Even-regular MV3 scale: Difference between revisions

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A '''diregular scale''' is a type of [[ternary scale]] with an even number of 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 2''k''-note diregular scale. Another characterization of diregular scales is that it is a ternary one-to-one detempering of a 2-period MOS word M(X, z) which has the form w(x, y, z)w(y, x, z) for some ternary word w and some permutation x, y, z of L, m, s where x and y always alternate in the scale. One diregular scale is the achiral variant of [[diachrome]].

A '''diregular scale''' is a type of [[ternary scale]] with an even number of 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 2''k''-note diregular scale.

== Notable diregular scales ==

* Achiral [[diachrome]] (dia5s)

* [[Penslen]] (slen5m)

* [[Mosh3s]]

== Properties ==

Another characterization of diregular scales is that it is a ternary one-to-one detempering of a 2-period MOS word M(X, z) which has the form w(x, y, z)w(y, x, z) for some ternary word w and some permutation x, y, z of L, m, s where x and y always alternate in the scale. One diregular scale is the achiral variant of [[diachrome]].

In terms of [[guide frame]]s and interleaved scales, in diregular scales the [[interleaved scale|interleaving offset]] is generated by the guided generator sequence GS(g), and the 2-note strand scale [0, len(scale)/2-step] is the offset for the guide frame. 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.

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== Terminology ==

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

~~== Notable diregular scales ==~~

* Achiral [[diachrome]] (dia5s)

* [[Penslen]] (slen5m)

* [[Mosh3s]]

[[Category:Aberrismic theory]]

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-A '''diregular scale''' is a type of [[ternary scale]] with an even number of 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 2''k''-note diregular scale. Another characterization of diregular scales is that it is a ternary one-to-one detempering of a 2-period MOS word M(X, z) which has the form w(x, y, z)w(y, x, z) for some ternary word w and some permutation x, y, z of L, m, s where x and y always alternate in the scale. One diregular scale is the achiral variant of [[diachrome]].
+A '''diregular scale''' is a type of [[ternary scale]] with an even number of 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 2''k''-note diregular scale.
+== Notable diregular scales ==
+* Achiral [[diachrome]] (dia5s)
+* [[Penslen]] (slen5m)
+* [[Mosh3s]]
+== Properties ==
+Another characterization of diregular scales is that it is a ternary one-to-one detempering of a 2-period MOS word M(X, z) which has the form w(x, y, z)w(y, x, z) for some ternary word w and some permutation x, y, z of L, m, s where x and y always alternate in the scale. One diregular scale is the achiral variant of [[diachrome]].
 In terms of [[guide frame]]s and interleaved scales, in diregular scales the [[interleaved scale|interleaving offset]] is generated by the guided generator sequence GS(g), and the 2-note strand scale [0, len(scale)/2-step] is the offset for the guide frame. 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.
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 == Terminology  ==
 The term ''diregular'' has been coined by akselai and Inthar.
-== Notable diregular scales ==
-* Achiral [[diachrome]] (dia5s)
-* [[Penslen]] (slen5m)
-* [[Mosh3s]]
 [[Category:Aberrismic theory]]