Xen concepts for beginners: Difference between revisions

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* [[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, such as [[5L 4s]] and [[4L 3s]].

* [[26edo]]: Has a fifth even flatter than that of 19edo, at 9.6{{c}} flat, and an even softer diatonic mos than 19edo, so much that the diatonic major third is nearly exactly [[26/21]] and the diatonic minor second is nearly exactly [[13/12]]. The [[7/4]] is also nearly exact, and the edo also has a good [[10/9]], [[14/11]], and [[11/8]].

* [[27edo]]: Even harder diatonic mos than 22edo; at 9.2{{c}} sharp of just, the fifth is approximately about as sharp as 26edo's is flat. It has 12edo's [[5/4]], a near-exact [[7/6]], and an approximate [[16/13]] neutral third. Four fifths give a supermajor ~~thirdand~~ three fourths give a subminor third, just like in 22edo.

* [[27edo]]: Even harder diatonic mos than 22edo; at 9.2{{c}} sharp of just, the fifth is approximately about as sharp as 26edo's is flat. It has 12edo's [[5/4]], a near-exact [[7/6]], and an approximate [[16/13]] neutral third. Four fifths give a supermajor third and three fourths give a subminor third, just like in 22edo.

* [[29edo]]: First edo with a perfect fifth closer to just intonation than 12edo. The minor third is extremely close to just [[13/11]]. It offers a tuning of 7L 1s with more consonant fifths than 15edo or 22edo before it. Its diatonic scale has similar melodic properties to 17edo, although subtler.

* [[31edo]]: One of the most popular meantone edos. 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.

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 * [[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, such as [[5L&nbsp;4s]] and [[4L&nbsp;3s]].
 * [[26edo]]: Has a fifth even flatter than that of 19edo, at 9.6{{c}} flat, and an even softer diatonic mos than 19edo, so much that the diatonic major third is nearly exactly [[26/21]] and the diatonic minor second is nearly exactly [[13/12]]. The [[7/4]] is also nearly exact, and the edo also has a good [[10/9]], [[14/11]], and [[11/8]].
-* [[27edo]]: Even harder diatonic mos than 22edo; at 9.2{{c}} sharp of just, the fifth is approximately about as sharp as 26edo's is flat. It has 12edo's [[5/4]], a near-exact [[7/6]], and an approximate [[16/13]] neutral third. Four fifths give a supermajor thirdand three fourths give a subminor third, just like in 22edo.
+* [[27edo]]: Even harder diatonic mos than 22edo; at 9.2{{c}} sharp of just, the fifth is approximately about as sharp as 26edo's is flat. It has 12edo's [[5/4]], a near-exact [[7/6]], and an approximate [[16/13]] neutral third. Four fifths give a supermajor third and three fourths give a subminor third, just like in 22edo.
 * [[29edo]]: First edo with a perfect fifth closer to just intonation than 12edo. The minor third is extremely close to just [[13/11]]. It offers a tuning of 7L&nbsp;1s with more consonant fifths than 15edo or 22edo before it. Its diatonic scale has similar melodic properties to 17edo, although subtler.
 * [[31edo]]: One of the most popular meantone edos. 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.