1778edo

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1778edo
Prime factorization 2 × 7 × 127
Step size 0.6749¢
Fifth 1040\1778 (520\889)
Consistency limit 7

The 1778 equal divisions of the octave (1778edo), or the 1778-tone equal temperament (1778tet), 1778 equal temperament (1778et) when viewed from a regular temperament perspective, divides the octave into 1778 equal parts of about 0.675 cents each.

Theory

Approximation of odd harmonics in 1778edo
Harmonic 3 5 7 9 11 13 15 17 19 21
Error absolute (¢) -0.043 -0.262 -0.322 -0.085 +0.088 -0.258 -0.305 +0.331 +0.125 +0.310
relative (%) -6 -39 -48 -13 +13 -38 -45 +49 +18 +46
Steps
(reduced)
2818
(1040)
4128
(572)
4991
(1435)
5636
(302)
6151
(817)
6579
(1245)
6946
(1612)
7268
(156)
7553
(441)
7810
(698)

Prime harmonics with less than 1 standard deviation in 1778edo are: 2, 3, 11, 23, 43, 47, 61. As such, it is best for use with the 2.3.11.23.43.47.61 subgroup.

In the 7-limit, in which it is consistent, it provides the optimal patent val for the neptune temperament.