Distributional evenness: Difference between revisions

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A scale with two step sizes is '''distributionally even''' ('''DE''') if it has its two step sizes distributed as evenly as possible. This turns out to be equivalent to the property of having [[maximum variety]] 2; that is, each [[interval class]] ("seconds", "thirds", and so on) contains no more than two sizes.

A scale with two step sizes is '''distributionally even''' ('''DE''') if it has its two step sizes distributed as evenly as possible (i.e. each step size is distributed in a [[maximal evenness|maximally even]] pattern among the steps of the scale). This turns out to be equivalent to the property of having [[maximum variety]] 2; that is, each [[interval class]] ("seconds", "thirds", and so on) contains no more than two sizes.

In practice, such scales are often referred to as "[[MOS scale]]s", but some consider this usage to be technically incorrect because a MOS as defined by [[Erv Wilson]] was to have ''exactly'' two specific intervals for each class other than multiples of the octave. When Wilson discovered MOS scales and found numerous examples, DE scales with period a fraction of an octave such as [[pajara]], [[augmented]], [[diminished]], etc. were not among them.

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 {{Distinguish|Maximal evenness}}
-A scale with two step sizes is '''distributionally even''' ('''DE''') if it has its two step sizes distributed as evenly as possible. This turns out to be equivalent to the property of having [[maximum variety]] 2; that is, each [[interval class]] ("seconds", "thirds", and so on) contains no more than two sizes.
+A scale with two step sizes is '''distributionally even''' ('''DE''') if it has its two step sizes distributed as evenly as possible (i.e. each step size is distributed in a [[maximal evenness|maximally even]] pattern among the steps of the scale). This turns out to be equivalent to the property of having [[maximum variety]] 2; that is, each [[interval class]] ("seconds", "thirds", and so on) contains no more than two sizes.
 In practice, such scales are often referred to as "[[MOS scale]]s", but some consider this usage to be technically incorrect because a MOS as defined by [[Erv Wilson]] was to have ''exactly'' two specific intervals for each class other than multiples of the octave. When Wilson discovered MOS scales and found numerous examples, DE scales with period a fraction of an octave such as [[pajara]], [[augmented]], [[diminished]], etc. were not among them.