https://en.xen.wiki/index.php?action=history&feed=atom&title=User%3AInthar%2FMaximal_consistent_set 2026-07-02T23:34:41Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=User:Inthar/Maximal_consistent_set&diff=230216&oldid=prev 2026-05-13T20:27:08Z

<p>Move &#039;maximal consistent set&#039; to user space as it hasn&#039;t been used in any example on the Wiki or been mentioned on either the Xengrove Discord or Xenharmonic Alliance Discord.</p> <p><b>New page</b></p><div>Related to [[consistency]].<br /> <br /> Non-technically, a &#039;&#039;&#039;maximal consistent set&#039;&#039;&#039; (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.<br /> <br /> Formally, given &#039;&#039;N&#039;&#039;-edo, a consistent chord &#039;&#039;C&#039;&#039; and a [[JI subgroup]] &#039;&#039;G&#039;&#039; [[generator|generated]] by the octave and the intervals in &#039;&#039;C&#039;&#039;, a &#039;&#039;maximal consistent set&#039;&#039; is a connected set &#039;&#039;S&#039;&#039;(connected via intervals that occur in C) such that adding another interval adjacent to &#039;&#039;S&#039;&#039; via an interval in &#039;&#039;C&#039;&#039; results in a chord that is inconsistent in &#039;&#039;N&#039;&#039;-edo. The &#039;&#039;maximal connected neighborhood&#039;&#039; (MCN) of &#039;&#039;C&#039;&#039; is a maximal consistent set containing &#039;&#039;C&#039;&#039;.</div>

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