669edo: Difference between revisions
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{{EDO intro|669}} | {{EDO intro|669}} | ||
669edo is consistent in the 7-odd-limit, although it has significant errors on the 3rd and the 5th | 669edo is [[consistent]] in the [[7-odd-limit]], although it has significant errors on the [[3/1|3rd]] and the [[5/1|5th]] [[harmonic]]s. Besides that, 669c [[val]] is a tuning for the [[sensipent]] temperament in the 5-limit. | ||
669edo appears | 669edo appears better at approximating higher harmonics, with harmonics 37 through 53 all having an error of 20% or less, with a [[comma basis]] for the 2.37.41.43.47.53 [[subgroup]] being {75809/75776, 1874161/1873232, 151124317/151101728, 9033613312/9032089499, 9795995841727/9788230467584}. Overall, the subgroup which provides satisfactory results for 669edo is 2.7.19.29.37.41.43.47.53. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|669}} | |||
=== | |||
{{ | |||
Revision as of 08:31, 22 October 2023
| ← 668edo | 669edo | 670edo → |
669edo is consistent in the 7-odd-limit, although it has significant errors on the 3rd and the 5th harmonics. Besides that, 669c val is a tuning for the sensipent temperament in the 5-limit.
669edo appears better at approximating higher harmonics, with harmonics 37 through 53 all having an error of 20% or less, with a comma basis for the 2.37.41.43.47.53 subgroup being {75809/75776, 1874161/1873232, 151124317/151101728, 9033613312/9032089499, 9795995841727/9788230467584}. Overall, the subgroup which provides satisfactory results for 669edo is 2.7.19.29.37.41.43.47.53.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.610 | -0.663 | -0.216 | +0.574 | -0.645 | +0.728 | +0.521 | +0.874 | +0.245 | -0.826 | -0.472 |
| Relative (%) | -34.0 | -37.0 | -12.0 | +32.0 | -36.0 | +40.6 | +29.0 | +48.7 | +13.6 | -46.0 | -26.3 | |
| Steps (reduced) |
1060 (391) |
1553 (215) |
1878 (540) |
2121 (114) |
2314 (307) |
2476 (469) |
2614 (607) |
2735 (59) |
2842 (166) |
2938 (262) |
3026 (350) | |