User:Zhenlige/EDO impressions: Difference between revisions
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*[[22edo|22]]: The smallest EDO with decent [[11-limit]] and the smallest non-meantone EDO with decent [[5-limit]]. [[Superpyth]] and [[porcupine]]. Close to optimal 2.3.7 [[archy]] with compression. With pure octaves it is almost the best archy can give, since archy highly relies on octave compression. The upper bound of a good fifth. The best you can get with [[50/49]] tempered out. | *[[22edo|22]]: The smallest EDO with decent [[11-limit]] and the smallest non-meantone EDO with decent [[5-limit]]. [[Superpyth]] and [[porcupine]]. Close to optimal 2.3.7 [[archy]] with compression. With pure octaves it is almost the best archy can give, since archy highly relies on octave compression. 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. Nearly optimal for 2.3.11.19 tempering out [[243/242]] and [[513/512]], where the next EDO that significanly improves is [[89edo]]. | ||
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*[[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]]. | *[[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]]. | ||
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*[[72edo|72]]: The ultimate extension of [[12edo]] and [[24edo]]. Its [[11-limit]] is very accurate with a slightly flat tendency that works well with 12edo's flat [[3/1|3]]. A real [[miracle]] (pun intended). The only reasonable way of extending [[compton]] to 11-limit. Some higher limit intervals are also usable. The only notable [[13-limit]] non-[[akea]] EDO around this size. A powerful tool for modulating quartertones, which can be difficult in 24edo itself. Suitable for octave stretching if only [[17-limit]] or below is used. Playable by using three 24edo instruments or six 12edo instruments. | *[[72edo|72]]: The ultimate extension of [[12edo]] and [[24edo]]. Its [[11-limit]] is very accurate with a slightly flat tendency that works well with 12edo's flat [[3/1|3]]. A real [[miracle]] (pun intended). The only reasonable way of extending [[compton]] to 11-limit. Some higher limit intervals are also usable. The only notable [[13-limit]] non-[[akea]] EDO around this size. A powerful tool for modulating quartertones, which can be difficult in 24edo itself. Suitable for octave stretching if only [[17-limit]] or below is used. Playable by using three 24edo instruments or six 12edo instruments. | ||
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*[[74edo|74]]: [[37edo]] with meantone fifths. Close to [[tungsten meantone]]. The intrinsic error of meantone becomes a problem at this size, making [[9/1|9]] inconsistent. | *[[74edo|74]]: [[37edo]] with [[meantone]] fifths. Close to [[tungsten meantone]]. The intrinsic error of meantone becomes a problem at this size, making [[9/1|9]] inconsistent. | ||
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*[[77edo|77]]: Good for [[valentine]]. Its slightly flat [[3/2]] gives a good [[19/1|19]] via [[boethius | *[[77edo|77]]: Good for [[valentine]] therefore containing [[Carlos Alpha]]. Its slightly flat [[3/2]] gives a good [[19/1|19]] via [[boethius]]. [[40/27]] as 4\[[7edo|7]] aka [[absurdity]]. Usable for high limit JI. At this size even some inconsistent intervals are usable via val mapping since its step size is only ~16 cents. | ||
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*[[81edo|81]]: The [[optimal patent val]] for [[meantone]] and some of its higher-limit extentions, but I won't use such a large EDO for a temperament with relatively low accuracy, and rather use [[golden meantone]] instead, which is simpler and more elegant mathematically. | *[[81edo|81]]: The [[optimal patent val]] for [[meantone]] and some of its higher-limit extentions, but I won't use such a large EDO for a temperament with relatively low accuracy, and rather use [[golden meantone]] instead, which is simpler and more elegant mathematically. | ||