1880edo

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← 1879edo1880edo1881edo →
Prime factorization 23 × 5 × 47
Step size 0.638298¢
Fifth 1100\1880 (702.128¢) (→55\94)
Semitones (A1:m2) 180:140 (114.9¢ : 89.36¢)
Consistency limit 7
Distinct consistency limit 7

1880 equal divisions of the octave (1880edo), or 1880-tone equal temperament (1880tet), 1880 equal temperament (1880et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1880 equal parts of about 0.638 ¢ each.

1880 = 20 × 94, and 1880edo shares its harmonic 3 with 94edo. It is consistent in the 7-odd-limit, and is overall a decent 13-limit system, although its 9/8 is off the stack of two 3/2's by one step, which prevents consistency in the 9-odd-limit.

In the 13-limit, it tempers out 6656/6655 and supports the 2.5.7.11.13 subgroup eternal revolutionary temperament.

Odd harmonics

Approximation of odd harmonics in 1880edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +0.173 -0.144 +0.110 -0.293 +0.171 +0.111 +0.029 -0.275 -0.066 +0.283 -0.189
relative (%) +27 -22 +17 -46 +27 +17 +5 -43 -10 +44 -30
Steps
(reduced)
2980
(1100)
4365
(605)
5278
(1518)
5959
(319)
6504
(864)
6957
(1317)
7345
(1705)
7684
(164)
7986
(466)
8258
(738)
8504
(984)

Subsets and supersets

Since 1880 factors into 23 × 5 × 47, 1880edo has subset edos 2, 4, 5, 8, 10, 20, 40, 47, 94, 188, 235, 376, 470, and 940.