1778edo
Jump to navigation
Jump to search
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
| ← 1777edo | 1778edo | 1779edo → |
1778 equal divisions of the octave (1778edo), or 1778-tone equal temperament (1778tet), 1778 equal temperament (1778et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1778 equal parts of about 0.675 ¢ each.
Theory
| 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 | -39 | -48 | -13 | +13 | -38 | -45 | +49 | +18 | +46 | +11 | |
| Steps (reduced) |
2818 (1040) |
4128 (572) |
4991 (1435) |
5636 (302) |
6151 (817) |
6579 (1245) |
6946 (1612) |
7268 (156) |
7553 (441) |
7810 (698) |
8043 (931) | |
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.