1880edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 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.

Theory

1880edo 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 3/2s 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.

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)