1778edo

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← 1777edo1778edo1779edo →
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.