1776edo

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← 1775edo1776edo1777edo →
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.