Collection of EDO impressions: Difference between revisions

: '''Bozu''': Elemental hyperpent. You can actually play a couple of melodies in the tuning, but it gets exhausted after an hour or two. Good tuning for percussive-melodic instruments like gamelan, woodblock, etc., but it can get grating on its own.

: '''Nicolai''': Equipentatonic. Nothing too original.

: '''Keenan''': 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.

: '''Mike''':  

: '''Bozu''': Elemental hypopent. The experience here is sort of like playing in 5edo, but it's more like a tuning where you have one complete scale to play with. For me, this is the smallest edo with which I would consider composing. But it's still overconstrained when it comes to trying to modulate anything.

: '''Nicolai''': Equiheptatonic. Again, nothing too original.

: '''Keenan''': Cool in many of the ways that 5 is. Regular temperament model of a scale used in Thai music.

: '''Mike''':  

: '''Bozu''': kind of a cool diminished scale, but it suffers from the same problems as other drone-like edo's, in terms of options and constraints.

: '''Nicolai''': First EDO with some kind of quarter tone interval.

: '''Keenan''': A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2).

: '''Mike''':  

: '''Aura''': The only things I know for a fact about this EDO come from my understanding of 3edo, as the same techniques available in 3edo are also viable here. However, I can't say much about the other aspects of this EDO due to lack of other relevant experience on my part.

: '''Bozu''': 3rd order augmented scale. I want to like this tuning, but I can't see any value in it beyond noodling.

: '''Keenan''': 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.

: '''Mike''':  

: '''Bozu''': Hyperpent with something resembling the chromatic scale. This is the smallest edo set that has anything worthwhile to offer. Constraints are within the critical range where melody, harmony, and chord changes can make some kind of sense. It's not my favourite edo, but it has its own characteristics.

: '''Nicolai''': The first ''actually'' usable EDO. Decent chords & decent melodic ideas. Sevish's ''Vidya'' is a good example of how it can sound.

: '''Keenan''': 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").

: '''Mike''':  

: '''Bozu''': This one is one of the three edo's that don't really fit any distinct category, and it shows. In my opinion, it's the second most difficult to use. Lots of possibilities of notes, unlike anything smaller than 9edo, but nothing seems to sound particularly great, not that it sounds particularly awful, either.

: '''Nicolai''': This is probably a good example of where you should use secundal harmony rather than tertial harmony.

: '''Keenan''': Every other note of [[22edo|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&#x20;and&#x20;http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 <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>]

: '''Mike''':  

: '''Bozu''': Honestly, the best edo. Not too many notes, not too few. What notes are there sound great. It's the lowest composite hypopent, as well as the lowest composite of augmented and diminished. You can use it to affect major, minor, augmented, and diminished tonalities very well. The only place it truly falls short is anything beyond that. It's not too great at approximating higher order harmonics, nor does it offer any neutral intervals. It'd be sort of silly to think of a beginner musician starting with anything other than this or some form of meantone or JI that 12edo approximates.

: '''Nicolai''': I probably shouldn't have listed this.

: '''Keenan''': 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.

: '''Mike''': 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: [https://www.youtube.com/watch?v=CaPeks0H3_s 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!!)

: '''Bozu''': To me, this one is the most difficult edo to bend to my will. Like 11edo, it doesn't fit any category, but the tones all just sound off to me.

: '''Nicolai''': Extremely dissonant, but at least the major chord sounds somewhat decent. Not much decent, but its better than nothing.

: '''Keenan''': 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]].

: '''Mike''':  

: '''Bozu''': 2nd order hypopent. It's like the scale from 7edo has some different colours added to its palette. Not super easy to wield, but it does have a nice spacey sound that makes sense to the ears in a weird way.

: '''Nicolai''': Cool chords. People say that its really dissonant, but I don't hear anything out of the ordinary.

: '''Keenan''': 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!

: '''Mike''':  

: '''Bozu''': 3rd order hyperpent, also with the augmented tonalities pasted in. Perhaps one of the most user-friendly edo's, it has a lot to offer, but also makes composers accustomed to 12edo think outside of the box.

: '''Nicolai''': 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.

: '''Keenan''': Very interesting for [[blackwood]], [[porcupine]], and others. A good all-around EDO. If you want to internalize [[Porcupine intervals|porcupine interval categories]], use 15edo.

: '''Mike''': 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

: '''Bozu''': diminished mayhem with extra mayhem. Check out Last Sacrament to see what this bad boy can do. It's not super user-friendly, in my experience, but it has a distinct sound that seems to pervade everything you can put together within its constraints.

: '''Nicolai''': Chromatic version of 9EDO's mavila. Also cool approximation of 7/4.

: '''Keenan''': [[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]].)

: '''Mike''': 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.

: '''Bozu''': Totally awesome composite hyperpent. Great fifths, it can sound maqam-ish or western-ish, depending on how you use it. So many possibilities.

: '''Nicolai''': The smallest EDO with more consonant harmony than the previous ones.

: '''Keenan''': 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.

: '''Mike''': superpyth machine blah blah

: '''Bozu''': Augmented scale sliced into thirds. Doesn't really offer any sort of semblance of a perfect fourth or fifth, but doesn't seem to be a one-trick pony, either. I'm just not sure what to do with it.

: '''Nicolai''': Nothing particularly interesting in this.

: '''Keenan''': Almost totally useless.

: '''Mike''': 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

: '''Bozu''': This is my personal favourite. Composite hypopent, awesome thirds and sixths and a decent fourth and fifth. Kind of leaves somethign to be desired with sevenths and seconds/ninths. Can play well within the western music idiom, and has plenty of tonal options outside of that, but doesn't really offer any of the cool maqam-esque tones of 17edo or any of the weird spacey tones of 14edo. I really think this should be the intermediate step between "standard tuning" (whatever you consider that to be) and "xenharmonic tuning" (whatever you consider that to be). This really sits between those two ideas for me.

: '''Nicolai''': 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.

: '''Keenan''': 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.

: '''Mike''': 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

: '''Bozu''': Excellent composite hyperpent tuning. Tons and tons of possibilities with western-esque and raga-esque tones. Notation starts getting more difficult than 17edo or 19edo.

: '''Nicolai''': Its cool, but again, nothing particularly interesting.

: '''Keenan''': First usable (sub-optimal) [[whitewood]] EDO, not much else.

: '''Yourmusic Productions''': 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.

: '''Bozu''': Excellent composite hyperpent tuning. Tons and tons of possibilities with western-esque and raga-esque tones. Notation starts getting more difficult than 17edo or 19edo.

: '''Nicolai''': Smallest cool superpyth EDO. I think there's orwell in there, too, but don't quote me on that.

: '''Keenan''': 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.

: '''Mike''': 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.

: '''Bozu''': This one defies my categorization as well as 11edo and 13edo, but with so many options for notes, maybe there is something there. I haven't really deemed this one worth much time investigating. To my ears, after playing with it for a couple of minutes, everything just sounds off, but not weird enough to pique my interest.

: '''Nicolai''': Hyperchromatic version of 9EDO's mavila.

: '''Keenan''': Mavila system similar to 16, but has [[superpelog]] in addition. Nothing to write home about.

: '''Mike''': same as the above but with mavila and 16-EDO and some other stuff too.

: '''Bozu''': This is where almost everyone outside of the xenharmonic community sends their minds when you mention "microtonal music." It's used in traditional maqam music. I've personally used it myself a bit, but, in my opinion, what gets added to 12edo is fairly limited. It opens up a couple of new worlds of a few consonant intervals that play really well with familiar ones, and also some really skunky dissonant ones that drive the neighbours crazy. But it's definitely not what I recommend for beginning a journey into alternative tuning.

: '''Nicolai''': 12EDO, but fancy.

: '''Keenan''': 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).

: '''Mike''': 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.

: '''Bozu''': Hyperpent. Not really sure what to do with it, honestly. I'd rather use 22edo.

: '''Nicolai''': Great approximation of 5/4, but its another hyperchromatic version of 9EDO's mavila.

: '''Keenan''': 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?

: '''Mike''': dunno

: '''Bozu''': Composite hypopent. This has some really cool possibilities and some pretty good consonant intervals, but doesn't seem (in my experience) to get too much love from xenharmonic composers. Dave Trombly has done some text-to-music stuff with it that shows how even randomly-generated notes and intervals sound quite musical, but other than that, I haven't really come across any in-depth projects exploring it. My own noodling around with it makes me think that it'd be pretty easy to use. Maybe there are better options for many specific approaches, though.

: '''Nicolai''': 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.

: '''Keenan''': 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]].

: '''Mike''': 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.

: '''Bozu''': Comte hyperpent. Another one with tons of usable tonal possibilities that seems to get little actual use.

: '''Nicolai''': 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.

: '''Keenan''': 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.

: '''Yourmusic Productions''': 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.

: '''Bozu''': Awesome fifths and great overall set of usable tones with some really unstable-sounding ones in between. I think this is a great intermediate-difficulty not-too-many-notes-but-kind-of-a-lot tuning set.

: '''Nicolai''': Similar to 27EDO, but this is a bit better since the fifth is a little bit better compared to 27EDO.

: '''Yourmusic Productions''': 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.

: '''Bozu''': This is sort of the gold standard of meantone tuning. Composite hypopent. Great thirds and fifths and everything else used to make western-esque music, and also some really nifty other spicier options. Very user-friendly. If you start with 12edo and go to 19edo and like it, this would be the obvious next recommendation. My only complaint here is that we are starting to get into the territory of having too many notes to easily perform on a guitar or standard black-and-white-key two row keyboard. Going with subsets at this point is beneficial, but those provide new challenges.

: '''Nicolai''': Meantone quarter tones.

: '''Yourmusic Productions''': 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.

: '''Bozu''': Composite hyperpent. Offers the same as 17edo, except more stable modal tones. This one is a gem. I have no idea how to handle notation, though, but it's one of the most useful.

: '''Nicolai''': 17EDO, but now there's a good third.

: '''Yourmusic Productions''': 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.

: '''Bozu''': Lots of notes, but all of the bases seem to be covered. Probably the only edo between 35 and 49 worth all of the trouble of dealing with so many notes.

: '''Nicolai''': Smaller version of 53EDO.

== [[42edo]] ==

: '''ArrowHead''': Has good approximations to the first 16 harmonics of the harmonic series like 43 does, and major triads with a very nice and buzzy sound, but is somewhat difficult to work with.

: '''Bozu''': Hyperpent composite. Same thing where it looks great on paper, but I feel underwhelmed noodling around with it.

: '''Nicolai''': You either get 5EDO or 7EDO, but there is a middle.