Even-regular MV3 scale: Difference between revisions

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A '''diregular scale''' is a type of scale with even notes. A diregular scale consists of two identical generator chains, where all generators are identical and subtend the same [[interval class|step class]]. The two chains are offset by an interval that subtends k steps in a 2k-note diregular scale. One example is the achiral variant of [[diachrome]].

In terms of [[guide frame]]s, diregular scales are one type of generator-offset scales where the interleaving offset is generated by GS(g), and the 2-note strand scale [0, len(scale)/2-step] is the "offset". The other type of generator-offset scale is represented by scales including bipentatonic scales (such as [[blackdye]]), where the strand is generated by GS(g) and the interleaving offset is the offset.

In terms of [[guide frame]]s, diregular scales are one type of [[generator-offset property|generator-offset]] scales where the interleaving offset is generated by GS(g), and the 2-note strand scale [0, len(scale)/2-step] is the "offset". The other type of generator-offset scale is represented by scales including bipentatonic scales (such as [[blackdye]]), where the strand is generated by GS(g) and the interleaving offset is the offset.

The term ''diregular'' has been coined by akselai and Inthar.

By the [[ternary scale theorems|MV3 classification theorem]], a balanced MV3 scale that has an even number of notes is always diregular and has step signature aXaYbZ where b is even.

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 A '''diregular scale''' is a type of scale with even notes. A diregular scale consists of two identical generator chains, where all generators are identical and subtend the same [[interval class|step class]]. The two chains are offset by an interval that subtends k steps in a 2k-note diregular scale. One example is the achiral variant of [[diachrome]].
-In terms of [[guide frame]]s, diregular scales are one type of generator-offset scales where the interleaving offset is generated by GS(g), and the 2-note strand scale [0, len(scale)/2-step] is the "offset". The other type of generator-offset scale is represented by scales including bipentatonic scales (such as [[blackdye]]), where the strand is generated by GS(g) and the interleaving offset is the offset.
+In terms of [[guide frame]]s, diregular scales are one type of [[generator-offset property|generator-offset]] scales where the interleaving offset is generated by GS(g), and the 2-note strand scale [0, len(scale)/2-step] is the "offset". The other type of generator-offset scale is represented by scales including bipentatonic scales (such as [[blackdye]]), where the strand is generated by GS(g) and the interleaving offset is the offset.
 The term ''diregular'' has been coined by akselai and Inthar.
 By the [[ternary scale theorems|MV3 classification theorem]], a balanced MV3 scale that has an even number of notes is always diregular and has step signature aXaYbZ where b is even.