User:Zhenlige/EDO impressions: Difference between revisions

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*[[3edo|3]]: 12edo augmented chords.

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

*[[5edo|5]]: Equalized [[2L 3s|pentatonic]] scale. Kinda familiar but everything is warped. The ~~first~~ EDO containing an interval that roughly resembles [[3/2]]. Not very noticeable harmonically.

*[[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 containing an interval that roughly resembles [[3/2]]. Not very noticeable harmonically.

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

*[[7edo|7]]: Equalized [[5L 2s|diatonic]] scale. Similar to 5edo.

*[[7edo|7]]: Equalized [[5L 2s|diatonic]] scale. 3-limit [[whitewood]]. Similar to 5edo. It sounds like out-of-tone [[3L 4s|neutral scale]] music.

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

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

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

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

*[[12edo|12]]: Equalized [[chromatic]] scale. The boundary between [[meantone]] and [[schismatic]]. It deserves its position. A good tuning for almost all types of music, tho sometimes not perfect. Very excellent [[3/2]] as well as prime [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/4]] and worse [[7/4]]. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup really deserves more exploration (something “xenharmonic” but not “microtonal”).

*[[12edo|12]]: Equalized [[chromatic]] scale. The boundary between [[meantone]] and [[schismatic]]. The smallest [[5L 2s|diatonic]] EDO. It deserves its position. A good tuning for almost all types of music, tho sometimes not perfect. 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 really deserves more exploration (something “xenharmonic” but not “microtonal”). Its thirds do not accurately approximate common JI intervals.

*...

*[[15edo|15]]: Better than it seems to be, tho still rough. A heavily stretched [[Carlos Alpha]] scale.

*[[15edo|15]]: Better than it seems to be, tho still rough. [[Blackwood]] [[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.

*...

*[[17edo|17]]: A circle of fifths in [[34edo]]. Interesting sharp fifths. The boundary between neogothic and superpyth. ~~The fact that~~ its thirds do not approximate any simple ratios well ~~is a pity~~. ~~(or benefit? I don't know)~~ I don't know how to write harmonies here.

*[[17edo|17]]: A circle of fifths in [[34edo]]. Interesting sharp fifths. The smallestt diatonic EDO with neutral intervals. The boundary between neogothic and superpyth. Like 12edo, its thirds do not approximate any simple ratios well. I don't know how to write harmonies here.

*[[18edo|18]]: Incomplete [[36edo]].

*[[19edo|19]]: Very different tradeoffs from 12edo. Usable but imperfect for many temperaments. [[Meantone]] or [[magic]], but with a too flat fifth. Strangely large minor 2nds. Also a compressed [[Carlos Beta]]. For meantone [[31edo]] is more preferable, and for magic [[41edo]]. The lower bound of a good fifth. It benefits from stretching. Good as a subset of [[enneadecal]].

*[[19edo|19]]: Very different tradeoffs from 12edo. Usable but imperfect for many temperaments. [[Meantone]] or [[magic]], but with a too flat fifth. Strangely large minor 2nds. Also a compressed [[Carlos Beta]]. For meantone [[31edo]] is more preferable, and for magic [[41edo]]. The lower bound of a good fifth. It benefits from stretching. A stack of [[5/3]]. Good as a subset of [[enneadecal]].

*[[20edo|20]]: The fact that [[41edo]] is good indicates that 20- and 21edo are probably bad. Does anyone really think ~~an inconsistent 27 can be used with~~ a ~~3 or~~ 9?

*[[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 ~9 and ~27 which are inconsistent to each other? It will break the regular temperament structure.

*...

*[[22edo|22]]: The ~~simplest~~ non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The only reasonable superpyth EDO. The upper bound of a good fifth.

*[[22edo|22]]: The smallest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The only reasonable superpyth EDO. The upper bound of a good fifth.

*[[23edo|23]]: Incomplete [[46edo]].

*[[23edo|23]]: Incomplete [[46edo]]. The largest EDO with no diatonic, blackwood or whitewood fifth.

*[[24edo|24]]: What many 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]]. Meantone but tuned terribly. Incomplete [[130edo]].

*[[26edo|26]]: A stack of [[7/4]]. Other intervals suck. Meantone but tuned terribly. Incomplete [[130edo]].

*[[27edo|27]]: Worse than both 12- and 22edo for 5-limit. 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. Use [[108edo]] to make it really a 7-limit EDO, and [[270edo]] is excellent. When I hear its ~[[10:12:15]] and ~[[6:7:9]] chord I feel the fifth is obviously off. I have listened to both 22edo and 27edo and I feel the former is better. It is distinct in 7-limit tho, but that is like thinking 0.1 is better represented as 1 than 0. There are beatings here and there. It really needs compression. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.

*...

*[[28edo|28]]: [[Whitewood]] [[diminished]]. Kinda opposite from [[15edo]]. The best you can get with [[whitewood]].

*[[29edo|29]]: A circle of fifths in [[mystery]], which supports [[pele]].

*[[29edo|29]]: A circle of fifths in [[mystery]], which supports [[pele]]. The smallest EDO with a better fifth than 12edo. Not so useful on its own.

*...

*[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. The meantone flat fifth makes its neutral thirds close to [[11/9]] (tho there is the JI subgroup problem since 11 and 9 themselves are not so close). Also [[valentine]] and [[miracle]]. IMO the best meantone EDO. For other temperaments its flat fifth may be a drawback.

@@ Line 11: / Line 11: @@
 *[[3edo|3]]: 12edo augmented chords.
 *[[4edo|4]]: 12edo diminished seventh chords.
-*[[5edo|5]]: Equalized [[2L 3s|pentatonic]] scale. Kinda familiar but everything is warped. The first EDO containing an interval that roughly resembles [[3/2]]. Not very noticeable harmonically.
+*[[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 containing an interval that roughly resembles [[3/2]]. Not very noticeable harmonically.
 *[[6edo|6]]: Incomplete [[12edo]]. Also a heavily stretched [[didacus]] chain.
-*[[7edo|7]]: Equalized [[5L 2s|diatonic]] scale. Similar to 5edo.
+*[[7edo|7]]: Equalized [[5L 2s|diatonic]] scale. 3-limit [[whitewood]]. Similar to 5edo. It sounds like out-of-tone [[3L 4s|neutral scale]] music.
 *[[8edo|8]]: Incomplete [[24edo]].
 *[[9edo|9]]: A subset of [[ennealimmal]].
 *[[10edo|10]]: A stack of [[13/8]]. A subset of [[130edo]] and [[270edo]].
 *[[11edo|11]]: Incomplete [[22edo]].
-*[[12edo|12]]: Equalized [[chromatic]] scale. The boundary between [[meantone]] and [[schismatic]]. It deserves its position. A good tuning for almost all types of music, tho sometimes not perfect. Very excellent [[3/2]] as well as prime [[17/1|17]] and [[19/1|19]] for its size, but inaccurate [[5/4]] and worse [[7/4]]. Suitable for symmetric scales. Easy to make [[../12neji|accurate NEJIs]]. Its 2.3.17.19 subgroup really deserves more exploration (something “xenharmonic” but not “microtonal”).
+*[[12edo|12]]: Equalized [[chromatic]] scale. The boundary between [[meantone]] and [[schismatic]]. The smallest [[5L 2s|diatonic]] EDO. It deserves its position. A good tuning for almost all types of music, tho sometimes not perfect. 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 really deserves more exploration (something “xenharmonic” but not “microtonal”). Its thirds do not accurately approximate common JI intervals.
 *...
-*[[15edo|15]]: Better than it seems to be, tho still rough. A heavily stretched [[Carlos Alpha]] scale.
+*[[15edo|15]]: Better than it seems to be, tho still rough. [[Blackwood]] [[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.
 *...
-*[[17edo|17]]: A circle of fifths in [[34edo]]. Interesting sharp fifths. The boundary between neogothic and superpyth. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know) I don't know how to write harmonies here.
+*[[17edo|17]]: A circle of fifths in [[34edo]]. Interesting sharp fifths. The smallestt diatonic EDO with neutral intervals. The boundary between neogothic and superpyth. Like 12edo, its thirds do not approximate any simple ratios well. I don't know how to write harmonies here.
 *[[18edo|18]]: Incomplete [[36edo]].
-*[[19edo|19]]: Very different tradeoffs from 12edo. Usable but imperfect for many temperaments. [[Meantone]] or [[magic]], but with a too flat fifth. Strangely large minor 2nds. Also a compressed [[Carlos Beta]]. For meantone [[31edo]] is more preferable, and for magic [[41edo]]. The lower bound of a good fifth. It benefits from stretching. Good as a subset of [[enneadecal]].
+*[[19edo|19]]: Very different tradeoffs from 12edo. Usable but imperfect for many temperaments. [[Meantone]] or [[magic]], but with a too flat fifth. Strangely large minor 2nds. Also a compressed [[Carlos Beta]]. For meantone [[31edo]] is more preferable, and for magic [[41edo]]. The lower bound of a good fifth. It benefits from stretching. A stack of [[5/3]]. Good as a subset of [[enneadecal]].
-*[[20edo|20]]: The fact that [[41edo]] is good indicates that 20- and 21edo are probably bad. Does anyone really think an inconsistent 27 can be used with a 3 or 9?
+*[[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 ~9 and ~27 which are inconsistent to each other? It will break the regular temperament structure.
 *...
-*[[22edo|22]]: The simplest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The only reasonable superpyth EDO. The upper bound of a good fifth.
+*[[22edo|22]]: The smallest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The only reasonable superpyth EDO. The upper bound of a good fifth.
-*[[23edo|23]]: Incomplete [[46edo]].
+*[[23edo|23]]: Incomplete [[46edo]]. The largest EDO with no diatonic, blackwood or whitewood fifth.
 *[[24edo|24]]: What many 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]]. Meantone but tuned terribly. Incomplete [[130edo]].
+*[[26edo|26]]: A stack of [[7/4]]. Other intervals suck. Meantone but tuned terribly. Incomplete [[130edo]].
 *[[27edo|27]]: Worse than both 12- and 22edo for 5-limit. 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. Use [[108edo]] to make it really a 7-limit EDO, and [[270edo]] is excellent. When I hear its ~[[10:12:15]] and ~[[6:7:9]] chord I feel the fifth is obviously off. I have listened to both 22edo and 27edo and I feel the former is better. It is distinct in 7-limit tho, but that is like thinking 0.1 is better represented as 1 than 0. There are beatings here and there. It really needs compression. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.
-*...
+*[[28edo|28]]: [[Whitewood]] [[diminished]]. Kinda opposite from [[15edo]]. The best you can get with [[whitewood]].
-*[[29edo|29]]: A circle of fifths in [[mystery]], which supports [[pele]].
+*[[29edo|29]]: A circle of fifths in [[mystery]], which supports [[pele]]. The smallest EDO with a better fifth than 12edo. Not so useful on its own.
 *...
 *[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. The meantone flat fifth makes its neutral thirds close to [[11/9]] (tho there is the JI subgroup problem since 11 and 9 themselves are not so close). Also [[valentine]] and [[miracle]]. IMO the best meantone EDO. For other temperaments its flat fifth may be a drawback.