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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''.

== 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.

# 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}.

# For any periodic scale ''S'' with equave E, if δ is an offset and Fl(''S''; δ) exists, then Fl(''S''; δ) = Fl(''S''; E - δ) = Fl(''S''; δ + E). Thus, taking the equave complement of an offset in a polyoffset does not change the flought scale, nor does shifting any individual offset by equaves.

# Given an E-equivalent scale ''S'', offsets δ within (0, min({step sizes in ''S''})) are called ''small'' in the context of floughtening ''S''. Small offsets are significant because the resulting flought scale has a structure that closely mimics the underlying scale structure: if ''S'' is a circular word <math>w(a_1, a_2, ..., a_n)</math> 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 <math>w(\delta b_1, \delta b_2, ..., \delta b_n)</math> where <math>b_i = a_i - \delta</math>.

# A flought scale is not always CS, even when the strand is CS and the scale has a [[generator sequence]] where every generator subtends the same number of steps. 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 [[GS]](32/25 125/96 32/25 5/4).

== Some flought scales ==

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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''.
 == 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.
+# 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}.
 # For any periodic scale ''S'' with equave E, if δ is an offset and Fl(''S''; δ) exists, then Fl(''S''; δ) = Fl(''S''; E - δ) = Fl(''S''; δ + E). Thus, taking the equave complement of an offset in a polyoffset does not change the flought scale, nor does shifting any individual offset by equaves.
 # Given an E-equivalent scale ''S'', offsets δ within (0, min({step sizes in ''S''})) are called ''small'' in the context of floughtening ''S''. Small offsets are significant because the resulting flought scale has a structure that closely mimics the underlying scale structure: if ''S'' is a circular word <math>w(a_1, a_2, ..., a_n)</math> 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 <math>w(\delta b_1, \delta b_2, ..., \delta b_n)</math> where <math>b_i = a_i - \delta</math>.
 # A flought scale is not always CS, even when the strand is CS and the scale has a [[generator sequence]] where every generator subtends the same number of steps. 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 [[GS]](32/25 125/96 32/25 5/4).
 == Some flought scales ==