641edo: Difference between revisions
The assesssment of subgroups was too hasty and arbitrary. For edos like this an analysis on the tuning profile is required. |
m →Theory: -typo |
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641edo is only [[consistent]] to the [[5-odd-limit]]. Since both [[harmonic]]s [[7/1|7]] and [[11/1|11]] are about halfway between its steps, and since harmonic [[5/1|5]] is also off by more than a third step, it can be used as a dual-5 dual-7 dual-11 temperament. Alternatively, it can be used as a 2.3.5.13.17.19 [[subgroup]] temperament, as it is consistent in the no-7 no-11 19-odd-limit. | 641edo is only [[consistent]] to the [[5-odd-limit]]. Since both [[harmonic]]s [[7/1|7]] and [[11/1|11]] are about halfway between its steps, and since harmonic [[5/1|5]] is also off by more than a third step, it can be used as a dual-5 dual-7 dual-11 temperament. Alternatively, it can be used as a 2.3.5.13.17.19 [[subgroup]] temperament, as it is consistent in the no-7 no-11 19-odd-limit. | ||
To start with, consider the 641d val {{val| 641 1016 1488 '''1799''' 2217 2372 }} in the 13-limit, which [[tempering out|tempers out]] [[625/624]], [[2200/2197]], [[4459/4455]], 14641/14625, and [[19712/19683]]. The alternative 641df val, {{val| 641 1016 1488 '''1799''' 2217 '''2371''' }}, tempers out [[676/675]], [[1001/1000]], 19712/19683, [[31213/31104]], and 983125/979776. The 641ce val, {{val| 641 1016 ''' | To start with, consider the 641d val {{val| 641 1016 1488 '''1799''' 2217 2372 }} in the 13-limit, which [[tempering out|tempers out]] [[625/624]], [[2200/2197]], [[4459/4455]], 14641/14625, and [[19712/19683]]. The alternative 641df val, {{val| 641 1016 1488 '''1799''' 2217 '''2371''' }}, tempers out [[676/675]], [[1001/1000]], 19712/19683, [[31213/31104]], and 983125/979776. The 641ce val, {{val| 641 1016 '''1489''' 1800 '''2218''' 2372 }}, tempers out 676/675, 1001/1000, [[6144/6125]], [[10985/10976]], and 85294/85184. | ||
=== Odd harmonics === | === Odd harmonics === | ||