User:Zhenlige/EDO impressions: Difference between revisions

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*[[10edo|10]]: A stack of [[13/8]]. A subset of [[130edo]] and [[270edo]].

*[[11edo|11]]: Incomplete [[22edo]].

*[[12edo|12]]: Equalized [[5L 7s|chromatic]] scale. Both [[augmented (temperament)|augmented]] and [[diminished (temperament)|diminished]]. The smallest EDO with decent [[3-limit|3-]], [[5-limit|5-]] and [[7-limit]]. The only reasonable tuning for the [[dominant (temperament)|dominant]] temperament, ignoring the difference of overall streching. A sharper fifth makes [[garibaldi]] better and a flatter fifth makes [[septimal meantone]] better. The boundary between [[meantone]] and [[schismatic]]. The smallest [[5L 2s|diatonic]] EDO. Efficient at its size. Very excellent [[3/1|3]] as well as good [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/1|5]] and worse [[7/1|7]]. Since its 7 is around twice as off as 5, adding a comma-sized generator gives [[7-limit]] [[compton]], a simple and accurate rank-2 temperament. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup deserves more exploration (something “xenharmonic” but not “microtonal”). Its thirds do not accurately approximate common JI intervals. A [[well temperament]] can make some of them do better. AFAIK 12edo and [[17edo]] are the most suitable EDOs for making well temperaments.

*[[12edo|12]]: Equalized [[5L 7s|chromatic]] scale. Both [[augmented (temperament)|augmented]] and [[diminished (temperament)|diminished]]. The smallest EDO with decent [[3-limit|3-]], [[5-limit|5-]] and [[7-limit]]. The only reasonable tuning for the [[dominant (temperament)|dominant]] temperament, ignoring the difference of overall streching. A sharper fifth makes [[garibaldi]] better and a flatter fifth makes [[septimal meantone]] better. The boundary between [[meantone]] and [[schismatic]]. The smallest [[5L 2s|diatonic]] EDO. Efficient at its size. Very excellent [[3/1|3]] as well as good [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/1|5]] and worse [[7/1|7]]. Since its 7 is around twice as off as 5, adding a comma-sized generator gives [[7-limit]] [[compton]], a simple and accurate rank-2 temperament which is friendly to 12edo-based softwares. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup deserves more exploration (something “xenharmonic” but not “microtonal”). Its thirds do not accurately approximate common JI intervals. A [[well temperament]] can make some of them do better. AFAIK 12edo and [[17edo]] are the most suitable EDOs for making well temperaments.

*...

*[[15edo|15]]: Better than it seems to be, tho still rough. [[Blackwood]] [[augmented (temperament)|augmented]]. A heavily stretched [[Carlos Alpha]] scale. The best you can get with blackwood. I don't know why there are “people fond of” such inaccurate temperaments.

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*[[65edo|65]]: A circle of fifths in [[130edo]].

*...

*[[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]]~~, and some~~ higher limit intervals are also usable~~. [[Compton]] which is useful in 12edo-based programs~~. The only notable [[13-limit]] non-[[akea]] EDO around this size. A powerful tool for modulating quartertones, which can be difficult in 24edo itself~~. Good for [[miracle]]~~. 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.

*...

*[[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.

@@ Line 25: / Line 25: @@
 *[[10edo|10]]: A stack of [[13/8]]. A subset of [[130edo]] and [[270edo]].
 *[[11edo|11]]: Incomplete [[22edo]].
-*[[12edo|12]]: Equalized [[5L 7s|chromatic]] scale. Both [[augmented (temperament)|augmented]] and [[diminished (temperament)|diminished]]. The smallest EDO with decent [[3-limit|3-]], [[5-limit|5-]] and [[7-limit]]. The only reasonable tuning for the [[dominant (temperament)|dominant]] temperament, ignoring the difference of overall streching. A sharper fifth makes [[garibaldi]] better and a flatter fifth makes [[septimal meantone]] better. The boundary between [[meantone]] and [[schismatic]]. The smallest [[5L 2s|diatonic]] EDO. Efficient at its size. Very excellent [[3/1|3]] as well as good [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/1|5]] and worse [[7/1|7]]. Since its 7 is around twice as off as 5, adding a comma-sized generator gives [[7-limit]] [[compton]], a simple and accurate rank-2 temperament. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup deserves more exploration (something “xenharmonic” but not “microtonal”). Its thirds do not accurately approximate common JI intervals. A [[well temperament]] can make some of them do better. AFAIK 12edo and [[17edo]] are the most suitable EDOs for making well temperaments.
+*[[12edo|12]]: Equalized [[5L 7s|chromatic]] scale. Both [[augmented (temperament)|augmented]] and [[diminished (temperament)|diminished]]. The smallest EDO with decent [[3-limit|3-]], [[5-limit|5-]] and [[7-limit]]. The only reasonable tuning for the [[dominant (temperament)|dominant]] temperament, ignoring the difference of overall streching. A sharper fifth makes [[garibaldi]] better and a flatter fifth makes [[septimal meantone]] better. The boundary between [[meantone]] and [[schismatic]]. The smallest [[5L 2s|diatonic]] EDO. Efficient at its size. Very excellent [[3/1|3]] as well as good [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/1|5]] and worse [[7/1|7]]. Since its 7 is around twice as off as 5, adding a comma-sized generator gives [[7-limit]] [[compton]], a simple and accurate rank-2 temperament which is friendly to 12edo-based softwares. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup deserves more exploration (something “xenharmonic” but not “microtonal”). Its thirds do not accurately approximate common JI intervals. A [[well temperament]] can make some of them do better. AFAIK 12edo and [[17edo]] are the most suitable EDOs for making well temperaments.
 *...
 *[[15edo|15]]: Better than it seems to be, tho still rough. [[Blackwood]] [[augmented (temperament)|augmented]]. A heavily stretched [[Carlos Alpha]] scale. The best you can get with blackwood. I don't know why there are “people fond of” such inaccurate temperaments.
@@ Line 66: / Line 66: @@
 *[[65edo|65]]: A circle of fifths in [[130edo]].
 *...
-*[[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]], and some higher limit intervals are also usable. [[Compton]] which is useful in 12edo-based programs. The only notable [[13-limit]] non-[[akea]] EDO around this size. A powerful tool for modulating quartertones, which can be difficult in 24edo itself. Good for [[miracle]]. 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.
 *...
 *[[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.