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Consistency: Difference between revisions

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Re-organize. Put the alt definition in the math section
Move 'maximal consistent set' to user space as it hasn't been used in any example on the Wiki or been mentioned on either the Xengrove Discord or Xenharmonic Alliance Discord.
 
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Examples of more advanced concepts that build on this are [[telicity]] and [[#Maximal consistent set|maximal consistent set]]s.
Examples of more advanced concepts that build on this are [[telicity]] and [[#User:Inthar/Maximal_consistent_set|maximal consistent set]]s.
 
== Maximal consistent set ==
Non-technically, a '''maximal consistent set''' (MCS) is a piece of a [[JI subgroup]] such that when you add another interval which is adjacent to the piece (viewed as a chord), then the piece becomes inconsistent in the edo.
 
Formally, given ''N''-edo, a consistent chord ''C'' and a [[JI subgroup]] ''G'' [[generator|generated]] by the octave and the intervals in ''C'', a ''maximal consistent set'' is a connected set ''S''(connected via intervals that occur in C) such that adding another interval adjacent to ''S'' via an interval in ''C'' results in a chord that is inconsistent in ''N''-edo. The ''maximal connected neighborhood'' (MCN) of ''C'' is a maximal consistent set containing ''C''.


== For non-octave tunings ==
== For non-octave tunings ==
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