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 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 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. | 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 the ambient edo can get to representing the smaller edo. | ||
== Formal definition == | == Formal definition == | ||