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]]. | 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 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. | In terms of [[guide frame]]s, diregular scales are one type of [[generator-offset property|generator-offset]] scales where the [[interleaved scale|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. | 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. | 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. | ||
Revision as of 13:52, 9 August 2024
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 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 frames, 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.
The term diregular has been coined by akselai and Inthar.
By the 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.