User:Zhenlige/EDO impressions: Difference between revisions

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*[[0edo|0]]: A fancy way to say “no melody”. The only tuning of the [[Single-pitch tuning|Om]] temperament. Important in theory, useless in practice.

*[[1edo|1]]: Equivalent to [[2-limit]] JI, unless you want to temper some other JI intervals into octaves. Not much about ~~harmony. Possibly useful for a transition between different tunings~~.

*[[1edo|1]]: [[2/1|Octaves]]. Equivalent to [[2-limit]] JI, unless you want to temper some other JI intervals into octaves. Not much to talk about.

*[[2edo|2]]: [[sqrt(2)|Half octaves]] aka symmetric [[tritone]]s. Some notable approximations are [[7/5]], [[17/12]] and [[99/70]]. ~~The key to tritone substitution, although sometimes asymmetric tritones or even non~~-~~tritone intervals can also be used~~.

*[[2edo|2]]: [[sqrt(2)|Half octaves]] aka symmetric [[tritone]]s. The key to tritone substitution, although sometimes asymmetric tritones or even non-tritone intervals can also be used. Some notable approximations are [[7/5]], [[17/12]] and [[99/70]], the final one giving [[kalismic temperaments|kalismic]]. 2n-edos within 1000 that do not support kalismic are probably bad in [[11-limit]].

*[[3edo|3]]: [[12edo]] augmented ~~chords~~. Treating its steps as [[63/50]] gives [[landscape]]. 3n-edos within 1000 that do not support landscape are probably bad in [[7-limit]].

*[[3edo|3]]: [[12edo]] major thirds. 2.5 subgroup [[augmented (temperament)|augmented]]. The smallest EDO with decent 2.5 subgroup. Treating its steps as [[63/50]] gives [[landscape]]. 3n-edos within 1000 that do not support landscape are probably bad in [[7-limit]].

*[[4edo|4]]: [[12edo]] ~~diminished seventh chords~~.

*[[4edo|4]]: [[12edo]] minor thirds.

*[[5edo|5]]: Equalized [[2L 3s|pentatonic]] scale. [[3-limit]] [[blackwood]]. Kinda familiar but everything is warped. To me as a Chinese, it sounds like out-of-tone traditional Chinese music. The smallest EDO that roughly represents [[3-limit]] or 2.3.7 subgroup.

*[[6edo|6]]: ~~Incomplete~~ [[12edo]]. Also a heavily stretched [[didacus]] chain.

*[[6edo|6]]: [[12edo]] whole tones. Incomplete 12edo. Also a heavily stretched [[didacus]] chain.

*[[7edo|7]]: Equalized [[5L 2s|diatonic]] scale. 3-limit [[whitewood]]. It sounds like out-of-tone [[3L 4s|neutral scale]] music. The smallest EDO that roughly represents [[5-limit]].

*[[8edo|8]]: Incomplete [[24edo]].

*[[9edo|9]]: A subset of [[ennealimmal]].

*[[9edo|9]]: A stack of [[7/6]]. A subset of [[ennealimmal]].

*[[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 ~~that gives~~ decent [[7-limit]]. The only reasonable tuning for the [[dominant (temperament)|dominant]] temperament ignoring 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 prime [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/1|5]] and worse [[7/1|7]]. 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.

*[[12edo|12]]: Equalized [[5L 7s|chromatic]] scale. Both [[augmented (temperament)|augmented]] and [[diminished (temperament)|diminished]]. The smallest edo with decent [[7-limit]]. The only reasonable tuning for the [[dominant (temperament)|dominant]] temperament ignoring 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 prime [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/1|5]] and worse [[7/1|7]]. 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.

*...

*[[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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*[[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?

*...

*[[22edo|22]]: The smallest non-meantone EDO with ~~reasonable~~ [[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.

*[[22edo|22]]: The smallest non-meantone EDO with decent [[5-limit]]. The smallest EDO with decent [[11-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.

*[[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.

*...

*[[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]].

*[[27edo|27]]: ~~A stack of [[7/6]].~~ Worse than both [[12edo]] and [[22edo]] for [[5-limit]]. ~~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]] to make it a true [[7-limit]] EDO, and [[270edo]] is excellent. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.

*[[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. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.

*[[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]].

@@ Line 12: / Line 12: @@
 *[[0edo|0]]: A fancy way to say “no melody”. The only tuning of the [[Single-pitch tuning|Om]] temperament. Important in theory, useless in practice.
-*[[1edo|1]]: Equivalent to [[2-limit]] JI, unless you want to temper some other JI intervals into octaves. Not much about harmony. Possibly useful for a transition between different tunings.
+*[[1edo|1]]: [[2/1|Octaves]]. Equivalent to [[2-limit]] JI, unless you want to temper some other JI intervals into octaves. Not much to talk about.
-*[[2edo|2]]: [[sqrt(2)|Half octaves]] aka symmetric [[tritone]]s. Some notable approximations are [[7/5]], [[17/12]] and [[99/70]]. The key to tritone substitution, although sometimes asymmetric tritones or even non-tritone intervals can also be used.
+*[[2edo|2]]: [[sqrt(2)|Half octaves]] aka symmetric [[tritone]]s. The key to tritone substitution, although sometimes asymmetric tritones or even non-tritone intervals can also be used. Some notable approximations are [[7/5]], [[17/12]] and [[99/70]], the final one giving [[kalismic temperaments|kalismic]]. 2n-edos within 1000 that do not support kalismic are probably bad in [[11-limit]].
-*[[3edo|3]]: [[12edo]] augmented chords. Treating its steps as [[63/50]] gives [[landscape]]. 3n-edos within 1000 that do not support landscape are probably bad in [[7-limit]].
+*[[3edo|3]]: [[12edo]] major thirds. 2.5 subgroup [[augmented (temperament)|augmented]]. The smallest EDO with decent 2.5 subgroup. Treating its steps as [[63/50]] gives [[landscape]]. 3n-edos within 1000 that do not support landscape are probably bad in [[7-limit]].
-*[[4edo|4]]: [[12edo]] diminished seventh chords.
+*[[4edo|4]]: [[12edo]] minor thirds.
 *[[5edo|5]]: Equalized [[2L 3s|pentatonic]] scale. [[3-limit]] [[blackwood]]. Kinda familiar but everything is warped. To me as a Chinese, it sounds like out-of-tone traditional Chinese music. The smallest EDO that roughly represents [[3-limit]] or 2.3.7 subgroup.
-*[[6edo|6]]: Incomplete [[12edo]]. Also a heavily stretched [[didacus]] chain.
+*[[6edo|6]]: [[12edo]] whole tones. Incomplete 12edo. Also a heavily stretched [[didacus]] chain.
 *[[7edo|7]]: Equalized [[5L 2s|diatonic]] scale. 3-limit [[whitewood]]. It sounds like out-of-tone [[3L 4s|neutral scale]] music. The smallest EDO that roughly represents [[5-limit]].
 *[[8edo|8]]: Incomplete [[24edo]].
-*[[9edo|9]]: A subset of [[ennealimmal]].
+*[[9edo|9]]: A stack of [[7/6]]. A subset of [[ennealimmal]].
 *[[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 that gives decent [[7-limit]]. The only reasonable tuning for the [[dominant (temperament)|dominant]] temperament ignoring 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 prime [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/1|5]] and worse [[7/1|7]]. 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.
+*[[12edo|12]]: Equalized [[5L 7s|chromatic]] scale. Both [[augmented (temperament)|augmented]] and [[diminished (temperament)|diminished]]. The smallest edo with decent [[7-limit]]. The only reasonable tuning for the [[dominant (temperament)|dominant]] temperament ignoring 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 prime [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/1|5]] and worse [[7/1|7]]. 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.
 *...
 *[[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 32: / Line 32: @@
 *[[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?
 *...
-*[[22edo|22]]: The smallest non-meantone EDO with reasonable [[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.
+*[[22edo|22]]: The smallest non-meantone EDO with decent [[5-limit]]. The smallest EDO with decent [[11-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.
 *[[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.
 *...
 *[[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]].
-*[[27edo|27]]: A stack of [[7/6]]. Worse than both [[12edo]] and [[22edo]] for [[5-limit]]. 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]] to make it a true [[7-limit]] EDO, and [[270edo]] is excellent. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.
+*[[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. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.
 *[[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]].