1059edo

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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.

Theory

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

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.