38/21 |
| 41 | 1053.8 | 720.3 | |
| 42 | 1079.5 | 737.8 | |
| 43 | 1105.2 | 755.4 | |
| 44 | 1130.9 | 773 | |
| 45 | 1156.6 | 790.5 | 37/19 |
| 46 | 1182.3 | 808.1 | |
| 47 | 1208 | 825.7 | |
| 48 | 1233.7 | 843.2 | |
| 49 | 1259.4 | 860.8 | 29/14, 31/15 |
| 50 | 1285.1 | 878.4 | 21/10 |
| 51 | 1310.8 | 895.9 | |
| 52 | 1336.5 | 913.5 | 13/6 |
| 53 | 1362.2 | 931.1 | |
| 54 | 1387.9 | 948.6 | 29/13 |
| 55 | 1413.6 | 966.2 | |
| 56 | 1439.3 | 983.8 | 23/10 |
| 57 | 1465 | 1001.4 | 7/3 |
| 58 | 1490.7 | 1018.9 | 26/11 |
| 59 | 1516.4 | 1036.5 | |
| 60 | 1542.1 | 1054.1 | |
| 61 | 1567.8 | 1071.6 | |
| 62 | 1593.5 | 1089.2 | |
| 63 | 1619.2 | 1106.8 | 28/11 |
| 64 | 1644.9 | 1124.3 | |
| 65 | 1670.6 | 1141.9 | |
| 66 | 1696.3 | 1159.5 | |
| 67 | 1722 | 1177 | 27/10 |
| 68 | 1747.7 | 1194.6 | |
| 69 | 1773.4 | 1212.2 | |
| 70 | 1799.1 | 1229.7 | |
| 71 | 1824.8 | 1247.3 | |
| 72 | 1850.6 | 1264.9 | |
| 73 | 1876.3 | 1282.4 | |
| 74 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.0 | +0.0 | -9.7 | -10.5 | +8.0 | -1.9 | -1.7 | +0.0 | -2.5 | +12.4 | -9.7 |
| Relative (%) | +31.1 | +0.0 | -37.8 | -40.8 | +31.1 | -7.2 | -6.6 | +0.0 | -9.7 | +48.3 | -37.8 | |
| Steps (reduced) |
47 (47) |
74 (0) |
93 (19) |
108 (34) |
121 (47) |
131 (57) |
140 (66) |
148 (0) |
155 (7) |
162 (14) |
167 (19) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.9 | +6.1 | -10.5 | +6.3 | +4.1 | +8.0 | -8.5 | +5.5 | -1.9 | -5.3 | -5.1 |
| Relative (%) | +23.1 | +23.9 | -40.8 | +24.5 | +16.1 | +31.1 | -33.1 | +21.4 | -7.2 | -20.6 | -20.0 | |
| Steps (reduced) |
173 (25) |
178 (30) |
182 (34) |
187 (39) |
191 (43) |
195 (47) |
198 (50) |
202 (54) |
205 (57) |
208 (60) |
211 (63) | |