Xen concepts for beginners: Difference between revisions

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* 18edo: has two fifths, 733c and 667c, that are nearly equally off from 3/2.

* 19edo: the smallest edo after 12edo which supports Meantone. Just major and minor thirds are better approximated than in 12edo. First [[interordinal]] diatonic edo (interordinals are semifourths, semisixths, semitenths, and semitwelfths).

* 22edo: diatonic MOS with a fifth so sharp that it has supermajor and subminor thirds for its major and minor thirds. Has a 5-limit major third which *cannot* be reached by stacking four fifths. Supports Superpyth like 27edo.

* 22edo: diatonic MOS with a fifth so sharp that it has supermajor and subminor thirds 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 (350c) and semifourths (250c), each of these lending itself to different harmony. Has 12edo MOS scales as well as new ones.

* 29edo: weird flat neogothic edo.

* 31edo: often considered the best Meantone edo. Close to historical quarter-comma meantone. Not only is its 5/4 ~~close to just~~, it also matches 7/4 well, also approximating other JI ratios like 6/5, 7/6, and 25/16.

* 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 (sibminor third), and 25/16 (classical augmented fifth).

* 34edo: good for the 5-limit (2.3.5), as it doesn't temper out 81/80 and has a good 5/4.

* 36edo: good for primes 3 and 7.

* 37edo: good for primes 5, 7, 11 and 13, in return for a sharp 3/2.

* 41edo: good 3; flat 5 and 7; sharp 11 and 13. Known for Kite guitar.

* 41edo: good 3; flat 5 and 7; sharp 11 and 13. Known for [[Kite guitar]].

* 46edo: neogothic 3; sharp 5; flat 7, 11, and 13; good 17. Supports Parapyth. Some favor it over 41edo.

* 46edo: neogothic 3; sharp 5; flat 7, 11, and 13; good 17. Supports [[Parapyth]]. Some favor it over 41edo.

* 53edo: is a stack of near-just 3/2's which also approximates primes 5, 7, 13, and 19.

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 * 18edo: has two fifths, 733c and 667c, that are nearly equally off from 3/2.
 * 19edo: the smallest edo after 12edo which supports Meantone. Just major and minor thirds are better approximated than in 12edo. First [[interordinal]] diatonic edo (interordinals are semifourths, semisixths, semitenths, and semitwelfths).
-* 22edo: diatonic MOS with a fifth so sharp that it has supermajor and subminor thirds for its major and minor thirds. Has a 5-limit major third which *cannot* be reached by stacking four fifths. Supports Superpyth like 27edo.
+* 22edo: diatonic MOS with a fifth so sharp that it has supermajor and subminor thirds 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 (350c) and semifourths (250c), each of these lending itself to different harmony. Has 12edo MOS scales as well as new ones.
 * 29edo: weird flat neogothic edo.
-* 31edo: often considered the best Meantone edo. Close to historical quarter-comma meantone. Not only is its 5/4 close to just, it also matches 7/4 well, also approximating other JI ratios like 6/5, 7/6, and 25/16.
+* 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 (sibminor third), and 25/16 (classical augmented fifth).
 * 34edo: good for the 5-limit (2.3.5), as it doesn't temper out 81/80 and has a good 5/4.
 * 36edo: good for primes 3 and 7.
 * 37edo: good for primes 5, 7, 11 and 13, in return for a sharp 3/2.
-* 41edo: good 3; flat 5 and 7; sharp 11 and 13. Known for Kite guitar.
+* 41edo: good 3; flat 5 and 7; sharp 11 and 13. Known for [[Kite guitar]].
-* 46edo: neogothic 3; sharp 5; flat 7, 11, and 13; good 17. Supports Parapyth. Some favor it over 41edo.
+* 46edo: neogothic 3; sharp 5; flat 7, 11, and 13; good 17. Supports [[Parapyth]]. Some favor it over 41edo.
 * 53edo: is a stack of near-just 3/2's which also approximates primes 5, 7, 13, and 19.