Interleaving: Difference between revisions

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A scale is a (''k''-)'''interleaving''' or a (''k''-)'''floughtening''' (''flought'' is pronounced /flɔːt/, rhymes with ''bought''; this is a neo-Anglish term cognate with German ''geflochten'' 'braided') if it is made of ''k'' > 1 copies (called ''strands'') of an ''n''-note [[periodic scale]] ''s'', and ''any two copies'' of ''s'' are interleaved so that any note of the first copy falls strictly between two notes of the other copy. We also say that the scale is (''k''-)''interleaved'' ''s''. The set of offsets that separate the strands from a fixed strand is a chord called the ''polyoffset'', which is determined up to inversion and [[equave]]-equivalence for a given interleaved scale. An interleaved scale is thus a [[cross-set]] with a little additional structure. One can '''interleave''' or '''floughten''' a scale ''s'' by a certain polyoffset Δ (or: "Δ ''interleaves'' ''s''" or "''s'' is ''interleavable'' by Δ") if ''s'' is the strand scale of an interleaved scale with polyoffset Δ. Such a scale is denoted {{nowrap|Interleave(''s''; Δ)}}. The concept of interleaved scales is a generalization of [[bipentatonic scale]]s.

A scale is a(n) (''k''-)'''interleaving''' or a (''k''-)'''floughtening''' (''flought'' is pronounced /flɔːt/, rhymes with ''bought''; this is a neo-Anglish term cognate with German ''geflochten'' 'braided') if it is made of ''k'' > 1 copies (called ''strands'') of an ''n''-note [[periodic scale]] ''s'', and ''any two copies'' of ''s'' are interleaved so that any note of the first copy falls strictly between two notes of the other copy. We also say that the scale is (''k''-)''interleaved'' ''s''. The set of offsets that separate the strands from a fixed strand is a chord called the ''polyoffset'', which is determined up to inversion and [[equave]]-equivalence for a given interleaved scale. An interleaved scale is thus a [[cross-set]] with a little additional structure. One can '''interleave''' or '''floughten''' a scale ''s'' by a certain polyoffset Δ (or: "Δ ''interleaves'' ''s''" or "''s'' is ''interleavable'' by Δ") if ''s'' is the strand scale of an interleaved scale with polyoffset Δ. Such a scale is denoted {{nowrap|Interleave(''s''; Δ)}}. The concept of interleaved scales is a generalization of [[bipentatonic scale]]s.

[[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.

Revision as of 17:28, 10 January 2025 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,636 edits m Inthar moved page Interleaved scale to Interleaving over redirect ← Older edit		Revision as of 17:28, 10 January 2025 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,636 edits No edit summary Newer edit →
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	A scale is a (''k''-)'''interleaving''' or a (''k''-)'''floughtening''' (''flought'' is pronounced /flɔːt/, rhymes with ''bought''; this is a neo-Anglish term cognate with German ''geflochten'' 'braided') if it is made of ''k'' > 1 copies (called ''strands'') of an ''n''-note [[periodic scale]] ''s'', and ''any two copies'' of ''s'' are interleaved so that any note of the first copy falls strictly between two notes of the other copy. We also say that the scale is (''k''-)''interleaved'' ''s''. The set of offsets that separate the strands from a fixed strand is a chord called the ''polyoffset'', which is determined up to inversion and [[equave]]-equivalence for a given interleaved scale. An interleaved scale is thus a [[cross-set]] with a little additional structure. One can '''interleave''' or '''floughten''' a scale ''s'' by a certain polyoffset Δ (or: "Δ ''interleaves'' ''s''" or "''s'' is ''interleavable'' by Δ") if ''s'' is the strand scale of an interleaved scale with polyoffset Δ. Such a scale is denoted {{nowrap\|Interleave(''s''; Δ)}}. The concept of interleaved scales is a generalization of [[bipentatonic scale]]s.		A scale is a(n) (''k''-)'''interleaving''' or a (''k''-)'''floughtening''' (''flought'' is pronounced /flɔːt/, rhymes with ''bought''; this is a neo-Anglish term cognate with German ''geflochten'' 'braided') if it is made of ''k'' > 1 copies (called ''strands'') of an ''n''-note [[periodic scale]] ''s'', and ''any two copies'' of ''s'' are interleaved so that any note of the first copy falls strictly between two notes of the other copy. We also say that the scale is (''k''-)''interleaved'' ''s''. The set of offsets that separate the strands from a fixed strand is a chord called the ''polyoffset'', which is determined up to inversion and [[equave]]-equivalence for a given interleaved scale. An interleaved scale is thus a [[cross-set]] with a little additional structure. One can '''interleave''' or '''floughten''' a scale ''s'' by a certain polyoffset Δ (or: "Δ ''interleaves'' ''s''" or "''s'' is ''interleavable'' by Δ") if ''s'' is the strand scale of an interleaved scale with polyoffset Δ. Such a scale is denoted {{nowrap\|Interleave(''s''; Δ)}}. The concept of interleaved scales is a generalization of [[bipentatonic scale]]s.

	[[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.