Maximal evenness: Difference between revisions

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A [[periodic scale|periodic]] [[binary scale]] is '''maximally even''' ('''ME''') with respect to an [[equal-step tuning]] if it is the result of rounding a smaller [[equal tuning]] to the nearest notes of the parent equal tuning with the same equave. Equivalently, a scale is maximally even if its two [[step]] sizes are [[Distributional evenness|evenly distributed]] within its [[step pattern]] and differ by exactly one step of the parent tuning. In other words, such a scale satisfies the property of '''maximal evenness'''. The first condition implies that ME scales are [[MOS scale]]s, and the second condition implies that the scale's [[step ratio]] is [[superparticular]].

A [[periodic scale|periodic]] [[binary scale]] is '''maximally even''' ('''ME''') with respect to an [[equal-step tuning]] if it is the result of rounding a smaller equal tuning to the nearest notes of the parent equal tuning with the same equave. Equivalently, a scale is maximally even if its two [[step]] sizes are [[Distributional evenness|evenly distributed]] within its [[step pattern]] and differ by exactly one step of the parent tuning. In other words, such a scale satisfies the property of '''maximal evenness'''. The first condition implies that ME scales are [[MOS scale]]s, and the second condition implies that the scale's [[step ratio]] is [[superparticular]].

In particular, within every [[edo]], one can specify such a scale for every smaller number of notes. An ''m''-note maximally even scale in ''n''-edo is the closest ''n''-edo can get to representing ''m''-edo.

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 {{Distinguish|Distributional evenness}}
 {{Wikipedia}}
-A [[periodic scale|periodic]] [[binary scale]] is '''maximally even''' ('''ME''')  with respect to an [[equal-step tuning]] if it is the result of rounding a smaller [[equal tuning]] to the nearest notes of the parent equal tuning with the same equave. Equivalently, a scale is maximally even if its two [[step]] sizes are [[Distributional evenness|evenly distributed]] within its [[step pattern]] and differ by exactly one step of the parent tuning. In other words, such a scale satisfies the property of '''maximal evenness'''. The first condition implies that ME scales are [[MOS scale]]s, and the second condition implies that the scale's [[step ratio]] is [[superparticular]].
+A [[periodic scale|periodic]] [[binary scale]] is '''maximally even''' ('''ME''')  with respect to an [[equal-step tuning]] if it is the result of rounding a smaller equal tuning to the nearest notes of the parent equal tuning with the same equave. Equivalently, a scale is maximally even if its two [[step]] sizes are [[Distributional evenness|evenly distributed]] within its [[step pattern]] and differ by exactly one step of the parent tuning. In other words, such a scale satisfies the property of '''maximal evenness'''. The first condition implies that ME scales are [[MOS scale]]s, and the second condition implies that the scale's [[step ratio]] is [[superparticular]].
 In particular, within every [[edo]], one can specify such a scale for every smaller number of notes. An ''m''-note maximally even scale in ''n''-edo is the closest ''n''-edo can get to representing ''m''-edo.