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Minimal consistent EDOs: Difference between revisions

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mirrored main consistency definition (my previous attempt wrong)
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An [[EDO]] N is [[consistent]] with respect to a set of rational numbers s if the [[direct approximation]] of every element of s is the closest N-EDO approximation. It is [[distinctly consistent]] if every element of s is mapped to a distinct value. If the set s is the q [[odd limit]], we say N is q-limit consistent and q-limit distinctly consistent, respectively. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135.
An [[EDO]] N is [[consistent]] with respect to the q-odd-limit if the closest approximations of the odd harmonics of the q-odd-limit in that edo also give the closest approximations of all the differences between these odd harmonics. It is [[distinctly consistent]] if every one of those closest approximations is a distinct value. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135.


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