Interleaving: Difference between revisions

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== Generalizations ==

=== Co-interleavability (?) ===

Periodic scales <math>S, T : \mathbb{Z} \to \mathbb{R}</math> of the same length and equave are ''co-interleavable'' (the ''co-'' is not meant to suggest any kind of duality) if there exists <math>\delta\in\mathbb{R}</math> such that ''S'' and ''T'' + δ are interleaved. Note that though a given 2''n''-note scale being a co-~~interleaveed~~ result of some pair of scales may be trivial, a given pair of scales being co-interleavable is less so: for example, '''MMMM''' and '''Lsss''' are not co-interleavable when '''s''' is too small.

Periodic scales <math>S, T : \mathbb{Z} \to \mathbb{R}</math> of the same length and equave are ''co-interleavable'' (the ''co-'' is not meant to suggest any kind of duality) if there exists <math>\delta\in\mathbb{R}</math> such that ''S'' and ''T'' + δ are interleaved. Note that though a given 2''n''-note scale being a co-interleaved result of some pair of scales may be trivial, a given pair of scales being co-interleavable is less so: for example, '''MMMM''' and '''Lsss''' are not co-interleavable when '''s''' is too small.

A ''contrainterleaved'' scale is a co-~~interleaveed~~ pair of the two chiralities of a [[chiral scale]].

A ''contrainterleaved'' scale is a co-interleaved pair of the two chiralities of a [[chiral scale]].

[[Category:Scale]]

[[Category:Terms]]

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 == Generalizations ==
 === Co-interleavability (?) ===
-Periodic scales <math>S, T : \mathbb{Z} \to \mathbb{R}</math> of the same length and equave are ''co-interleavable'' (the ''co-'' is not meant to suggest any kind of duality) if there exists <math>\delta\in\mathbb{R}</math> such that ''S'' and ''T'' + δ are interleaved. Note that though a given 2''n''-note scale being a co-interleaveed result of some pair of scales may be trivial, a given pair of scales being co-interleavable is less so: for example, '''MMMM''' and '''Lsss''' are not co-interleavable when '''s''' is too small.
+Periodic scales <math>S, T : \mathbb{Z} \to \mathbb{R}</math> of the same length and equave are ''co-interleavable'' (the ''co-'' is not meant to suggest any kind of duality) if there exists <math>\delta\in\mathbb{R}</math> such that ''S'' and ''T'' + δ are interleaved. Note that though a given 2''n''-note scale being a co-interleaved result of some pair of scales may be trivial, a given pair of scales being co-interleavable is less so: for example, '''MMMM''' and '''Lsss''' are not co-interleavable when '''s''' is too small.
-A ''contrainterleaved'' scale is a co-interleaveed pair of the two chiralities of a [[chiral scale]].
+A ''contrainterleaved'' scale is a co-interleaved pair of the two chiralities of a [[chiral scale]].
 [[Category:Scale]]
 [[Category:Terms]]