Ed4: Difference between revisions

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	Equal Divisions of the Double Octave -- frequency ratio 4/1, aka "Quadruple" -- are closely related to Equal Divisions of the Octave -- frequency ratio 2/1, aka "Duple" -- in other words, ED2 or [[EDO]] scales. Given any odd-numbered ED2, an ED4 can be generated by taking every other tone of the ED2. Such a tuning ~~will show~~ the pathological trait of inconsistency in any non-trivial integer limit. For example, given 5ED2 (aka [[5edo]]), two octaves of which, in cents are:		Equal Divisions of the Double Octave -- frequency ratio 4/1, aka "Quadruple" -- are closely related to Equal Divisions of the Octave -- frequency ratio 2/1, aka "Duple" -- in other words, ED2 or [[EDO]] scales. Given any odd-numbered ED2, an ED4 can be generated by taking every other tone of the ED2. Such a tuning shows the pathological trait of inconsistency in any non-trivial integer limit. For example, given 5ED2 (aka [[5edo]]), two octaves of which, in cents are:

	0 240 480 720 960 1200 1440 1680 1920 2160 2400...		0 240 480 720 960 1200 1440 1680 1920 2160 2400...