User:Zhenlige/EDO impressions: Difference between revisions
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*[[41edo|41]]: Prime steps in an octave and highly composite steps in a 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 steps in an octave and highly composite steps in a 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|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 coarse EDO won't give anything very notable. | *[[44edo|44]]: Like [[38edo]], doubling a coarse EDO won't give anything very notable. | ||
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*[[53edo|53]]: A stack of [[3/2]]. Almost just [[3/1|3]], accurate [[5-limit]], and decent [[7-limit]]. The smallest EDO that shows the accuracy of [[schismatic]] like [[12edo]] for [[meantone]]. Good for music that emphasizes [[5-limit]]. | *[[53edo|53]]: A stack of [[3/2]]. Almost just [[3/1|3]], accurate [[5-limit]], and decent [[7-limit]]. The smallest EDO that shows the accuracy of [[schismatic]] like [[12edo]] for [[meantone]]. Good for music that emphasizes [[5-limit]]. | ||
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*[[60edo|60]]: [[12edo]] with [[13/1|13]] and [[magic]]-tempered [[5/1|5]] added. | *[[60edo|60]]: [[12edo]] with [[13/1|13]] and [[magic]]-tempered [[5/1|5]] added. 5, [[7/1|7]] and [[11/1|11]] are quite off. Streching can help but it damages the good 13. | ||
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*[[65edo|65]]: A circle of fifths in [[130edo]]. | *[[65edo|65]]: A circle of fifths in [[130edo]]. | ||
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*[[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. | *[[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 | *[[81edo|81]]: The [[optimal patent val]] for [[meantone]] and some of its higher-limit extentions, but like [[50edo]], I will rather use [[golden meantone]] instead. | ||
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*[[84edo|84]]: An alternate [[compton]] EDO besides [[72edo]], with better [[5/1|5]] and [[13/1|13]] with the expense of [[11/1|11]]. It has a sharp tendency instead of 72edo's flat. | *[[84edo|84]]: An alternate [[compton]] EDO besides [[72edo]], with better [[5/1|5]] and [[13/1|13]] with the expense of [[11/1|11]]. It has a sharp tendency instead of 72edo's flat. | ||
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*[[118edo|118]]: The relationship of [[53edo|53]]-118-[[171edo]] for [[schismatic]] is similar to [[12edo|12]]-[[19edo|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 slightly overtempered (outside 5-odd-limit [[diamond tradeoff]]), and 171 and 31 are ideal. So like 19, I won't appreciate it much. | *[[118edo|118]]: The relationship of [[53edo|53]]-118-[[171edo]] for [[schismatic]] is similar to [[12edo|12]]-[[19edo|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 slightly overtempered (outside 5-odd-limit [[diamond tradeoff]]), and 171 and 31 are ideal. So like 19, I won't appreciate it much. | ||
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*[[130edo|130]]: Good [[13-limit]] EDO. It doesn't support [[akea]] and has a flat [[3/1|3]] instead of sharp, unlike smaller 13-limit EDOs. | *[[130edo|130]]: Good [[13-limit]] EDO. It doesn't support [[akea]] and has a flat [[3/1|3]] instead of sharp, unlike smaller 13-limit EDOs. It may need more exploration. | ||
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*[[171edo|171]]: The ultimate EDO for approximating [[7-limit]] JI. It suggests very slight stretching. If you don't need some ridiculous high precision or specific microtemperaments, there is no need to go any further. [[Schismatic]], [[gammic]], [[ennealimmal]] and [[enneadecal]]. Containing a better [[Carlos Gamma]] scale than [[34edo]]. At this size level, EDOs are more like free pitch, rather than either JI or a stable temperament. Ideal for free-pitch-like music that emphasizes 7-limit. | *[[171edo|171]]: The ultimate EDO for approximating [[7-limit]] JI. It suggests very slight stretching. If you don't need some ridiculous high precision or specific microtemperaments, there is no need to go any further. [[Schismatic]], [[gammic]], [[ennealimmal]] and [[enneadecal]]. Containing a better [[Carlos Gamma]] scale than [[34edo]]. At this size level, EDOs are more like free pitch, rather than either JI or a stable temperament. Ideal for free-pitch-like music that emphasizes 7-limit. | ||