Collection of EDO impressions: Difference between revisions

: '''Vector:''' Not as "trivial" as some people think. The 2-limit sorta forces you to think of the octave as less of an equivalence than in higher limits.  

: '''MisterShafXen:''' Very bland, not worth using.  

== [[2edo]] ==

: '''Fumica:''' An exposition of consonance and dissonance.  

: '''Glitchydarkness:''' Diminished harmony without the thirds, It's interesting, but there's not enough notes yet.

== [[3edo]] ==

: '''Fumica:''' Augmented chord.  

: '''Glitchydarkness:''' You can make chords with this one! I'll name a few: Augmented ...  ...Augmented... Yeah you can't really do much, but it's neat! It's still the first EDO to actually have chords, and it's better than whatever 2edo was!

== [[4edo]] ==

: '''Fumica:''' Diminished chord.  

: '''Glitchydarkness:''' Has some good melodic movement for its size, and can play the diminished chord! Who cares if it's contained within 12edo, you could name any EDO and it's contained in another higher one too, it's a property of numbers!

== [[5edo]] ==

: '''Glitchydarkness:''' Really good for its size, and is the first EDO to have multiple types of chords! There are now sus2 and sus4 chords to be used, the harmony is evolving! We also get some more variety over at the melodic aspect of the scale, and overall everything is better then all previous edos. Even better, we have a perfect fifth! The key to harmony! Overall the best tiny EDO

: '''Vector:''' This is the best 2.3.7 edo by far for its size. Other than that, it's equipentatonic, and so you get the first hint of diatonic-style melody in this edo. It's a subset of 15edo.

== [[6edo]] ==

: '''Fumica:''' Whole tone scale.  

: '''Vector:''' Whole tone scale. It's interesting because it has basically all the basic consonances of 12edo except the fifths. I usually end up harmonizing with tritones; it doesn't even sound that dissonant because I'm already using the wholetone scale.

== [[7edo]] ==

: '''Carmen14edo/Bragtime:''' The basis of knowsur's melody and harmony on the 14edo album NANA WODORI, and thus one of my personal favorites.

: '''Fumica:''' Equalized diatonic scale.  

== [[8edo]] ==

: '''Deja Igliashon:''' Do you like 24edo? Do you think a chord of 0-400-550-700-850-1000¢ sounds close enough to 8:10:11:12:13:14? Great! Now play just the 10:11:12:13:14 part of the chord--it's 0-150-300-450-600¢, which also happens to be five consecutive notes of 8edo. Say what?! A decently-concordant 5-note chord in an 8-note tuning that everyone thinks is awful?! Who knew?? You can even extend it to 10:11:12:13:14:17 if you like that spicy 17th-harmonic flavor: just add 900¢ to the chord, and enjoy playing 3/4 of all the notes in the tuning at once and still sounding good!

: '''Fumica:''' The first nontrivial nondiatonic edo. Since neither the fifth nor the major second passes as consonance, quintal harmony isn't available, not to mention tertian harmony. From here the more complex ratios it approximates on paper generally lack the context to make them ring, so with the very sparse harmonic resource, it forces an approach that focuses on rhythm, texture – anything but harmony. Of course, some resource is there if you try hard enough, but suspending the idea of treating it as more than two diminished chords will spare you a demoralizing fight. Ultimately, I just believe music that sounds good in it sounds good despite it, not because of it; this isn't different from any of the previous edos.

== [[9edo]] ==

: '''Fumica:''' Similar to 8edo, its harmonic resource is quite sparse. Treat it as augmented chords. Good news is there are three.  

: '''Vector:''' Our first mavila edo! I'm not a huge fan of this tuning, because of all the enharmonic notes it gives in mavila.  It's the first time we have a distinction between normal major and minor chords, though.

== [[10edo]] ==

: '''Deja Igliashon:''' How is nobody talking about how awesome this tuning is for 8:13:14:15 chords? Like if you understand 15-limit JI at all, and you look at the intervals of this tuning, the harmonic series implications should just be slapping you across the face with an ice-cold salmon straight from the river. Lots of big accurate EDOs like 50edo and 60edo get their approximations to the 7th, 13th, and 15th harmonics from 10edo. And jeez, give a blues guitarist a 10edo guitar and she'll absolutely shred it without thinking twice because so many blues guitar gestures work just great in 10edo.

: '''Fumica:''' The first serious edo. Expressivity in the classical and/or septimal chords are neutralized, but harmonic 13 is accurately approximated and offers a critical advantage over 12edo. Imo the best edo for serialism. A-tier.  

== [[11edo]] ==

: '''Deja Igliashon:''' Mike mostly said it, but also: if you like 22edo's approximation to 4:5:6:7:9:11:15:17, all you gotta do is leave out the 5/4 and 3/2 and everything else is in 11edo. If ya wanna make really zonky xenharmonic music and don't care to keep the 3rd and 5th harmonics around, 11edo absolutely rules. Heck, even if you try playing tertian triads, i.e. 0-3-7 and 0-4-7, you're still more or less approximating 9:11:14 and 7:9:11, which aren't even that weird. Why are people so scared of this tuning??

: '''Fumica:''' Every other step of 22edo. It hits harmonics 7, 9, 11, and 15, and that's quite something. The 9 allows a form of quintal harmony. The 15 has good voice-leading utility. Of course, those properties are but implications of it being next to 10- and 12edo, both of which have those and can do much more. It just happens they're enough to make 11edo my favorite strictly nondiatonic edo. B-tier.

== [[12edo]] ==

: '''Fumica:''' A no-brainer. Fully laid-back, like a good font to an article – never to get in the way, never to show itself off. It disappears. It lets you forget about it and focus on the musical contents instead. S-tier.  

: '''Vector:''' The tuning I write most of my music in. It's good enough for writing the kind of music I want to write, as long as that kind of music isn't "xenharmonic". 12edo theory is my inspiration for my 15edo theory system, and my general approach to xenharmony. (It also brought with it a fair share of misconceptions: for a while, I assumed "sharp" just meant "1 edostep", and after I was corrected wtih 17edo I assumed it meant "between whatever intervals are (true) minor and major".)

== [[13edo]] ==

: '''Carmen14edo/Bragtime:''' The other one I'll probably never explore out of sheer fear

: '''Deja Igliashon:''' I'm amazed that people are actually using the random scale names I put on the 13edo wiki page (archeotonic, oneirotonic, etc.)! That's so cool! I love 13edo and I'm happy some other folks do too. It's fantastic for approximating 8:9:10:11:13:17:21 for such a small number of notes. 13edo's approximation to 13/8 also happens to be quite close to acoustic phi, for those who are into that sort of thing--stretch the octave a few cents sharp and you can get some really interesting phi-based combination tones.

== [[14edo]] ==

: '''Deja Igliashon:''' Semaphore--the temperament where 49/48 vanishes and therefor 7/6=8/7=half of a perfect 4th--has to be one of the most underappreciated temperaments, and 14edo is my favorite tuning of it. A chain of the 257¢ intervals generates both a 5-note MOS scale and a 9-note one, and the 9-note scale is incredibly rich in subminor (6:7:9) and supermajor (14:18:21) triads! How rich, you ask? On 7 of the 9 notes, you can build either a subminor triad, supermajor triad, or BOTH--mostly both, actually. And unlike 5-limit triads where the minor 3rd and major 3rd are a semitone apart, these septimal 3rds here are a whole-tone apart, which makes moving between triad types on a single root feel less wonky-chromatic and more akin to the vibe of moving from (say) a sus2 to a major triad or a sus4 to a minor triad. The triadic lattice is so hyperconnected in this temperament that common-tone chord progressions are basically everywhere, and you can drastically alter the mood without modulating to a different key while ALSO retaining a scale that feels melodically very similar to the diatonic, rather than a chromatic scale or a diatonic scale with extra passing tones. You can even selectively omit 2 of the 9 notes to play melodic gestures that essentially sound diatonic. Not to mention that since the Semaphore generator is half of a perfect 4th, there are 2 chains of fifths/fourths in this scale that are separated by subminor 3rds, so there are lots of possible chord progressions involving root movements by 4ths or 5ths. Okay, sure, these are the same shaky 4ths and 5ths as in 7edo, but there are plenty of musical contexts where that doesn't really matter.  

: '''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.  

== [[15edo]] ==

: '''Fumica:''' The error of the fifth is getting quite large for its step size, particularly if you compare it with 10edo. Either this or 10edo can be viewed as the opposite of 14edo, so I think of this as the direct competitor of 10edo. As for which I prefer? I have no idea. A-tier.  

: '''Vector:''' A shining example of why the chain of fifths is not suitable as a universal model. 15edo has a diatonic scale (the zarlino scale of 2313231) that makes for a much more familiar interpretation of the tuning than inflecting the 5edo notes up and down. In terms of just intonation, it approximates simple intervals of the 11-limit, and tempers the infamous zarlino wolf fifth flat enough that it merges with the concordant 11th subharmonic, thereby solving the main problem that zarlino itself has.

== [[16edo]] ==

: '''Fumica:''' Potentially useful as every other step of 32edo. Besides that, it has armodue, basically an extremely flat fifth that doesn't sound like the 3rd harmonic at all. "Fifthiness" is useless if not for approximating the 3rd harmonic, so I'm afraid I don't consider this approach to have much value. D-tier.

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

== [[17edo]] ==

: '''Deja Igliashon:''' Another one of my all-time favorite and most-used tunings! You literally cannot find a better temperament for the no-5s 13-limit unless you give an incredibly high weight to accuracy, in which case 207edo finally edges it out. (Or so little weight to accuracy that 9edo eventually beats it). It is just so accurate AND so small that any mathematical approach to quantifying temperament badness practically cannot help but declare 17edo the true lord and savior of the 2.3.7.11.13 subgroup. And if you can stop moaning about how out-of-tune the major triads sound long enough to actually mess around with other harmonic possibilities, you'll quickly discover that practically anywhere you put your fingers, you're stumbling on something that hums and buzzes with that wonderful cold and alien 13-limit energy. Oh, and this is also the smallest EDO that can distinctly represent the rough melodic shapes of all the maqamat from Maqam World, since it is the smallest EDO that has neutral 2nds (half of a minor 3rd), neutral 3rds (half of a perfect 5th), AND good perfect 4ths and perfect 5ths.

: '''Fumica:''' This edo contains an impressive diatonic scale which is nice for both melody and harmony. Semiquartal harmony, that is using the contrast between 7/4 and 12/7 as the basis of tonality, works exceptionally well in this system. S-tier.

== [[18edo]] ==

: '''Deja Igliashon:''' Of all of the EDOs I've played in or looked at, this is definitely one of them. Normally I'm able to find some compelling subset of harmonics 8-16 (or at least 16-32) that every EDO really excels at approximating better than anything else near it in size. For 18edo the best I can find is 11:12:13:14:15:17, which looks good at first until you realize the 11:12:13:14:15 part of it is all 9edo, and adding that 17 to the end just doesn't really expand the possibilities very much at all. 18edo is also really good for 16:18:20:21 chords, but 13edo is also pretty good at those AND can extend them to include the 11th, 13th, and 17th harmonics, so it's hard to make the case that 18edo is a better choice, since it is also BIGGER.

: '''Fumica:''' Potentially useful as every other step of 36edo. D-tier.  

== [[19edo]] ==

: '''Deja Igliashon:''' I have tried SO HARD to like this tuning, but I just can't. Yeah, it's a very nice meantone and those syrupy-sweet 5-limit harmonies are delicious. It also supports Semaphore temperament, which I gushed over when talking about 14edo, and in fact it even adds a teensy bit of 5-limit grounding to Semaphore (making it Godzilla). But the fact that it's just so good at 5-limit diatonic music, and so not-so-good at most things involving the 7th, 11th, and/or 13th harmonics, makes me feel like I'm getting zapped by a shock collar any time I try to step from meantone into something more esoteric. There aren't any 7- to 10-note scales that really allow 5-limit harmony to expand to include higher primes very well...Magic[10] is probably the most rich in harmonic possibilities, but it's so melodically awkward! That said, I've heard musicians who are much better than me pull some spectacular sounds from 19edo by indulging in forms of chromaticism that are lost on my jazz-illiterate self. Then again, 19edo has so many fans and cheerleaders that I feel like it's my sacred duty to diss it and hype up the less-popular EDOs instead.

: '''Fumica:''' This edo is where my microtonal journey began. Extremely versatile yet friendly to beginners. Using it as a tuning of meantone, the tuning profile is sort of opposite to 12edo, but with seven more pitch classes, the expressive possibility explodes. Presence of an exact hemitwelfth sets it apart from many other meantone edos. S-tier.

== [[20edo]] ==

: '''Deja Igliashon:''' People be SLEEPING on this absolute xenharmonic powerhouse! "Oh, it has terrible renditions of the 3rd and 5th harmonic, and there are smaller EDOs that have good renditions of them, so why would anyone use 20edo?" Honey. Darling. Sweetheart! You have NO IDEA! The harmonic series goes so much further, WHY are you stopping at the 5th harmonic? Does 20edo do a good 7th harmonic? Yes. 11th? Sure! 13th? Almost perfect! 15th? Less than 9 cents off! 17th? Eh, passably. 19th? You bet! 21st? Oooh yeah, 10 cents isn't that far off. 23rd? Meh, 12 cents is pushing it, but... 25th? Hell yeah! 27th? Yes ma'am! 29th? Also within 10 cents! 31st? You bet your neon tutu! Yes fam, I am telling you, 20edo does a better job at 4:7:9:11:13:15:17:19:21:23:25:27:29:31 than just about anything that is less than twice its size, and if you omit its weaker 9th, 17th, and 23rd harmonics, it is absolutely BREATHTAKING in its accuracy. So okay, you give up harmonics 3, 5, 9, 17, and 23, and in exchange you get 7, 11, 13, 15, 19, 21, 25, 27, 29, and 31? And there's still only 20 notes in the whole tuning? That's a hell of a bargain IMO, especially considering that the larger the otonal chord you are playing, the less it matters if one or two harmonics are out of tune, so realistically you can absolutely keep the 17th and 23rd harmonics in there.

: '''Fumica:''' 15edo but worse. F-tier.  

== [[21edo]] ==

: '''Deja Igliashon:''' 21edo is an enigma to me, because I ADORE it, I think it sounds amazing and I've made some of my best music with it, but I have NO IDEA how to explain that in terms of theory. It is solidly mediocre as a 7-limit temperament, not any better or worse as an 11- or 13-limit one, starts to look better as a no-3's 13-limit temperament since its approximations to harmonics 5, 7, 11, and 13 all lean sharp. I suppose one thing it has going for it is that it really is the poster child for tempering out 36/35, thereby making 7/6=6/5 and 5/4=9/7, such that the utonal counterpart of 4:5:6 becomes 6:7:9, and that's cool. But it doesn't really have any MOS scales that grab me--I usually approach it with tetrachordal scales in mind rather than MOS scales. It kinda seems like it might maximize a lot of harmonic entropy, since most of its intervals are smack in between a pair of adjacent simple ratios. Everything is kinda blurry and washy and watery and woozy except for the 7th harmonic, and I really can't think of any other ET that is just so good at that kind of ambiguity. Which is the kind of vibe I generally aspire to, honestly.

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

== [[22edo]] ==

: '''Deja Igliashon:''' 22edo not being a meantone does NOT mean you're forced into unfamiliar territory, at least not any more than pure 5-limit JI forces you into unfamiliar territory. Yes indeed 22edo OFFERS lots of fun new exciting possibilities, particularly in approximating the 11-limit with some very simple chordal/scalar structures, but you can absolutely make the most banal, trite, pedestrian music you want to as well. Don't let anyone scare you away from this tuning! Sure, certain chord progressions from popular songs written in 12edo don't work the same way, but if you're into microtonality enough to be looking at this page, you're probably not super concerned with playing faithful renditions of traditional songs.

: '''Fumica:''' The least evil solution to porcupine and less so to superpyth. I happen to have experience working with porcupine and it felt quite alright, except that I often found myself struggling to combat its out-of-tune nature. B-tier.  

== [[23edo]] ==

: '''Deja Igliashon:''' 23edo is the first EDO I've liked enough to write two full albums in, exclusively. It is probably my favorite EDO ever, I've even thought about getting the 23edo circle of flat fifths tattooed on my lower back! At first I thought 23edo was like 21edo, i.e. "it sounds better than it looks like it should", but then I realized I just wasn't looking at it the right way. It has amazingly-accurate representations of 3:5:7:11:19:27:29 and 9:13:15:17:21:23:25:31:33 (I'm probably missing some additional harmonics TBH)...because OH YEAH it's simply half of 46edo, and 46edo is a phenomenal rank-1 temperament for super-extended JI! It's actually surprisingly easy to stumble into some really smooth near-JI harmonies in 23edo, provided you're not trying to play basic 5-limit triads. Although honestly even 23edo's version of Mavila temperament sounds unexpectedly smooth...I think there's something funky going on with those 678¢ fifths where a whole bunch of clashing partials all have nearly identical beat frequencies or something? IDK, but either way I have found 23edo to be the most inspiring, deep, and intriguing EDO I've laid hands on (and I've laid hands on a LOT).  

: '''Fumica:''' Potentially useful as every other step of 46edo. D-tier.  

== [[24edo]] ==

: '''Deja Igliashon:''' it is an absolute crime that Western academic composers got into 24edo during the period when atonality was in vogue, and approached it with no care or consideration for the wealth of concordant harmonic possibilities it presents. It is really just awesome at no-7s 19-limit JI, like just try 0-200-400-550-700-850-1100-1300-1500¢, and tell me it's not doing just as good at approximating 8:9:10:11:12:13:15:17:19, as any other EDOs of similar size or smaller are doing at whatever harmonic series approximations they're known for. 24edo just gives you all kinds of fun ways to tack the 11th and 13th harmonics onto boring ol' 12edo 12-tone harmonies, and it really deserves to be recognized for that, not for its tradition of dreadful atonal discordance.

: '''Fumica:''' This is kind of a normie's edo, but also the most accessible. Quartertones in my otherwise 12edo works often go unnoticed by the audience. A natural next step of 12edo with a structurally beautiful 2.3.5.11.17.19 subgroup interpretation. A-tier.

== [[25edo]] ==

: '''Yourmusic Productions:''' 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.

: '''Fumica:''' 26edo but worse. F-tier.  

== [[34edo]] ==

: '''Yourmusic Productions:''' 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.

: '''Fumica:''' The idea of adding third tones to plain 12edo music is interesting, but none of my attempts have been successful as I generally find them to sound forced. I think this edo is more difficult to use than it appears. C-tier.

== [[37edo]] ==