Collection of EDO impressions

This page contains impressions and thoughts of several wiki authors (and others) about selected edos.

1edo

Aura: The framework for all other EDOs. As it offers only 2-limit consonance, all notes belong to the same pitch class, and this can get boring pretty quickly, though admittedly not as boring as if you only had one note to play.

Nicolai: The harmony of the cavemen.

Keenan: People ought to write more 2-limit music. (Or not.)

Yourmusic Productions: Contained within 12 and so not worth talking about.

Carmen14edo/Bragtime: It's just a single note m8, but somehow it's all we need

Fumica: An exposition of pitch.

Glitchydarkness: Perfect, but eventually it gets boring, you can only rely on timbre for so long! I'd know it's all i do

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.

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

Zhenlige: Octaves. Equivalent to 2-limit JI, unless you want to temper some other JI intervals into octaves. Not much to talk about.

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

2edo

Aura: This EDO is very simple, offering only the perfect consonance of the octave and perfect dissonance of the tritone. The brute force contrast between the antitonic (my name for the diatonic function of pitches located at or around 600 cents away from the tonic) and the tonic does make for good minimalistic harmonic progression, but to use this to its maximum potential requires some of the same techniques needed to master traditional music theory's Locrian mode, and even then, this EDO's limited note palette only ensures that it gets boring rather quickly.

Bozu: 0th order diminished. Nothing interesting, too constrained.

Nicolai: The worse harmony of the cavemen.

Yourmusic Productions: Contained within 12 and so not worth talking about.

Carmen14edo/Bragtime: It's just a tritone m8, but 12edo and fellow even edos just wouldn't be the same without it

Fumica: An exposition of consonance and dissonance.

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

MisterShafXen: Nowhere near enough notes.

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

Zhenlige: Half octaves aka symmetric tritones. The key to tritone substitution, although sometimes asymmetric tritones or even non-tritone intervals can also be used. Some notable approximations are 7/5, 17/12 and 99/70, the final one giving kalismic. 2n-edos within 1000 that do not support kalismic are probably bad in 11-limit.

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

3edo

Aura: This EDO is also quite simple, and it relies on the perfect consonance of the octave to obtain resolution, with the dominant harmony consisting only of the two steps surrounding the octave. Like with 2edo, 3edo does make for good minimalistic harmonic progression, but to use it to its maximum potential requires serious skills, and its limited note palette again ensures that it gets boring rather quickly.

Bozu: Elemental augmented type tuning. Fun for a minute or two, boring after that. Sounds augmented no matter what you play.

Nicolai: Augmented chord.

Yourmusic Productions: Contained within 12 and so not worth talking about.

Carmen14edo/Bragtime: Honestly I've just never been much of a fan of this one.

Fumica: Augmented chord.

MisterShafXen: Finally, at least one chord! Although it is dissonant…

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!

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

Zhenlige: 12edo major thirds. 2.5 subgroup augmented. The smallest EDO with decent 2.5 subgroup. Treating its steps as 63/50 gives landscape. 3n-edos within 1000 that do not support landscape are probably bad in 7-limit.

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

4edo

Aura: This EDO is twice as complicated as 2edo, but no more than that. Again, it relies on the perfect consonance of the octave to obtain any type of resolution, and the brute force contrast between the antitonic and the tonic makes for good minimalistic harmonic progression. This time, however, the pitch directly above the tonic can be used in conjunction with the tonic and the octave to create a surprisingly decent tonic chord- more or less the exact means of obtaining resolution in the strictest forms of traditional music theory's Locrian mode. However, given that there are only two other pitch classes to work with, a chord like this is best saved for the end of a piece. Unlike 2edo, 4edo has more of a melodic structure to work with, but again, this requires skills, and this EDO is liable to get boring rather quickly in the hands of an unskilled composer.

Bozu: Elemental diminished type tuning. Fun for a minute or two, boring after that. Sounds diminished no matter what you play.

Nicolai: Diminished chord. It, surprisingly, has interesting melodic movement despite only being four notes.

Yourmusic Productions: Contained within 12 and so not worth talking about.

Carmen14edo/Bragtime: UH OH IT'S A TRAIN A-COMING 💀

Fumica: Diminished chord.

MisterShafXen: It’s… okay. Only 1 tetrad, but at least there are 3 triads!

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!

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

Zhenlige: 12edo minor thirds.

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

5edo

Aura: This EDO is the smallest one commonly used and is the first one that allows the usage of the fifth above the tonic as part of a resolved tonic harmony, though this admittedly sounds dirty, and furthermore the note a fifth above the dominant acts more like a second than a third in this case. Thankfully, this EDO doesn't take as much skill to work with as the previous three EDOs, and it is not quite as dissonant in terms of its note palette either. Beyond this, and the fact that it provides the framework for the varicant and contravaricant functions, I can't say much more about this EDO than what has already been said by others who have used it, as the only reason I know anything beyond what I've mentioned here is due to observations of others' work on this EDO.

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.

MisterShafXen: Equipentatonic, has a shell of a 4:5:6:7 chord (no 5/4).

Mike:

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: Sevish - Fifteen (15 tone microtonal music) - YouTube

2. equipentatonic, which is trippy.

Yourmusic Productions: 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.)

Carmen14edo/Bragtime: As the others have already explained, this one is a certified hood classic. I second what Bozu and Keenan said.

Fumica: Equalized pentic scale.

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.

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

Zhenlige: Equalized pentatonic scale. 3-limit blackwood. Kinda familiar but everything is warped. To me as a Chinese, it sounds like out-of-tone traditional Chinese music. The smallest EDO that roughly represents 3-limit or 2.3.7 subgroup.

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

6edo

Aura: This EDO requires a mixture of the aforementioned techniques for 2edo and 3edo for proper harmonizing, along with knowledge of the whole tone scale from 12edo, as that scale is exactly what this EDO is. I'd really like to see someone take on this challenge, especially as there are more options for this EDO than for either 2edo or 3edo- particularly in the realm of melody.

Bozu: Smallest 2nd order tuning set - augmented in whole steps. There are a number of possibilities, but trying to create any sort of tonal movement is useless, modality is useless, and overall, it's overconstrained.

Nicolai: Whole tone scale. Take out 4\6 and you have a pentatonic subset of the lydian dominant scale.

Keenan: 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.

Mike: the whole tone scale. But, if you flatten the octaves, you can get almost perfect 4:5:7:11 chords, which is worth noting.

Yourmusic Productions: A universe in monochrome. You can make things out, but so much is missing.

Carmen14edo/Bragtime: wooOO the main character's having a flashback or a dream! *always visually accompanied by a ripple effect*

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.

MisterShafXen: Augmented in whole tones. So much missing.

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

Zhenlige: 12edo whole tones. Incomplete 12edo. Also a heavily stretched didacus chain.

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

7edo

ArrowHead: I find 7edo to be great for blowing people's minds since it completely eliminates any concept of "minor" or "major" in the diatonic scale. Everything is neutral.

Aura: This EDO provides the framework for all the diatonic functions and most of the paradiatonic functions. Beyond that, the fact that all triads are essentially neutral in this EDO, and the fact that this EDO supports Amity, I have very little to comment on.

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 5edo is. Regular temperament model of a scale used in Thai music. (disputed)

Mike:

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

MisterShafXen: Yay, diatonic! Oh no, it's all neutral (2.3.11.13.29 subgroup, anyone?)

Yourmusic Productions: The emancipation from harmony, but now with recognisable, if bland diatonic melodies.

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.

Vector: This... could honestly fit in as a diatonic tuning. It's the first kind of tuning where we have functional harmony, although all the chords are neutral.

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

Zhenlige: Equalized diatonic scale. 3-limit whitewood. It sounds like out-of-tone neutral scale music. The smallest EDO that roughly represents 5-limit.

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

8edo

Aura: The only things I knew for a fact about this EDO going in were from my understanding of 4edo- namely that the same techniques available in 4edo are also viable here, with the added bonus of being able to use the Locrian-style tonic harmony in other ways due to there being more available pitch contrasts. It is true that one has to omit the fifth from most chords for harmony in this EDO to be useful, but I have to say I was pleasantly surprised when I found out not only that the antitonic harmony could now be fortified with what is effectively a supermajor third rather than simply another instance of the tonic, but also that the pitch immediately above the antitonic could serve as a good set-up for the antitonic harmony thanks to also having this same supermajor third above the root in the form of the tonic itself. Suffice to say I now have a new xenharmonic trick up my sleeve.

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:

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

Yourmusic Productions: Any combination of more than 2 notes sounds bad, and most 2 note combinations sound bad too. Just vile.

Carmen14edo/Bragtime: I'm convinced anyone who thinks this edo legitimately sounds good are lying.

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.

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

Zhenlige: Incomplete 24edo.

Eufalesio: Having no diatonic fifths is useless to me.

9edo

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. Listening to others' antidiatonic scales in this EDO does have my curiosity peaked, but at the same time, the lack of a good fifth is a turn-off for me.

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:

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)

Yourmusic Productions: Marvellously elegant little system. More than enough room for complex melodies and fortifying them with double-stopped 3rds and 6ths sounds awesome.

Carmen14edo/Bragtime: The only song I ever heard in this edo was from the video "1 to 11 tone Equal temperament songs" by 5 hideya, but it sounded like anxiety on steroids.

Deja Igliashon: Do you like 36edo? Do you think a chord of 0-400-567-700-833-967-1100¢ sounds close enough to 8:10:11:12:13:14:15? Rad! Now play just the 11:12:13:14:15 part of the chord--it's 0-133-267-400-533¢, which also happens to be five consecutive notes of 9edo. You can even extend it to approximate 11:12:13:14:15:19 if you're into that kinky 19-limit stuff, just add 933¢ on top!

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.

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

Zhenlige: A stack of 7/6. A subset of ennealimmal.

Eufalesio: Because this system does not support diatonic, I consider it useless. On its own. However, as a subset of other edos, it absolutely rules, as it is the basis for ennealimmal. A great deal of nineven edos are top-tier, because of this. Alone, rank: F. As a subset, rank: A.

10edo

Aura: With the discovery that this EDO tempers out the punctisma, and that it creates part of the structure that 24edo inherits, I'm interested in finding ways to put an approximation of this EDO to use.

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:

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

Yourmusic Productions: 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.

Carmen14edo/Bragtime: Apparently it's pretty cool.

Bill Sethares: If God Had Intended Us To Play In Ten Tones Per Octave, Then He Would Have Given Us Ten Fingers.

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.

Vector: This EDO is a decent 2.3.5.7 system, somehow, despite only having neutral thirds. It tunes its fifth exactly sharp enough that the neutral third just peeks into the major third range, and as 5/4 is on the flatter end of major thirds, it's just enough to latch on.

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

Zhenlige: A stack of 13/8. A subset of 130edo and 270edo.

11edo

Aura: Potentially useful in terms of its pitch-hue palette due to it being every other step of 22edo- the lack of a diatonic fifth is a turn-off.

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. 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

Mike:

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.

Yourmusic Productions: 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.

Carmen14edo/Bragtime: One of the only ones I'll probably never explore out of sheer fear

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.

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

Zhenlige: Incomplete 22edo.

Eufalesio: Having no diatonic fifths is useless to me. Use 22edo instead.

12edo

ArrowHead: The smallest one that does 5-limit well, and is right on the midpoint of the regular diatonic tuning spectrum, separating meantone from Parapythagorean and Superpythagorean. Has the largest possible contrast between major and minor for a meantone tuning, though since the wide major thirds and narrow minor thirds can sound quite sludgy on certain timbres such as organs I feel like 12 is far from optimal tuning for many areas of Western music. While I do feel that Western music education should cover the mathematics of tuning before college, and talk about Pythagorean tuning and other meantones to encourage Western musicians to explore other tunings and prevent people from thinking that 12 is the only correct way to tune, I do admit that these should come after people get familiar with the common practice chords and scales, and 12edo is without a doubt the best starting point for introducing stuff.

Aura: Finally! The EDO I have the most extensive experience with. All my direct, first-hand experience with 1edo, 2edo, 3edo, 4edo and 6edo prior to me finishing this page came about because I have access to a 12edo instrument- my grandmother's piano. It is also from here that I've taken the bulk of my ideas on tonality- including my idea for Treble-Down tonality. I still use this EDO as a basis for forming harmonic and melodic ideas, however, now that I've grown accustomed to having microtonal gestures available, I find it rather anemic in terms of its expressive potential.

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: 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!!)

Yourmusic Productions: The more I study it, the more it's flaws and limitations irritate me.

Carmen14edo/Bragtime: For all the hate others have for 12edo, I have love and respect. I believe we microtonal musicians take it for granted, and while it's not the best edo to be the western standard regarding sheer possibilities in this tuning, it's very far from the worst choice imo, and I'd personally choose it as western culture's standard tuning over most all other edos of a similar size.

Deja Igliashon: why is no one talking about how good the 8:9:10:12:15:17:19 chords are in this tuning? You can even sneak a 14th harmonic in there at 1000¢ and it won't harsh the sound very noticeably.

Fumica: 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".)

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

Zhenlige: Equalized chromatic scale. Both augmented and diminished. The smallest edo with decent 7-limit. The only reasonable tuning for the dominant temperament ignoring overall streching. A sharper fifth makes garibaldi better and a flatter fifth makes septimal meantone better. The boundary between meantone and schismatic. The smallest diatonic EDO. Efficient at its size. Very excellent 3 as well as 17 and 19 for its size, but inaccurate 5 and worse 7. Suitable for symmetric scales. Easy to make accurate NEJIs. Its 2.3.17.19 subgroup deserves more exploration (something "xenharmonic" but not "microtonal"). Its thirds do not accurately approximate common JI intervals. A well temperament can make some of them do better.

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

13edo

Aura: Has a basic oneirotonic scale, but since there's no diatonic fifth to work with when I need it, I don't want to stay here.

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. 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:

1. 13edo 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

Yourmusic Productions: 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.

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.

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

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

Eufalesio: Having no diatonic fifths is useless to me.

14edo

Aura: I have to admit that I was surprised to learn from others that one can replicate dialtones in this EDO, and it was that knowledge that made me want to incorporate a 159edo-based approximation of it. Suffice to say that based on my work with said approximation, this is a pretty strange EDO overall as you don't have as much of the familiar to rely on.

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:

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

Yourmusic Productions: The opposite of 10edo - 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 12edo, 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.

Carmen14edo/Bragtime: Need I say anything? It used to be my bae, and will forever have a special spot in my heart.

Deja Igliashon: Semaphore--the temperament where 49/48 vanishes and therefore 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.

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

Eufalesio: Having no diatonic fifths is useless to me.

15edo

Aura: I've since found that this EDO supports a variation on my traditional diatonic scale, however, tempering the 40/27 to a large tritone, as this system does, causes its fair share of problems.

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 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.

Yourmusic Productions: 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.

Carmen14edo/Bragtime: Blackwood[10] is like the coolest scale ever, change my mind (you won't)

Deja Igliashon: One of my all-time favorite and most-used tunings. It absolutely RULES on guitar, it's so easy, it's so fun, it's so versatile, everyone should try it! Also, why is no one talking about the fact that 15edo is essentially the smallest EDO that can recognizably render harmonics 2, 3, 5, 7, and 11? Yeah, Blackwood[10] is rad AF for having an unbroken circular chain of alternating major and minor 5-limit triads with no wolf intervals, but like...have you seen Triforce[9]? It has three 8:10:11:12:14:15 hexads! That's UNHINGED. Sure they are not tuned super accurately, but you can practically just mash random combinations of pitches in that scale and end up with some recognizable 11-limit harmony. Also, 15edo supports Orgone temperament, like 11edo and 26edo, but unlike those other two, 15edo tempers out 56/55, making 5/4=14/11, and making the utonal counterpart of 8:11:14 equal to 4:5:7. That gives Orgone[7] some extra concordance.

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.

Budjarn Lambeth: Offers exciting melodic shapes. Still requires careful attention to timbre, but it's more forgiving on that front than most similar sized tunings. The smallest equal tuning that approximates the entire 11-limit, so it's a great starting point for exploring new consonances which can't be found in 12.

Zhenlige: Better than it seems to be, tho still rough. Blackwood augmented. A heavily stretched Carlos Alpha scale. The best you can get with blackwood. I don't know why there are "people fond of" such inaccurate temperaments.

16edo

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.

Yourmusic Productions: 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.

Carmen14edo/Bragtime: I want Easley Blackwood's "16 notes: Andantino" to play at my funeral

Deja Igliashon: There's lots of cool stuff happening in 16edo, but a surprising amount of it is basically just inherited from 8edo. What 16edo adds to the mix is a nice 5-limit major 3rd and a nice approximation to the 7th harmonic, and also the freaky-funky Mavila[7] inside-out diatonic (where major chords become minor, minor chords become major, diminished chords become augmented, and mice chase cats). But IDK, despite my high tolerance for tunings with awful or non-existent perfect 5ths, I've yet to find anything I can do in 16edo that I don't feel like I can do better in a different tuning.

Fumica: Potentially useful as every other step of 32edo or every third step of 48edo. Besides that, it has armodue, basically an extremely flat fifth that doesn't sound like the 3rd harmonic at all. "Fifthiness" is pointless 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)

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

Eufalesio: Supposedly, it would be one of the best antidiatonic systems, next to 9edo, but if an edo does not have diatonic, I consider it useless. Unlike 9edo which forms the basis for ennealimmal, I don't know of any good temperaments with a 1/16 octave period. 2^n edos suck in general. Rank: D.

17edo

Aura: Like 14edo this EDO is pretty strange as you don't have as much of the familiar to rely on, though it does better than 12edo in some respects. Judging from my experience with the 159edo-based approximation of it, I can surmise that trying to work with Neapolitan-type scales in this EDO makes for an interesting experience.

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

Yourmusic Productions: Interestingly alien, but with good 2nd's, 4ths & 5ths to retreat too when you're not sure what to do next.

Carmen14edo/Bragtime: Some people like that one guy who wrote a paper argue this is better for diatonic melody & counterpoint, but at what cost? The answer is concordant triadic harmony lol

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 is characterized by its hard diatonic scale, with more contrasting step sizes than 12edo's basic diatonic scale. This gives it more intense voice leading and more cathartic resolutions. Traditional tertian harmony works pretty well here, but semiquartal harmony, that is using the contrast between 7/4 and 12/7 as the basis of tonality, does even better. S-tier.

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

Zhenlige: A circle of fifths in 34edo. Interesting sharp fifths. The smallest diatonic EDO with neutral intervals. The boundary between neogothic and superpyth. Like 12edo, its diatonic thirds do not approximate any simple ratios well, and a well temperament may help. Its 13 is good, and 11 and 7 have a similar precision to 12edo's 5. It benefits from compression.

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

18edo

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

Yourmusic Productions: 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.

Carmen14edo/Bragtime: I'll go out on a limb and guess this is one of the least used and least liked edos. I have nothing against it, but I have nothing for it.

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.

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

Zhenlige: Incomplete 36edo.

Eufalesio: Having no diatonic fifths is useless to me.

19edo

ArrowHead: Has a radically different sound than 12edo and is a great alternative tuning to get into when starting out with microtonality and alternate tunings. Somewhat loose diatonic scale, but much tighter pentatonic. However, its sound is much more jarring compared to 31edo or 43edo, and so it can take quite of getting used to.

Aura: Judging from my experience with the 159edo-based approximation of it, I can surmise that this EDO is a little easier to work with than 17edo, but again, trying to work with Neapolitan-type scales in this EDO makes for an interesting experience.

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.

Yourmusic Productions: 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.

Carmen14edo/Bragtime: I'd rate it 10/10 if it didn't have such a shite approximation of 7/4, but 9.5/10 is still quite good. Sunsrise by SAGA and the cover Sunsrise v2 on YouTube have made my brain explode in the best way possible.

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. Octave stretch solves the intonational problem to a large extent. S-tier.

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

Zhenlige: A stack of 5/3. Very different tradeoffs from 12edo. Usable but imperfect for many temperaments. Meantone or magic, but with a too flat fifth. Strangely large minor 2nds off from 16/15 even more than 12edo's. A compressed Carlos Beta scale. For meantone 31edo is more preferable, and for magic 41edo. The lower bound of a good fifth. It benefits from stretching. Good as a subset of enneadecal.

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

20edo

Bozu: Hyperpent. On paper, it looks okay, but seems really difficult to use musically.

Nicolai: Nothing particularly interesting.

Keenan: 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.

Yourmusic Productions: 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.

Carmen14edo/Bragtime: Once edos get this big, they no longer offer me the inherent "woah I'm a small number edo" appeal, and that's when having other redeemable qualities must kick in. I'm yet to hear of such qualities with this edo.

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.

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

Zhenlige: The fact that 41edo is good indicates that 20- and 21edo are probably bad. Does anyone really think it is OK for a chord to contain a lot of inconsistent mappings involving 3?

Eufalesio: Having no diatonic fifths is useless to me.

21edo

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 14edo but moreso. Dramatically exaggerated harmonic expressiveness, shares the relatively nice major 3rd with 12edo 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 19edo for familiar sounding intervals, but still really rather nice.

Carmen14edo/Bragtime: Once edos get this big, they no longer offer me the inherent "woah I'm a small number edo" appeal, and that's when having other redeemable qualities must kick in. I'm yet to hear of such qualities with this edo, but I've heard inthar compose very pretty music in it. All that said, it's a multiple of 7edo so I should be a fan of it.

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.

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

22edo

ArrowHead294: Basically the opposite of meantone (specifically 31edo) when it comes to 5 vs. 7, since you find 7/6 subminor thirds in places where you'd normally expect 6/5 minor thirds and 9/7 supermajor thirds where you'd expect 5/4 major thirds. A great way to break out of the meantone way of thinking for most people, and probably the most optimal and practical tuning for superpythagorean temperament. Minor sevenths being 7/4 makes septimal harmony easy to reach and is a really cool effect IMO. However, although the 5-limit minor and major thirds are tuned closer to JI than in 12edo, the minor third is sharp instead of flat and the major third is flat instead of sharp, which gives 5-limit chords a lot of "zonk" to them.

Aura: I have to say that judging from the 159edo-based approximation that I'm using, the pentatonic scales actually sound pretty good, but the fact that this EDO forces its users to explore unfamiliar harmonic territory is a double-edged sword, and the diatonic fifth that this system offers is more like a 128/85 than a 3/2.

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 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.

Yourmusic Productions: Like 24edo, only the new harmonic options are actually more in tune than the familiar ones rather than less. Better than 12edo but still not quite as good as 19edo overall.

Carmen14edo/Bragtime: Gleam was the first microtonal song for me. I have no words to describe it other than ear candy of the future, peering into an alternate world with music better than our own. That aside, having concordant major and minor triads and a usable 11/8 approximation is really nice, but lacking a really concordant and non-septimal diatonic scale is a deal-breaker for me regarding me composing in it & exploring it.

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 just intonation 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.

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

Zhenlige: The smallest EDO with decent 11-limit and the smallest non-meantone EDO with decent 5-limit. Superpyth and porcupine. The only reasonable superpyth EDO. The upper bound of a good fifth. The best you can get with 50/49 tempered out.

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

23edo

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 16edo 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.

Yourmusic Productions: Not enough songs using this to get a proper opinion. Definitely one of the tougher ones to get to grips with.

Carmen14edo/Bragtime: Thanks, I hate it. Eikositriophobia exists for a reason.

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.

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

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

Eufalesio: Having no diatonic fifths is useless to me.

24edo

ArrowHead: For a while, 24 was the only microtonal tuning I ever knew about. It's very convenient as a microtonal tuning, since it's meantone and preserves all the familiar intervals of 12edo. The ability to use the 11th and 13th harmonics and their intervals (without 7) as consonances is a huge bonus. Also supports semaphore with alternating whole steps and quarter tones, allowing for tons of new progressions and modulatory possibilities. Unfortunately it's far from the best tuning to get into for introducing microtonality, since it doesn't do 7 well at all, though, and I've found that most Westerners consider the sound of 11/8 and 13/8 to be much weirder compared to 7/4.

Aura: This EDO served as my first personal foray into the world of microtonality- namely through my song "Folly of a Drunk". It is also from here that I learned a good chunk of what I know about the 11-limit, and given its telic fifth inherited from 12edo, it still holds a place in my musical practice. However, while its pitch-hue palette is richer than that of 12edo, and I've finally settled on an interpretation of my signature simul half cadence for this system, I still feel the need to branch out some.

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.

Yourmusic Productions: Double the complexity, but considerably less than double the number of good-sounding combinations. A lot of extra work for little extra return.

Carmen14edo/Bragtime: Many people in the microtonal community write it off due to the notoriousness of "quarter tone music", but I'm particularly attracted to the new 12edo-polyphony key changes possible in this tuning.

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.

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

Zhenlige: What some non-microtonalists think microtonality is. 12edo with neutrals. Good for prime 11. Accurate in subgroup 2.3.11.17.19.

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

25edo

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.

Yourmusic Productions: 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.

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

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

Eufalesio: Having no diatonic fifths is useless to me.

26edo

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 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.

Yourmusic Productions: Definitely deserves more attention than it's got so far.

Deja Igliashon: I just don't have much to say about this one. It's sort of the opposite of 21edo to me: looks like it should be really cool and good on paper, but I just don't really enjoy the sound. Most of what it's good at can be done in smaller EDOs too, and that's usually what I'd rather choose.

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

Zhenlige: The fact that 53edo is good indicates that 26- and 27edo are probably bad. A stack of 7/4. Good for 2.7.11 subgroup. Other intervals suck. Since it is relatively small, consistency does not implies high accuracy. Meantone in 5-limit but tuned terribly. Incomplete 130edo.

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

27edo

ArrowHead: Similar to 22edo, 27 is basically the opposite of meantone (specifically 19edo) when it comes to 5 vs. 7, with subminor and supermajor thirds and sixths in places where minor and major thirds and sixths usually are. Criminally underrated and underutilised for what it is. Fifths are very bright and shimmery but not wolf-sounding like 5edo is. Its 5-limit minor and major thirds are more familiar and forgiving than 22edo, and it has a very good 13th harmonic. Overall a great place to explore xenharmony with temperaments like Tetracot.

Aura: Not going to lie, given how underexplored this EDO is, I felt it necessary to try working with a 159edo-based retuning of it. Judging from my experience with that, it should suffice to say that working with Superlocrian in this EDO is another interesting experience.

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.

Deja Igliashon: if this EDO got as much attention as 31edo, the world would be a better place. For many EDOs, getting into the particulars of how they temper extended JI is kind of unnecessary to really appreciate them, but 27edo is just so disgustingly ELEGANT in how it tempers that it makes it SO MUCH EASIER to navigate extended JI than darn near anything that can approach it in accuracy. First, consider the unison vector 64/63: just like 5, 10, 15, 20, 22, and 25edo (and I guess 12d?), tempering this out makes it so you can divide 7/4 into two equal parts that are each equal to 4/3, so even a short chain of fifths just automagically incorporates a bunch of ratios of 7. Then you've got 128/125, aka the Augmented comma, aka the diesis or something, which makes it so three approximate 5/4s span exactly one octave--if you simply follow a chain of 5/4s, you literally can't get lost in the tuning! So far so good but also 15edo can do both of these as well, so what else do we have? How about the holy trinity of 144/143, 169/168, and 196/195, the vanishing of which make it so 12/11=13/12=14/13=15/14? This is the trinity that really gives 9edo its mojo, and in 27edo we have three parallel closed circles of 9edo, offset from one another by 1 and 2 steps of 27edo (respectively). Why is this cool? Because if you have a root note on one chain of 9edo, you have a 5/4 above it on the same chain, and then you have 11/8, 3/2, 13/8, 7/4, and 15/8 on the next chain of 9edo that's 1\27 higher. So you can just arpeggiate a bunch of harmonics using motion by a single uniform step size, and if you keep moving by that same step size, instead of getting lost or circulating through ALL THE NOTES OF THE TUNING, you end up back at familiar territory after just a few off-kilter notes. Basically 27edo just makes it really easy not to get lost in 15-odd-limit JI, because you have can find your way between harmonics with simple motions on small closed circles. Just AMAZING!

Fumica: The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 subgroup with the sole exception of harmonic 15 tuned way too sharp, for I prefer a flat tuning of 15 or at least no sharper than 12edo's to improve its stability as a consonant major seventh. Other than that it's pretty good. Octave compression gives better intonation. A-tier.

Zhenlige: Worse than both 12edo and 22edo for 5-limit. It generally sounds worse than 22edo. Its fifth sucks and its diatonic scale makes little sense. Its 7/3 and 7/5 are good, but 3, 5 and 7 are off. When I hear its ~10:12:15 and ~6:7:9 chord I feel the fifth is obviously off. Use 108edo (not landscape) to make it a true 7-limit EDO, and 270edo is excellent.

28edo

Bozu: Hypopent and diminished, I'm not really sure what else this has to offer other than some funky neutralish intervals and diminished mayhem.

Yourmusic Productions: 14edo, 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.

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

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

Eufalesio: The hyper-accurate 5/4 alone and nothing else makes it useless. Rank: FF

29edo

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: 12edo'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 24edo Another definite favourite.

Fumica: The first edo that sounds like Pythagorean tuning with distinct chromatic and diatonic semitones, such that most contemporary 12edo music will sound alright if retempered to this through dominant. The patent-val interpretation is underwhelming. Otherwise it's a good framework as every other step of 58edo and every third step of 87edo. C-tier.

Zhenlige: A circle of fifths in mystery, which supports pele (and is close to its optimal tuning), a convenient temperament with 5, 7, 11 and 13 on the same chain of fifths. Near pure 13/11. The smallest EDO with a better 3/2 than 12edo.

30edo

Bozu: Hyperpent. Augmented. Meh, too many seemingly useless intervals.

Yourmusic Productions: Whole tone + Blackwood. Like 24edo, mainly just adds more ways to sound bad compared to 15edo and not worth the hassle.

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

Budjarn Lambeth: The most simple dual-fifth edo, not as "in-tune" as bigger ones, but a good introduction to the dual-fifth concept. It's kind of underrated because, while it doesn't have the same precise, luminous JI chords as 29 or 31, its wolf intervals are fewer and have less bite than 29 or 31 - so 30edo is actually relatively easy to noodle around in without hitting any really sour notes. It's not a good system for the JI-centric, regular temperament-centric approach that works for other big edos - but if you meet 30edo on its own terms, it's actually surprisingly approachable, and you can get a surprising amount of sweetness out of it. It kind of sounds like if JI was muffled underwater, if that makes sense? Everything's a little murky, but in a 'smooth' way - not necessarily unpleasant. Bryan Deister has lots of good Lumatone pieces in 30edo. Don't get me wrong, it's not as useful as 29 or 31, but it's much more useful than it's made out to be.

31edo

ArrowHead: The second alternative tuning I knew about after 24edo, I got interested in it through Baroque and Renaissance music due to it being an excellent representation of quarter-comma meantone that offers good approximations to all intervals of 11 (and even a few involving 13). Personally, I think this is the best alternative tuning for most non-classical Western musicians to use. Since everything sounds more mellow and calm compared to 12edo, I think that many, if not most, contemporary worship songs would sound better in 31 compared to 12. I also think it's a better tuning for songs with largely pentatonic melodies, such as Hillsong's Highlands, than 12edo is, since the pentatonic scale is noticeably tighter. The number of notes is not overly unwieldy (though it is pushing the limits of practicality on guitars and basses, it's still doable for chords), and the differences between its sound and 12edo's sound are big enough that people will notice (and therefore they might actually care) but not so big that it sounds jarring like 19edo can be (and often is). It also allows many interesting symmetry breaks and comma pumps over 12 that to me are an extremely interesting effect. If A is still 440 Hz, to me, keys from A major and F♯ minor onwards among the sharps sound noticeably darker in 31 and more energetic in 12, D and G major and their relative minor keys sound similar, while flat keys sound noticeably brighter in 31 and more "serious" in 12. Great for temperaments like Orwell that allow for easy exploration of more exotic harmonies.

Aura: Working with Superlocrian in this EDO is again interesting, but it's easier to do with this EDO than with 27edo. Apart from that, I'm not too thrilled with the lack of the telic fifth, nor the nature of this tuning system's approximation of the 11-prime.

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.

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

Zhenlige: Ideal for pure-octave meantone, combining lots of 11-limit extensions in a single tuning. The meantone flat fifth makes its neutral thirds close to 11/9 (tho there is the JI subgroup problem since 11 and 9 themselves are not so good). Also valentine and miracle. IMO the best meantone EDO. Nearly the best meantone can give for high limit. For other temperaments its flat fifth may be a drawback, making 9 bad.

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

32edo

Bozu: Composite hyperpent. diminished. Kind of user-antagonistic on first impression. Not picking up anything of striking value.

Nicolai: Same as 27 & 29EDO, but the fifth now is sharper than 27EDO.

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

Fumica: 27edo but worse. F-tier.

33edo

ArrowHead: Good representation of 1/2-comma meantone, a very flat meantone tuning where the whole tone is exclusively 10/9. Sounds really strange since there's so little contrast between major and minor and because the fifth is the absolute flattest that it can get before it starts to sound out of tune.

Bozu: Composite hypopent. Augmented. Same impression as 32edo, except maybe even less valuable.

Nicolai: 11EDO, but with a better fifth.

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.

Budjarn Lambeth: If you love the melodic shape of 7edo, but you wish it was a little more "in-tune", and you wish there were some subtle little variations between its modes, then 33edo's flattertone[7] scale is perfect for that. Once you get used to flattertone[7], you can explore the bigger flattertone MOS scales to sprinkle in even more colour. Or try approximating some overtone scales as close as possible in 33edo to take advantage of its lush, high-limit harmonies, and mix those with flattertone to really make it pop! The best piece I've written was tuned to 33edo: Enchanted Shopping Mall (2024).

34edo

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 31edo, 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.

Fumica: This is to 17edo what 24edo is to 12edo. While 17edo is often good enough, this offers some more sophisticated solutions such as tetracot. Even the harmonics 7 and 11, which come from 17edo and are commonly cited as relatively poor in this edo, are convincing enough to me, since when I worked with modus I never had a problem with the intonation at all, unlike with porcupine. The sound is better than the structure. B-tier.

Zhenlige: 17edo with 5 and 17 added, making a good 2.3.5.13.17 system. A slightly stretched Carlos Gamma scale.

Eufalesio: 17edo, but good. By splitting the edo in two, we get a great ya, the best so far. Fails at 7 and 11, which is sad, but at least is a very good yatha, as it also supports kleismic. And diaschismic. I've used this to retune some classical pieces. It's good for its grain, but it's not the best. Rank: B+.

35edo

Aura: Interestingly enough, this EDO has a heptatonic scale that consists of the following steps- 5\35, 7\35, 14\35, 21\35, 26\35, 30\35, 35\35. I found this scale while trying to find a good scale to use in a 159edo-based approximation of this EDO. All in all, this particular scale has a quality mostly evocative of something akin to Dorian mode despite obvious tuning differences that seem to give a sort of middle ground between the 5edo qualities and the 7edo of this EDO. So much for some of the claims of some other microtonalists about this one…

Bozu: Smallest amphipent edo (both hyperpent and hypopent).

Nicolai: You either get 5EDO or 7EDO, there is no middle.

Yourmusic Productions: 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.

Fumica: Potentially useful as every other step of 70edo. D-tier.

Budjarn Lambeth: A very good dual-fifth edo.

Zhenlige: The largest non-diatonic EDO.

36edo

ArrowHead: This is a great microtonal tuning which is also a great gateway into microtonality for Western musicians. Has true harmonic sevenths, along with very accurate and distinct approximations to septimal subminor and supermajor thirds and sixths. Since the 7th harmonic and all of its intervals are all pretty much variations on familiar intervals, from my experience many people consider the sound of the new intervals in 36edo to be more forgiving, whereas the "new" intervals in 24edo tend to sound much more jarring and weird in comparison.

Aura: I keep hearing about how this EDO has a good 7-limit, but given that the fifth is not telic, and the fact that there's no good 11-prime, I'm not inclined to use this EDO outside of approximations.

Bozu: 12edo slashed into thirds.

Nicolai: 12EDO, but better.

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 sixth 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.

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

Zhenlige: Good for 2.3.7.13.17.19.23.29 subroup. Avoid 5 here because it is almost completely missed. Otherwise incomplete 72edo.

37edo

Bozu: Amphipent with a lot of notes.

Nicolai: Same situation as 35EDO, but the 5EDO fifth is now just a superpyth fifth. Also good approximations of intervals.

Fumica: Potentially useful as every other step of 74edo or every third step of 111edo. Besides that, it has a good 2.5.7.11.13 subgroup interpretation, tho I have no idea how harmony in this subgroup is supposed to work. D-tier.

Budjarn Lambeth: A very good dual-fifth edo.

Zhenlige: A strong no-3 system, which is kinda hard to use since the only isoharmonic chords are subsets of the 3n+1 and 3n+2 series, and there are not many useful scales.

38edo

Bozu: 19edo slashed into halves.

Fumica: This is to 19edo what 24edo is to 12edo. On paper it adds decent approximation to harmonics 11, 17, and 19, but in practice I never had a situation where I felt I needed these additional notes when working with 19edo. C-tier.

Zhenlige: 19edo with neutrals. Near pure 11/9. Doubling such a coarse EDO won't give anything very notable, and the acceptable error of 19edo really becomes a problem at this size.

39edo

Bozu: Hyperpent augmented with a lot of notes.

Nicolai: You either get mavila or superpyth, there is no middle.

Fumica: 1/5-comma quasisuper, most notable for tuning the minor second to 28/27 (with the 39d val) which I feel is where the tension peaks for voice leading. Such an overlooked system despite the similarity to 27edo in many ways. B-tier.

40edo

Bozu: Amphipent diminished. Can't really find a good use for this one.

Eufalesio: Having no diatonic fifths is useless to me.

41edo

Aura: Using Ultralocrian mode in this EDO is a challenge, but apparently quite well worth it. It's tendencies to temper 15/11 and 27/20 together and similarly tempering their octave complements together make for giving my traditional diatonic music an unexpected edge, however, the lack of a telic fifth means this system is just not for me.

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.

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

Zhenlige: Prime octave and highly composite fifth, opposite from 12edo, thus good for fifth-dividing temperaments. Containing Bohlen-Pierce scale. Good for magic. The Kite guitar shows its elegance, with many simple intervals evenly spaced. Also garibaldi and miracle. The largest problem is its relatively inaccurate 5. From here on, most EDOs with good 13-limit support akea.

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

42edo

Bozu: Amphipent augmented.

Nicolai: You either get 7EDO or superpyth, there is no middle.

Zhenlige: Incomplete 84edo.

43edo

ArrowHead: By far my favourite alternative tuning for post-Mediæval Western music where 12edo's enharmonics aren't critical, and perhaps the most optimal meantone tuning. It has the fifths tuned flat and major thirds tuned sharp with almost exactly the same deviation from just intonation on both of them and the minor third is tuned flat by twice that amount. It's also good for microtonality involving higher-order harmonic complexes since it approximates most of the intervals involving 7, and 11, and 13 well, and has a somewhat better approximation of the first 16 harmonics of the harmonic series than 31edo. However, with so many notes, in practice it's best suited for keyboards (Lumatone et al). For guitar and bass players, I don't even think it's practical to put 87 frets on any real-world guitar or bass of reasonable size; at this point I think most guitar or bass players who want to use 43 would go fretless.

Bozu: Hypopent composite. Looks great on paper, but is a lot of notes and is either difficult to use or perhaps not as good in practice as it ought to be.

Nicolai: The other step-sibling of meantone.

Fumica: 1/5-comma meantone, not a bad meantone tuning in the 5-limit. The 3 and 5 are equally off, making up a beautifully pure 15. Unfortunately the diesis is too small to achieve good septimal and undecimal harmony. B-tier.

Budjarn Lambeth: Better than 12edo for most pop or earlier classical music that doesn't have lots of key changes in the one piece. The fifths are still pretty good, but the thirds and sixths sound so much warmer and more expressively. But, it is unsuitable if you want to use lots of key changes (like in jazz, later classical, or prog rock). Japanese pentatonic scales with semitones in them sound gorgeous in 43edo. I recommend the meantone[19] MOS scale in 43edo to composers who want to dip their toes into microtonality without getting in too deep.

Zhenlige: Close to 1/5-comma meantone which gives pure 15/8. Not very notable besides that. Its fifth is too sharp for septimal meantone.

Eufalesio: This meantone edo may have a seemingly good val to approximate higher limits, but doing so from a meantone framework is dumb. Apart from that, the lower limits, ones that I hold to high standards, are worsely tuned than in 31edo. In my opinion, the best meantones are the golden meantones, and from 31edo on, the peak has already been reached. E.

44edo

Bozu: Amphipent diminished.

Fumica: This edo adds decent approximation to harmonic 13 on top of 22edo's 11-limit, which is pretty tense to start with. At this point it just all breaks down. D-tier.

Zhenlige: Like 38edo, doubling a coarse EDO won't give anything very notable.

45edo

Bozu: Amphipent augmented.

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

46edo

ArrowHead: Has good approximations to the first 16 harmonics of the harmonic series like 43edo 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.

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

Zhenlige: 13-limit diaschismic and valentine. Near pure 11/7. It has quartertones similar to 22edo but approximates JI intervals more accurately. Its 30::36 are all 2 steps apart.

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

47edo

Bozu: Amphipent augmented.

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

Zhenlige: Incomplete 94edo.

48edo

Bozu: 12edo with eighth-tones.

Nicolai: 12EDO, but more fancy.

Fumica: More appropriate as an interval category scheme than anything else. C-tier.

Zhenlige: A not-so-good multiple of 12edo.

49edo

Bozu: Amphipent with two different choices of crummy fifths. Not really obviously useful, in my opinion.

50edo

ArrowHead: I think this is the optimal tuning for most music with largely pentatonic melodies, since having the major third be slightly flat (2–4¢) helps bring out the greater contrast between the whole tones and minor third without sounding jarring like 19edo can. Keyboard players can play this on the Lumatone or any other isomorphic keyboard. Putting 101 frets on a guitar or string bass, on the other hand, is a different story, so ultimately 31edo is more practical, especially for contemporary worship musicians who don't often deal with much complex music.

Bozu: This is a great option for meantone. Notations seems to be less of a pain, but 53edo is almost better in every way.

Nicolai: I consider this an optimal meantone EDO, due to a wealthy collection of notes here.

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

Zhenlige: Meantone with a flatter fifth than 31edo, but I usually use golden meantone (with slight octave stretching) for this range.

Eufalesio: Still a good meantone edo, and though it is a much better approximant for golden meantone, I prefer using golden meantone as a rank-2, and not buying the entire gamut. The 19-limit usability is very surprising, still. However, having all those new intervals inside a meantone edo feels in my opinion strangely unnatural, as we're stretching the meantone chain-of-fifths beyond what's supposed to. The meantone chain of fifths already hits its apex with 31edo. – For finer edos in this range, meantone ceases to do it for me, but I respect this one. Rank: C-.

51edo

Bozu: Not as versatile as 50edo.

Fumica: 17edo with a major third from the augmented temperament, which can be a useful combo. Otherwise it has little tone efficiency. C-tier.

52edo

Bozu: Not as versatile as 51edo.

53edo

ArrowHead: Works great as an extended Pythagorean tuning, making it well-suited for Mediæval music. Also suited for those wanting to experiment with true 5-limit just intonation but also having the ability to modulate. It is also perhaps the most optimal equal temperament tuning supporting Orwell, due to its fifth being almost indistinguishable from just, the fact that it has a good approximation of the 13^th harmonic (which 31edo does only an okay job at and 22edo lacks entirely), and 84edo has so many notes that it really does get unwieldy. Turkish music theory is also based on 53edo. However, this is truly near the stopping point for physical instruments and 107 frets isn't practical for almost any real-world guitar or bass.

Aura: Most of my experience with this EDO comes from my discovery of its admirable performiance in the 5-limit, and this will likely continue to be the case, since while it has a telic fifth, the lack of good approximations other than the 2.3.5.13 subgroup- particularly its bad 11-prime- is a turn-off, and, to be honest, I wasn't sure how to get around that issue until I discovered 159edo.

Bozu: Generally the stopping point. If you are comfortable with >50 tones, then this tuning offers almost everything you will need. If not, stick with 31edo or something smaller.

Nicolai: JI: The Book.

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

Zhenlige: A stack of 3/2. Almost just 3, accurate 5-limit, and decent 7-limit. Good for 5-limit schismatic with occasional garibaldi 7.

Eufalesio: Pythagorean tuning incarnate, and astounding ya. Yathana is especially potent, but the -zatwetha is still very much usable, even the yazalatha! It feels less tempered than 41edo, so it feels like a less compromised system, still, I feel bad for the rest of the edos near this one, because this trumps a lot of the competition. But what can I say? Suck it losers! Rank: SS.

55edo

ArrowHead: A standardisation and representation of 1/6-comma meantone, proposed by Telemann as a theoretical basis for analysing the intervals of meantone. Works well for most of Western music written since the Renaissance and even works today for songs that don't presuppose 12edo's enharmonics, but in practice I think it's really best suited for certain classical works as it's gotten to the point of diminishing returns. For non-classical musicians, the sound is likely to be far too similar to 12edo to justify the significant extra complexity, especially since 43edo and 50edo are already pushing it.

Fumica: This edo is out of the optimal range of meantone. Septimal meantone feels dumb here since we know 43edo is sharp enough. It can be used for mohaha, but that feels so similar to 24edo that I'd just go with the latter. D-tier.

Eufalesio: Even worse than 43edo. In fact, it's a zeta valley edo, which means that it does a bad job at approximating JI, and that in my eyes is a failed edo. I don't know what the Mozarts were on while they suggested a meantone this sharp... it's not good at all! Rank: FF

56edo

Fumica: A hemicommatic edo with a rather messed-up tuning profile. Nothing notable about it. D-tier.

58edo

Fumica: The fourth essential comma-level edo. Being the first edo with full 11-odd-limit distinction, this one is easily adorable. Whereas 41edo tunes the fifth to 24 steps, this edo tunes the fourth to 24 steps, and the implication is its 2.3.5.7.13.29 subgroup is analogous to 41edo's 2.3.5.7.11.19 subgroup. This edo is best as a 2.3.5.7.11.13.29-subgroup system, but it has more to offer. Specifically, the harmonics 19 and 23 in the 58hi val are surprisingly convincing, and although the 17 doesn't blend quite well it at least looks good on paper. Everything considered, it is virtually the first full 23-limit system. All that bugs me is the minor fact that 11/8 and 7/5 are tuned too close to each other, only one comma apart. A-tier.

59edo

Bozu: Seems to have some interesting options, but it's a lot of notes, and other neighbouring edo's can do some more versatile things.

60edo

Bozu: 12edo, with each note sliced into five pieces. Not a bad option, except for the myriad of notes to navigate.

Fumica: This edo has a particularly problematic fifth, in that it closes after twelve steps, tempering out the Pythagorean comma. As the first thing I leave meantone is to look for a fifth that leads to a positive Pythagorean comma, this edo is clearly not my thing. C-tier.

61edo

Fumica: Can be used to tune modus. Otherwise not bearing much utility. D-tier.

62edo

Fumica: The ultimate 23-limit meantone tuning. It re-tunes harmonics 13, 17, and 19, and paves the path to the 23 from 31edo. I find these additions to 31edo's 11-limit very favorable. A-tier.

Eufalesio: Keeps all the 11-limit goodness from 31edo and greatly improves on primes from 13 and beyond. It can be used all the way to the 23-limit, with monotonic error. Interesting, but approaching higher limits from a meantone framework is dumb. Like 50edo, I still give it my respect, but mainly because it's a multiple of 31edo. C-.

63edo

Fumica: Similar to 56edo, nothing notable about it. D-tier.

65edo

Bozu: There are so many tonal options, but many of them are very useful. Maybe this could rival 53edo for versatility. There are some limitations, though.

Fumica: As every other step of 130edo, this edo is excellent in the 2.3.5.11.19.23-subgroup, but the contrast between that and the poor approximations to 7 and 13 is fatal. Still, it allows a dual-7 dual-13 approach, not very satisfying at this level but better than nothing. C-tier.

Zhenlige: A circle of fifths in 130edo.

67edo

Fumica: A disastrous meantone tuning. F-tier.

68edo

Fumica: While this edo contains 17edo and if we compare it with 51edo, it clearly hits more harmonic targets, it should be noted that linearly dividing the steps into four is a weaker move than into two or three, as quarter-step offsets don't tend to create new categories, unlike third- or half-step offsets. This is especially true of this edo, as 34edo hits lots of harmonic targets already. Another obvious flaw is the awkward situation with prime 11. C-tier.

70edo

Fumica: As every other step of 140edo, this edo's structure allows lots of niche uses. Unfortunately none of them is interesting enough to make me stay very long. C-tier.

72edo

Aura: While I don't recall making many songs with this EDO, I did compile a private list of Just Intervals, and I was quite fascinated with it for a time, as this EDO has better 5-limit and 7-limit approximations than both 12edo and 24edo, with the latter being inherited from 36edo. However, the fifth is not telic, which is a problem for me in its own right.

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

Zhenlige: The ultimate extension of 12edo and 24edo. Its 11-limit is very accurate with a slightly flat tendency that works well with 12edo's flat 3, and some higher limit intervals are also usable. Compton which is useful in 12edo-based programs. The only notable 13-limit non-akea EDO around this size. A powerful tool for modulating quartertones, which can be difficult in 24edo itself. Good for miracle. Suitable for octave stretching if only 17-limit or below is used. Playable by using three 24edo instruments or six 12edo instruments.

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

73edo

Fumica: A strange sharp-tending hemicommatic system that seems to allow some niche uses. C-tier.

74edo

Fumica: A good meantone tuning. Not much else to offer. D-tier.

Zhenlige: 37edo with meantone fifths. Close to tungsten meantone. The intrinsic error of meantone becomes a problem at this size, making 9 inconsistent.

75edo

Fumica: A good tetracot tuning. Otherwise nothing notable. D-tier.

77edo

Fumica: This edo is very sophisticated and hard to evaluate. It's an ideal tuning for the valentine temperament, obviously. It also seems to be capable of somewhat approximating the full 23-limit. Overall, the structure is a tight fit, with lots of quirks, but that's not too troublesome – they may as well be turned into advantages in the right circumstances. B-tier.

Zhenlige: Good for valentine. Its slightly flat 3/2 gives a good 19 via boethius. Containing Carlos Alpha. 40/27 as 4\7 aka absurdity. Usable for high limit JI. At this size even some inconsistent intervals are usable via val mapping since its step size is only ~16 cents.

79edo

Fumica: A disastrous non-meantone tuning. F-tier.

81edo

Zhenlige: The optimal patent val for meantone and some of its higher-limit extentions, but I won't use such a large EDO for a temperament with relatively low accuracy, and rather use golden meantone instead, which is simpler and more elegant mathematically.

Eufalesio: 81edo is already the absolute maximum for golden meantone, as anything finer and the patent val fifth stops supporting it. If 50edo was already a bit too much, 81edo and beyond are definitely too much. At that point, it's better to not buy the entire gamut and just use rank-2 golden meantone. D.

84edo

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

Zhenlige: An alternate compton EDO besides 72edo, with better 5 and 13 with the expense of 11. It has a sharp tendency instead of 72edo's flat.

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

87edo

Bozu: 29edo with each interval sliced into three. You can do some nifty stuff with it, but the number of notes is too crazy to cover much with midi unless you choose a subset. Pushing a continuum beyond this.

Zhenlige: Good mystery EDO. Useful for high limit JI. Playable by using three 29edo instruments.

Eufalesio: Theory says that it is a really strong 13-limit edo. So much so, that it is the first edo with distinct consistency and pure consistency in the 13-odd-limit, and normal consistency in the 15-odd-limit, and for that, I give it my respects. However, I like my fifths to have minimal error, and being a subset of 29edo, the fifths are good, but not as good. Rank: C+.

94edo

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

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

Eufalesio: GOAT. The combination of the two coarsest schismic edos, which are both incredibly solid choices. However, 41edo is a tad too tempered and 53edo is a tad too untempered and too close to using pythagorean tuning as if it were yazalatha. However, 94edo is tempered just enough, into a neatly optimized cassandra package. I am heavily biased towards this, as it represents the ultimate cassandra, the simplest extended chain-of-fifths framework which I find extremely easy to work with. – Naturals for prime 3 or 19. ±1 for 17 or 23. ∓2 for 5 or 7. ±4 for 11 or 13. Throughout many different peer-reviewed experiments and in many on my compositions, I've found that this edo is good enough for most xen purposes. Still a tiny smidge innacurate in the ya, but since it is flat and not sharp, I find it much more palatable, as I like slightly wide minor thirds. I really only use it for the yazalathana, but the 23-limit goodness is no joke. Rank: Perfect.

99edo

Zhenlige: Efficient near-argent EDO. It suggests slight compression. Good for hemififths. It completely misses 11 and 13.

111edo

Zhenlige: 37edo with 3 added.

118edo

Zhenlige: The relationship of 53-118-171edo for schismatic is similar to 12-19-31edo for meantone. 53 and 12 are the simplest reasonable EDO with very mildly tempered fifths, 118 and 19 are better over all but slightly overtempered (outside 5-odd-limit diamond tradeoff), and 171 and 31 are ideal. So like 19, I won't appreciate it much.

120edo

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

130edo

Eufalesio: I haven't composed in it, but theory screams to me that this edo is a beast. I like to think of it as 65edo, but good. It has a very accurate yazalatha, and a schismic chain-of-fifths framework? Cool. Only problem... It's rastmic. Rastmic is a tad innacurate of a framework for an edo in the hundreds, but oh well. Rank: S

159edo

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

Eufalesio: Aura's favorite tuning. He does have a point, it takes an extremely good edo, and tripling it makes it even better! 29-limit goodness! I don't care as much for the insanely accurate ila, as I care for the entire yazalatha, on which it is worse than other alternatives, as primes 7 and 13 are relatively innacurate. I've composed stuff with it, and it isn't as easy to do as in other edos, but the result is still decent. Rank: SS-

171edo

Zhenlige: The ultimate EDO for approximating 7-limit JI. It suggests very slight stretching. If you don't need some ridiculous high precision or specific microtemperaments, there is no need to go any further. Schismatic, gammic, ennealimmal and enneadecal. Containing a better Carlos Gamma scale than 34edo. At this size level, EDOs are more like free pitch, rather than either JI or a stable temperament. Ideal for free-pitch-like music that emphasizes 7-limit.

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

217edo

Eufalesio: It's the septuple of 31edo, and that is nothing less than a miracle (though it doesn't support miracle). I've done some tests on it, and it's 31-limit is incredible. It's a simple high-accuracy system with very useful subsets. It introduces the cassaschismic framework in which you have to use 3-5 cent steps apart from the pyth spine, but apart from that, it's still within the realms of manageability. Also, it has an incredible yazatha, which I really respect. Rank: S+

224edo

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

Eufalesio: A cousin to 217edo which is still schismic, dare I say the ultimate schismic edo, though still harder to conceptualize. Theory tells me that the yazalatha is extremely accurate, even more than the 217edo, and for that I think it deserves praise. However, 217edo has 31edo as a subset, whilst 224edo only has powers of 2 which suck ass as subsets. Rank: B+

270edo

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

Eufalesio: Ultimate low complexity JIoid edo. Though a tad fine now, consistency and accuracy within its yazalathana is insane. I've done some tests with this and this is straight up unbeatable. For practically all musical purposes, this sounds like JI. There is literally no edo better than this within reason, as its step size is still discernible (by me (in mid frequency range)). Rank: Perfect.

311edo

Zhenlige: Good for very high limit JI.

Eufalesio: Ultimate ultra-high-limit JI. Absolute error is a smidge worse than 270edo, but it makes up by being consistent to the goddamn 41-odd-limit. Since its yazalathana mappings are the same as 270edo, it can be used to retune pieces for much more in tune otonality, but I'm not one to do that. This is my boundary of practicality. From this point on, edosteps begin to blend with each other and using JI is most surely a better option. Rank: SS

665edo

Eufalesio: Ultimate pyth. It has an unfathomably perfect 2.3, and I say that in an almost literal sense. It is very much fathomable, obviously: the beat period of 665edo's fifth is 5077906.80060 s*Hz with two sawtooth waves in perfect sync, which would be around 3 hours, 12 minutes 21 seconds at f=440. 3 fucking hours. That's what it would take you to hear the beating of 665edo. It is, for all intents and purposes, unfathomable to focused human perception. Or, you could make a 3-hour track out of this and sell it to connoisseurs disenchanted with the mainstream. However, this is not why you would use 665edo, as this essentially allows you to extend the precision limit of the chain of fifths from very good to extreme, by adding the mercator (+53 fifths) and an equalized qian comma (+306/-359 fifths) into the mix, also working as a schisma. Yes, it has a bad prime 11, but it is surprisingly good in the rest of primes up to the 27-odd-limit, which is very surprising for a convergent. I will likely never use this, but since I do greatly care about the chain of fifths as a theoretical construct, I think this is good. Rank: A.

7315edo

Eufalesio: Undecupling 665edo results in what I believe to be one of the potentially theoretically most robust yet precise JI-oid systems. Splitting the equalized qian comma in 11s greatly amplifies the accuracy of this edo and allows you to keep the unfathomably accurate chain of fifths as a strong backbone, and thirteenths of a qian comma serving as nanoalterations. I will likely never use this due to the insane precision it demands, but I have nothing other than respect for this behemoth of an edo. S.

8539edo

Eufalesio: If 311edo was my boundary of practicality, 8539edo is my boundary of sanity. The precision of this behemoth is unfathomable. I firmly believe no sane person would compose anything requiring a tuning precision higher than what this offers. And I'm one to ogle at impossibly gargantuan edos, I'll admit, but that ogling is only theoretical. Beyond here... there be monsters... and hot sauce. Rank: C

190537edo

Eufalesio: This is the next edo in the list of record k-strong telicity, and it starts to get scary from this point. This is unadulterated cosmic horror disguised as math in the 3-limit, forget about the rest of primes. The beat period of this fifth is 984 572 779 224.54 s*Hz with two sawtooth waves in perfect sync, which would be around 70 years and 331 days at f=440. This edo has a fifth that is accurate to a level that is quite possibly beyond the scope of a human lifetime. Think about it. There is a chance you'll die before listening to 190537edo's fifth beat, at f=440. – If you say that you need accuracy to this precision, I am, beyond a reasonable doubt, wholly confident you are not human, or not anymore. Perhaps in a couple centuries, posthumanity will be able to comprehend this near-perfection, but as we stand right now, it is impossible to comprehend. Unrankable.

Sources

Listed here are edo impression pages of individuals (if available).

• Aura's EDO Impressions
• Bozu's opinions of various edos
• User:Flirora/EDO_impressions
• Fumica's edo impressions
• Keenan's EDO impressions
• Mike's EDO impressions
• Nicolai's EDO Impressions
• Sevish's scale impressions (external site, Sevish.com)
• Yourmusic Productions' opinion of various edos
• User:Zhenlige/EDO impressions
• User:Eufalesio/EDO impressions