Balanced word: Difference between revisions
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{{distinguish|perfect balance}} | {{distinguish|perfect balance}}{{Todo|rework|inline=1|text=this can probably be explained without invoking "words"}} | ||
An abstract scale pattern is '''balanced''' if it satisfies a certain (quite strong) restriction on how much the intervals within any of the scale's interval classes can differ; by one characterization of the property, it stipulates that for any step size, no two ''k''-steps can differ too much in how many times the step size occurs in them. The simplest non-trivial examples of balanced scales are [[MOS scales]], and balanced words are one of many possible generalizations of [[MOS scale]]s to scales with three or more step sizes. | An abstract scale pattern is '''balanced''' if it satisfies a certain (quite strong) restriction on how much the intervals within any of the scale's interval classes can differ; by one characterization of the property, it stipulates that for any step size, no two ''k''-steps can differ too much in how many times the step size occurs in them. The simplest non-trivial examples of balanced scales are [[MOS scales]], and balanced words are one of many possible generalizations of [[MOS scale]]s to scales with three or more step sizes. | ||
== Mathematical definition == | == Mathematical definition == | ||