Consistency: Difference between revisions
| Line 86: | Line 86: | ||
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. | 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 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''. | Formally, given ''N''-edo, a consistent 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 == | ||