669edo: Difference between revisions

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~~{{novelty}}{{stub}}~~{{Infobox ET}}

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 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 ~~much more useful as a~~ higher~~-limit system~~, 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}.

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.

~~Overall, the subgroup which provides satisfactory results for 669edo is 2.7.19.29.37.41.43.47.53.~~

=== Odd harmonics ===

===~~Harmonics~~===

=== Subsets and supersets ===

Since 669 factors into {{factorization|669}}, 669edo contains [[3edo]] and [[223edo]] as subsets.

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-{{novelty}}{{stub}}{{Infobox ET}}
+{{Infobox ET}}
-{{EDO intro|669}}
+{{ED intro}}
-edo 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.
+edo 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.
-edo appears much more useful as a higher-limit system, 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}.
+edo 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.
-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}}
+{{Harmonics in equal|669|start=12|collapsed=1}}
+{{Harmonics in equal|669|start=23|collapsed=1}}
-===Harmonics===
+=== Subsets and supersets ===
-{{harmonics in equal|669}}
+Since 669 factors into {{factorization|669}}, 669edo contains [[3edo]] and [[223edo]] as subsets.