Interleaving: Difference between revisions
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[[Blackdye]], [[Zil]][14], and [[bicycle]] are examples of interleaved scales, because they each have two interleaved strands, respectively Pyth[5], Zarlino, and 8:9:10:11:13:14. The terminology, however, is intended to cover any number of strands and any choice of strand scale. | [[Blackdye]], [[Zil]][14], and [[bicycle]] are examples of interleaved scales, because they each have two interleaved strands, respectively Pyth[5], Zarlino, and 8:9:10:11:13:14. The terminology, however, is intended to cover any number of strands and any choice of strand scale. | ||
Given a ternary [[step signature]] of the form {{nowrap|''a'''''X'''''b'''''Y'''(''a'' + ''b'')'''Z'''}}, there exists a unique interleaved ternary scale with that step signature, made of an interleaved pair of two {{nowrap|''a''('''X''' + '''Z''')''b''('''Y''' + '''Z''')}} | Given a ternary [[step signature]] of the form {{nowrap|''a'''''X'''''b'''''Y'''(''a'' + ''b'')'''Z'''}}, there exists a unique interleaved ternary scale with that step signature, made of an interleaved pair of two {{nowrap|''a''('''X''' + '''Z''')''b''('''Y''' + '''Z''')}} subsets. | ||
== Some interleaved scales == | == Some interleaved scales == | ||
Interleaved scales can easily be built from a harmonic series mode as the strand: for example, if ''n''::2''n'' is the strand, then (2''n'' + 1)/''2n'' always works as the offset (e.g. strand 5:6:7:8:9:10, offset 10:11). Here are some other examples: | Interleaved scales can easily be built from a harmonic series mode as the strand: for example, if ''n''::2''n'' is the strand, then (2''n'' + 1)/''2n'' always works as the offset (e.g. strand 5:6:7:8:9:10, offset 10:11). Here are some other examples: | ||