1059edo: Difference between revisions
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{{EDO intro|1059}} | {{EDO intro|1059}} | ||
1059edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps, lending itself to a 2.9.5.7 [[subgroup]] interpretation. | 1059edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|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. | 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. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
[[2118edo]], which divides the edostep in two, provides a good correction for 3rd and 11th harmonics. | Since 1059 factors into {{factorization|1059}}, 1059edo contains [[3edo]] and [[353edo]] as subsets. [[2118edo]], which divides the edostep in two, provides a good correction for 3rd and 11th harmonics. | ||
Revision as of 10:53, 31 October 2023
| ← 1058edo | 1059edo | 1060edo → |
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 (%) | -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.