Interleaving: Difference between revisions

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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 ''offset chord'', 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 offset chord Δ (or: "Δ ''interleaves'' ''s''" or "''s'' is ''interleavable'' by Δ") if ''s'' is the strand scale of an interleaved scale with offset chord 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''' 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 ''offset chord'', 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 offset chord Δ (or: "Δ ''interleaves'' ''s''" or "''s'' is ''interleavable'' by Δ") if ''s'' is the strand scale of an interleaved scale with offset chord 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 00:49, 1 January 2026 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,677 edits →Mutual interleavability ← Older edit		Revision as of 00:50, 1 January 2026 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,677 edits No edit summary Tag: Visual edit Newer edit →
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	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 ''offset chord'', 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 offset chord Δ (or: "Δ ''interleaves'' ''s''" or "''s'' is ''interleavable'' by Δ") if ''s'' is the strand scale of an interleaved scale with offset chord 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''' 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 ''offset chord'', 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 offset chord Δ (or: "Δ ''interleaves'' ''s''" or "''s'' is ''interleavable'' by Δ") if ''s'' is the strand scale of an interleaved scale with offset chord 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.