User:Zhenlige/EDO impressions: Difference between revisions

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== General patterns ==

*If (2n+1)-edo is good, then n-edo and (n+1)-edo are probably bad, or at least heavily inconsistent, because many intervals near the half octave (especially [[3/2]]) will be off.

*If m-edo and n-edo are good, and most intervals are either accurate enough or off in the opposite directions, then (m+n)-edo is probably good.

== Details ==

In terms of accuracy, assuming harmonic overtone.

*[[0edo|0]]: A fancy way to say “pitchless”.

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*...

*[[26edo|26]]: A stack of [[7/4]]. Meantone but tuned terribly. Incomplete [[130edo]].

*[[27edo|27]]: Worse than both 12- and 22edo for 5-limit. It is distinct in 7-limit tho, but that is like thinking 0.1 is better represented as 1 than 0. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.

*[[27edo|27]]: Worse than both 12- and 22edo for 5-limit. It is distinct in 7-limit tho, but that is like thinking 0.1 is better represented as 1 than 0. There are beatings here and there. It really needs compression. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.

*...

*[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. Also [[valentine]] and [[miracle]]. IMO the best meantone EDO. For other temperaments its flat fifth may be a drawback.

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+== General patterns ==
+*If (2n+1)-edo is good, then n-edo and (n+1)-edo are probably bad, or at least heavily inconsistent, because many intervals near the half octave (especially [[3/2]]) will be off.
+*If m-edo and n-edo are good, and most intervals are either accurate enough or off in the opposite directions, then (m+n)-edo is probably good.
+== Details ==
 In terms of accuracy, assuming harmonic overtone.
 *[[0edo|0]]: A fancy way to say “pitchless”.
@@ Line 26: / Line 31: @@
 *...
 *[[26edo|26]]: A stack of [[7/4]]. Meantone but tuned terribly. Incomplete [[130edo]].
-*[[27edo|27]]: Worse than both 12- and 22edo for 5-limit. It is distinct in 7-limit tho, but that is like thinking 0.1 is better represented as 1 than 0. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.
+*[[27edo|27]]: Worse than both 12- and 22edo for 5-limit. It is distinct in 7-limit tho, but that is like thinking 0.1 is better represented as 1 than 0. There are beatings here and there. It really needs compression. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.
 *...
 *[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. Also [[valentine]] and [[miracle]]. IMO the best meantone EDO. For other temperaments its flat fifth may be a drawback.