User:Zhenlige/EDO impressions: Difference between revisions

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

*[[1edo|1]]: Equivalent to [[2-limit]] JI. Not much about harmony. Possibly useful for a transition between different tunings.

*[[2edo|2]]:

*[[2edo|2]]: Tritones.

*[[3edo|3]]: 12edo augmented chords.

*[[4edo|4]]: 12edo diminished seventh chords.

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*[[15edo|15]]: Better than it seems to be, tho still rough. A heavily stretched [[Carlos Alpha]] scale.

*...

*[[17edo|17]]: Interesting sharp fifths. The fact that its thirds do not approximate any simple ratios well is a pity, or benefit? I don't know.

*[[17edo|17]]: Interesting sharp fifths. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know)

*...

*[[19edo|19]]: [[Meantone]], but with a too flat fifth. Strangely large minor 2nds. Also a compressed [[Carlos Beta]]. 31edo is more preferable. The lower bound of a good fifth.

*[[19edo|19]]: Usable but imperfect for many temperaments. [[Meantone]], but with a too flat fifth. Strangely large minor 2nds. Also a compressed [[Carlos Beta]]. For meantone 31edo is more preferable. The lower bound of a good fifth.

*...

*[[22edo|22]]: Good [[superpyth]] and [[porcupine]] tuning. The higher bound of a good fifth.

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*[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. For other temperaments its flat fifth is a drawback.

*...

*[[34edo|34]]: 17edo with prime [[5/1|5]]. Also a stretched [[Carlos Gamma]].

*[[34edo|34]]: 17edo with prime [[5/1|5]], but no [[7/1|7]]. Also a stretched [[Carlos Gamma]].

*...

*[[36edo|36]]: Good for 2.3.7.13.17.19.23.29 subroup. Otherwise incomplete 72edo.

*[[37edo|37]]: Everything but prime [[3/1|3]]. Maybe interesting though.

*...

*[[41edo|41]]: Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals equidistantly spreaded.

*...

*[[50edo|50]]: Good flatter meantone, but I usually just go for [[golden meantone]] at this level of precision.

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*[[53edo|53]]: Almost just [[3/2]], and accurate [[7-limit]]. Purely an approximation of JI.

*...

*[[72edo|72]]: An excellent extension of 12- and 24edo. The relative error is within 1/3 steps ~~for even~~ large primes except a few including 13, 53 and 59. Suitable for octave stretching in 17-limit.

*[[72edo|72]]: An excellent extension of 12- and 24edo. The relative error of primes is within 1/3 steps up to large primes except a few including 13, 53 and 59. Suitable for octave stretching in 17-limit.

*...

*[[77edo|77]]: Good [[valentine]] and [[boethius]].

*...

*[[171edo|171]]: Ideal for approximating 7-limit JI. At this size level, EDOs are more like free pitch, rather than either JI or a stable temperament.

@@ Line 2: / Line 2: @@
 *[[0edo|0]]: A fancy way to say “pitchless”.
 *[[1edo|1]]: Equivalent to [[2-limit]] JI. Not much about harmony. Possibly useful for a transition between different tunings.
-*[[2edo|2]]:
+*[[2edo|2]]: Tritones.
 *[[3edo|3]]: 12edo augmented chords.
 *[[4edo|4]]: 12edo diminished seventh chords.
@@ Line 15: / Line 15: @@
 *[[15edo|15]]: Better than it seems to be, tho still rough. A heavily stretched [[Carlos Alpha]] scale.
 *...
-*[[17edo|17]]: Interesting sharp fifths. The fact that its thirds do not approximate any simple ratios well is a pity, or benefit? I don't know.
+*[[17edo|17]]: Interesting sharp fifths. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know)
 *...
-*[[19edo|19]]: [[Meantone]], but with a too flat fifth. Strangely large minor 2nds. Also a compressed [[Carlos Beta]]. 31edo is more preferable. The lower bound of a good fifth.
+*[[19edo|19]]: Usable but imperfect for many temperaments. [[Meantone]], but with a too flat fifth. Strangely large minor 2nds. Also a compressed [[Carlos Beta]]. For meantone 31edo is more preferable. The lower bound of a good fifth.
 *...
 *[[22edo|22]]: Good [[superpyth]] and [[porcupine]] tuning. The higher bound of a good fifth.
@@ Line 25: / Line 25: @@
 *[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. For other temperaments its flat fifth is a drawback.
 *...
-*[[34edo|34]]: 17edo with prime [[5/1|5]]. Also a stretched [[Carlos Gamma]].
+*[[34edo|34]]: 17edo with prime [[5/1|5]], but no [[7/1|7]]. Also a stretched [[Carlos Gamma]].
 *...
 *[[36edo|36]]: Good for 2.3.7.13.17.19.23.29 subroup. Otherwise incomplete 72edo.
 *[[37edo|37]]: Everything but prime [[3/1|3]]. Maybe interesting though.
+*...
+*[[41edo|41]]: Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals equidistantly spreaded.
 *...
 *[[50edo|50]]: Good flatter meantone, but I usually just go for [[golden meantone]] at this level of precision.
@@ Line 34: / Line 36: @@
 *[[53edo|53]]: Almost just [[3/2]], and accurate [[7-limit]]. Purely an approximation of JI.
 *...
-*[[72edo|72]]: An excellent extension of 12- and 24edo. The relative error is within 1/3 steps for even large primes except a few including 13, 53 and 59. Suitable for octave stretching in 17-limit.
+*[[72edo|72]]: An excellent extension of 12- and 24edo. The relative error of primes is within 1/3 steps up to large primes except a few including 13, 53 and 59. Suitable for octave stretching in 17-limit.
 *...
 *[[77edo|77]]: Good [[valentine]] and [[boethius]].
+*...
+*[[171edo|171]]: Ideal for approximating 7-limit JI. At this size level, EDOs are more like free pitch, rather than either JI or a stable temperament.