User:Inthar/Maximal consistent set

Related to consistency.

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 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.