User:Zhenlige/EDO impressions: Difference between revisions

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*[[27edo|27]]: A stack of [[7/6]]. Worse than both 12- and 22edo for 5-limit. Its fifth sucks and its diatonic scale makes little sense. Its 7/3 and 7/5 are good, but 3, 5 and 7 are off. Use [[108edo]] to make it really a 7-limit EDO, and [[270edo]] is excellent. When I hear its ~[[10:12:15]] and ~[[6:7:9]] chord I feel the fifth is obviously off. I have listened to both 22edo and 27edo and I feel the former is better. Compared to 22edo, it is like fixing 7 by ruining 5 and partly 3. There are beatings here and there. It really needs compression. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.

*[[28edo|28]]: [[Whitewood]] [[diminished]]. Kinda opposite from [[15edo]]. The best you can get with [[whitewood]].

*[[29edo|29]]: A circle of fifths in [[mystery]], which supports [[pele]]. The smallest EDO with a better fifth than 12edo. Not so useful on its own.

*[[29edo|29]]: A circle of fifths in [[mystery]], which supports [[pele]] (and is close to its optimal tuning), a convenient temperament with 5, 7, 11 and 13 on the same chain of fifths. The smallest EDO with a better fifth than 12edo. Not so useful on its own.

*...

*[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. The meantone flat fifth makes its neutral thirds close to [[11/9]] (tho there is the JI subgroup problem since 11 and 9 themselves are not so close). Also [[valentine]] and [[miracle]]. IMO the best meantone EDO. For other temperaments its flat fifth may be a drawback, making 9 bad.

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 *[[27edo|27]]: A stack of [[7/6]]. Worse than both 12- and 22edo for 5-limit. Its fifth sucks and its diatonic scale makes little sense. Its 7/3 and 7/5 are good, but 3, 5 and 7 are off. Use [[108edo]] to make it really a 7-limit EDO, and [[270edo]] is excellent. When I hear its ~[[10:12:15]] and ~[[6:7:9]] chord I feel the fifth is obviously off. I have listened to both 22edo and 27edo and I feel the former is better. Compared to 22edo, it is like fixing 7 by ruining 5 and partly 3. There are beatings here and there. It really needs compression. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.
 *[[28edo|28]]: [[Whitewood]] [[diminished]]. Kinda opposite from [[15edo]]. The best you can get with [[whitewood]].
-*[[29edo|29]]: A circle of fifths in [[mystery]], which supports [[pele]]. The smallest EDO with a better fifth than 12edo. Not so useful on its own.
+*[[29edo|29]]: A circle of fifths in [[mystery]], which supports [[pele]] (and is close to its optimal tuning), a convenient temperament with 5, 7, 11 and 13 on the same chain of fifths. The smallest EDO with a better fifth than 12edo. Not so useful on its own.
 *...
 *[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. The meantone flat fifth makes its neutral thirds close to [[11/9]] (tho there is the JI subgroup problem since 11 and 9 themselves are not so close). Also [[valentine]] and [[miracle]]. IMO the best meantone EDO. For other temperaments its flat fifth may be a drawback, making 9 bad.