Interleaving: Difference between revisions

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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''.
== Terminology ==
== Terminology ==
Given an E-equivalent scale, scale s, offsets between 0 and min({step sizes in s}) (equivalently, between max{len(s)-1-steps in s} and E) are called ''small''. Small offsets are significant because it copies the underlying scale structure: if s = w(a1, a2, ..., an) then Fl(s; δ) = w(δ b1, δ b2, ..., δ bn) where bi = ai - δ.
Given an E-equivalent scale, scale s, offsets between 0 and min({step sizes in s}) (equivalently, between max{len(s)-1-steps in s} and E) are called ''small''. Small offsets are significant because it copies the underlying scale structure: if s is a circular word w(a1, a2, ..., an) then Fl(s; δ) uses the same circular word but with δ followed by the difference between δ and every step size in w, namely w(δ b1, δ b2, ..., δ bn) where bi = ai - δ.
 
== Properties ==
== Properties ==
* A flought scale is not always CS, even when the strand is CS and the scale has an [[AGS]]. One such scale is Fl(Zarlino, 32/25) = 25/24 9/8 75/64 5/4 125/96 4/3 375/256 3/2 25/16 5/3 225/128 15/8 125/64 2/1 which has [[AGS]](32/25 125/96 32/25 5/4).
* A flought scale is not always CS, even when the strand is CS and the scale has an [[AGS]]. One such scale is Fl(Zarlino, 32/25) = 25/24 9/8 75/64 5/4 125/96 4/3 375/256 3/2 25/16 5/3 225/128 15/8 125/64 2/1 which has [[AGS]](32/25 125/96 32/25 5/4).