# 1778edo

 ← 1777edo 1778edo 1779edo →
Prime factorization 2 × 7 × 127
Step size 0.674916¢
Fifth 1040\1778 (701.912¢) (→520\889)
Semitones (A1:m2) 168:134 (113.4¢ : 90.44¢)
Consistency limit 9
Distinct consistency limit 9

1778 equal divisions of the octave (abbreviated 1778edo or 1778ed2), also called 1778-tone equal temperament (1778tet) or 1778 equal temperament (1778et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1778 equal parts of about 0.675 ¢ each. Each step represents a frequency ratio of 21/1778, or the 1778th root of 2.

1778edo is consistent to the 9-odd-limit, but the errors of both harmonics 5 and 7 are quite large. It is enfactored in the 5-limit, with the same tuning as 889edo, tempering out [-29 -11 20 (gammic comma) and [-69 45 -1 (counterschisma). In the 7-limit, the equal temperament tempers out 2401/2400 (breedsma) and 48828125/48771072 (neptunisma). It provides the optimal patent val for the 7-limit neptune temperament.

For higher harmonics, it is suitable for a 2.3.11.19.23.43.47.61 subgroup interpretation.

### Odd harmonics

Approximation of odd harmonics in 1778edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.043 -0.262 -0.322 -0.085 +0.088 -0.258 -0.305 +0.331 +0.125 +0.310 +0.072
Relative (%) -6.3 -38.8 -47.7 -12.7 +13.1 -38.2 -45.1 +49.1 +18.5 +46.0 +10.7
Steps
(reduced)
2818
(1040)
4128
(572)
4991
(1435)
5636
(302)
6151
(817)
6579
(1245)
6946
(1612)
7268
(156)
7553
(441)
7810
(698)
8043
(931)

### Subsets and supersets

Since 1778 factors into 2 × 7 × 127, 1778edo has subset edos 2, 7, 14, 127, 254, and 889.