Collection of EDO impressions: Difference between revisions

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Created page with "{| class="wikitable" |- |edo |Keenan's EDO impressions |Mike's EDO impressions |Piotr's edo impressions |- |1edo |People ought to write more 2-limit music...."
 
CritDeathX (talk | contribs)
Added all of the current EDO impressions. I recommend people make similar lists, whether it be small comments or extreme dives!
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|[[edo]]
|[[edo]]
|[[User:CritDeathX/Sam's EDO Impressions|Sam's EDO Impressions]]
|[[Keenan's EDO impressions]]
|[[Keenan's EDO impressions]]
|[[Mike's EDO impressions]]
|[[Mike's EDO impressions]]
|[[Piotr's edo impressions]]
|[[Piotr's edo impressions]]
|[[Yourmusic Productions' opinion of various edos]]
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|[[1edo]]
|[[1edo]]
|The harmony of the cavemen.
|People ought to write more 2-limit music. (Or not.)
|People ought to write more 2-limit music. (Or not.)
|lol
|lol
|Infinite octave consonance!
|Infinite octave consonance!
|Contained within 12 and so not worth talking about.
|-
|2edo
|The worse harmony of the cavemen.
|Boring
|lol
|Infinite tritave dissonance!
|Contained within 12 and so not worth talking about.
|-
|3edo
|Augmented chord.
|Boring
|lol
|While it does have a major third, it's weak otherwise.
|Contained within 12 and so not worth talking about.
|-
|4edo
|Diminished chord. It, surprisingly, has interesting melodic movement despite only being four notes.
|Boring
|lol
|uh,
|Contained within 12 and so not worth talking about.
|-
|5edo
|Equipentatonic. Nothing too original.
|Smallest useful EDO, and it's really cool. Basically 2.3.7 limit (no hint of the 5th harmonic at all), and a great candidate for a scale people can just bang away on. Regular temperament model of slendro.
|1. smallest EDO that has something resembling 3/2. Has a great approximation of the 7th harmonic. Really awesome, stretched out, equal pentatonic scale. Sevish features it here as a prominent subset of 15-EDO: http://www.youtube.com/watch?v=rPmuKUm2kJg
2. equipentatonic, which is trippy
|5edo.
|The emancipation from harmony. Nothing clashes with anything else, so you're free to play any combination of notes and concentrate on rhythm, arrangement and instrumentation instead. (and you really need to push those other areas to keep it from getting boring.)
|-
|6edo
|Whole tone scale. Take out 4\6 and you have a pentatonic subset of the lydian dominant scale.
|Boring as a subset of 12edo, but useful as a very simple 2.9.5.7 temperament. Most of the good 2.9.... scales have 6-note MOSes for this reason.
|the whole tone scale. But, if you flatten the octaves, you can get almost perfect 4:5:7:11 chords, which is worth noting.
|6edo.
|A universe in monochrome. You can make things out, but so much is missing.
|-
|7edo
|Equiheptatonic. Again, nothing too original.
|Cool in many of the ways that 5 is. Regular temperament model of a scale used in Thai music.
|1. next-smallest EDO that has something resembling 3/2. This sounds like an "equalized" diatonic scale, so that there are no more "major" or "minor" thirds, but just "thirds." 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, mohajira/maqamic[7] and its MODMOS's, porcupine[7], tetracot[7], and mavila[7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you stretch the octaves to about 1230 cents, you get something which is like every other step of the popular nonoctave [[88cET]], and which can also be thought of as a nonoctave version of [[Tetracot family|tetracot temperament]], with really good 2:3:5 chords.
2. equidiatonic, which is trippy
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|The emancipation from harmony, but now with recognisable, if bland diatonic melodies.
|-
|8edo
|First EDO with some kind of quarter tone interval.
|A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2).
|1. An EDO that's often dismissed as an equalized diminished[8] scale, yet contains a lot more. For starters, it's also an equalized sensi[8] (especially if viewed as existing in the 2.9/7.5/3 subgroup, and has, for its size, excellent approximations to the tempered 1/1-9/7-5/3 [[Sensamagic chords|sensamagic chord]]), made of two 450 cent "supermajor thirds" on top of one another. This chord provides a great contrast to the usual diminished chord, as it's much less intense and "evil" sounding, and much more floaty and abstract. I also tend to enjoy huge stacks of 450 cent intervals, which I think are beautiful. Stacks of 750 cent intervals can also be very beautiful: I don't know whether they "approximate 3/2 poorly" or "approximate 14/9 well" or whatever it is, but they sound really good. They're two things that categorically sound to me like sharp fifths mixed with minor sixths, and two of them gets you a minor tenth; this is another way to get away from making it sound "diminished." Lastly, I also note that 8-EDO is an equalized porcupine[8], so for those who are used to porcupine, 2 1 1 1 1 1 1 may trip you out as being sort of like porcupine but with 4:5:6 replaced with 7:9:11. With sensamagic chords, diminished chords, and 7:9:11 chords - all of which differ in consonance - there's no reason why you can't use this tuning to make beautiful, programmatic, and to my ears somewhat "spacy" sounding music.
2. 8-EDO is a great tuning but I dunno if it has a ton of specifically categorically interesting stuff
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|Any combination of more than 2 notes sounds bad, and most 2 note combinations sound bad too. Just vile.
|-
|9edo
|Cool approximation of 7/6. I also consider it something of the parent scale of gamelan music.
|On the one hand you can treat the 667 cent intervals as 3/2, yielding an extreme version of [[mavila]] (or 7-limit [[armodue]]) which is a very acceptable tuning for pelog selisir. On the other hand you can treat it has having no 3rd harmonics, as something like a 2.5.7/3 temperament. (Treating it as a super-accurate 2.27/25.7/3 temperament makes no sense to me.) First EDO with '''recognizable''' "major" and "minor" chords.
|1. If we're considering the 667 cent intervals to be 3/2, then this is the first EDO that doesn't temper out 25/24 in the 5-limit, and as such distinguishes between 4:5:6 and 10:12:15. However you want to view it, it's definitely the first EDO to my ears where I can hear distinct "major" and "minor" chords, as detuned as they may be. This is also the first EDO that supports [[Pelogic family|mavila]] and [[Pelogic family|pelogic]] temperament, and the 7-note MOS's are of prime interest here. Because of that, it's the first EDO I know how to create something like "functional harmony" in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: <nowiki>http://www.youtube.com/watch?v=KV_MzdtU2WQ</nowiki>. Also, like mavila in general, it also allows for common practice music to be translated into this tuning, where major chords become minor and vice versa; however, this experience can be unpleasant if one uses a harsh timbre or isn't prepared for the more discordant harmonies. Examples of that here: <nowiki>http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/</nowiki>. Random other things: it has a great 7/6 and can also be viewed as an equalized version of superpelog[9] and orwell[9] and augmented[9], contains an interesting augmented[6] where the "minor thirds" are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).
2. has a lot of what 16-EDO does but with less notes. However, 3/2 is weaker. comparing 9-EDO to 16-EDO can let you compare less notes + easier categorization vs more notes + better accuracy. Smallest EDO with major and minor chords (unless you count 8-EDO but that's kind of out there)
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|Marvellously elegant little system. More than enough room for complex melodies and fortifying them with double-stopped 3rds and 6ths sounds awesome.
|-
|10edo
|The first ''actually'' usable EDO. Decent chords & decent melodic ideas. Sevish's ''Vidya'' is a good example of how it can sound.
|Like [[blackwood]], except with neutral thirds. Or, blackwood intersects [[dicot]]. Same circle-of-3/2s structure as 5edo, but now there are 360-cent "neutral thirds" and 600-cent "tritones". It's easy to trick people into thinking that [[decimal]] MODMOSes are the familiar "blues scale" (and for that matter, that 0 360 960 cents is a "dominant seventh").
|1. A neutral triad version of [[blackwood]], or a "neutral tetrad" version of [[pajara]], or a neutral [[negri]], or a neutral [[lemba]]. Elaine Walker's written some great stuff in this. I have the feeling that this is a great base scale for "diatonic"-style melodies, but haven't explored it as much yet. Also an equalized [[Trienstonic clan|octokaidecal]][10]. Need to play more
2. don't know a lot about it, but 10-note scales are interesting for also being something in which major and minor can share a triad class, which may be of semi-categorical relevance
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|A universe that's recognisable, but everything is distorted and the people have no faces. The merging of 3rds and 6ths removes one of the primary forms of textural expressiveness in 12, leaving it disconcertingly emotionally flat.
|-
|11edo
|This is probably a good example of where you should use secundal harmony rather than tertial harmony.
|Every other note of [[22edo|22]]. This makes it a great 2.9.7.11 temperament. Includes [[machine]], [[orgone]], <nowiki>http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11</nowiki> and <nowiki>http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11</nowiki>
|1. Amazing and totally underrated EDO. It supports excellent 4:7:9:11 chords, as well as 4:7:9:11:15:17:19 chords if you're into that thing. Was once thought to be mostly "atonal" for lacking 3/2, but revealed as a low-numbered EDO of prime interest after the Great Subgroup Revolution Of 2011. Giving you decently accurate tetradic harmony for only 11 notes is almost a miracle. Supports [[machine]] temperament, of which the 2 2 1 2 2 2 MOS is of interest for being stable and sounding like a "warped diatonic." Example here that loosely uses it:
http://www.youtube.com/watch?v=AhPjsCoMy-Q. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another "warped diatonic" scale. An example of this:
http://soundcloud.com/mikebattagliaexperiments/sets/tonal-study-in-orgone-temperament/. Also, much like 8-EDO supports the excellent and underrated 2.9/7.5/3 version of sensi temperament.
2. has machine[6] which is a key warped diatonic scale, and orgone[7]. I'd say 11-EDO is way up there in terms of key things to learn for categories because it's small, has great 4:7:9:11 triads, and has warped diatonic scales.
|
|It can almost pass for 12 as long as you only play one note at at time, but more than that and it's limitations become painfully clear.
|-
|12edo
|I probably shouldn't have listed this.
|Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant]] temperament. Also [[augmented]] and [[diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.
|If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable 5-limit harmony, has a debatably passable representation of the 7-limit, and can sort of "hint" at 11, as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: http://www.youtube.com/watch?v=CaPeks0H3_s. Our theory places "12-EDO" and "meantone" as one example of an infinite series of musical tunings, all of which are of potential interest - however, care must be taken to not unfairly diminish 12-EDO's value in a mathematical sense because one may simply be bored with it. Many feel that everything in it "has already been done"; I have a different perspective as a jazz musician in NYC, where people do new and interesting things with 12-EDO every time I go to Smalls'. (Be more creative!!)
|Widely used...
|The more I study it, the more it's flaws and limitations irritate me.
|-
|13edo
|Extremely dissonant, but at least the major chord sounds somewhat decent. Not much decent, but its better than nothing.
|Every other note of [[26edo|26]]. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[uncle]] and [[dicot]].
|1. [[13edo|13]] is insane. I can't get my head wrapped around it, but I love it at the same time. 13 wreaks havoc on my brain because it constantly sends crazy signals about my 12-EDO categories which misfire in fantastic ways. 11-EDO does the same thing, but 13-EDO is worse for no particular reason. You can use this to a particular effect by coming up with warped diatonic scales which have the pattern 2212221, but in which the "octave" now becomes more like a major 7th. Other than that, 13 is also notable for having a bunch of exceedingly beautiful scales which can generate some of the most far out harmonies you've ever heard, and is also simultaneously notable for being totally ignored in this capacity because a long time ago it got a reputation for being harmonically inaccurate and that reputation stuck. The crown jewel in the 13, uh, crown, is father[8], which is an amazingly vivid and bright scale, which for me evokes the imagery of galaxies in deep space and underwater coral reefs and stuff, but it's been largely ignored because it has an interval which is 30 cents off from 3/2 and which sounds bad if you expect it to be 3/2. Despite all that, I like the 738 cent interval for just being the color it is - treat it with caution but use it as an "extension" in chords and such. You can also treat it as 32/21, which means you're treating the inverse as 21/16, at which point you'll probably realize that this scale isn't bad at all - it's just the 2.9.7/3 version of mothra temperament, which Igs has called "A-team." Other nice scales include 2222212, which is glacial[7], and some other stuff. Oh yeah, and also the 738 cent interval is an augmented fifth in 26-EDO, which is twice 13. No comment. It also has good 13/8 and 11/8, and a good 7/6, and a decent 9/8, and a bunch of other random stuff. The circle of not-quite-3/2's hits a ton of those intervals.
2. 13-EDO and 11-EDO both have warped diatonic scales with stretched/compressed octaves
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|All the various kinds of 9thno5 chords work, and have interesting new flavours compared to their 12edo equivalents. Well worth getting to grips with the cluster based harmony needed to make it sound nice.
|-
|14edo
|Cool chords. People say that its really dissonant, but I don't hear anything out of the ordinary.
|Jamesbond, [[bug]]/[[semaphore]], etc. (Quite bad whitewood tuning.) Pretty much misses "minor" and "major" thirds entirely, going straight from "subminor" to "neutral" to "supermajor", which makes it very xenharmonic (thought not necessarily *pleasant*). Also don't forget the presence of DTMF ("touch tone") tones. Any phone number is a two-part piece of music!
|1. [[14edo|14-EDO]] has frickin touch tone noises! Holy shit! Just play two 7-EDO chains a b9 apart and you'll hear it! It's also interesting for not having 5/4 or 6/5 in any real capacity, but having 11/9 and 9/7 and a passable 7/6. So if you think about the way a 14-EDO native listener would hear the harmonic series, instead of hearing the sequence of intervals like octave-fifth-fourth-major third-minor third-smaller minor third, they'd probably hear octave-fifth-fourth-large neutral third-small neutral third-large subminor third-small subminor third-etc. Note that they'd probably not use names like "neutral" and "subminor" though, since those are just our names for those things. It also has a really interesting version of hedgehog temperament which makes the 5:6 in 5:6:7 out to be a neutral third; this is great for categories and then when you move into hedgehog[8] in 22-EDO, the scalar structure remains intelligible despite the intonation shifting under it. A great tuning I also wish I knew more about.
2. has the whole "kloog" slash "kleeg" thing going on, and also has touch tone noises as intervals for you to try and categorize
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|The opposite of 10 - recognisable, but distorted so there's three types of 3rd and 6th with exaggerated expressive qualities. Even though it's best intervals aren't as in tune as 12, it sounds much less dissonant when playing all the notes at once, so it seems a natural home for Schoenberg influenced serialism and extended chords.
|-
|15edo
|Probably the most popular small EDO. Great chords, good approximation of 6/5, and supports some nice temperaments. Also I kinda introduced Weigel to a Hanson keyboard, and then he made it into his keyboard, so I feel a little happy about telling him about that.
|Very interesting for [[blackwood]], [[porcupine]], and others. A good all-around EDO. If you want to internalize [[Porcupine intervals|porcupine interval categories]], use 15edo.
|has 5-limit harmony plus a 5 note circle of 3/2's, which is crazy in terms of "tonality," which would seem to be peripherally relevant
|
|Like 14, not as good at simple harmonies as 12, but some glorious extended blackwood chords that combine more notes than you can in 12 and still sound good. Porcupine looks simpler, but I actually find it more of a struggle than blackwood to use.
|-
|16edo
|Chromatic version of 9EDO's mavila. Also cool approximation of 7/4.
|[[Mavila]]/armodue. Really versatile and interesting - if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, [[gorgo]].)
|is notable for being the first EDO (to me) where the 3 step interval can sound like "a step" instead of "a leap." Example is machine: 3 3 1 3 3 3. Much like 3 3 1 3 3 3 1 in 17-EDO, machine[6] in 16-EDO has L/s = 3/1 but the 3-step interval still sounds like "a second." It sounds like 16-EDO is an "enharmonic" scale for machine[11], which I (sort of) perceive as the true "background" for 331333, much like I perceive 19-EDO as an enharmonic underpinning for meantone[12] or whatever.
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|12's evil twin. Scales are recognisable but inverted and everything but the mellowest of timbres or simplest of harmonies sounds horrible once you start combining notes.
|-
|17edo
|The smallest EDO with more consonant harmony than the previous ones.
|Really good no-5's system; [[supra]], [[bleu]], etc. The lack of 5-limit harmony forces you to think xenharmonically, but the nice accurate 3/2s form a solid familiar backbone you can depend on when things get too crazy. Also, neutral third scales are awesome. Compatible (not perfectly, of course) with a large number of maqamat.
|superpyth machine blah blah
|
|Interestingly alien, but with good 2nd's, 4ths & 5ths to retreat too when you're not sure what to do next.
|-
|18edo
|Nothing particularly interesting in this.
|Almost totally useless.
|has a really useful 10 note scale called "supersharp" which is 2 2 2 2 1 2 2 2 2 1, which has major/minor/diminished chords which are a bit sharp
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|A universe in monochrome, but with extended dynamic range. There's enough complexity in other areas to keep it interesting, but I'm still aware in the back of my mind that something's missing.
|-
|19edo
|The smallest EDO with a really nice meantone fifth. I consider this the smallest EDO to use if you want to make pop music into microtonal music.
|First EDO with a meantone diatonic scale (5L2s proper), but not only meantone! [[Negri]] is awesome, [[godzilla]] is awesome, [[sensi]] is awesome, and [[keemun]] and [[magic]] are both quite interesting. Excellent EDO to promote to newcomers because it works beautifully with standard meantone notation and familiar meantone harmony is possible, but again, it's so much more than meantone. Xenharmonic scales and comma pumps abound.
|needs to be in there for the above reason about enharmonic-sized EDOs in general, but also because learning to differentiate things like #4's and b5's is easy and attainable and a good "first step." I hear A# and Bb as different notes in 19-EDO now - the first fits into things like E lydian, the second fits into things like E diminished, etc. Then you can experiment with melodic diesis movements
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|The more I study it, the more I love how elegantly everything fits together, how you can use standard notation, but things that are equivalent in 12 actually have proper meaning here, how familiar tunes are transferable and recognisable but the emphasis on intervals is subtly shifted to making minor chords and melodies sound more stable and consonant than major ones. It still has it's limitations, power chord based heavy rock in particular suffers from the weaker 5ths, but just works so much better than 12 in general.
|-
|20edo
|Nothing particularly interesting.
|More-complicated version of [[blackwood]], not much else. Instead of [5edo interval], minor, major, [5edo interval] it now goes [5edo interval], minor, neutral, major, [5edo interval]. Big deal. I'd choose 15 over 20 any day because it has porcupine.
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|
|Looking at the math on paper, it should be possible to create pleasant music in this one, but nothing I've heard has actually managed it yet.
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|21edo
|Its cool, but again, nothing particularly interesting.
|First usable (sub-optimal) [[whitewood]] EDO, not much else.
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|Like 14 but moreso. Dramatically exaggerated harmonic expressiveness, shares the relatively nice major 3rd with 12 rather than the horrible tritone, and the highest edo that works with standard notation without having to add more letters or learn new kinds of accidental. Not as good as 19 for familiar sounding intervals, but still really rather nice.
|-
|22edo
|Smallest cool superpyth EDO. I think there's orwell in there, too, but don't quote me on that.
|Amazing and mind-blowing; many great [[22edo#Theory-Properties of 22 equal temperament-Linear Temperaments|temperaments]]. Not much reason to use more notes per octave than this, if you ask me.
|in keeping with the above note about enharmonic EDOs, can be thought of as an enharmonic scale for something like porcupine, so that you can perceive a 15-note background but have better intonation - the same way you can perceive a 12-note background in 19 (meantone[12]) but have better intonation than 12. You can do the same with orwell and perceive an orwell[13]-note background, but have much better intonation for orwell than 13-EDO itself. There's other stuff too. Also has superpyth[7] which is good for revealing the diatonic scale in a different intonational context.
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|Like 24, only the new harmonic options are actually more in tune than the familiar ones rather than less. Better than 12 but still not quite as good as 19 overall.
|-
|23edo
|Hyperchromatic version of 9EDO's mavila.
|Mavila system similar to 16, but has [[superpelog]] in addition. Nothing to write home about.
|same as the above but with mavila and 16-EDO and some other stuff too.
|
|Not enough songs using this to get a proper opinion. Definitely one of the tougher ones to get to grips with.
|-
|24edo
|12EDO, but fancy.
|Very worthwhile, and underrated because of its long history of "microtonal" (rather than "xenharmonic") use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones).
|allows you to take a sound you all intuitively know (the blues) and make it "real" and "tangible" and manipulate it to see what comes of it
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|Double the complexity, but considerably less than double the number of good-sounding combinations. A lot of extra work for little extra return.
|-
|25edo
|Great approximation of 5/4, but its another hyperchromatic version of 9EDO's mavila.
|Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider "the fifth" or "3/2". Too many notes for either one of them - why not use 15 or 16 instead?
|dunno
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|The whole-tone version of 50EDO's golden meantone. Lots and lots of bad options but like 6 vs 12, missing most of the good combinations.
|-
|26edo
|The step-sibling of the meantone series. Its twice of 13EDO though, so the closest approximation of 5/4 is still trash. 14/11 is cool, though, so lets use that.
|The forgotten meantone EDO, and the first true [[flattone]] EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because [[Flattone12|flattone[12]]] is much easier to hear as unequal than meantone[12]. Also has [[injera]] and [[cynder]]/[[mothra]].
|has meantone but the intonation is bad. However, the minor sixths are really good 13/8's. Also, the half steps are 138 cents, which is pretty big - but they still function as leading tones and all that. This behavior is exacerbated in 33-EDO. Good for messing with your head and also revealing the diatonic scale in a different intonational context.
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|Definitely deserves more attention than it's got so far.
|-
|27edo
|Amazing approximations of intervals like 7/6, 6/5, 5/4 (but its the same as 12EDO), 3/2, 5/3, and 7/4. Its weird how it manages to work this much with being a power of 3.
|First true [[tetracot]]/[[modus]] EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.
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|Like all pure powers of 3, unusually good for it's size. All the melodic coolness of 9 plus decent minor and neutral intervals and an acceptable 5th. Definitely my favourite superpyth system of manageable size.
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|28edo
|Meh.
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|14, only with a really in tune major 3rd and lots of other really interesting extra intervals. Really want an instrument that can do this one justice, probably an 8-string guitar tuned in it's slightly stretched 5ths so the top string is 3 octaves up from the bottom, and a 28-30" fanned fret multiscale fretboard that makes all the chords isomorphic.
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|29edo
|Similar to 27EDO, but this is a bit better since the fifth is a little bit better compared to 27EDO.
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|12's evil twin, but in an awesome way. About the same amount of error but in opposite directions means similar kinds of psychoacoustic beating, majors and minors are still clearly recognisable, and everything sounds deceptively familiar right up until it does something awesome that 12 can't. When you do focus on xen intervals and chords, it still sounds much better than 24. Another definite favourite.
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|30edo
|Meh.
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|Whole tone + Blackwood. Like 24, mainly just adds more ways to sound bad compared to 15 and not worth the hassle.
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|31edo
|Meantone quarter tones.
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|It definitely sounds nice, but I don't hear much actual songwriting going on in it, just people building enormous washes of harmony and luxuriating in them. Maybe it has too LITTLE tension in it, or maybe it's just past the point of complexity that the human mind can fully comprehend. In any case, it definitely hasn't been used to it's full potential yet.
|-
|32edo
|Same as 27 & 29EDO, but the fifth now is sharper than 27EDO.
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|Like all pure powers of 2, unusually bad for it's size.
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|33edo
|11EDO, but with a better fifth.
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|Interesting, but another one that's too big to explore properly without better equipment, and nothing I've heard yet has really managed to do it justice.
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|34edo
|17EDO, but now there's a good third.
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|Even better for 5-limit music than 31, with it's gorgeous thirds, actually defined different sizes of whole tone and still sour harmonic 7, yet even more underused. Definitely deserves more attention. Maybe a half-kite guitar, with full frets up to the perfect 4th or 5th, then 17edo above that point, with adjacent strings tuned so the full range of higher notes can still be played would make it feasible.
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|35edo
|You either get 5EDO or 7EDO, there is no middle.
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|The highest EDO that absolutely refuses to fit into a diatonic framework and forces you to work with it on it's own terms. If you do, it's ability to combine whitewood and blackwood make it incredibly flexible, with very interesting extended harmonies. Something like a 14 string chapman stick with one side tuned in 3 octaves of stretched 4ths and the other in 2 octaves of compressed ones would properly highlight and take advantage of it's unique strengths.
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|36edo
|12EDO, but better.
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|12, only with lots of extra harmonic options that actually sound good and are much easier to slip into an otherwise normal track than 24's.
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|37edo
|Same situation as 35EDO, but the 5EDO fifth is now just a superpyth fifth. Also good approximations of intervals.
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|38edo
|Meh.
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|39edo
|You either get mavila or superpyth, there is no middle.
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|40edo
|Meh.
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|41edo
|Smaller version of 53EDO.
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|42edo
|You either get 7EDO or superpyth, there is no middle.
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|43edo
|The other step-sibling of meantone.
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|44edo
|Meh.
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|45edo
|Meh.
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|46edo
|You either get 5EDO or 7EDO, but there is a middle.
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|47edo
|You either get 7EDO or superpyth, but there's a nice third.
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|48edo
|12EDO, but more fancy.
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|49edo
|Meh.
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|50edo
|I consider this an optimal meantone EDO, due to a wealthy collection of notes here.
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|51edo
|Meh.
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|52edo
|Meh.
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|53edo
|JI: The Book.
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|84edo
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|12, 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.
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Revision as of 02:46, 27 July 2020

edo Sam's EDO Impressions Keenan's EDO impressions Mike's EDO impressions Piotr's edo impressions Yourmusic Productions' opinion of various edos
1edo The harmony of the cavemen. People ought to write more 2-limit music. (Or not.) lol Infinite octave consonance! Contained within 12 and so not worth talking about.
2edo The worse harmony of the cavemen. Boring lol Infinite tritave dissonance! Contained within 12 and so not worth talking about.
3edo Augmented chord. Boring lol While it does have a major third, it's weak otherwise. Contained within 12 and so not worth talking about.
4edo Diminished chord. It, surprisingly, has interesting melodic movement despite only being four notes. Boring lol uh, Contained within 12 and so not worth talking about.
5edo Equipentatonic. Nothing too original. Smallest useful EDO, and it's really cool. Basically 2.3.7 limit (no hint of the 5th harmonic at all), and a great candidate for a scale people can just bang away on. Regular temperament model of slendro. 1. smallest EDO that has something resembling 3/2. Has a great approximation of the 7th harmonic. Really awesome, stretched out, equal pentatonic scale. Sevish features it here as a prominent subset of 15-EDO: http://www.youtube.com/watch?v=rPmuKUm2kJg

2. equipentatonic, which is trippy

5edo. The emancipation from harmony. Nothing clashes with anything else, so you're free to play any combination of notes and concentrate on rhythm, arrangement and instrumentation instead. (and you really need to push those other areas to keep it from getting boring.)
6edo Whole tone scale. Take out 4\6 and you have a pentatonic subset of the lydian dominant scale. Boring as a subset of 12edo, but useful as a very simple 2.9.5.7 temperament. Most of the good 2.9.... scales have 6-note MOSes for this reason. the whole tone scale. But, if you flatten the octaves, you can get almost perfect 4:5:7:11 chords, which is worth noting. 6edo. A universe in monochrome. You can make things out, but so much is missing.
7edo Equiheptatonic. Again, nothing too original. Cool in many of the ways that 5 is. Regular temperament model of a scale used in Thai music. 1. next-smallest EDO that has something resembling 3/2. This sounds like an "equalized" diatonic scale, so that there are no more "major" or "minor" thirds, but just "thirds." 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, mohajira/maqamic[7] and its MODMOS's, porcupine[7], tetracot[7], and mavila[7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you stretch the octaves to about 1230 cents, you get something which is like every other step of the popular nonoctave 88cET, and which can also be thought of as a nonoctave version of tetracot temperament, with really good 2:3:5 chords.

2. equidiatonic, which is trippy

The emancipation from harmony, but now with recognisable, if bland diatonic melodies.
8edo First EDO with some kind of quarter tone interval. A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2). 1. An EDO that's often dismissed as an equalized diminished[8] scale, yet contains a lot more. For starters, it's also an equalized sensi[8] (especially if viewed as existing in the 2.9/7.5/3 subgroup, and has, for its size, excellent approximations to the tempered 1/1-9/7-5/3 sensamagic chord), made of two 450 cent "supermajor thirds" on top of one another. This chord provides a great contrast to the usual diminished chord, as it's much less intense and "evil" sounding, and much more floaty and abstract. I also tend to enjoy huge stacks of 450 cent intervals, which I think are beautiful. Stacks of 750 cent intervals can also be very beautiful: I don't know whether they "approximate 3/2 poorly" or "approximate 14/9 well" or whatever it is, but they sound really good. They're two things that categorically sound to me like sharp fifths mixed with minor sixths, and two of them gets you a minor tenth; this is another way to get away from making it sound "diminished." Lastly, I also note that 8-EDO is an equalized porcupine[8], so for those who are used to porcupine, 2 1 1 1 1 1 1 may trip you out as being sort of like porcupine but with 4:5:6 replaced with 7:9:11. With sensamagic chords, diminished chords, and 7:9:11 chords - all of which differ in consonance - there's no reason why you can't use this tuning to make beautiful, programmatic, and to my ears somewhat "spacy" sounding music.

2. 8-EDO is a great tuning but I dunno if it has a ton of specifically categorically interesting stuff

Any combination of more than 2 notes sounds bad, and most 2 note combinations sound bad too. Just vile.
9edo Cool approximation of 7/6. I also consider it something of the parent scale of gamelan music. On the one hand you can treat the 667 cent intervals as 3/2, yielding an extreme version of mavila (or 7-limit armodue) which is a very acceptable tuning for pelog selisir. On the other hand you can treat it has having no 3rd harmonics, as something like a 2.5.7/3 temperament. (Treating it as a super-accurate 2.27/25.7/3 temperament makes no sense to me.) First EDO with recognizable "major" and "minor" chords. 1. If we're considering the 667 cent intervals to be 3/2, then this is the first EDO that doesn't temper out 25/24 in the 5-limit, and as such distinguishes between 4:5:6 and 10:12:15. However you want to view it, it's definitely the first EDO to my ears where I can hear distinct "major" and "minor" chords, as detuned as they may be. This is also the first EDO that supports mavila and pelogic temperament, and the 7-note MOS's are of prime interest here. Because of that, it's the first EDO I know how to create something like "functional harmony" in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: http://www.youtube.com/watch?v=KV_MzdtU2WQ. Also, like mavila in general, it also allows for common practice music to be translated into this tuning, where major chords become minor and vice versa; however, this experience can be unpleasant if one uses a harsh timbre or isn't prepared for the more discordant harmonies. Examples of that here: http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/. Random other things: it has a great 7/6 and can also be viewed as an equalized version of superpelog[9] and orwell[9] and augmented[9], contains an interesting augmented[6] where the "minor thirds" are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).

2. has a lot of what 16-EDO does but with less notes. However, 3/2 is weaker. comparing 9-EDO to 16-EDO can let you compare less notes + easier categorization vs more notes + better accuracy. Smallest EDO with major and minor chords (unless you count 8-EDO but that's kind of out there)

Marvellously elegant little system. More than enough room for complex melodies and fortifying them with double-stopped 3rds and 6ths sounds awesome.
10edo The first actually usable EDO. Decent chords & decent melodic ideas. Sevish's Vidya is a good example of how it can sound. Like blackwood, except with neutral thirds. Or, blackwood intersects dicot. Same circle-of-3/2s structure as 5edo, but now there are 360-cent "neutral thirds" and 600-cent "tritones". It's easy to trick people into thinking that decimal MODMOSes are the familiar "blues scale" (and for that matter, that 0 360 960 cents is a "dominant seventh"). 1. A neutral triad version of blackwood, or a "neutral tetrad" version of pajara, or a neutral negri, or a neutral lemba. Elaine Walker's written some great stuff in this. I have the feeling that this is a great base scale for "diatonic"-style melodies, but haven't explored it as much yet. Also an equalized octokaidecal[10]. Need to play more

2. don't know a lot about it, but 10-note scales are interesting for also being something in which major and minor can share a triad class, which may be of semi-categorical relevance

A universe that's recognisable, but everything is distorted and the people have no faces. The merging of 3rds and 6ths removes one of the primary forms of textural expressiveness in 12, leaving it disconcertingly emotionally flat.
11edo This is probably a good example of where you should use secundal harmony rather than tertial harmony. Every other note of 22. This makes it a great 2.9.7.11 temperament. Includes machine, orgone, http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 and http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 1. Amazing and totally underrated EDO. It supports excellent 4:7:9:11 chords, as well as 4:7:9:11:15:17:19 chords if you're into that thing. Was once thought to be mostly "atonal" for lacking 3/2, but revealed as a low-numbered EDO of prime interest after the Great Subgroup Revolution Of 2011. Giving you decently accurate tetradic harmony for only 11 notes is almost a miracle. Supports machine temperament, of which the 2 2 1 2 2 2 MOS is of interest for being stable and sounding like a "warped diatonic." Example here that loosely uses it:

http://www.youtube.com/watch?v=AhPjsCoMy-Q. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another "warped diatonic" scale. An example of this:

http://soundcloud.com/mikebattagliaexperiments/sets/tonal-study-in-orgone-temperament/. Also, much like 8-EDO supports the excellent and underrated 2.9/7.5/3 version of sensi temperament.

2. has machine[6] which is a key warped diatonic scale, and orgone[7]. I'd say 11-EDO is way up there in terms of key things to learn for categories because it's small, has great 4:7:9:11 triads, and has warped diatonic scales.

It can almost pass for 12 as long as you only play one note at at time, but more than that and it's limitations become painfully clear.
12edo I probably shouldn't have listed this. Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular dominant temperament. Also augmented and diminished. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles. If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable 5-limit harmony, has a debatably passable representation of the 7-limit, and can sort of "hint" at 11, as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: http://www.youtube.com/watch?v=CaPeks0H3_s. Our theory places "12-EDO" and "meantone" as one example of an infinite series of musical tunings, all of which are of potential interest - however, care must be taken to not unfairly diminish 12-EDO's value in a mathematical sense because one may simply be bored with it. Many feel that everything in it "has already been done"; I have a different perspective as a jazz musician in NYC, where people do new and interesting things with 12-EDO every time I go to Smalls'. (Be more creative!!) Widely used... The more I study it, the more it's flaws and limitations irritate me.
13edo Extremely dissonant, but at least the major chord sounds somewhat decent. Not much decent, but its better than nothing. Every other note of 26. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including uncle and dicot. 1. 13 is insane. I can't get my head wrapped around it, but I love it at the same time. 13 wreaks havoc on my brain because it constantly sends crazy signals about my 12-EDO categories which misfire in fantastic ways. 11-EDO does the same thing, but 13-EDO is worse for no particular reason. You can use this to a particular effect by coming up with warped diatonic scales which have the pattern 2212221, but in which the "octave" now becomes more like a major 7th. Other than that, 13 is also notable for having a bunch of exceedingly beautiful scales which can generate some of the most far out harmonies you've ever heard, and is also simultaneously notable for being totally ignored in this capacity because a long time ago it got a reputation for being harmonically inaccurate and that reputation stuck. The crown jewel in the 13, uh, crown, is father[8], which is an amazingly vivid and bright scale, which for me evokes the imagery of galaxies in deep space and underwater coral reefs and stuff, but it's been largely ignored because it has an interval which is 30 cents off from 3/2 and which sounds bad if you expect it to be 3/2. Despite all that, I like the 738 cent interval for just being the color it is - treat it with caution but use it as an "extension" in chords and such. You can also treat it as 32/21, which means you're treating the inverse as 21/16, at which point you'll probably realize that this scale isn't bad at all - it's just the 2.9.7/3 version of mothra temperament, which Igs has called "A-team." Other nice scales include 2222212, which is glacial[7], and some other stuff. Oh yeah, and also the 738 cent interval is an augmented fifth in 26-EDO, which is twice 13. No comment. It also has good 13/8 and 11/8, and a good 7/6, and a decent 9/8, and a bunch of other random stuff. The circle of not-quite-3/2's hits a ton of those intervals.

2. 13-EDO and 11-EDO both have warped diatonic scales with stretched/compressed octaves

All the various kinds of 9thno5 chords work, and have interesting new flavours compared to their 12edo equivalents. Well worth getting to grips with the cluster based harmony needed to make it sound nice.
14edo Cool chords. People say that its really dissonant, but I don't hear anything out of the ordinary. Jamesbond, bug/semaphore, etc. (Quite bad whitewood tuning.) Pretty much misses "minor" and "major" thirds entirely, going straight from "subminor" to "neutral" to "supermajor", which makes it very xenharmonic (thought not necessarily *pleasant*). Also don't forget the presence of DTMF ("touch tone") tones. Any phone number is a two-part piece of music! 1. 14-EDO has frickin touch tone noises! Holy shit! Just play two 7-EDO chains a b9 apart and you'll hear it! It's also interesting for not having 5/4 or 6/5 in any real capacity, but having 11/9 and 9/7 and a passable 7/6. So if you think about the way a 14-EDO native listener would hear the harmonic series, instead of hearing the sequence of intervals like octave-fifth-fourth-major third-minor third-smaller minor third, they'd probably hear octave-fifth-fourth-large neutral third-small neutral third-large subminor third-small subminor third-etc. Note that they'd probably not use names like "neutral" and "subminor" though, since those are just our names for those things. It also has a really interesting version of hedgehog temperament which makes the 5:6 in 5:6:7 out to be a neutral third; this is great for categories and then when you move into hedgehog[8] in 22-EDO, the scalar structure remains intelligible despite the intonation shifting under it. A great tuning I also wish I knew more about.

2. has the whole "kloog" slash "kleeg" thing going on, and also has touch tone noises as intervals for you to try and categorize

The opposite of 10 - recognisable, but distorted so there's three types of 3rd and 6th with exaggerated expressive qualities. Even though it's best intervals aren't as in tune as 12, it sounds much less dissonant when playing all the notes at once, so it seems a natural home for Schoenberg influenced serialism and extended chords.
15edo Probably the most popular small EDO. Great chords, good approximation of 6/5, and supports some nice temperaments. Also I kinda introduced Weigel to a Hanson keyboard, and then he made it into his keyboard, so I feel a little happy about telling him about that. Very interesting for blackwood, porcupine, and others. A good all-around EDO. If you want to internalize porcupine interval categories, use 15edo. has 5-limit harmony plus a 5 note circle of 3/2's, which is crazy in terms of "tonality," which would seem to be peripherally relevant Like 14, not as good at simple harmonies as 12, but some glorious extended blackwood chords that combine more notes than you can in 12 and still sound good. Porcupine looks simpler, but I actually find it more of a struggle than blackwood to use.
16edo Chromatic version of 9EDO's mavila. Also cool approximation of 7/4. Mavila/armodue. Really versatile and interesting - if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, gorgo.) is notable for being the first EDO (to me) where the 3 step interval can sound like "a step" instead of "a leap." Example is machine: 3 3 1 3 3 3. Much like 3 3 1 3 3 3 1 in 17-EDO, machine[6] in 16-EDO has L/s = 3/1 but the 3-step interval still sounds like "a second." It sounds like 16-EDO is an "enharmonic" scale for machine[11], which I (sort of) perceive as the true "background" for 331333, much like I perceive 19-EDO as an enharmonic underpinning for meantone[12] or whatever. 12's evil twin. Scales are recognisable but inverted and everything but the mellowest of timbres or simplest of harmonies sounds horrible once you start combining notes.
17edo The smallest EDO with more consonant harmony than the previous ones. Really good no-5's system; supra, bleu, etc. The lack of 5-limit harmony forces you to think xenharmonically, but the nice accurate 3/2s form a solid familiar backbone you can depend on when things get too crazy. Also, neutral third scales are awesome. Compatible (not perfectly, of course) with a large number of maqamat. superpyth machine blah blah Interestingly alien, but with good 2nd's, 4ths & 5ths to retreat too when you're not sure what to do next.
18edo Nothing particularly interesting in this. Almost totally useless. has a really useful 10 note scale called "supersharp" which is 2 2 2 2 1 2 2 2 2 1, which has major/minor/diminished chords which are a bit sharp A universe in monochrome, but with extended dynamic range. There's enough complexity in other areas to keep it interesting, but I'm still aware in the back of my mind that something's missing.
19edo The smallest EDO with a really nice meantone fifth. I consider this the smallest EDO to use if you want to make pop music into microtonal music. First EDO with a meantone diatonic scale (5L2s proper), but not only meantone! Negri is awesome, godzilla is awesome, sensi is awesome, and keemun and magic are both quite interesting. Excellent EDO to promote to newcomers because it works beautifully with standard meantone notation and familiar meantone harmony is possible, but again, it's so much more than meantone. Xenharmonic scales and comma pumps abound. needs to be in there for the above reason about enharmonic-sized EDOs in general, but also because learning to differentiate things like #4's and b5's is easy and attainable and a good "first step." I hear A# and Bb as different notes in 19-EDO now - the first fits into things like E lydian, the second fits into things like E diminished, etc. Then you can experiment with melodic diesis movements The more I study it, the more I love how elegantly everything fits together, how you can use standard notation, but things that are equivalent in 12 actually have proper meaning here, how familiar tunes are transferable and recognisable but the emphasis on intervals is subtly shifted to making minor chords and melodies sound more stable and consonant than major ones. It still has it's limitations, power chord based heavy rock in particular suffers from the weaker 5ths, but just works so much better than 12 in general.
20edo Nothing particularly interesting. More-complicated version of blackwood, not much else. Instead of [5edo interval], minor, major, [5edo interval] it now goes [5edo interval], minor, neutral, major, [5edo interval]. Big deal. I'd choose 15 over 20 any day because it has porcupine. Looking at the math on paper, it should be possible to create pleasant music in this one, but nothing I've heard has actually managed it yet.
21edo Its cool, but again, nothing particularly interesting. First usable (sub-optimal) whitewood EDO, not much else. Like 14 but moreso. Dramatically exaggerated harmonic expressiveness, shares the relatively nice major 3rd with 12 rather than the horrible tritone, and the highest edo that works with standard notation without having to add more letters or learn new kinds of accidental. Not as good as 19 for familiar sounding intervals, but still really rather nice.
22edo Smallest cool superpyth EDO. I think there's orwell in there, too, but don't quote me on that. Amazing and mind-blowing; many great temperaments. Not much reason to use more notes per octave than this, if you ask me. in keeping with the above note about enharmonic EDOs, can be thought of as an enharmonic scale for something like porcupine, so that you can perceive a 15-note background but have better intonation - the same way you can perceive a 12-note background in 19 (meantone[12]) but have better intonation than 12. You can do the same with orwell and perceive an orwell[13]-note background, but have much better intonation for orwell than 13-EDO itself. There's other stuff too. Also has superpyth[7] which is good for revealing the diatonic scale in a different intonational context. Like 24, only the new harmonic options are actually more in tune than the familiar ones rather than less. Better than 12 but still not quite as good as 19 overall.
23edo Hyperchromatic version of 9EDO's mavila. Mavila system similar to 16, but has superpelog in addition. Nothing to write home about. same as the above but with mavila and 16-EDO and some other stuff too. Not enough songs using this to get a proper opinion. Definitely one of the tougher ones to get to grips with.
24edo 12EDO, but fancy. Very worthwhile, and underrated because of its long history of "microtonal" (rather than "xenharmonic") use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones). allows you to take a sound you all intuitively know (the blues) and make it "real" and "tangible" and manipulate it to see what comes of it Double the complexity, but considerably less than double the number of good-sounding combinations. A lot of extra work for little extra return.
25edo Great approximation of 5/4, but its another hyperchromatic version of 9EDO's mavila. Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider "the fifth" or "3/2". Too many notes for either one of them - why not use 15 or 16 instead? dunno The whole-tone version of 50EDO's golden meantone. Lots and lots of bad options but like 6 vs 12, missing most of the good combinations.
26edo The step-sibling of the meantone series. Its twice of 13EDO though, so the closest approximation of 5/4 is still trash. 14/11 is cool, though, so lets use that. The forgotten meantone EDO, and the first true flattone EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because flattone[12] is much easier to hear as unequal than meantone[12]. Also has injera and cynder/mothra. has meantone but the intonation is bad. However, the minor sixths are really good 13/8's. Also, the half steps are 138 cents, which is pretty big - but they still function as leading tones and all that. This behavior is exacerbated in 33-EDO. Good for messing with your head and also revealing the diatonic scale in a different intonational context. Definitely deserves more attention than it's got so far.
27edo Amazing approximations of intervals like 7/6, 6/5, 5/4 (but its the same as 12EDO), 3/2, 5/3, and 7/4. Its weird how it manages to work this much with being a power of 3. First true tetracot/modus EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs. Like all pure powers of 3, unusually good for it's size. All the melodic coolness of 9 plus decent minor and neutral intervals and an acceptable 5th. Definitely my favourite superpyth system of manageable size.
28edo Meh. 14, only with a really in tune major 3rd and lots of other really interesting extra intervals. Really want an instrument that can do this one justice, probably an 8-string guitar tuned in it's slightly stretched 5ths so the top string is 3 octaves up from the bottom, and a 28-30" fanned fret multiscale fretboard that makes all the chords isomorphic.
29edo Similar to 27EDO, but this is a bit better since the fifth is a little bit better compared to 27EDO. 12's evil twin, but in an awesome way. About the same amount of error but in opposite directions means similar kinds of psychoacoustic beating, majors and minors are still clearly recognisable, and everything sounds deceptively familiar right up until it does something awesome that 12 can't. When you do focus on xen intervals and chords, it still sounds much better than 24. Another definite favourite.
30edo Meh. Whole tone + Blackwood. Like 24, mainly just adds more ways to sound bad compared to 15 and not worth the hassle.
31edo Meantone quarter tones. It definitely sounds nice, but I don't hear much actual songwriting going on in it, just people building enormous washes of harmony and luxuriating in them. Maybe it has too LITTLE tension in it, or maybe it's just past the point of complexity that the human mind can fully comprehend. In any case, it definitely hasn't been used to it's full potential yet.
32edo Same as 27 & 29EDO, but the fifth now is sharper than 27EDO. Like all pure powers of 2, unusually bad for it's size.
33edo 11EDO, but with a better fifth. Interesting, but another one that's too big to explore properly without better equipment, and nothing I've heard yet has really managed to do it justice.
34edo 17EDO, but now there's a good third. Even better for 5-limit music than 31, with it's gorgeous thirds, actually defined different sizes of whole tone and still sour harmonic 7, yet even more underused. Definitely deserves more attention. Maybe a half-kite guitar, with full frets up to the perfect 4th or 5th, then 17edo above that point, with adjacent strings tuned so the full range of higher notes can still be played would make it feasible.
35edo You either get 5EDO or 7EDO, there is no middle. The highest EDO that absolutely refuses to fit into a diatonic framework and forces you to work with it on it's own terms. If you do, it's ability to combine whitewood and blackwood make it incredibly flexible, with very interesting extended harmonies. Something like a 14 string chapman stick with one side tuned in 3 octaves of stretched 4ths and the other in 2 octaves of compressed ones would properly highlight and take advantage of it's unique strengths.
36edo 12EDO, but better. 12, only with lots of extra harmonic options that actually sound good and are much easier to slip into an otherwise normal track than 24's.
37edo Same situation as 35EDO, but the 5EDO fifth is now just a superpyth fifth. Also good approximations of intervals.
38edo Meh.
39edo You either get mavila or superpyth, there is no middle.
40edo Meh.
41edo Smaller version of 53EDO.
42edo You either get 7EDO or superpyth, there is no middle.
43edo The other step-sibling of meantone.
44edo Meh.
45edo Meh.
46edo You either get 5EDO or 7EDO, but there is a middle.
47edo You either get 7EDO or superpyth, but there's a nice third.
48edo 12EDO, but more fancy.
49edo Meh.
50edo I consider this an optimal meantone EDO, due to a wealthy collection of notes here.
51edo Meh.
52edo Meh.
53edo JI: The Book.
84edo 12, 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.