1059edo

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← 1058edo1059edo1060edo →
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 (abbreviated 1059edo or 1059ed2), also called 1059-tone equal temperament (1059tet) or 1059 equal temperament (1059et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1059 equal parts of about 1.13 ¢ each. Each step represents a frequency ratio of 21/1059, or the 1059th root of 2.

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 (%) -47.5 +7.8 +1.1 +4.9 +46.2 +23.4 -39.7 +37.7 +44.5 -46.4 -45.2
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.