68edt
Division of the third harmonic into 68 equal parts (68EDT) is related to 43 edo (meride tuning), but with the 3/1 rather than the 2/1 being just. The octave is about 2.7068 cents stretched and the step size is about 27.9699 cents. Unlike 43edo, it is only consistent up to the 6-integer-limit, with discrepancy for the 7th harmonic.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 28 | 19.1 | |
| 2 | 55.9 | 38.2 | 31/30, 32/31 |
| 3 | 83.9 | 57.4 | 22/21 |
| 4 | 111.9 | 76.5 | 16/15 |
| 5 | 139.8 | 95.6 | 13/12 |
| 6 | 167.8 | 114.7 | |
| 7 | 195.8 | 133.8 | 19/17 |
| 8 | 223.8 | 152.9 | 33/29 |
| 9 | 251.7 | 172.1 | 22/19, 37/32 |
| 10 | 279.7 | 191.2 | 27/23 |
| 11 | 307.7 | 210.3 | 31/26, 37/31 |
| 12 | 335.6 | 229.4 | 17/14 |
| 13 | 363.6 | 248.5 | 21/17, 37/30 |
| 14 | 391.6 | 267.6 | |
| 15 | 419.5 | 286.8 | 14/11 |
| 16 | 447.5 | 305.9 | 22/17, 35/27 |
| 17 | 475.5 | 325 | 29/22 |
| 18 | 503.5 | 344.1 | |
| 19 | 531.4 | 363.2 | 19/14 |
| 20 | 559.4 | 382.4 | 29/21 |
| 21 | 587.4 | 401.5 | |
| 22 | 615.3 | 420.6 | |
| 23 | 643.3 | 439.7 | |
| 24 | 671.3 | 458.8 | 28/19 |
| 25 | 699.2 | 477.9 | 3/2 |
| 26 | 727.2 | 497.1 | 35/23 |
| 27 | 755.2 | 516.2 | 17/11, 31/20 |
| 28 | 783.2 | 535.3 | 11/7 |
| 29 | 811.1 | 554.4 | 8/5 |
| 30 | 839.1 | 573.5 | 13/8 |
| 31 | 867.1 | 592.6 | 28/17 |
| 32 | 895 | 611.8 | |
| 33 | 923 | 630.9 | 29/17 |
| 34 | 951 | 650 | 26/15 |
| 35 | 978.9 | 669.1 | |
| 36 | 1006.9 | 688.2 | 34/19 |
| 37 | 1034.9 | 707.4 | |
| 38 | 1062.9 | 726.5 | 24/13, 37/20 |
| 39 | 1090.8 | 745.6 | 15/8 |
| 40 | 1118.8 | 764.7 | 21/11 |
| 41 | 1146.8 | 783.8 | 31/16, 33/17 |
| 42 | 1174.7 | 802.9 | |
| 43 | 1202.7 | 822.1 | 2/1 |
| 44 | 1230.7 | 841.2 | |
| 45 | 1258.6 | 860.3 | 29/14, 31/15 |
| 46 | 1286.6 | 879.4 | |
| 47 | 1314.6 | 898.5 | 32/15 |
| 48 | 1342.6 | 917.6 | |
| 49 | 1370.5 | 936.8 | |
| 50 | 1398.5 | 955.9 | |
| 51 | 1426.5 | 975 | |
| 52 | 1454.4 | 994.1 | 37/16 |
| 53 | 1482.4 | 1013.2 | 33/14 |
| 54 | 1510.4 | 1032.4 | |
| 55 | 1538.3 | 1051.5 | 17/7 |
| 56 | 1566.3 | 1070.6 | 37/15 |
| 57 | 1594.3 | 1089.7 | |
| 58 | 1622.3 | 1108.8 | 23/9 |
| 59 | 1650.2 | 1127.9 | |
| 60 | 1678.2 | 1147.1 | 29/11 |
| 61 | 1706.2 | 1166.2 | |
| 62 | 1734.1 | 1185.3 | |
| 63 | 1762.1 | 1204.4 | 36/13 |
| 64 | 1790.1 | 1223.5 | |
| 65 | 1818 | 1242.6 | |
| 66 | 1846 | 1261.8 | |
| 67 | 1874 | 1280.9 | |
| 68 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.7 | +0.0 | +5.4 | +10.7 | +2.7 | -12.4 | +8.1 | +0.0 | +13.4 | -11.8 | +5.4 |
| Relative (%) | +9.7 | +0.0 | +19.4 | +38.2 | +9.7 | -44.5 | +29.0 | +0.0 | +47.9 | -42.1 | +19.4 | |
| Steps (reduced) |
43 (43) |
68 (0) |
86 (18) |
100 (32) |
111 (43) |
120 (52) |
129 (61) |
136 (0) |
143 (7) |
148 (12) |
154 (18) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +6.7 | -9.7 | +10.7 | +10.8 | -10.2 | +2.7 | -7.0 | -11.9 | -12.4 | -9.1 | -2.1 |
| Relative (%) | +23.9 | -34.8 | +38.2 | +38.7 | -36.5 | +9.7 | -25.0 | -42.5 | -44.5 | -32.4 | -7.5 | |
| Steps (reduced) |
159 (23) |
163 (27) |
168 (32) |
172 (36) |
175 (39) |
179 (43) |
182 (46) |
185 (49) |
188 (52) |
191 (55) |
194 (58) | |