User:Zhenlige/EDO impressions: Difference between revisions
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*[[0edo|0]]: A fancy way to say “pitchless”. | *[[0edo|0]]: A fancy way to say “pitchless”. | ||
*[[1edo|1]]: Equivalent to [[2-limit]] JI. Not much about harmony. Possibly useful for a transition between different tunings. | *[[1edo|1]]: Equivalent to [[2-limit]] JI. Not much about harmony. Possibly useful for a transition between different tunings. | ||
*[[2edo|2]]: | *[[2edo|2]]: Equally-divided tritones. | ||
*[[3edo|3]]: 12edo augmented chords. | *[[3edo|3]]: 12edo augmented chords. | ||
*[[4edo|4]]: 12edo diminished seventh 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]]. | *[[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. | ||
*[[6edo|6]]: Incomplete [[12edo]]. | *[[6edo|6]]: Incomplete [[12edo]]. | ||
*... | *[[7edo|7]]: Equalized [[5L 2s|diatonic]] scale. Similar to 5edo. | ||
*[[8edo|8]]: Incomplete [[24edo]]. | |||
*[[9edo|9]]: A subset of [[ennealimmal]]. | *[[9edo|9]]: A subset of [[ennealimmal]]. | ||
*[[10edo|10]]: A stack of [[13/8]]. | *[[10edo|10]]: A stack of [[13/8]]. A subset of [[130edo]] and [[270edo]]. | ||
*[[11edo|11]]: Incomplete [[22edo]]. | *[[11edo|11]]: Incomplete [[22edo]]. | ||
*[[12edo|12]]: It deserves its position. A good tuning for almost all types of music, though 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 exploration. | *[[12edo|12]]: It deserves its position. A good tuning for almost all types of music, though 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 exploration. | ||
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*[[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. A heavily stretched [[Carlos Alpha]] scale. | ||
*... | *... | ||
*[[17edo|17]]: Interesting sharp fifths. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know) | *[[17edo|17]]: A circle of fifths in [[34edo]]. Interesting sharp fifths. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know) | ||
* | *[[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. 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. Good as a subset of [[enneadecal]]. | ||
*[[20edo|20]]: 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 an inconsistent 27 can be used with a 3 or 9? | ||
*... | *... | ||
*[[22edo|22]]: The simplest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The upper bound of a good fifth. | *[[22edo|22]]: The simplest non-meantone EDO with reasonable 5-limit. Good [[superpyth]] and [[porcupine]] tuning. The upper bound of a good fifth. | ||
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*... | *... | ||
*[[26edo|26]]: A stack of [[7/4]]. Incomplete [[130edo]]. | *[[26edo|26]]: A stack of [[7/4]]. Incomplete [[130edo]]. | ||
*[[27edo|27]]: Worse than both 12- and 22edo for 7-limit. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad. | |||
*... | *... | ||
*[[31edo|31]]: Ideal for pure-octave [[meantone]], combining lots of 11-limit extensions in a single tuning. 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. Also [[valentine]]. IMO the best meantone EDO. For other temperaments its flat fifth may be a drawback. | ||
*... | *... | ||
*[[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]]. | ||
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*[[41edo|41]]: Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals equidistantly spaced. Also good [[garibaldi]] and [[neutral]]. | *[[41edo|41]]: Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Good for [[magic]]. The [[Kite guitar]] shows its elegance, with many simple intervals equidistantly spaced. Also good [[garibaldi]] and [[neutral]]. | ||
*... | *... | ||
*[[50edo|50]]: | *[[46edo|46]]: Efficient [[gentle region|neogothic]] EDO. | ||
*... | |||
*[[50edo|50]]: Flatter meantone than [[31edo]], but I usually use [[golden meantone]] (with slight octave stretching) for this range. | |||
*... | *... | ||
*[[53edo|53]]: Almost just [[3/2]], and accurate [[7-limit]]. Purely an approximation of JI and not many efficient temperaments are supported. Good for 5-limit [[schismatic]] with occasional [[garibaldi]] [[7/1|7]]. | *[[53edo|53]]: Almost just [[3/2]], and accurate [[7-limit]]. Purely an approximation of JI and not many efficient temperaments are supported. Good for 5-limit [[schismatic]] with occasional [[garibaldi]] [[7/1|7]]. | ||
Revision as of 05:47, 11 June 2025
In terms of accuracy, assuming harmonic overtone.
- 0: A fancy way to say “pitchless”.
- 1: Equivalent to 2-limit JI. Not much about harmony. Possibly useful for a transition between different tunings.
- 2: Equally-divided tritones.
- 3: 12edo augmented chords.
- 4: 12edo diminished seventh chords.
- 5: Equalized pentatonic scale. Kinda familiar but everything is warped. The first EDO containing an interval that roughly resembles 3/2. Not very noticeable harmonically.
- 6: Incomplete 12edo.
- 7: Equalized diatonic scale. Similar to 5edo.
- 8: Incomplete 24edo.
- 9: A subset of ennealimmal.
- 10: A stack of 13/8. A subset of 130edo and 270edo.
- 11: Incomplete 22edo.
- 12: It deserves its position. A good tuning for almost all types of music, though not perfect. Very excellent 3/2 as well as prime 17 and 19 for its size, but inaccurate 5/4 and worse 7/4. Suitable for symmetric scales. Easy to make accurate NEJIs. Its 2.3.17.19 subgroup really deserves exploration.
- ...
- 15: Better than it seems to be, tho still rough. A heavily stretched Carlos Alpha scale.
- ...
- 17: A circle of fifths in 34edo. Interesting sharp fifths. The fact that its thirds do not approximate any simple ratios well is a pity. (or benefit? I don't know)
- 18: Incomplete 36edo.
- 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. Good as a subset of enneadecal.
- 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?
- ...
- 22: The simplest non-meantone EDO with reasonable 5-limit. Good superpyth and porcupine tuning. The upper bound of a good fifth.
- 23: Incomplete 46edo.
- 24: 12edo with neutral intervals. Good for prime 11. Accurate in subgroup 2.3.11.17.19.
- ...
- 26: A stack of 7/4. Incomplete 130edo.
- 27: Worse than both 12- and 22edo for 7-limit. The fact that 53edo is good indicates that 26- and 27edo are probably bad.
- ...
- 31: Ideal for pure-octave meantone, combining lots of 11-limit extensions in a single tuning. Also valentine. IMO the best meantone EDO. For other temperaments its flat fifth may be a drawback.
- ...
- 34: 17edo with prime 5, but no 7. Also a stretched Carlos Gamma.
- ...
- 36: Good for 2.3.7.13.17.19.23.29 subroup. Otherwise incomplete 72edo.
- 37: Everything but prime 3. Maybe interesting though.
- 38: 19edo with neutrals. Near pure 11/9. The acceptable error of 19edo really becomes a problem at this size.
- ...
- 41: Prime octave and highly composite fifth, opposite from 12edo, thus good for fifth-dividing temperaments. Good for magic. The Kite guitar shows its elegance, with many simple intervals equidistantly spaced. Also good garibaldi and neutral.
- ...
- 46: Efficient neogothic EDO.
- ...
- 50: Flatter meantone than 31edo, but I usually use golden meantone (with slight octave stretching) for this range.
- ...
- 53: Almost just 3/2, and accurate 7-limit. Purely an approximation of JI and not many efficient temperaments are supported. Good for 5-limit schismatic with occasional garibaldi 7.
- ...
- 65: A circle of fifths in 130edo.
- ...
- 72: An excellent extension of 12- and 24edo. Good for miracle. The relative error of primes is within 1/3 steps up to large primes except a few including 13, 53 and 59. Suitable for octave stretching in 17-limit.
- ...
- 77: Good for valentine and accurate boethius.
- ...
- 99: Efficient near-argent EDO. Suggests slight compression. Good for hemififths.
- ...
- 118: The relationship of 53-118-171edo for schismatic is similar to 12-19-31edo for meantone. 53 and 12 are the simplest reasonable EDO with very mildly tempered fifths, 118 and 19 are better over all but a bit overtempered (outside 5-odd-limit diamond tradeoff), and 171 and 31 are ideal. So like 19, I won't use it much.
- ...
- 171: Ideal for approximating 7-limit JI. Good as schismatic, gammic, ennealimmal and enneadecal. 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.
- ...
- 224: like 171 but with a slightly sharper (and closer to just) fifth, worse 7-limit but better 13-limit. Ideal for free-pitch-like music that emphasizes 13-limit.