1059edo
| ← 1058edo | 1059edo | 1060edo → |
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
| 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.