Interleaving: Difference between revisions

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[[Blackdye]], [[Zil]][14], and [[bicycle]] are examples of flought 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.

The term ''flought'' was coined by Inthar by evolving the Old English past participle ''(ġe)flohten'' of the verb ''fleohtan'' 'to weave; to plait' into a hypothetical Modern English word. It is cognate to the Modern English words ''plait'' and ''plexus''.

The term ''flought'' was coined by [[Inthar]] by evolving the Old English past participle ''(ġe)flohten'' of the verb ''fleohtan'' 'to weave; to plait' into a hypothetical Modern English word. It is cognate to the Modern English words ''plait'' and ''plexus''.

== Properties ==

# The following is a necessary and sufficient condition for floughtenability. Let ''S'' be a scale with equave ''E'', <math>\mathcal{D}_k(S)</math> be the set of all ''k''-step intervals of ''S'', and Δ be a chord such that every interval of Δ falls within (0, ''E''). Then the polyoffset chord Δ floughtens ''S'' if and only if no nonunison (positive) interval in Δ falls within <math> [\min \mathcal{D}_k(S), \max \mathcal{D}_k(S)]</math> for any ''k'' = 0, ... len(''S'') - 1.

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 [[Blackdye]], [[Zil]][14], and [[bicycle]] are examples of flought 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.
-The term ''flought'' was coined by Inthar by evolving the Old English past participle ''(ġe)flohten'' of the verb ''fleohtan'' 'to weave; to plait' into a hypothetical Modern English word. It is cognate to the Modern English words ''plait'' and ''plexus''.
+The term ''flought'' was coined by [[Inthar]] by evolving the Old English past participle ''(ġe)flohten'' of the verb ''fleohtan'' 'to weave; to plait' into a hypothetical Modern English word. It is cognate to the Modern English words ''plait'' and ''plexus''.
 == Properties ==
 # The following is a necessary and sufficient condition for floughtenability. Let ''S'' be a scale with equave ''E'', <math>\mathcal{D}_k(S)</math> be the set of all ''k''-step intervals of ''S'', and Δ be a chord such that every interval of Δ falls within (0, ''E''). Then the polyoffset chord Δ floughtens ''S'' if and only if no nonunison (positive) interval in Δ falls within <math> [\min \mathcal{D}_k(S), \max \mathcal{D}_k(S)]</math> for any ''k'' = 0, ... len(''S'') - 1.