70edt
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70 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 70edt or 70ed3), is a nonoctave tuning system that divides the interval of 3/1 into 70 equal parts of about 27.2 ¢ each. Each step represents a frequency ratio of 31/70, or the 70th root of 3.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 27.2 | 18.6 | |
| 2 | 54.3 | 37.1 | 31/30, 34/33 |
| 3 | 81.5 | 55.7 | 21/20, 22/21 |
| 4 | 108.7 | 74.3 | 33/31 |
| 5 | 135.9 | 92.9 | 13/12 |
| 6 | 163 | 111.4 | 11/10, 34/31 |
| 7 | 190.2 | 130 | 19/17 |
| 8 | 217.4 | 148.6 | 17/15 |
| 9 | 244.5 | 167.1 | 23/20 |
| 10 | 271.7 | 185.7 | 34/29 |
| 11 | 298.9 | 204.3 | |
| 12 | 326 | 222.9 | 35/29 |
| 13 | 353.2 | 241.4 | 27/22 |
| 14 | 380.4 | 260 | |
| 15 | 407.6 | 278.6 | 19/15 |
| 16 | 434.7 | 297.1 | 9/7 |
| 17 | 461.9 | 315.7 | 30/23 |
| 18 | 489.1 | 334.3 | |
| 19 | 516.2 | 352.9 | 27/20, 31/23 |
| 20 | 543.4 | 371.4 | 37/27 |
| 21 | 570.6 | 390 | |
| 22 | 597.8 | 408.6 | |
| 23 | 624.9 | 427.1 | 33/23 |
| 24 | 652.1 | 445.7 | |
| 25 | 679.3 | 464.3 | 34/23 |
| 26 | 706.4 | 482.9 | |
| 27 | 733.6 | 501.4 | 29/19 |
| 28 | 760.8 | 520 | 31/20 |
| 29 | 788 | 538.6 | 30/19 |
| 30 | 815.1 | 557.1 | |
| 31 | 842.3 | 575.7 | 13/8 |
| 32 | 869.5 | 594.3 | 33/20 |
| 33 | 896.6 | 612.9 | 37/22 |
| 34 | 923.8 | 631.4 | 29/17 |
| 35 | 951 | 650 | |
| 36 | 978.1 | 668.6 | 37/21 |
| 37 | 1005.3 | 687.1 | 34/19 |
| 38 | 1032.5 | 705.7 | 20/11 |
| 39 | 1059.7 | 724.3 | 24/13, 35/19 |
| 40 | 1086.8 | 742.9 | |
| 41 | 1114 | 761.4 | 19/10 |
| 42 | 1141.2 | 780 | 29/15 |
| 43 | 1168.3 | 798.6 | |
| 44 | 1195.5 | 817.1 | |
| 45 | 1222.7 | 835.7 | |
| 46 | 1249.9 | 854.3 | 35/17, 37/18 |
| 47 | 1277 | 872.9 | 23/11 |
| 48 | 1304.2 | 891.4 | |
| 49 | 1331.4 | 910 | 28/13 |
| 50 | 1358.5 | 928.6 | |
| 51 | 1385.7 | 947.1 | 20/9 |
| 52 | 1412.9 | 965.7 | |
| 53 | 1440.1 | 984.3 | 23/10 |
| 54 | 1467.2 | 1002.9 | 7/3 |
| 55 | 1494.4 | 1021.4 | |
| 56 | 1521.6 | 1040 | |
| 57 | 1548.7 | 1058.6 | 22/9 |
| 58 | 1575.9 | 1077.1 | |
| 59 | 1603.1 | 1095.7 | |
| 60 | 1630.2 | 1114.3 | |
| 61 | 1657.4 | 1132.9 | |
| 62 | 1684.6 | 1151.4 | 37/14 |
| 63 | 1711.8 | 1170 | |
| 64 | 1738.9 | 1188.6 | 30/11 |
| 65 | 1766.1 | 1207.1 | 36/13 |
| 66 | 1793.3 | 1225.7 | 31/11 |
| 67 | 1820.4 | 1244.3 | 20/7 |
| 68 | 1847.6 | 1262.9 | |
| 69 | 1874.8 | 1281.4 | |
| 70 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.5 | +0.0 | -9.0 | +12.3 | -4.5 | +0.4 | -13.5 | +0.0 | +7.8 | +5.8 | -9.0 |
| Relative (%) | -16.5 | +0.0 | -33.0 | +45.2 | -16.5 | +1.3 | -49.5 | +0.0 | +28.7 | +21.4 | -33.0 | |
| Steps (reduced) |
44 (44) |
70 (0) |
88 (18) |
103 (33) |
114 (44) |
124 (54) |
132 (62) |
140 (0) |
147 (7) |
153 (13) |
158 (18) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.7 | -4.1 | +12.3 | +9.2 | +13.0 | -4.5 | +10.6 | +3.3 | +0.4 | +1.3 | +5.9 |
| Relative (%) | -43.0 | -15.2 | +45.2 | +34.0 | +47.7 | -16.5 | +39.0 | +12.2 | +1.3 | +4.9 | +21.7 | |
| Steps (reduced) |
163 (23) |
168 (28) |
173 (33) |
177 (37) |
181 (41) |
184 (44) |
188 (48) |
191 (51) |
194 (54) |
197 (57) |
200 (60) | |