User:Zhenlige/EDO impressions: Difference between revisions
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*[[1edo|1]]: Equivalent to [[2-limit]] JI (unless you want to temper some higher-rank JI subgroups into octaves, which I think nobody will do). Not much about harmony. Possibly useful for a transition between different tunings. | *[[1edo|1]]: Equivalent to [[2-limit]] JI (unless you want to temper some higher-rank JI subgroups into octaves, which I think nobody will do). Not much about harmony. Possibly useful for a transition between different tunings. | ||
*[[2edo|2]]: Half octaves aka symmetric tritones. The key to tritone substitution, although sometimes asymmetric tritones or even non-tritone intervals can also be used. | *[[2edo|2]]: Half octaves aka symmetric tritones. The key to tritone substitution, although sometimes asymmetric tritones or even non-tritone intervals can also be used. | ||
*[[3edo|3]]: 12edo augmented chords. | *[[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. | ||
*[[4edo|4]]: 12edo diminished seventh chords. | *[[4edo|4]]: 12edo diminished seventh chords. | ||
*[[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. | *[[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. | ||
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*[[10edo|10]]: A stack of [[13/8]]. A subset of [[130edo]] and [[270edo]]. | *[[10edo|10]]: A stack of [[13/8]]. A subset of [[130edo]] and [[270edo]]. | ||
*[[11edo|11]]: Incomplete [[22edo]]. | *[[11edo|11]]: Incomplete [[22edo]]. | ||
*[[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. | *[[12edo|12]]: Equalized [[chromatic]] scale. Both [[augmented]] and [[diminished]]. The only reasonable tuning for [[dominant (temperament)|dominant]]. 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, but you can make a [[well temperament]] to make them approximate some. | ||
*... | *... | ||
*[[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. | *[[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 smallest 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. | *[[17edo|17]]: A circle of fifths in [[34edo]]. Interesting sharp fifths. The smallest 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. Only 3-limit seems to be good but still worse than 12. | ||
*[[18edo|18]]: Incomplete [[36edo]]. | *[[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. A stack of [[5/3]]. 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 it is OK for a chord to contain | *[[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. 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. | ||
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*[[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. | *[[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. | ||
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*[[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. | *[[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, making 9 bad. | ||
*... | *... | ||
*[[34edo|34]]: 17edo with prime [[5/1|5]], but no [[7/1|7]]. Also a stretched [[Carlos Gamma]]. | *[[34edo|34]]: 17edo with prime [[5/1|5]], but no [[7/1|7]]. Also a stretched [[Carlos Gamma]]. | ||
*[[35edo|35]]: The largest | *[[35edo|35]]: The largest non-diatonic EDO. | ||
*[[36edo|36]]: Good for 2.3.7.13.17.19.23.29 subroup. Avoid [[5/1|5]] here because it is almost completely missed. Otherwise incomplete 72edo. | *[[36edo|36]]: Good for 2.3.7.13.17.19.23.29 subroup. Avoid [[5/1|5]] here because it is almost completely missed. Otherwise incomplete 72edo. | ||
*[[37edo|37]]: Everything but prime [[3/1|3]]. | *[[37edo|37]]: Everything but prime [[3/1|3]]. | ||