Xen concepts for beginners: Difference between revisions

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* [[5edo]]: Equalized pentatonic ("equipentatonic").

* [[7edo]]: Equalized diatonic ("equiheptatonic").

* [[9edo]]: The simplest edo with a [[2L 5s]] mos (sssLssL). This mos is of interest because it can be viewed as a tuning of the diatonic scale where whole steps are smaller than half steps.

* [[9edo]]: The simplest edo with a [[2L 5s]] mos (sssLssL). This mos is of interest because it can be viewed as a tuning of the diatonic scale where whole steps are smaller than half steps (an "antidiatonic" scale). The corresponding temperament is [[mavila]], which is llike meantone except major and minor intervals are swapped. Some larger edos like 16edo and 23edo tune it better, though mavila has poor accuracy in general since the fifth is very flat.

* [[11edo]]: Stretched 12edo, has [[4L 3s]] mos (LLsLsLs) which is a stretched diatonic.

* [[13edo]]: Compressed 12edo having the [[5L 3s]] mos (LLsLLsLs) which is a compressed version of the diatonic scale.

* [[15edo]]: The smallest edo with a [[5L 5s]] mos (LsLsLsLsLs) commonly called the blackwood scale. Also the smallest with a [[7L 1s]] mos (LLLLsLLL). Both scales are known for supporting relatively familiar major and minor chords with relatively unfamiliar melodic structures.

* [[16edo]]: Has 2L 5s (sssLssL) and [[7L 2s]] (LLLsLLLLs).

* [[16edo]]: Has 2L 5s (sssLssL) and [[7L 2s]] (LLLsLLLLs), generated by the mavila temperament, for which it is a more accurate tuning than 9edo.

* [[17edo]]: The smallest edo after 12edo with a diatonic scale, and the smallest after 12edo to provide perfect fifths which are consonant for most purposes. Its major intervals are sharper and its minor intervals flatter than in 12edo, so it is often said to have a dramatic sound. First neutral diatonic edo (providing neutral seconds, thirds, sixths, and sevenths).

* [[18edo]]: Has two fifths, 733{{c}} and 667{{c}}, 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, but perfect fifths are represented significantly worse. 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 (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]] and 7L 1s.

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

* [[23edo]]: The largest edo without a diatonic, 5edo, or 7edo fifth. Supports mavila like 9edo and 16edo with the flat 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 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]].

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 * [[5edo]]: Equalized pentatonic ("equipentatonic").
 * [[7edo]]: Equalized diatonic ("equiheptatonic").
-* [[9edo]]: The simplest edo with a [[2L 5s]] mos (sssLssL). This mos is of interest because it can be viewed as a tuning of the diatonic scale where whole steps are smaller than half steps.
+* [[9edo]]: The simplest edo with a [[2L 5s]] mos (sssLssL). This mos is of interest because it can be viewed as a tuning of the diatonic scale where whole steps are smaller than half steps (an "antidiatonic" scale). The corresponding temperament is [[mavila]], which is llike meantone except major and minor intervals are swapped. Some larger edos like 16edo and 23edo tune it better, though mavila has poor accuracy in general since the fifth is very flat.
 * [[11edo]]: Stretched 12edo, has [[4L 3s]] mos (LLsLsLs) which is a stretched diatonic.
 * [[13edo]]: Compressed 12edo having the [[5L 3s]] mos (LLsLLsLs) which is a compressed version of the diatonic scale.
 * [[15edo]]: The smallest edo with a [[5L 5s]] mos (LsLsLsLsLs) commonly called the blackwood scale. Also the smallest with a [[7L 1s]] mos (LLLLsLLL). Both scales are known for supporting relatively familiar major and minor chords with relatively unfamiliar melodic structures.
-* [[16edo]]: Has 2L 5s (sssLssL) and [[7L 2s]] (LLLsLLLLs).
+* [[16edo]]: Has 2L 5s (sssLssL) and [[7L 2s]] (LLLsLLLLs), generated by the mavila temperament, for which it is a more accurate tuning than 9edo.
 * [[17edo]]: The smallest edo after 12edo with a diatonic scale, and the smallest after 12edo to provide perfect fifths which are consonant for most purposes. Its major intervals are sharper and its minor intervals flatter than in 12edo, so it is often said to have a dramatic sound. First neutral diatonic edo (providing neutral seconds, thirds, sixths, and sevenths).
 * [[18edo]]: Has two fifths, 733{{c}} and 667{{c}}, 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, but perfect fifths are represented significantly worse. 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 (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]] and 7L 1s.
-* [[23edo]]: The largest edo without a diatonic, 5edo, or 7edo fifth.
+* [[23edo]]: The largest edo without a diatonic, 5edo, or 7edo fifth. Supports mavila like 9edo and 16edo with the flat 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 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]].