Maximal evenness: Difference between revisions

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where the [[Wikipedia:Floor and ceiling functions|ceiling]] function fixes integers and rounds up non-integers to the next higher integer. It can be proven that ME(''n'', ''m'') is a [[MOS scale]] where the two step sizes differ by exactly 1\''m''⟨''E''⟩ when interpreted as a subset of ''m''-ed''E'', and that the indices for the two step sizes are themselves ME when considered as subsets of ''n''-ed''E'', satisfying the informal definition above. ME(''n'', ''m'') is the lexicographically brightest mode among its rotations.

It is easy to show that using round() (rounding half-integers up) gives an equivalent definition; floor() does too, since ME(''n'', ''m'') is a MOS and thus a[[~~chiral~~]].

It is easy to show that using round() (rounding half-integers up) gives an equivalent definition; floor() does too, since ME(''n'', ''m'') is a MOS and thus [[chirality|achiral]].

== Concoctic scales ==

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 where the [[Wikipedia:Floor and ceiling functions|ceiling]] function fixes integers and rounds up non-integers to the next higher integer. It can be proven that ME(''n'', ''m'') is a [[MOS scale]] where the two step sizes differ by exactly 1\''m''⟨''E''⟩ when interpreted as a subset of ''m''-ed''E'', and that the indices for the two step sizes are themselves ME when considered as subsets of ''n''-ed''E'', satisfying the informal definition above. ME(''n'', ''m'') is the lexicographically brightest mode among its rotations.
-It is easy to show that using round() (rounding half-integers up) gives an equivalent definition; floor() does too, since ME(''n'', ''m'') is a MOS and thus a[[chiral]].
+It is easy to show that using round() (rounding half-integers up) gives an equivalent definition; floor() does too, since ME(''n'', ''m'') is a MOS and thus [[chirality|achiral]].
 == Concoctic scales ==