Collection of EDO impressions: Difference between revisions

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: '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes.

: '''Zhenlige:''' 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.

: '''Eufalesio:''' Octaves. Extremely boring to use still, as octaves are hyperconsonant, so there is no inertia. You really have to get creative to make something cool in this. Ligeti pulled it off. But I won't care to try. F

== [[2edo]] ==

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: '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes.

: '''Zhenlige:''' Half octaves aka symmetric tritones. The key to tritone substitution, although sometimes asymmetric tritones or even non-tritone intervals can also be used.

: '''Eufalesio:''' Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. D

== [[3edo]] ==

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: '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes.

: '''Zhenlige:''' 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.

: '''Eufalesio''': Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. Though 3edo has a surprisingly accurate 5. C

== [[4edo]] ==

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: '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes.

: '''Zhenlige:''' 12edo diminished seventh chords.

: '''Eufalesio''': Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. D

== [[5edo]] ==

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: '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes.

: '''Zhenlige:''' 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.

: '''Eufalesio:''' The first usable edo and the first edo to have any semblance of a perfect fifth. It features an extremely simplified 2.3.7, forming a consistent circle of 8/7 and 3/2. Due to its extremely coarse grain, it is extremely simple to use, as each step is large enough that no cluttering will ever occur. It is horrible in all other limits... well... except... 2.3.7.37, but who here cares about that –Also due to its extremely coarse grain, you can play anything, short of bashing keys and sitting on the keyboard, and it will sound good. This is because the edostep is so large that it doesn't cause audible cluttering... unless you're playing too low. The sonic profile of this edo is immediately recognizable. – It greatly benefits from non-harmonic timbres, or bell-like sounds, much like that of slendro. Its melodic capabilities are basically the same as that of all pentatonic scales, which is to say: great! It would be wrong to only call 5edo innacurate. A better descriptor would be: coarse. The coarsest, in fact. And due to the fact that it is so coarse, but it is still quite relatively accurate, it is a great edo. A

== [[6edo]] ==

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: '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes.

: '''Zhenlige:''' Incomplete [[12edo]]. Also a heavily stretched [[didacus]] chain.

: '''Eufalesio''': Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. D

== [[7edo]] ==

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: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".

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

: '''Eufalesio:''' The second usable edo. Its fifth is a tad flat, but usable, and it is also the first edo to feature a heptatonic scale, obviously... an equalized diatonic. The edostep is now small enough so that cluttering ''can'' occur, but still somewhat bashable. The sonic profile is also immediately recognizable. While the 5-limit is not there, the melodic coolness you can pull of with this coarse edo are nothing to scoff at. C, not for accuracy, but for ''cool''.

== [[8edo]] ==

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: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".

: '''Zhenlige:''' Incomplete [[24edo]].

: '''Eufalesio:''' Useless. FF

== [[9edo]] ==

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: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to timbre to prevent it sounding "out of tune".

: '''Zhenlige:''' A subset of [[ennealimmal]].

: '''Eufalesio:''' Potentially useful, but I don't really like it. D

== [[10edo]] ==

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: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".

: '''Zhenlige:''' Incomplete [[22edo]].

: '''Eufalesio:''' Useless. Use 22edo instead. FF

== [[12edo]] ==

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: '''Budjarn Lambeth:''' An excellent [[5-limit]] tuning. It is simple and stays out of the composer's way for two reasons: it works with an impressively wide variety of timbres, and it avoids [[wolf interval]]s better than any larger tuning. I believe this elegant simplicity is the reason for its popularity.

: '''Zhenlige:''' 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 [[User:Zhenlige/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 some of them do.

: '''Eufalesio:''' It's easily one of the best edos. 12edo is many, many things all at once, and I would say that its place in mainstream music is well earned. It's the first edo that can deal with the 5-limit at all, and it also has an incredibly accurate fifth for its size, making it the only temperament that is both meantone and pythagorean at the same time... Super practical, and very easy to conceptualize. S

== [[13edo]] ==

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: '''Fumica:''' Every other step of 26edo. Like 11edo, quintal harmony can be used. Unlike 11edo, the intonation sucks. D-tier.

: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".

: '''Eufalesio:''' Useless. FF

== [[14edo]] ==

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: '''Fumica:''' I heard it too that this was the "most dissonant edo". The intonation surely has a lot of spice. Supports [[squares]] and [[godzilla]], making it important in theory. Perhaps works better as an interval category scheme than as sound to be listened to. B-tier.

: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".

: '''Eufalesio:''' Useless. FF

== [[15edo]] ==

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: '''Vector:''' Definitive proof that a fifth doesn't need to be a 3/2. (TBA)

: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".

: '''Eufalesio:''' Potentially useful, but I don't really like it. D

== [[17edo]] ==

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: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".

: '''Zhenlige:''' 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.

: '''Eufalesio''': Despite being the next edo with a usable fifth, the fact that it tempers the interval whose edostep best approximates it is the ultimate irony. I like the slightly sharp fifths and neo-gothic feel, but the lack of 5-limit is a hole I can't easily live without, and no matter how good it is on other limits (and it is ''great''), the lack of 5 is sad. C

== [[18edo]] ==

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: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".

: '''Zhenlige:''' Incomplete [[36edo]].

: '''Eufalesio:''' Useless. FF

== [[19edo]] ==

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: '''Budjarn Lambeth:''' The smallest equal tuning that approximates the entire [[43-limit]]. Its melodic similarity to 12edo makes it easier to find your bearings, but harder to break out of that diatonic comfort zone and explore all those intricate high limit harmonies it has to offer.

: '''Zhenlige:''' Very different tradeoffs from 12edo. Usable but imperfect for many temperaments. [[Meantone]] or [[magic]], but with a too flat fifth. Strangely large minor 2nds. A compressed [[Carlos Beta]] scale. 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]].

: '''Eufalesio:''' The next most easily accessible edo, and one that offers a change in perspective. It is meantone just like 12edo, but it has a completely different sonic profile, due to the flatter 5-limit, which I find very enjoyable. The near just minor thirds are definitely something to remark, though not as discernible as it is in its supersets. Great stuff! A

== [[20edo]] ==

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: '''Budjarn Lambeth:''' It has a lot of [[consonant]] intervals available, but they're mostly all very different to anything in 12edo. This makes it intimidating at first, but rewards exploration, ideal for composers looking for a wild world of new microtonal colours, without sounding as "sour" as some smaller EDOs do.

: '''Zhenlige:''' 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?

: '''Eufalesio:''' Useless. FF

== [[21edo]] ==

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: '''Fumica:''' 14edo but worse. F-tier.

: '''Budjarn Lambeth:''' If you like the melodic shapes of 7edo, but want some sweeter harmonies and smaller step sizes to mix them with, 21edo is ideal for that.

: '''Eufalesio:''' Useless. FF

== [[22edo]] ==

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: '''Budjarn Lambeth:''' It is the first EDO bigger than 12 which sounds equally as "in-tune" as 12, in my opinion. Though it does have some [[wolf interval]]s which can startle new composers; with experience one learns how to approach those. Its [[superpyth]] and [[pajara]] scales offer a familiar-but-not-too-familiar melodic structure where prior 12edo training is useful, but where exploration beyond it is rewarded with gorgeous new colours. In this sense, it offers the strengths of both 19 and 20 without the drawbacks of either.

: '''Zhenlige:''' 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.

: '''Eufalesio:''' While the change in perspective that 19edo offers is mixed with familiarity, 22edo is an entirely different beast. It features a very exaggerated non-meantone 5-limit, making it the ultimate porcupine, which is not a temperament known for its accuracy, but it's cool! It also supports magic, featuring a flatter 5, which I enjoy, though the incredibly sharp 6/5 is a tad excessive. – The 7-limit structure inside the diatonic scale is something very sui generis, though it's 11-limit is kinda meh, but what can I say, it's the first edo to be consistent in the 11-odd-limit! C, not for accuracy, but for ''cool''.

== [[23edo]] ==

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: '''Budjarn Lambeth:''' A great EDO to begin experimenting with [[octave stretching]] and squishing. With pure octaves, it sounds out of tune, but stretch it by about 10 [[cents]], and you get access to the full array of pretty no-13s [[59-limit]] harmonies. ''Compress'' it by about 10 cents, and you instead get access to the full array of no-19s [[37-limit]] harmonies. Both tunings punch far above their weight by having lots of consonances in only 23 notes. Experiment with both the stretched and squished versions of 23edo, to get a feeling for how stretching or squishing a scale can shift its underlying harmonies dramatically while preserving its melodic shape.

: '''Zhenlige:''' Incomplete [[46edo]]. The largest EDO without a diatonic, blackwood or whitewood fifth.

: '''Eufalesio:''' Useless. FF

== [[24edo]] ==

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: '''Budjarn Lambeth:''' Along with [[36edo]], it is one of the two possible ways to extend 12edo while preserving equal spacing, and keeping the number of notes somewhat manageable. 36edo is ideal if you want to add intervals involving the 7th harmonic into 12edo, while 24edo is ideal if you want to add intervals involving the 11th harmonic. Comparing and contrasting 24edo and 36edo can help you get a feel for the difference between the "vibe" of the 11th harmonic, and the "vibe" of the 7th harmonic. I recommend dipping your toes into each of the two. — Try using familar 12edo intervals in lower registers of your instrument(s)/mix, while mixing in some of the strange new 24edo intervals in the higher registers. Thus will mimic the shape of the [[harmonic series]] and sound nice and glittery.

: '''Zhenlige:''' What some non-microtonalists think microtonality is. 12edo with neutrals. Good for prime [[11/1|11]]. Accurate in subgroup 2.3.11.17.19.

: '''Eufalesio:''' Entry-level xenharmonic edo. A huge improvement to the 2.3.5.11, but nothing much more to remark. Probably the most common xenharmonic edo among non xen spaces, and for good reason. We've all used it. It's trivial to build it. – Still, some ensembles fail at playing quartertones accurately (singers are the worst, some can even fail to sing 12edo accurately, which is a feat...) C

== [[25edo]] ==

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: '''Deja Igliashon:''' 25edo might be "the one that got away" for me. It bears a lot of similarities to [[23edo]] by virtue of being half the notes of a large very-accurate ET (50edo), having half of the nice 2nds, 3rds, 6ths, and 7ths, but not the nice 4ths and 5ths. Lots of nice harmony to be had, but no 5-limit triads (or at least, none that are very nice). I've thought about having a [[guitar]] made in 25edo multiple times but always ended up going with something else for some reason. Anyway, it's really really good for 8:9:10:14:17:19:23:25 chords, as well as 11:12:13:15:21:27 chords, but you can't put the two together unless you are in 50edo.

: '''Fumica:''' Potentially useful as every other step of 50edo. D-tier.

: '''Eufalesio:''' Useless. FF

== [[26edo]] ==

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: '''Fumica:''' Just as [[19edo]] is the point separating [[meantone]] and [[flattone]], this is the point separating flattone and [[flattertone|a meantone extension that implies an even flatter fifth]]. Therefore it should share all the advantages of 12edo and 19edo, at least theoretically, that is if not for its poor intonation in the [[5-limit]]. C-tier.

: '''Zhenlige:''' 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 but tuned terribly. Incomplete [[130edo]].

: '''Eufalesio:''' Interesting, but unjustifiably inaccurate for me. D

== [[27edo]] ==

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: '''Fumica:''' Potentially useful as every other step of [[56edo]]. D-tier.

: '''Zhenlige:''' [[Whitewood]] [[diminished]]. Kinda opposite from [[15edo]]. The best you can get with [[whitewood]].

: '''Eufalesio:''' The hyper-accurate 5/4 alone makes it useless. FF

== [[29edo]] ==

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: '''Fumica:''' Potentially useful as every other step of [[60edo]]. D-tier.

: '''Budjarn Lambeth:''' The most simple [[dual-fifth]] edo, but not as "in-tune" as others.

: '''Eufalesio:''' Useless. FF

== [[31edo]] ==

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: '''Fumica:''' This is a great edo. Too great it's a little unfun to work with. It has a tuning profile close to what I consider the [[optimal tuning]] of meantone, and [[migration]], the [[meantone]] [[extension]] that maps harmonic 11 to the semi-augmented fourth, works almost perfectly in this system. [[Octave stretch]] gives better intonation. A-tier.

: '''Zhenlige:''' 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.

: '''Eufalesio:''' The best meantone edo. Manageable grain, incredible 11-limit. You can't get more juice out of meantone without diminishing returns. From this point on, it becomes hard to justify using a finer meantone gamut. SSS

== [[32edo]] ==

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: '''Yourmusic Productions:''' Like all pure powers of 2, unusually bad for it's size.

: '''Fumica:''' 27edo but worse. F-tier.

: '''Eufalesio:''' Useless. FF

== [[33edo]] ==

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: '''Budjarn Lambeth:''' A very good [[dual-fifth]] edo.

: ''Zhenlige:''' The largest non-diatonic EDO.

: '''Eufalesio:''' Useless. FF

== [[36edo]] ==

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== [[40edo]] ==

: '''Bozu:''' [[Amphipent]] [[diminished (temperament)|diminished]]. Can't really find a good use for this one.

: '''Eufalesio:''' Useless. FF

== [[41edo]] ==

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: '''Fumica:''' The first of the five essential comma-level edos, and the first edo to achieve [[9-odd-limit]] [[distinction]] and [[consistency]]. This is most significant for providing three flavors for each [[chromatic]] category: classical, Pythagorean, and septimal. In this case it is a [[schismic]] and [[garischismic]] system, so that all three kinds are separated by the same [[comma]] step and can be found on a stack of fifths. The comma step is somewhat larger than just, making the differences more pronounced, which is part of why I think this edo is pretty deep – the step isn't only a comma, but many things at once, including but not limited to the septimal dieses, as well as the chroma of the [[archaeotonic]] scale, the scale of [[Tetracot]][7]. The best [[subgroup]] of this edo is, actually, 2.3.5.7.11.19. [[Prime]] 13 is certainly plausible, but prime 19 fits way better. There's a unique uniform tuning for the [[harmonic segment]] 18::22, a fact related to the vanish of s10 = 100/99 and s9/s11 = 243/242. The beauty of this edo goes even beyond the structure, but also to the intonation: it has a very slightly sharp 3 and a more noticeably flat 5, making a flat, more stable 15; that is ideal for my music. Finally, it's an ideal tuning for the [[magic]] temperament. I can't compliment it enough. S-tier.

: '''Zhenlige:''' Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Containing [[Bohlen-Pierce scale]]. 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) 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]].

: '''Eufalesio:''' The first usable schismic edo (29edo and 17edo don't count because their 5/4's are wack). Still manageable grain, hyperaccurate fifths and the non-meantoneness is definitely welcome. It is the first edo to introduce a comma accidental framework, which in my opinion is one of the best frameworks for composition. The 11-limit is marvelous (pun intended) but the 13-limit is... lacking. However, since it tempers so many things together, it is extremely useful. – Still, even if the 5-limit is not that accurate, since the innacuracy is flatwards, I think it's much more enjoyable, as I like wide minor thirds. Also supports Bohlen Pierce, which is also incredibly cool. AC, not for air conditioner, but for ''accuracy'' and ''cool''.

== [[42edo]] ==

: '''Bozu:''' [[Amphipent]] [[augmented (temperament)|augmented]].

: '''Nicolai:''' You either get [[7edo|7EDO]] or [[superpyth]], there is no middle.

: '''Eufalesio:''' Useless. FF

== [[43edo]] ==

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: '''Bozu:''' [[Amphipent]] [[augmented (temperament)|augmented]].

: '''Fumica:''' The only legit edo tuning for [[flattone]]. Otherwise it has little utility. It has this weird structure of 9/8~10/9~11/10 all [[tempered]] together as a characteristic of flattone, but meanwhile the [[septimal comma]] is tuned to two steps, which feels a bit ugly. D-tier.

: '''Eufalesio:''' Useless. FF

== [[46edo]] ==

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: '''Fumica:''' The second essential comma-level edo. Five more notes than [[41edo]], offering the distinction of two types of [[neutral]] intervals at the cost of a narrower [[septimal diesis]]. As an eighth-tone system, it has a true [[quartertone]]. With that and all the accurate approximations, the expressive possibilities are endless. Best as a 2.3.5.7.11.17.23-[[subgroup]] temperament. A-tier.

: '''Zhenlige:''' Efficient [[parapyth]] EDO.

: '''Eufalesio:''' The best diaschismic. 13-limit stuff, though a bit sharp and not as accurate as 41-edo, it is good. I haven't composed anything with it, however, as I think diaschismic is kinda hard to conceptualize, and the sharpness of the 5 is something that I find less desirable. B

== [[47edo]] ==

: '''Bozu:''' [[Amphipent]] [[augmented (temperament)|augmented]].

: '''Nicolai:''' You either get [[7edo|7EDO]] or [[superpyth]], but there's a nice third.

: '''Eufalesio:''' Useless. FF

== [[48edo]] ==

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: '''Fumica:''' Close to [[2/7-comma meantone]] so it has a niche. Has the same problem as [[45edo]], though less severe. C-tier.

: '''Zhenlige:''' Flatter meantone than [[31edo]], but I usually use [[golden meantone]] (with slight octave stretching) for this range.

: '''Eufalesio:''' Still a good meantone edo, and though it is a much better approximant for golden meantone, I prefer using golden meantone as a rank-2, and not buying the entire gamut. The 19-limit usability is surprising, still. However, having all those new intervals inside a meantone edo feels in my opinion strangely unnatural, as we're stretching the meantone chain-of-fifths beyond what's supposed to. – For bigger edos in this range, meantone ceases to do it for me, but I respect it. C

== [[51edo]] ==

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: '''Fumica:''' The third essential comma-level edo. This one is kinda overrated. The best thing about it is the distinction of [[15/13]] and [[13/10]] from nearby [[7-limit|septimal]] intervals, which neither 41- nor 46edo does. What bugs me is that the fifth feels undertempered for pretty much every purpose, and while the 5-limit approximation is praiseworthy the rest deserves more love. Compared to [[41edo|41-]] or [[46edo]], it feels slack and doesn't convey a sense of tightly packed well-compromisedness. B-tier.

: '''Zhenlige:''' A stack of [[3/2]]. Almost just [[3/1|3]], and accurate [[7-limit]]. Its structure is not very elegant tho. Good for 5-limit [[schismatic]] with occasional [[garibaldi]] [[7/1|7]].

: '''Eufalesio:''' Pythagorean tuning incarnate, and astounding 5-limit. 2.3.5.13.19 is especially potent, but the .7.23 is still very much usable, even the .11! It doesn't temper as many things together as 41edo, so it feels like a less compromised system, still, I feel bad for the rest of the edos near this one, because this trumps a lot of the competition. But what can I say? Suck it losers! SS

== [[55edo]] ==

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: '''Fumica:''' The last essential comma-level edo. Has the same problem as [[60edo]]. Even tho it approximates [[JI]] way better and thus qualifies for an essential comma-level edo, most of its structural features have been provided by 41- and 58edo. B-tier.

: '''Zhenlige:''' 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. Playable by using three [[24edo]] instruments or six [[12edo]] instruments.

: '''Eufalesio:''' The first compton edo that achieves any semblance of JIoid goodness. This was one of the first finer edos I've composed in. It has an astounding 11-limit, and decent 19-limit! It's also a multiple of 12, so it is very transposing-friendly and building it is trivial! It's a miracle, and it also supports it! SSS

== [[73edo]] ==

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== [[81edo]] ==

: '''Zhenlige:''' The [[optimal patent val]] for [[meantone]] and some of its higher-limit extentions, but does anyone really want to use such a large EDO for a temperament with relatively low accuracy? Since it severely loses the convenience of EDOs, I will use [[golden meantone]] instead, which is simpler and more elegant mathematically.

: '''Eufalesio:''' Interesting, but rank-2 golden meantone is basically the same. D

== [[84edo]] ==

: '''Yourmusic Productions:''' [[12edo]] only each note is split into a full rainbow, which makes for awesome looking yet still easily comprehensible [[notation]]. The best multiple of 12 for [[5-limit]] music and my personal holy grail of edos to find a way to make playable.

: '''Eufalesio:''' I haven't composed anything in it, but theory tells me that it's a really good compton edo. The bad tuning of the 11 is a bit sad, but it can be useful all the way up to the 31-limit. The 2.3.5.7.13 here is instead a great subgroup, which is a good selling point for me. Had I known about it, I could have probably used this instead of 72edo, but I'm now not that interested in compton anymore. A

== [[87edo]] ==

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: '''Aura:''' Surprisingly, I have attempted to use this EDO before, and it is the first EDO I've attempted to use that wasn't some kind of superset of [[12edo]]. I've noticed just from working out the [[JI]] intervals that this EDO approximates that the [[7-limit]] for this EDO is really good- better than what this EDO has to offer in the [[5-limit]]. Furthermore, all of the pitches in this EDO are connected by a single, complicated circle of fifths. It is from working with this EDO that I learned the ways that the [[paradiatonic]] prime-limits (that would be the [[7-limit]], the [[11-limit]], and the [[13-limit]]) are connected with each other.

: '''Zhenlige:''' Good for high-limit JI with the [[garibaldi]] structure similar to [[41edo]] and [[53edo]]. Containing [[Carlos Beta]].

: '''Eufalesio:''' GOAT. The combination of the two smallest schismic edos, which are both incredibly solid choices, into one neatly rounded package that is very optimized. I am heavily '''biased''' towards this, as it represents the ultimate cassandra, and a chain-of-fifths framework that I find extremely easy to work with. It also tempers a lot of things together, much like 41edo, – Naturals for prime 3 or 19. ±1 for 17 or 23. ∓2 for 5 or 7. ±4 for 11 or 13. Throughout many different peer-reviewed experiments and in many on my compositions, I've found that this edo is good enough for most xen purposes. Still a tiny smidge innacurate in the 5-limit, but since it is flat and not sharp, I find it much more palatable, as I like wide minor thirds. I really only use it for the 2.3.5.7.11.13.19, but the 23-limit goodness is no joke. SSS

== [[99edo]] ==

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Line 643:

== [[120edo]] ==

: '''Aura:''' Just like with [[72edo]], I don't recall making many songs with this EDO, but again, I did compile a private list of [[JI]] intervals that this system approximates, and I was quite fascinated with it for a time. However, I eventually learned that you can't make a proper [[diatonic scale]] in this EDO without dealing with serious [[inconsistency]] in the [[3-limit]], and it was at that point that I realized that inconsistency in the 3-limit was a problem, which ultimately led to my formulation of [[telicity]].

== [[130edo]] ==

: '''Eufalesio:''' I haven't composed in it, but theory screams to me that this edo is a beast. I like to think of it as 65edo, but good. It has an extremely accurate 13-limit, and a schismic chain-of-fifths framework? Count me in! S

== [[159edo]] ==

: '''Aura:''' This is the main system I use in writing [[microtonal]] music. After finishing the list of [[JI]] equivalents of the various steps of this EDO, I have since found that not only is 159edo very good for those who like to make more just versions of the [[quartertone|quartertone-based intervals]] you see in [[24edo]], but is also very capable of approximating the steps of many lower EDOs within five [[cents]], making for some decent retunings of some of the more commonly used EDOs such as {{EDOs|22edo, 31edo, and even 41edo}}, which was part of the premise of "[[:File:Space Tour.mp3|Space Tour]]". Based on this discovery alone, I'd have to say that 159edo is not just a superset of [[53edo]], but rather, an EDO that is quite full of potential. However, the fact is that this EDO is [[consistent]] all the way up to the [[17-limit]], and has a good 23-[[prime]], and, should you skip the 17-prime, you have access to a decent 19-prime and 29-prime. This, and the fact that one has access to a bunch of [[microtemperament]]s in this EDO, all for a step-size that's slightly above the average [[JND]], means I can also perform other tricks in composition. I imagine at this point that some would ask me why I don't just use JI, and the answer is that even an EDO in the hundreds like 159edo is considerably more simple than JI, as you have to account for a lot of [[unnoticeable comma]]s in JI- a near-pointless endeavor as virtually nobody can hear such small differences in pitch.

: '''Eufalesio:''' Aura's favorite tuning. He does have a point, it takes an extremely good edo, and tripling it makes it even better! 29-limit goodness! I don't care as much for the insanely accurate 2.3.11, as I care for the entirety of the 2.3.5.7.11.13.19(.29). It really is that good. I've composed stuff with it, and it isn't as easy to do as in other edos, but the result is still worth it. SS

== [[171edo]] ==

: '''Zhenlige:''' The ultimate EDO for approximating [[7-limit]] JI. If you don't need some ridiculous high precision or specific microtemperaments, there is no need to go any further. Good as [[schismatic]], [[gammic]], [[ennealimmal]] and [[enneadecal]]. Containing a better [[Carlos Gamma]] scale than [[34edo]]. 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.

: '''Eufalesio:''' Ennealimmal, personified. I haven't composed in it directly, but since I did compose in 7-limit JI, it'd sound the same. It features a dead-accurate 7-limit that I cannot distinguish from just. It's that good. The great innacuracy of the 11 is a bit sad, though it still has a usable 13, which has that going for it. A

== [[217edo]] ==

: '''Eufalesio:''' It's the septuple of 31edo, and that is nothing less than a miracle (though it doesn't support miracle). I've done some tests on it, and it's 31-limit is incredible. It introduces an unfamiliar and slightly tedious gari-vulture-esque framework in which you have to use schisma-function steps apart from pythcommas, but apart from that, it's still within the realms of manageability. Also, it has an incredible 2.3.5.13, which I really respect. Also important to remark, from this point onward, edos start to sound more or less the same, as the absolute error gets lower and lower, and the difference between edosteps becomes harder to reliably hear. S

== [[224edo]] ==

: '''Zhenlige:''' Like 171edo but with a slightly sharper (and closer to just) fifth, worse 7-limit but better [[13-limit]].

: '''Eufalesio:''' A cousin to 217edo which is still schismic, dare I say the ultimate schismic edo, though still harder to conceptualize. Theory tells me that the 13-limit is extremely accurate, even more than the 217edo, and for that I think it deserves some attention. But 217edo is smaller, and it contains 31edo, so... I think I'll stick with the other one. B

== [[270edo]] ==

: '''Zhenlige:''' Better than 224edo if [[schismatic]] is not required. Ideal for free-pitch-like music that emphasizes 13-limit.

: '''Eufalesio:''' Ultimate low complexity JIoid edo. Though a tad large now, consistency within its 2.3.5.7.11.13.19 is insane. This trumps a lot of the competition. Using a finer gamut in the same subgroup becomes hard to justify. SSS

== [[311edo]] ==

: '''Zhenlige:''' Good for very high-limit JI.

: '''Eufalesio:''' Ultimate ultra-high-limit JI. Absolute error is a smidge worse than 270edo, but it makes up by being consistent to the goddamn 41-odd-limit. Serendipity personified. Very hard to justify using anything else other than this, as the difference between edosteps from this point on is definitely nigh impossible to hear. I see it as an ultimate tuning of sorts for practicality's sake. SSS

== [[1600edo]] ==

: '''Eufalesio:''' Now we've gone far tooo big. But... you know... 43-odd-limit... ah... round number... ah! It tickles special parts of my brain, even if it's not really practical to use it. I don't really know why I like it, I'm probably not going to use anything above the 29-limit... but what if...? B

== [[2460edo]] ==

:'''Eufalesio:''' The only reason I've put this one here is because it is a 12n edo, and that makes it ''slightly'' easier to work with, and very transposing friendly. It's astonishingly accurate, though dividing the semitone into 205ths is reasonably excessive. C

== [[8539edo]] ==

:'''Eufalesio:''' This level of fineness is at the bleeding edge of insanity. The precision of this behemoth is astounding. I firmly believe no sane person would compose anything requiring a tuning precision higher than what this offers. And I'm one to ogle at impossibly gargantuan edos, I'll admit, but that ogling is only theoretical. Beyond here... there be monsters... and hot sauce. C

== Sources ==

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* [[Yourmusic Productions' opinion of various edos]]

* [[User:Zhenlige/EDO impressions]]

* [[User:Eufalesio/EDO impressions]]

== Notes ==

[[Category:Impression]]

@@ Line 13: / Line 13: @@
 : '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes.
 : '''Zhenlige:''' 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.
+: '''Eufalesio:''' Octaves. Extremely boring to use still, as octaves are hyperconsonant, so there is no inertia. You really have to get creative to make something cool in this. Ligeti pulled it off. But I won't care to try. F
 == [[2edo]] ==
@@ Line 25: / Line 26: @@
 : '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes.
 : '''Zhenlige:''' Half octaves aka symmetric tritones. The key to tritone substitution, although sometimes asymmetric tritones or even non-tritone intervals can also be used.
+: '''Eufalesio:''' Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. D
 == [[3edo]] ==
@@ Line 37: / Line 39: @@
 : '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes.
 : '''Zhenlige:''' 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.
+: '''Eufalesio''': Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. Though 3edo has a surprisingly accurate 5. C
 == [[4edo]] ==
@@ Line 49: / Line 52: @@
 : '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes.
 : '''Zhenlige:''' 12edo diminished seventh chords.
+: '''Eufalesio''': Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. D
 == [[5edo]] ==
@@ Line 66: / Line 70: @@
 : '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes.
 : '''Zhenlige:''' 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.
+: '''Eufalesio:''' The first usable edo and the first edo to have any semblance of a perfect fifth. It features an extremely simplified 2.3.7, forming a consistent circle of 8/7 and 3/2. Due to its extremely coarse grain, it is extremely simple to use, as each step is large enough that no cluttering will ever occur. It is horrible in all other limits... well... except... 2.3.7.37, but who here cares about that –Also due to its extremely coarse grain, you can play anything, short of bashing keys and sitting on the keyboard, and it will sound good. This is because the edostep is so large that it doesn't cause audible cluttering... unless you're playing too low. The sonic profile of this edo is immediately recognizable. – It greatly benefits from non-harmonic timbres, or bell-like sounds, much like that of slendro. Its melodic capabilities are basically the same as that of all pentatonic scales, which is to say: great! It would be wrong to only call 5edo innacurate. A better descriptor would be: coarse. The coarsest, in fact. And due to the fact that it is so coarse, but it is still quite relatively accurate, it is a great edo. A
 == [[6edo]] ==
@@ Line 80: / Line 85: @@
 : '''Budjarn Lambeth:''' Lends itself to meditative, minimalist music: music where rhythm and timbre are the source of most of the interest, while melody and harmony are repetitive and change by small increments, forcing the listener to pay close attention to the most subtle changes.
 : '''Zhenlige:''' Incomplete [[12edo]]. Also a heavily stretched [[didacus]] chain.
+: '''Eufalesio''': Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively. D
 == [[7edo]] ==
@@ Line 96: / Line 102: @@
 : '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".
 : '''Zhenlige:''' Equalized [[5L 2s|diatonic]] scale. 3-limit [[whitewood]]. Similar to 5edo. It sounds like out-of-tone [[3L 4s|neutral scale]] music. The smallest EDO that roughly represents [[5-limit]].
+: '''Eufalesio:''' The second usable edo. Its fifth is a tad flat, but usable, and it is also the first edo to feature a heptatonic scale, obviously... an equalized diatonic. The edostep is now small enough so that cluttering ''can'' occur, but still somewhat bashable. The sonic profile is also immediately recognizable. While the 5-limit is not there, the melodic coolness you can pull of with this coarse edo are nothing to scoff at. C, not for accuracy, but for ''cool''.
 == [[8edo]] ==
@@ Line 111: / Line 118: @@
 : '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".
 : '''Zhenlige:''' Incomplete [[24edo]].
+: '''Eufalesio:''' Useless. FF
 == [[9edo]] ==
@@ Line 126: / Line 134: @@
 : '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to timbre to prevent it sounding "out of tune".
 : '''Zhenlige:''' A subset of [[ennealimmal]].
+: '''Eufalesio:''' Potentially useful, but I don't really like it. D
 == [[10edo]] ==
@@ Line 160: / Line 169: @@
 : '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".
 : '''Zhenlige:''' Incomplete [[22edo]].
+: '''Eufalesio:''' Useless. Use 22edo instead. FF
 == [[12edo]] ==
@@ Line 175: / Line 185: @@
 : '''Budjarn Lambeth:''' An excellent [[5-limit]] tuning. It is simple and stays out of the composer's way for two reasons: it works with an impressively wide variety of timbres, and it avoids [[wolf interval]]s better than any larger tuning. I believe this elegant simplicity is the reason for its popularity.
 : '''Zhenlige:''' 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 [[User:Zhenlige/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 some of them do.
+: '''Eufalesio:''' It's easily one of the best edos. 12edo is many, many things all at once, and I would say that its place in mainstream music is well earned. It's the first edo that can deal with the 5-limit at all, and it also has an incredibly accurate fifth for its size, making it the only temperament that is both meantone and pythagorean at the same time... Super practical, and very easy to conceptualize. S
 == [[13edo]] ==
@@ Line 189: / Line 200: @@
 : '''Fumica:''' Every other step of 26edo. Like 11edo, quintal harmony can be used. Unlike 11edo, the intonation sucks. D-tier.
 : '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".
+: '''Eufalesio:''' Useless. FF
 == [[14edo]] ==
@@ Line 203: / Line 215: @@
 : '''Fumica:''' I heard it too that this was the "most dissonant edo". The intonation surely has a lot of spice. Supports [[squares]] and [[godzilla]], making it important in theory. Perhaps works better as an interval category scheme than as sound to be listened to. B-tier.
 : '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".
+: '''Eufalesio:''' Useless. FF
 == [[15edo]] ==
@@ Line 229: / Line 242: @@
 : '''Vector:''' Definitive proof that a fifth doesn't need to be a 3/2. (TBA)
 : '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".
+: '''Eufalesio:''' Potentially useful, but I don't really like it. D
 == [[17edo]] ==
@@ Line 242: / Line 256: @@
 : '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".
 : '''Zhenlige:''' 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.
+: '''Eufalesio''': Despite being the next edo with a usable fifth, the fact that it tempers the interval whose edostep best approximates it is the ultimate irony. I like the slightly sharp fifths and neo-gothic feel, but the lack of 5-limit is a hole I can't easily live without, and no matter how good it is on other limits (and it is ''great''), the lack of 5 is sad. C
 == [[18edo]] ==
@@ Line 254: / Line 269: @@
 : '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".
 : '''Zhenlige:''' Incomplete [[36edo]].
+: '''Eufalesio:''' Useless. FF
 == [[19edo]] ==
@@ Line 268: / Line 284: @@
 : '''Budjarn Lambeth:''' The smallest equal tuning that approximates the entire [[43-limit]]. Its melodic similarity to 12edo makes it easier to find your bearings, but harder to break out of that diatonic comfort zone and explore all those intricate high limit harmonies it has to offer.
 : '''Zhenlige:''' Very different tradeoffs from 12edo. Usable but imperfect for many temperaments. [[Meantone]] or [[magic]], but with a too flat fifth. Strangely large minor 2nds. A compressed [[Carlos Beta]] scale. 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]].
+: '''Eufalesio:''' The next most easily accessible edo, and one that offers a change in perspective. It is meantone just like 12edo, but it has a completely different sonic profile, due to the flatter 5-limit, which I find very enjoyable. The near just minor thirds are definitely something to remark, though not as discernible as it is in its supersets. Great stuff! A
 == [[20edo]] ==
@@ Line 279: / Line 296: @@
 : '''Budjarn Lambeth:''' It has a lot of [[consonant]] intervals available, but they're mostly all very different to anything in 12edo. This makes it intimidating at first, but rewards exploration, ideal for composers looking for a wild world of new microtonal colours, without sounding as "sour" as some smaller EDOs do.
 : '''Zhenlige:''' 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?
+: '''Eufalesio:''' Useless. FF
 == [[21edo]] ==
@@ Line 289: / Line 307: @@
 : '''Fumica:''' 14edo but worse. F-tier.
 : '''Budjarn Lambeth:''' If you like the melodic shapes of 7edo, but want some sweeter harmonies and smaller step sizes to mix them with, 21edo is ideal for that.
+: '''Eufalesio:''' Useless. FF
 == [[22edo]] ==
@@ Line 303: / Line 322: @@
 : '''Budjarn Lambeth:''' It is the first EDO bigger than 12 which sounds equally as "in-tune" as 12, in my opinion.  Though it does have some [[wolf interval]]s which can startle new composers; with experience one learns how to approach those. Its [[superpyth]] and [[pajara]] scales offer a familiar-but-not-too-familiar melodic structure where prior 12edo training is useful, but where exploration beyond it is rewarded with gorgeous new colours. In this sense, it offers the strengths of both 19 and 20 without the drawbacks of either.
 : '''Zhenlige:''' 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.
+: '''Eufalesio:''' While the change in perspective that 19edo offers is mixed with familiarity, 22edo is an entirely different beast. It features a very exaggerated non-meantone 5-limit, making it the ultimate porcupine, which is not a temperament known for its accuracy, but it's cool! It also supports magic, featuring a flatter 5, which I enjoy, though the incredibly sharp 6/5 is a tad excessive. – The 7-limit structure inside the diatonic scale is something very sui generis, though it's 11-limit is kinda meh, but what can I say, it's the first edo to be consistent in the 11-odd-limit! C, not for accuracy, but for ''cool''.
 == [[23edo]] ==
@@ Line 315: / Line 335: @@
 : '''Budjarn Lambeth:''' A great EDO to begin experimenting with [[octave stretching]] and squishing. With pure octaves, it sounds out of tune, but stretch it by about 10 [[cents]], and you get access to the full array of pretty no-13s [[59-limit]] harmonies. ''Compress'' it by about 10 cents, and you instead get access to the full array of no-19s [[37-limit]] harmonies. Both tunings punch far above their weight by having lots of consonances in only 23 notes. Experiment with both the stretched and squished versions of 23edo, to get a feeling for how stretching or squishing a scale can shift its underlying harmonies dramatically while preserving its melodic shape.
 : '''Zhenlige:''' Incomplete [[46edo]]. The largest EDO without a diatonic, blackwood or whitewood fifth.
+: '''Eufalesio:''' Useless. FF
 == [[24edo]] ==
@@ Line 329: / Line 350: @@
 : '''Budjarn Lambeth:''' Along with [[36edo]], it is one of the two possible ways to extend 12edo while preserving equal spacing, and keeping the number of notes somewhat manageable. 36edo is ideal if you want to add intervals involving the 7th harmonic into 12edo, while 24edo is ideal if you want to add intervals involving the 11th harmonic. Comparing and contrasting 24edo and 36edo can help you get a feel for the difference between the "vibe" of the 11th harmonic, and the "vibe" of the 7th harmonic. I recommend dipping your toes into each of the two. — Try using familar 12edo intervals in lower registers of your instrument(s)/mix, while mixing in some of the strange new 24edo intervals in the higher registers. Thus will mimic the shape of the [[harmonic series]] and sound nice and glittery.
 : '''Zhenlige:''' What some non-microtonalists think microtonality is. 12edo with neutrals. Good for prime [[11/1|11]]. Accurate in subgroup 2.3.11.17.19.
+: '''Eufalesio:''' Entry-level xenharmonic edo. A huge improvement to the 2.3.5.11, but nothing much more to remark. Probably the most common xenharmonic edo among non xen spaces, and for good reason. We've all used it. It's trivial to build it. – Still, some ensembles fail at playing quartertones accurately (singers are the worst, some can even fail to sing 12edo accurately, which is a feat...) C
 == [[25edo]] ==
@@ Line 338: / Line 360: @@
 : '''Deja Igliashon:''' 25edo might be "the one that got away" for me. It bears a lot of similarities to [[23edo]] by virtue of being half the notes of a large very-accurate ET (50edo), having half of the nice 2nds, 3rds, 6ths, and 7ths, but not the nice 4ths and 5ths. Lots of nice harmony to be had, but no 5-limit triads (or at least, none that are very nice). I've thought about having a [[guitar]] made in 25edo multiple times but always ended up going with something else for some reason. Anyway, it's really really good for 8:9:10:14:17:19:23:25 chords, as well as 11:12:13:15:21:27 chords, but you can't put the two together unless you are in 50edo.
 : '''Fumica:''' Potentially useful as every other step of 50edo. D-tier.
+: '''Eufalesio:''' Useless. FF
 == [[26edo]] ==
@@ Line 348: / Line 371: @@
 : '''Fumica:''' Just as [[19edo]] is the point separating [[meantone]] and [[flattone]], this is the point separating flattone and [[flattertone|a meantone extension that implies an even flatter fifth]]. Therefore it should share all the advantages of 12edo and 19edo, at least theoretically, that is if not for its poor intonation in the [[5-limit]]. C-tier.
 : '''Zhenlige:''' 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 but tuned terribly. Incomplete [[130edo]].
+: '''Eufalesio:''' Interesting, but unjustifiably inaccurate for me. D
 == [[27edo]] ==
@@ Line 365: / Line 389: @@
 : '''Fumica:''' Potentially useful as every other step of [[56edo]]. D-tier.
 : '''Zhenlige:''' [[Whitewood]] [[diminished]]. Kinda opposite from [[15edo]]. The best you can get with [[whitewood]].
+: '''Eufalesio:''' The hyper-accurate 5/4 alone makes it useless. FF
 == [[29edo]] ==
@@ Line 378: / Line 403: @@
 : '''Fumica:''' Potentially useful as every other step of [[60edo]]. D-tier.
 : '''Budjarn Lambeth:''' The most simple [[dual-fifth]] edo, but not as "in-tune" as others.
+: '''Eufalesio:''' Useless. FF
 == [[31edo]] ==
@@ Line 387: / Line 413: @@
 : '''Fumica:''' This is a great edo. Too great it's a little unfun to work with. It has a tuning profile close to what I consider the [[optimal tuning]] of meantone, and [[migration]], the [[meantone]] [[extension]] that maps harmonic 11 to the semi-augmented fourth, works almost perfectly in this system. [[Octave stretch]] gives better intonation. A-tier.
 : '''Zhenlige:''' 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.
+: '''Eufalesio:''' The best meantone edo. Manageable grain, incredible 11-limit. You can't get more juice out of meantone without diminishing returns. From this point on, it becomes hard to justify using a finer meantone gamut. SSS
 == [[32edo]] ==
@@ Line 393: / Line 420: @@
 : '''Yourmusic Productions:''' Like all pure powers of 2, unusually bad for it's size.
 : '''Fumica:''' 27edo but worse. F-tier.
+: '''Eufalesio:''' Useless. FF
 == [[33edo]] ==
@@ Line 417: / Line 445: @@
 : '''Budjarn Lambeth:''' A very good [[dual-fifth]] edo.
 : ''Zhenlige:''' The largest non-diatonic EDO.
+: '''Eufalesio:''' Useless. FF
 == [[36edo]] ==
@@ Line 447: / Line 476: @@
 == [[40edo]] ==
 : '''Bozu:''' [[Amphipent]] [[diminished (temperament)|diminished]]. Can't really find a good use for this one.
+: '''Eufalesio:''' Useless. FF
 == [[41edo]] ==
@@ Line 454: / Line 484: @@
 : '''Fumica:''' The first of the five essential comma-level edos, and the first edo to achieve [[9-odd-limit]] [[distinction]] and [[consistency]]. This is most significant for providing three flavors for each [[chromatic]] category: classical, Pythagorean, and septimal. In this case it is a [[schismic]] and [[garischismic]] system, so that all three kinds are separated by the same [[comma]] step and can be found on a stack of fifths. The comma step is somewhat larger than just, making the differences more pronounced, which is part of why I think this edo is pretty deep – the step isn't only a comma, but many things at once, including but not limited to the septimal dieses, as well as the chroma of the [[archaeotonic]] scale, the scale of [[Tetracot]][7]. The best [[subgroup]] of this edo is, actually, 2.3.5.7.11.19. [[Prime]] 13 is certainly plausible, but prime 19 fits way better. There's a unique uniform tuning for the [[harmonic segment]] 18::22, a fact related to the vanish of s10 = 100/99 and s9/s11 = 243/242. The beauty of this edo goes even beyond the structure, but also to the intonation: it has a very slightly sharp 3 and a more noticeably flat 5, making a flat, more stable 15; that is ideal for my music. Finally, it's an ideal tuning for the [[magic]] temperament. I can't compliment it enough. S-tier.
 : '''Zhenlige:''' Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Containing [[Bohlen-Pierce scale]]. 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) 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]].
+: '''Eufalesio:''' The first usable schismic edo (29edo and 17edo don't count because their 5/4's are wack). Still manageable grain, hyperaccurate fifths and the non-meantoneness is definitely welcome. It is the first edo to introduce a comma accidental framework, which in my opinion is one of the best frameworks for composition. The 11-limit is marvelous (pun intended) but the 13-limit is... lacking. However, since it tempers so many things together, it is extremely useful. – Still, even if the 5-limit is not that accurate, since the innacuracy is flatwards, I think it's much more enjoyable, as I like wide minor thirds. Also supports Bohlen Pierce, which is also incredibly cool. AC, not for air conditioner, but for ''accuracy'' and ''cool''.
 == [[42edo]] ==
 : '''Bozu:''' [[Amphipent]] [[augmented (temperament)|augmented]].
 : '''Nicolai:''' You either get [[7edo|7EDO]] or [[superpyth]], there is no middle.
+: '''Eufalesio:''' Useless. FF
 == [[43edo]] ==
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 : '''Bozu:''' [[Amphipent]] [[augmented (temperament)|augmented]].
 : '''Fumica:''' The only legit edo tuning for [[flattone]]. Otherwise it has little utility. It has this weird structure of 9/8~10/9~11/10 all [[tempered]] together as a characteristic of flattone, but meanwhile the [[septimal comma]] is tuned to two steps, which feels a bit ugly. D-tier.
+: '''Eufalesio:''' Useless. FF
 == [[46edo]] ==
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 : '''Fumica:''' The second essential comma-level edo. Five more notes than [[41edo]], offering the distinction of two types of [[neutral]] intervals at the cost of a narrower [[septimal diesis]]. As an eighth-tone system, it has a true [[quartertone]]. With that and all the accurate approximations, the expressive possibilities are endless. Best as a 2.3.5.7.11.17.23-[[subgroup]] temperament. A-tier.
 : '''Zhenlige:''' Efficient [[parapyth]] EDO.
+: '''Eufalesio:''' The best diaschismic. 13-limit stuff, though a bit sharp and not as accurate as 41-edo, it is good. I haven't composed anything with it, however, as I think diaschismic is kinda hard to conceptualize, and the sharpness of the 5 is something that I find less desirable. B
 == [[47edo]] ==
 : '''Bozu:''' [[Amphipent]] [[augmented (temperament)|augmented]].
 : '''Nicolai:''' You either get [[7edo|7EDO]] or [[superpyth]], but there's a nice third.
+: '''Eufalesio:''' Useless. FF
 == [[48edo]] ==
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 : '''Fumica:''' Close to [[2/7-comma meantone]] so it has a niche. Has the same problem as [[45edo]], though less severe. C-tier.
 : '''Zhenlige:''' Flatter meantone than [[31edo]], but I usually use [[golden meantone]] (with slight octave stretching) for this range.
+: '''Eufalesio:''' Still a good meantone edo, and though it is a much better approximant for golden meantone, I prefer using golden meantone as a rank-2, and not buying the entire gamut. The 19-limit usability is surprising, still. However, having all those new intervals inside a meantone edo feels in my opinion strangely unnatural, as we're stretching the meantone chain-of-fifths beyond what's supposed to. – For bigger edos in this range, meantone ceases to do it for me, but I respect it. C
 == [[51edo]] ==
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 : '''Fumica:''' The third essential comma-level edo. This one is kinda overrated. The best thing about it is the distinction of [[15/13]] and [[13/10]] from nearby [[7-limit|septimal]] intervals, which neither 41- nor 46edo does. What bugs me is that the fifth feels undertempered for pretty much every purpose, and while the 5-limit approximation is praiseworthy the rest deserves more love. Compared to [[41edo|41-]] or [[46edo]], it feels slack and doesn't convey a sense of tightly packed well-compromisedness. B-tier.
 : '''Zhenlige:''' A stack of [[3/2]]. Almost just [[3/1|3]], and accurate [[7-limit]]. Its structure is not very elegant tho. Good for 5-limit [[schismatic]] with occasional [[garibaldi]] [[7/1|7]].
+: '''Eufalesio:''' Pythagorean tuning incarnate, and astounding 5-limit. 2.3.5.13.19 is especially potent, but the .7.23 is still very much usable, even the .11! It doesn't temper as many things together as 41edo, so it feels like a less compromised system, still, I feel bad for the rest of the edos near this one, because this trumps a lot of the competition. But what can I say? Suck it losers! SS
 == [[55edo]] ==
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 : '''Fumica:''' The last essential comma-level edo. Has the same problem as [[60edo]]. Even tho it approximates [[JI]] way better and thus qualifies for an essential comma-level edo, most of its structural features have been provided by 41- and 58edo. B-tier.
 : '''Zhenlige:''' 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. Playable by using three [[24edo]] instruments or six [[12edo]] instruments.
+: '''Eufalesio:''' The first compton edo that achieves any semblance of JIoid goodness. This was one of the first finer edos I've composed in. It has an astounding 11-limit, and decent 19-limit! It's also a multiple of 12, so it is very transposing-friendly and building it is trivial! It's a miracle, and it also supports it! SSS
 == [[73edo]] ==
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 == [[81edo]] ==
 : '''Zhenlige:''' The [[optimal patent val]] for [[meantone]] and some of its higher-limit extentions, but does anyone really want to use such a large EDO for a temperament with relatively low accuracy? Since it severely loses the convenience of EDOs, I will use [[golden meantone]] instead, which is simpler and more elegant mathematically.
+: '''Eufalesio:''' Interesting, but rank-2 golden meantone is basically the same. D
 == [[84edo]] ==
 : '''Yourmusic Productions:''' [[12edo]] only each note is split into a full rainbow, which makes for awesome looking yet still easily comprehensible [[notation]]. The best multiple of 12 for [[5-limit]] music and my personal holy grail of edos to find a way to make playable.
+: '''Eufalesio:''' I haven't composed anything in it, but theory tells me that it's a really good compton edo. The bad tuning of the 11 is a bit sad, but it can be useful all the way up to the 31-limit. The 2.3.5.7.13 here is instead a great subgroup, which is a good selling point for me. Had I known about it, I could have probably used this instead of 72edo, but I'm now not that interested in compton anymore. A
 == [[87edo]] ==
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 : '''Aura:''' Surprisingly, I have attempted to use this EDO before, and it is the first EDO I've attempted to use that wasn't some kind of superset of [[12edo]].  I've noticed just from working out the [[JI]] intervals that this EDO approximates that the [[7-limit]] for this EDO is really good- better than what this EDO has to offer in the [[5-limit]].  Furthermore, all of the pitches in this EDO are connected by a single, complicated circle of fifths.  It is from working with this EDO that I learned the ways that the [[paradiatonic]] prime-limits (that would be the [[7-limit]], the [[11-limit]], and the [[13-limit]]) are connected with each other.
 : '''Zhenlige:''' Good for high-limit JI with the [[garibaldi]] structure similar to [[41edo]] and [[53edo]]. Containing [[Carlos Beta]].
+: '''Eufalesio:''' GOAT. The combination of the two smallest schismic edos, which are both incredibly solid choices, into one neatly rounded package that is very optimized. I am heavily '''biased''' towards this, as it represents the ultimate cassandra, and a chain-of-fifths framework that I find extremely easy to work with. It also tempers a lot of things together, much like 41edo, – Naturals for prime 3 or 19. ±1 for 17 or 23. ∓2 for 5 or 7. ±4 for 11 or 13. Throughout many different peer-reviewed experiments and in many on my compositions, I've found that this edo is good enough for most xen purposes. Still a tiny smidge innacurate in the 5-limit, but since it is flat and not sharp, I find it much more palatable, as I like wide minor thirds. I really only use it for the 2.3.5.7.11.13.19, but the 23-limit goodness is no joke. SSS
 == [[99edo]] ==
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 == [[120edo]] ==
 : '''Aura:''' Just like with [[72edo]], I don't recall making many songs with this EDO, but again, I did compile a private list of [[JI]] intervals that this system approximates, and I was quite fascinated with it for a time. However, I eventually learned that you can't make a proper [[diatonic scale]] in this EDO without dealing with serious [[inconsistency]] in the [[3-limit]], and it was at that point that I realized that inconsistency in the 3-limit was a problem, which ultimately led to my formulation of [[telicity]].
+== [[130edo]] ==
+: '''Eufalesio:''' I haven't composed in it, but theory screams to me that this edo is a beast. I like to think of it as 65edo, but good. It has an extremely accurate 13-limit, and a schismic chain-of-fifths framework? Count me in! S
 == [[159edo]] ==
 : '''Aura:''' This is the main system I use in writing [[microtonal]] music.  After finishing the list of [[JI]] equivalents of the various steps of this EDO, I have since found that not only is 159edo very good for those who like to make more just versions of the [[quartertone|quartertone-based intervals]] you see in [[24edo]], but is also very capable of approximating the steps of many lower EDOs within five [[cents]], making for some decent retunings of some of the more commonly used EDOs such as {{EDOs|22edo, 31edo, and even 41edo}}, which was part of the premise of "[[:File:Space Tour.mp3|Space Tour]]".  Based on this discovery alone, I'd have to say that 159edo is not just a superset of [[53edo]], but rather, an EDO that is quite full of potential.  However, the fact is that this EDO is [[consistent]] all the way up to the [[17-limit]], and has a good 23-[[prime]], and, should you skip the 17-prime, you have access to a decent 19-prime and 29-prime.  This, and the fact that one has access to a bunch of [[microtemperament]]s in this EDO, all for a step-size that's slightly above the average [[JND]], means I can also perform other tricks in composition.  I imagine at this point that some would ask me why I don't just use JI, and the answer is that even an EDO in the hundreds like 159edo is considerably more simple than JI, as you have to account for a lot of [[unnoticeable comma]]s in JI- a near-pointless endeavor as virtually nobody can hear such small differences in pitch.
+: '''Eufalesio:''' Aura's favorite tuning. He does have a point, it takes an extremely good edo, and tripling it makes it even better! 29-limit goodness! I don't care as much for the insanely accurate 2.3.11, as I care for the entirety of the 2.3.5.7.11.13.19(.29). It really is that good. I've composed stuff with it, and it isn't as easy to do as in other edos, but the result is still worth it. SS
 == [[171edo]] ==
 : '''Zhenlige:''' The ultimate EDO for approximating [[7-limit]] JI. If you don't need some ridiculous high precision or specific microtemperaments, there is no need to go any further. Good as [[schismatic]], [[gammic]], [[ennealimmal]] and [[enneadecal]]. Containing a better [[Carlos Gamma]] scale than [[34edo]]. 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.
+: '''Eufalesio:''' Ennealimmal, personified. I haven't composed in it directly, but since I did compose in 7-limit JI, it'd sound the same. It features a dead-accurate 7-limit that I cannot distinguish from just. It's that good. The great innacuracy of the 11 is a bit sad, though it still has a usable 13, which has that going for it. A
+== [[217edo]] ==
+: '''Eufalesio:''' It's the septuple of 31edo, and that is nothing less than a miracle (though it doesn't support miracle). I've done some tests on it, and it's 31-limit is incredible. It introduces an unfamiliar and slightly tedious gari-vulture-esque framework in which you have to use schisma-function steps apart from pythcommas, but apart from that, it's still within the realms of manageability. Also, it has an incredible 2.3.5.13, which I really respect. Also important to remark, from this point onward, edos start to sound more or less the same, as the absolute error gets lower and lower, and the difference between edosteps becomes harder to reliably hear. S
 == [[224edo]] ==
 : '''Zhenlige:''' Like 171edo but with a slightly sharper (and closer to just) fifth, worse 7-limit but better [[13-limit]].
+: '''Eufalesio:''' A cousin to 217edo which is still schismic, dare I say the ultimate schismic edo, though still harder to conceptualize. Theory tells me that the 13-limit is extremely accurate, even more than the 217edo, and for that I think it deserves some attention. But 217edo is smaller, and it contains 31edo, so... I think I'll stick with the other one. B
 == [[270edo]] ==
 : '''Zhenlige:''' Better than 224edo if [[schismatic]] is not required. Ideal for free-pitch-like music that emphasizes 13-limit.
+: '''Eufalesio:''' Ultimate low complexity JIoid edo. Though a tad large now, consistency within its 2.3.5.7.11.13.19 is insane. This trumps a lot of the competition. Using a finer gamut in the same subgroup becomes hard to justify. SSS
 == [[311edo]] ==
 : '''Zhenlige:''' Good for very high-limit JI.
+: '''Eufalesio:''' Ultimate ultra-high-limit JI. Absolute error is a smidge worse than 270edo, but it makes up by being consistent to the goddamn 41-odd-limit. Serendipity personified. Very hard to justify using anything else other than this, as the difference between edosteps from this point on is definitely nigh impossible to hear. I see it as an ultimate tuning of sorts for practicality's sake. SSS
+== [[1600edo]] ==
+: '''Eufalesio:''' Now we've gone far tooo big. But... you know... 43-odd-limit... ah... round number... ah! It tickles special parts of my brain, even if it's not really practical to use it. I don't really know why I like it, I'm probably not going to use anything above the 29-limit... but what if...? B
+== [[2460edo]] ==
+:'''Eufalesio:''' The only reason I've put this one here is because it is a 12n edo, and that makes it ''slightly'' easier to work with, and very transposing friendly. It's astonishingly accurate, though dividing the semitone into 205ths is reasonably excessive. C
+== [[8539edo]] ==
+:'''Eufalesio:''' This level of fineness is at the bleeding edge of insanity. The precision of this behemoth is astounding. I firmly believe no sane person would compose anything requiring a tuning precision higher than what this offers. And I'm one to ogle at impossibly gargantuan edos, I'll admit, but that ogling is only theoretical. Beyond here... there be monsters... and hot sauce. C
 == Sources ==
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 * [[Yourmusic Productions' opinion of various edos]]
 * [[User:Zhenlige/EDO impressions]]
+* [[User:Eufalesio/EDO impressions]]
 == Notes ==
 [[Category:Impression]]