Consistency: Difference between revisions

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For example, 4:5:6:7 is consistent to distance 2 in [[31edo]]. However, 4:5:6:7:11 is only consistent to distance 0 because 11/5 is mapped too inaccurately (rel error 26.2%). This shows that 31edo is especially strong in the 2.3.5.7 subgroup and weaker in 2.3.5.7.11.

Examples of more advanced concepts that build on this are [[telicity]] and [[Consistent#~~maximal~~ consistent ~~neighborhood~~|~~maximal~~ consistent ~~neighborhood~~]]s.

Examples of more advanced concepts that build on this are [[telicity]] and [[Consistent#maximally consistent set|maximally consistent set]]s.

== ~~Maximal~~ consistent set ==

== Maximally consistent set ==

(''Under construction'')

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 '''maximally 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 [[equave]] 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''.

@@ Line 42: / Line 42: @@
 For example, 4:5:6:7 is consistent to distance 2 in [[31edo]]. However, 4:5:6:7:11 is only consistent to distance 0 because 11/5 is mapped too inaccurately (rel error 26.2%). This shows that 31edo is especially strong in the 2.3.5.7 subgroup and weaker in 2.3.5.7.11.
-Examples of more advanced concepts that build on this are [[telicity]] and [[Consistent#maximal consistent neighborhood|maximal consistent neighborhood]]s.
+Examples of more advanced concepts that build on this are [[telicity]] and [[Consistent#maximally consistent set|maximally consistent set]]s.
-== Maximal consistent set ==
+== Maximally consistent set ==
 (''Under construction'')
-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 '''maximally 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 [[equave]] 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''.