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).
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) | |