# 1776edo

 ← 1775edo 1776edo 1777edo →
Prime factorization 24 × 3 × 37
Step size 0.675676¢
Fifth 1039\1776 (702.027¢)
Semitones (A1:m2) 169:133 (114.2¢ : 89.86¢)
Consistency limit 15
Distinct consistency limit 15

1776 equal divisions of the octave (abbreviated 1776edo or 1776ed2), also called 1776-tone equal temperament (1776tet) or 1776 equal temperament (1776et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1776 equal parts of about 0.676 ¢ each. Each step represents a frequency ratio of 21/1776, or the 1776th root of 2.

1776edo is consistent in the 15-odd-limit, and has good representation of it, with errors less than 26%. In the 2.5.7.11.13 subgroup, it is enfactored with the same mapping as 888edo, and corrects the latter's mapping for harmonic 3. A comma basis for the 13-limit is {4096/4095, 9801/9800, 67392/67375, 250047/250000, 531674/531441}.

In the 5-limit, it supports the squarschmidt temperament, tempering out the [61 4 -29 comma, and it also tempers out [55 -64 -20, [6, 68, -49, [116, -60, -9.

### Prime harmonics

Approximation of prime harmonics in 1776edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.072 +0.173 +0.093 +0.033 +0.013 -0.226 -0.216 +0.104 +0.153 +0.235
Relative (%) +0.0 +10.7 +25.6 +13.8 +4.9 +1.9 -33.4 -31.9 +15.4 +22.6 +34.7
Steps
(reduced)
1776
(0)
2815
(1039)
4124
(572)
4986
(1434)
6144
(816)
6572
(1244)
7259
(155)
7544
(440)
8034
(930)
8628
(1524)
8799
(1695)

### Subsets and supersets

Since 1776 factors as 24 × 3 × 37, it has subset edos 1, 2, 3, 4, 6, 8, 12, 16, 24, 37, 48, 74, 111, 148, 222, 296, 444, 592, 888.