Consistency: Difference between revisions
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Non-technically, a '''maximal consistent set''' (MCS) is a chord in a [[JI subgroup]] such that when you add another interval which is adjacent to the chord, then the chord becomes inconsistent in the edo. | Non-technically, a '''maximal consistent set''' (MCS) is a chord in a [[JI subgroup]] such that when you add another interval which is adjacent to the chord, then the chord becomes inconsistent in the edo. | ||
Formally, given ''N''-edo, a chord ''C'' and a [[JI subgroup]] ''G'' [[generator|generated]] by the octave and the dyads in ''C'', a ''maximal consistent set'' is a connected set ''S'' (connected via dyads in C) such that adding another interval adjacent to ''S'' via a dyad 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''. | Formally, given ''N''-edo, a chord ''C'' and a [[JI subgroup]] ''G'' [[generator|generated]] by the octave and the dyads in ''C'', a ''maximal consistent set'' is a connected set ''S'' (connected via dyads that occur in C) such that adding another interval adjacent to ''S'' via a dyad 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''. | ||
==Generalization to non-octave scales== | ==Generalization to non-octave scales== | ||