Xen concepts for beginners: Difference between revisions

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* [[22edo]]: Diatonic MOS with a fifth so sharp that it has supermajor and subminor thirds (approximately [[9/7]] and [[7/6]]) for its major and minor thirds. Has a 5-limit major third (approximate [[5/4]]) which *cannot* be reached by stacking four fifths. Supports [[Superpyth]] like [[27edo]].

* [[23edo]]: The largest edo without a diatonic, 5edo, or 7edo fifth.

* [[24edo]]: Has both neutral thirds (and other neutral intervals) and semifourths (and other interordinals), each of these lending itself to different harmony. Has 12edo MOS scales as well as new ones.

* [[26edo]]: Even softer diatonic MOS than 19edo, so much that the "5/4" is nearly exactly [[26/21]]. Has near-exact [[13/12]] and [[7/4]], and good [[14/11]], and [[11/8]].

* [[27edo]]: Even harder diatonic MOS than 22edo; has a near-exact [[7/6]] and splits the sharp fifth into two approximate [[16/13]] sharp neutral thirds.

* [[29edo]]: Weird flat neogothic edo.

* [[31edo]]: Often considered the best Meantone edo. Close to historical [[quarter-comma meantone]]. Not only is its major third close to just [[5/4]], it also matches the harmonic seventh [[7/4]] well, also approximating other JI ratios like [[6/5]] (just minor third), [[7/6]] (septimal subminor third), and [[25/16]] (classical augmented fifth).

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 * [[22edo]]: Diatonic MOS with a fifth so sharp that it has supermajor and subminor thirds (approximately [[9/7]] and [[7/6]]) for its major and minor thirds. Has a 5-limit major third (approximate [[5/4]]) which *cannot* be reached by stacking four fifths. Supports [[Superpyth]] like [[27edo]].
 * [[23edo]]: The largest edo without a diatonic, 5edo, or 7edo fifth.
 * [[24edo]]: Has both neutral thirds (and other neutral intervals) and semifourths (and other interordinals), each of these lending itself to different harmony. Has 12edo MOS scales as well as new ones.
+* [[26edo]]: Even softer diatonic MOS than 19edo, so much that the "5/4" is nearly exactly [[26/21]]. Has near-exact [[13/12]] and [[7/4]], and good [[14/11]], and [[11/8]].
+* [[27edo]]: Even harder diatonic MOS than 22edo; has a near-exact [[7/6]] and splits the sharp fifth into two approximate [[16/13]] sharp neutral thirds.
 * [[29edo]]: Weird flat neogothic edo.
 * [[31edo]]: Often considered the best Meantone edo. Close to historical [[quarter-comma meantone]]. Not only is its major third close to just [[5/4]], it also matches the harmonic seventh [[7/4]] well, also approximating other JI ratios like [[6/5]] (just minor third), [[7/6]] (septimal subminor third), and [[25/16]] (classical augmented fifth).