User:Zhenlige/EDO impressions: Difference between revisions
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*[[20edo|20]]: The fact that [[41edo]] is good indicates that 20- and 21edo are probably bad. Does anyone really think it is OK for a chord to contain a lot of inconsistent mappings involving 3? | *[[20edo|20]]: The fact that [[41edo]] is good indicates that 20- and 21edo are probably bad. Does anyone really think it is OK for a chord to contain a lot of inconsistent mappings involving 3? | ||
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*[[22edo|22]]: The smallest | *[[22edo|22]]: The smallest EDO with decent [[11-limit]] and the smallest non-meantone EDO with decent [[5-limit]]. [[Superpyth]] and [[porcupine]]. The only reasonable superpyth EDO. The upper bound of a good fifth. The best you can get with [[50/49]] tempered out. | ||
*[[23edo|23]]: Incomplete [[46edo]]. The largest EDO without a [[5L 2s|diatonic]], [[5edo|blackwood]] or [[7edo|whitewood]] fifth. | *[[23edo|23]]: Incomplete [[46edo]]. The largest EDO without a [[5L 2s|diatonic]], [[5edo|blackwood]] or [[7edo|whitewood]] fifth. | ||
*[[24edo|24]]: What some non-microtonalists think microtonality is. 12edo with neutrals. Good for prime [[11/1|11]]. Accurate in subgroup 2.3.11.17.19. | *[[24edo|24]]: What some non-microtonalists think microtonality is. 12edo with neutrals. Good for prime [[11/1|11]]. Accurate in subgroup 2.3.11.17.19. | ||
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*[[26edo|26]]: A stack of [[7/4]]. Good for 2.7.11 subgroup. Other intervals suck. Since it is relatively small, consistency does not implies high accuracy. Meantone in [[5-limit]] but tuned terribly. Incomplete [[130edo]]. | *[[26edo|26]]: The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad. A stack of [[7/4]]. Good for 2.7.11 subgroup. Other intervals suck. Since it is relatively small, consistency does not implies high accuracy. [[Meantone]] in [[5-limit]] but tuned terribly. Incomplete [[130edo]]. | ||
*[[27edo|27]]: Worse than both [[12edo]] and [[22edo]] for [[5-limit]]. It generally sounds worse than 22edo. 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. When I hear its ~[[10:12:15]] and ~[[6:7:9]] chord I feel the fifth is obviously off. Use [[108edo]] (not [[landscape]]) to make it a true [[7-limit]] EDO, and [[270edo]] is excellent | *[[27edo|27]]: Worse than both [[12edo]] and [[22edo]] for [[5-limit]]. It generally sounds worse than 22edo. 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. When I hear its ~[[10:12:15]] and ~[[6:7:9]] chord I feel the fifth is obviously off. Use [[108edo]] (not [[landscape]]) to make it a true [[7-limit]] EDO, and [[270edo]] is excellent. | ||
*[[28edo|28]]: [[Whitewood]] [[diminished (temperament)|diminished]]. Kinda opposite from [[15edo]]. The best you can get with whitewood. | *[[28edo|28]]: [[Whitewood]] [[diminished (temperament)|diminished]]. Kinda opposite from [[15edo]]. The best you can get with whitewood. | ||
*[[29edo|29]]: A circle of fifths in [[mystery]], which supports [[pele]] (and is close to its optimal tuning), a convenient temperament with [[5/1|5]], [[7/1|7]], [[11/1|11]] and [[13/1|13]] on the same chain of fifths. Near pure [[13/11]]. The smallest EDO with a better [[3/2]] than [[12edo]]. | *[[29edo|29]]: A circle of fifths in [[mystery]], which supports [[pele]] (and is close to its optimal tuning), a convenient temperament with [[5/1|5]], [[7/1|7]], [[11/1|11]] and [[13/1|13]] on the same chain of fifths. Near pure [[13/11]]. The smallest EDO with a better [[3/2]] than [[12edo]]. | ||
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*[[35edo|35]]: The largest non-[[5L 2s|diatonic]] EDO. | *[[35edo|35]]: The largest non-[[5L 2s|diatonic]] EDO. | ||
*[[36edo|36]]: Good for 2.3.7.13.17.19.23.29 subroup. Avoid [[5/1|5]] here because it is almost completely missed. Otherwise incomplete [[72edo]]. | *[[36edo|36]]: Good for 2.3.7.13.17.19.23.29 subroup. Avoid [[5/1|5]] here because it is almost completely missed. Otherwise incomplete [[72edo]]. | ||
*[[37edo|37]]: | *[[37edo|37]]: A strong no-[[3/1|3]] system, which is kinda hard to use since the only isoharmonic chords are subsets of the 3n+1 and 3n+2 series, and there are not many useful scales. | ||
*[[38edo|38]]: [[19edo]] with neutrals. Near pure [[11/9]]. | *[[38edo|38]]: [[19edo]] with neutrals. Near pure [[11/9]]. Doubling such a coarse EDO won't give anything very notable, and the acceptable error of 19edo really becomes a problem at this size. | ||
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*[[41edo|41]]: Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Containing [[Bohlen-Pierce scale]]. Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals evenly spaced. Also [[garibaldi]] and [[miracle]]. The largest problem is its relatively inaccurate [[5/1|5]]. From here on, most EDOs with good [[13-limit]] support [[akea]]. | *[[41edo|41]]: Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Containing [[Bohlen-Pierce scale]]. Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals evenly spaced. Also [[garibaldi]] and [[miracle]]. The largest problem is its relatively inaccurate [[5/1|5]]. From here on, most EDOs with good [[13-limit]] support [[akea]]. | ||
*[[42edo|42]]: Incomplete [[84edo]]. | *[[42edo|42]]: Incomplete [[84edo]]. | ||
*[[43edo|43]]: Close to 1/5-comma [[meantone]] which gives pure [[15/8]]. Not very notable besides that. Its fifth is too sharp for [[septimal meantone]]. | *[[43edo|43]]: Close to 1/5-comma [[meantone]] which gives pure [[15/8]]. Not very notable besides that. Its fifth is too sharp for [[septimal meantone]]. | ||
*[[44edo|44]]: Like [[38edo]], doubling a | *[[44edo|44]]: Like [[38edo]], doubling a coarse EDO won't give anything very notable. | ||
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*[[46edo|46]]: [[13-limit]] [[diaschismic]] and [[valentine]]. Near pure [[11/7]]. It has quartertones similar to [[22edo]] but approximates JI intervals more accurately. Its 30::36 are all 2 steps apart. | *[[46edo|46]]: [[13-limit]] [[diaschismic]] and [[valentine]]. Near pure [[11/7]]. It has quartertones similar to [[22edo]] but approximates JI intervals more accurately. Its 30::36 are all 2 steps apart. | ||
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*[[48edo|48]]: A not-so-good multiple of [[12edo]]. | *[[48edo|48]]: A not-so-good multiple of [[12edo]]. | ||
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*[[50edo|50]]: Meantone with a flatter fifth than [[31edo]], but I usually use [[golden meantone]] (with slight octave stretching) for this range. | *[[50edo|50]]: [[Meantone]] with a flatter fifth than [[31edo]], but I usually use [[golden meantone]] (with slight octave stretching) for this range. | ||
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*[[53edo|53]]: A stack of [[3/2]]. Almost just [[3/1|3]], accurate [[5-limit]], and decent [[7-limit]]. Good for 5-limit [[schismatic]] with occasional [[garibaldi]] [[7/1|7]]. | *[[53edo|53]]: A stack of [[3/2]]. Almost just [[3/1|3]], accurate [[5-limit]], and decent [[7-limit]]. Good for 5-limit [[schismatic]] with occasional [[garibaldi]] [[7/1|7]]. | ||