78edt

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← 77edt 78edt 79edt →
Prime factorization 2 × 3 × 13
Step size 24.384 ¢ 
Octave 49\78edt (1194.82 ¢)
Consistency limit 7
Distinct consistency limit 7

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

Approximation of prime harmonics in 78edt
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)