78edt
| ← 77edt | 78edt | 79edt → |
78EDT is the equal division of the third harmonic into 78 parts of 24.3840 cents each, corresponding to 49.2125 edo. It has a distinct flat tendency, in the sense that if 3 is pure, 2 (octave), 5, 7, 11, 13, 17, and 19 are all flat. It is consistent to the no-twos 19-limit, tempering out 245/243 and 3125/3087 in the 7-limit; 1331/1323, 6655/6561, and 9375/9317 in the 11-limit; 275/273, 847/845, 1575/1573, and 2197/2187 in the 13-limit; 875/867 and 2025/2023 in the 17-limit; 325/323, 363/361, 665/663, 935/931, and 1547/1539 in the 19-limit (no-twos subgroup).
78EDT is related to 49 edo, but with octave compression of 5.1821 cents. Patent vals match through the 11-limit, tempering out 64/63, 100/99, 245/243, and 1331/1323. 78EDT tempers out 144/143, 196/195, 275/273, 325/324, 364/363, and 572/567 in the 13-limit; 120/119, 136/135, 154/153, 170/169, and 224/221 in the 17-limit; 96/95, 190/189, and 210/209 in the 19-limit (full integer limit).
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 24.384 | |
| 2 | 48.768 | 34/33, 35/34, 36/35, 37/36, 38/37 |
| 3 | 73.152 | 25/24 |
| 4 | 97.536 | 18/17, 37/35 |
| 5 | 121.92 | 15/14, 29/27 |
| 6 | 146.304 | 37/34 |
| 7 | 170.688 | 21/19 |
| 8 | 195.072 | 19/17, 28/25, 37/33 |
| 9 | 219.456 | 17/15, 25/22 |
| 10 | 243.84 | 38/33 |
| 11 | 268.224 | 7/6 |
| 12 | 292.608 | |
| 13 | 316.993 | 6/5 |
| 14 | 341.377 | |
| 15 | 365.761 | 21/17, 37/30 |
| 16 | 390.145 | |
| 17 | 414.529 | 14/11, 33/26 |
| 18 | 438.913 | |
| 19 | 463.297 | 17/13 |
| 20 | 487.681 | |
| 21 | 512.065 | 35/26, 39/29 |
| 22 | 536.449 | 15/11 |
| 23 | 560.833 | 18/13, 29/21 |
| 24 | 585.217 | 7/5 |
| 25 | 609.601 | 27/19, 37/26 |
| 26 | 633.985 | 13/9, 36/25 |
| 27 | 658.369 | 19/13 |
| 28 | 682.753 | |
| 29 | 707.137 | |
| 30 | 731.521 | 29/19 |
| 31 | 755.905 | 17/11 |
| 32 | 780.289 | 11/7 |
| 33 | 804.673 | 35/22 |
| 34 | 829.057 | 21/13 |
| 35 | 853.441 | 18/11 |
| 36 | 877.825 | |
| 37 | 902.209 | 37/22 |
| 38 | 926.593 | 29/17 |
| 39 | 950.978 | 26/15 |
| 40 | 975.362 | |
| 41 | 999.746 | |
| 42 | 1024.13 | 38/21 |
| 43 | 1048.514 | 11/6 |
| 44 | 1072.898 | 13/7 |
| 45 | 1097.282 | |
| 46 | 1121.666 | 21/11 |
| 47 | 1146.05 | 33/17 |
| 48 | 1170.434 | |
| 49 | 1194.818 | |
| 50 | 1219.202 | |
| 51 | 1243.586 | 39/19 |
| 52 | 1267.97 | 25/12, 27/13 |
| 53 | 1292.354 | 19/9 |
| 54 | 1316.738 | 15/7 |
| 55 | 1341.122 | 13/6 |
| 56 | 1365.506 | 11/5 |
| 57 | 1389.89 | 29/13, 38/17 |
| 58 | 1414.274 | 34/15 |
| 59 | 1438.658 | 39/17 |
| 60 | 1463.042 | |
| 61 | 1487.426 | 26/11, 33/14 |
| 62 | 1511.81 | |
| 63 | 1536.194 | 17/7 |
| 64 | 1560.578 | 37/15 |
| 65 | 1584.963 | 5/2 |
| 66 | 1609.347 | 38/15 |
| 67 | 1633.731 | 18/7 |
| 68 | 1658.115 | |
| 69 | 1682.499 | 37/14 |
| 70 | 1706.883 | |
| 71 | 1731.267 | 19/7 |
| 72 | 1755.651 | |
| 73 | 1780.035 | 14/5 |
| 74 | 1804.419 | 17/6 |
| 75 | 1828.803 | |
| 76 | 1853.187 | 35/12 |
| 77 | 1877.571 | |
| 78 | 1901.955 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.2 | +0.0 | -6.5 | -3.8 | -6.0 | -2.6 | -3.8 | -1.2 | +9.4 | -1.8 | +4.7 |
| Relative (%) | -21.3 | +0.0 | -26.8 | -15.7 | -24.7 | -10.8 | -15.4 | -5.1 | +38.4 | -7.3 | +19.2 | |
| Steps (reduced) |
49 (49) |
78 (0) |
114 (36) |
138 (60) |
170 (14) |
182 (26) |
201 (45) |
209 (53) |
223 (67) |
239 (5) |
244 (10) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -9.0 | +8.3 | -1.0 | -8.7 | +2.8 | -12.2 | +3.3 | +11.5 | +8.7 | +9.3 | -5.5 |
| Relative (%) | -37.0 | +34.1 | -4.0 | -35.5 | +11.5 | -50.0 | +13.3 | +47.2 | +35.5 | +38.3 | -22.5 | |
| Steps (reduced) |
256 (22) |
264 (30) |
267 (33) |
273 (39) |
282 (48) |
289 (55) |
292 (58) |
299 (65) |
303 (69) |
305 (71) |
310 (76) | |