User:Zhenlige/EDO impressions: Difference between revisions
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*[[22edo|22]]: The simplest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The upper bound of a good fifth. | *[[22edo|22]]: The simplest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The upper bound of a good fifth. | ||
*[[23edo|23]]: Incomplete [[46edo]]. | *[[23edo|23]]: Incomplete [[46edo]]. | ||
*[[24edo|24]]: 12edo with | *[[24edo|24]]: 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]]. Meantone but tuned terribly. Incomplete [[130edo]]. | *[[26edo|26]]: A stack of [[7/4]]. Meantone but tuned terribly. Incomplete [[130edo]]. | ||
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*[[50edo|50]]: Flatter meantone than [[31edo]], but I usually use [[golden meantone]] (with slight octave stretching) for this range. | *[[50edo|50]]: Flatter meantone than [[31edo]], but I usually use [[golden meantone]] (with slight octave stretching) for this range. | ||
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*[[53edo|53]]: Almost just [[3/2]], and accurate [[7-limit]]. | *[[53edo|53]]: Almost just [[3/2]], and accurate [[7-limit]]. Its structure is not very elegant tho. Good for 5-limit [[schismatic]] with occasional [[garibaldi]] [[7/1|7]]. | ||
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*[[65edo|65]]: A circle of fifths in [[130edo]]. | *[[65edo|65]]: A circle of fifths in [[130edo]]. | ||
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*[[72edo|72]]: An excellent extension of 12- and 24edo. Good for [[miracle]]. 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. | *[[72edo|72]]: An excellent extension of 12- and 24edo. Good for [[miracle]]. 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. | ||
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*[[74edo|74]]: [[37edo]] with meantone fifths. 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]] and accurate [[boethius]]. | *[[77edo|77]]: Good for [[valentine]] and accurate [[boethius]]. | ||
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*[[99edo|99]]: Efficient near-[[Logarithmic approximants#Argent temperament|argent]] EDO. Suggests slight compression. Good for [[hemififths]]. | *[[99edo|99]]: Efficient near-[[Logarithmic approximants#Argent temperament|argent]] EDO. Suggests slight compression. Good for [[hemififths]]. | ||
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*[[111edo|111]]: [[37edo]] with [[3/1|3]] added. | |||
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*[[118edo|118]]: The relationship of 53-118-171edo for [[schismatic]] is similar to 12-19-31edo for meantone. 53 and 12 are the simplest reasonable EDO with very mildly tempered fifths, 118 and 19 are better over all but a bit overtempered (outside 5-odd-limit [[diamond tradeoff]]), and 171 and 31 are ideal. So like 19, I won't use it much. | *[[118edo|118]]: The relationship of 53-118-171edo for [[schismatic]] is similar to 12-19-31edo for meantone. 53 and 12 are the simplest reasonable EDO with very mildly tempered fifths, 118 and 19 are better over all but a bit overtempered (outside 5-odd-limit [[diamond tradeoff]]), and 171 and 31 are ideal. So like 19, I won't use it much. | ||