User:Zhenlige/EDO impressions: Difference between revisions

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

*[[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.

*[[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]].

*[[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]]. Other intervals suck. Meantone but tuned terribly. Incomplete [[130edo]].

*[[27edo|27]]: A stack of [[7/6]]. 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. Compared to 22edo, it is like fixing 7 by ruining 5 and partly 3. There are beatings here and there. It really needs compression. The fact that [[53edo]] is good indicates that 26- and 27edo are probably bad.

*[[34edo|34]]: 17edo with prime [[5/1|5]], but no [[7/1|7]]. Also a stretched [[Carlos Gamma]].

*[[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. I have no idea how other similar-sized EDOs (namely 53 and 72) can be applied on a fretted string instrument. It's a pity that its [[5/1|5]] is not very good. Also [[garibaldi]] and [[neutral]].

*[[72edo|72]]: The ultimate extension of 12- and 24edo. A powerful tool for modulating quartertones, whis is difficult in [[24edo]] itself. 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.

*[[77edo|77]]: Good for [[valentine]] and accurate [[boethius]].

*[[87edo|87]]: Good [[mystery]] EDO. Useful for high-limit JI.

*[[171edo|171]]: The ultimate EDO for approximating [[7-limit]] JI. If you don't need some ridiculous high precision, there is no need to go any further. 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. For 11-limit maybe [[342edo|doubling]] is a good choice, and for 13-limit [[684edo|quadrupling]].