Interleaving: Difference between revisions

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== Properties ==

* For any periodic scale s with equave E, if Δ is a polyoffset and Fl(s; Δ) exists, then Fl(s; Δ) = Fl(s; E - Δ) where E - Δ = {E - δ : δ ∈ Δ}.

* Given an E-equivalent scale, scale s, offsets δ within (0, min({step sizes in s}~~)) (equivalently, (max{len(s)-1-steps in s}, E~~)) are called ''small''. Small offsets are significant because the resulting flought scale 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.

* Given an E-equivalent scale, scale s, offsets δ within (0, min({step sizes in s})) are called ''small''. Small offsets are significant because the resulting flought scale 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.

* 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).

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 == Properties ==
 * For any periodic scale s with equave E, if Δ is a polyoffset and Fl(s; Δ) exists, then Fl(s; Δ) = Fl(s; E - Δ) where E - Δ = {E - δ : δ ∈ Δ}.
-* Given an E-equivalent scale, scale s, offsets δ within (0, min({step sizes in s})) (equivalently, (max{len(s)-1-steps in s}, E)) are called ''small''. Small offsets are significant because the resulting flought scale 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.
+* Given an E-equivalent scale, scale s, offsets δ within (0, min({step sizes in s})) are called ''small''. Small offsets are significant because the resulting flought scale 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.
 * 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).