Interleaving: Difference between revisions

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Putting examples before mathematical facts to motivate the latter.
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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 native Modern English cognate to the 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 native Modern English cognate to the words ''plait'' and ''plexus''.
== Some flought scales ==
Flought scales can easily be built from a harmonic series mode as the strand: for example, if ''n''::2''n'' is the strand, then (2''n'' + 1)/''2n'' always works as the offset (e.g. strand 5:6:7:8:9:10, offset 10:11). Here are some other examples:
* Fl(12:14:16:18:21:24; 11:12)
* Fl(12:14:16:18:21:24; 12:13:22)
* Fl(12:14:16:18:21:24; 8:10:11)
** [[User:Userminusone/Userminusone's_11_limit_15_tone_scale]]
* Fl(12:14:16:18:21:24; 9:10:11)
** Note: detempered 11-limit Porcupine[15]; well-formed [[generator sequence]] GS(10/9, 11/10, 12/11, 10/9, 11/10, 12/11, 10/9, 11/10, 189/176)
* Fl(Pyth[5]; 8:10:11)
* Fl(Pyth[5]; 9:10:11)
** Note: detempered 2.3.5.11 Porcupine[15]; well-formed [[generator sequence]] GS(10/9, 11/10, 12/11)
* Fl(9/8-14/11-4/3-3/2-56/33-21/11-2/1; 9/7)
== Properties ==
== 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 dyads of ''S'', and Δ be a chord such that every dyad of Δ falls within the open interval (0, ''E''). Then the polyoffset chord Δ floughtens ''S'' if and only if no nonunison (positive) dyad 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 dyads of ''S'', and Δ be a chord such that every dyad of Δ falls within the open interval (0, ''E''). Then the polyoffset chord Δ floughtens ''S'' if and only if no nonunison (positive) dyad in Δ falls within <math> [\min \mathcal{D}_k(S), \max \mathcal{D}_k(S)]</math> for any ''k'' ∈ {0, ... len(''S'') - 1}.