# 1059edo

 ← 1058edo 1059edo 1060edo →
Prime factorization 3 × 353
Step size 1.13314¢
Fifth 619\1059 (701.416¢)
Semitones (A1:m2) 97:82 (109.9¢ : 92.92¢)
Dual sharp fifth 620\1059 (702.55¢)
Dual flat fifth 619\1059 (701.416¢)
Dual major 2nd 180\1059 (203.966¢) (→60\353)
Consistency limit 3
Distinct consistency limit 3

1059 equal divisions of the octave (1059edo), or 1059-tone equal temperament (1059tet), 1059 equal temperament (1059et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1059 equal parts of about 1.13 ¢ each.

1059edo is inconsistent to the 5-odd-limit and harmonic 3 is about halfway between its steps, lending itself to a 2.9.5.7.13 subgroup interpretation.

103 steps of 1059edo represent a continued fraction approximation for the secor generator interval in the form of 46/43. In the 2.3.5.7.11.23.43 subgroup this results in a 329 & 1059 temperament. The comma basis for such (assuming both patent vals) is 1376/1375, 2646/2645, 172032/171875, 16401231/16384000, 51759729/51536320.

### Odd harmonics

Approximation of odd harmonics in 1059edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) -0.539 +0.089 +0.013 +0.056 +0.523 +0.266 -0.450 +0.427 +0.504 -0.526 -0.512
relative (%) -48 +8 +1 +5 +46 +23 -40 +38 +44 -46 -45
Steps
(reduced)
1678
(619)
2459
(341)
2973
(855)
3357
(180)
3664
(487)
3919
(742)
4137
(960)
4329
(93)
4499
(263)
4651
(415)
4790
(554)

### Subsets and supersets

Since 1059 factors into 3 × 353, 1059edo contains 3edo and 353edo as subsets. 2118edo, which divides the edostep in two, provides a good correction for 3rd and 11th harmonics.