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

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

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

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

3edo

Aura: This EDO is also quite simple, and 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.

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

4edo

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 💀

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

5edo

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.

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

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

6edo

Aura: This EDO requires a mixture of the aforementioned techniques for 2edo and 3edo for proper harmonizing. 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*

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 5 is. Regular temperament model of a scale used in Thai music.

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

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.

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!

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. However, I can't say much about the other aspects of this EDO due to lack of other relevant experience on my part.

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

Keenan: On the one hand you can treat the 667 cent intervals as 3/2, yielding an extreme version of mavila (or 7-limit armodue) which is a very acceptable tuning for pelog selisir. On the other hand you can treat it has having no 3rd harmonics, as something like a 2.5.7/3 temperament. (Treating it as a super-accurate 2.27/25.7/3 temperament makes no sense to me.) First EDO with recognizable "major" and "minor" chords.

Mike:

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!

10edo

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.

11edo

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 22. This makes it a great 2.9.7.11 temperament. Includes machine, orgone, http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 and http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11

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??

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.

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.

13edo

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 26. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including uncle and dicot.

Mike:

1. 13 is insane. I can't get my head wrapped around it, but I love it at the same time. 13 wreaks havoc on my brain because it constantly sends crazy signals about my 12-EDO categories which misfire in fantastic ways. 11-EDO does the same thing, but 13-EDO is worse for no particular reason. You can use this to a particular effect by coming up with warped diatonic scales which have the pattern 2212221, but in which the "octave" now becomes more like a major 7th. Other than that, 13 is also notable for having a bunch of exceedingly beautiful scales which can generate some of the most far out harmonies you've ever heard, and is also simultaneously notable for being totally ignored in this capacity because a long time ago it got a reputation for being harmonically inaccurate and that reputation stuck. The crown jewel in the 13, uh, crown, is father[8], which is an amazingly vivid and bright scale, which for me evokes the imagery of galaxies in deep space and underwater coral reefs and stuff, but it's been largely ignored because it has an interval which is 30 cents off from 3/2 and which sounds bad if you expect it to be 3/2. Despite all that, I like the 738 cent interval for just being the color it is - treat it with caution but use it as an "extension" in chords and such. You can also treat it as 32/21, which means you're treating the inverse as 21/16, at which point you'll probably realize that this scale isn't bad at all - it's just the 2.9.7/3 version of mothra temperament, which Igs has called "A-team." Other nice scales include 2222212, which is glacial[7], and some other stuff. Oh yeah, and also the 738 cent interval is an augmented fifth in 26-EDO, which is twice 13. No comment. It also has good 13/8 and 11/8, and a good 7/6, and a decent 9/8, and a bunch of other random stuff. The circle of not-quite-3/2's hits a ton of those intervals.

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

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.

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 10 - recognisable, but distorted so there's three types of 3rd and 6th with exaggerated expressive qualities. Even though it's best intervals aren't as in tune as 12, it sounds much less dissonant when playing all the notes at once, so it seems a natural home for Schoenberg influenced serialism and extended chords.

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

15edo

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

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.

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.

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.

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.

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.

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 14 but moreso. Dramatically exaggerated harmonic expressiveness, shares the relatively nice major 3rd with 12 rather than the horrible tritone, and the highest edo that works with standard notation without having to add more letters or learn new kinds of accidental. Not as good as 19 for familiar sounding intervals, but still really rather nice.

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.

22edo

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.

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

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

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 16, but has superpelog in addition. Nothing to write home about.

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

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).

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. It is also from here that I learned what I have about the 11-limit.

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.

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.

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.

27edo

ArrowHead: Basically the opposite of meantone (specifically 19edo) when it comes to 5 vs. 7 (you find 7/6 in places where you'd normally expect 6/5 and 9/7 where you'd expect 5/4). 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!

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: 14, only with a really in tune major 3rd and lots of other really interesting extra intervals. Really want an instrument that can do this one justice, probably an 8-string guitar tuned in it's slightly stretched 5ths so the top string is 3 octaves up from the bottom, and a 28-30" fanned fret multiscale fretboard that makes all the chords isomorphic.

29edo

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

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

Yourmusic Productions: 12's evil twin, but in an awesome way. About the same amount of error but in opposite directions means similar kinds of psychoacoustic beating, majors and minors are still clearly recognisable, and everything sounds deceptively familiar right up until it does something awesome that 12 can't. When you do focus on xen intervals and chords, it still sounds much better than 24. Another definite favourite.

30edo

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

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

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. 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 12, 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.

Aura: Working with Superlocrian in this EDO is again interesting, but it's easier to do with this EDO than with 27edo.

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.

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.

33edo

ArrowHead: Good representation of ½-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.

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 31, with it's gorgeous thirds, actually defined different sizes of whole tone and still sour harmonic 7, yet even more underused. Definitely deserves more attention. Maybe a half-kite guitar, with full frets up to the perfect 4th or 5th, then 17edo above that point, with adjacent strings tuned so the full range of higher notes can still be played would make it feasible.

35edo

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.

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.

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.

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.

38edo

Bozu: 19edo slashed into halves.

39edo

Bozu: Hyperpent augmented with a lot of notes.

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

40edo

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

41edo

Aura: Using Ultralocrian mode in this EDO is a challenge, but apparently quite well worth it.

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

Nicolai: Smaller version of 53EDO.

42edo

Bozu: Amphipent augmented.

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

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.

44edo

Bozu: Amphipent diminished.

45edo

Bozu: Amphipent augmented.

46edo

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

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

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

47edo

Bozu: Amphipent augmented.

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

48edo

Bozu: 12edo eighth-tones.

Nicolai: 12EDO, but more fancy.

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 19 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.

51edo

Bozu: Not as versatile as 50edo.

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 JI but also having the ability to modulate without things getting too 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 current experiments with 159edo, and this will likely continue to be the case since this EDO doesn't have good approximations of the 11-limit.

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.

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 43 and 50 are already pushing it.

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.

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.

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.

84edo

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

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.

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.

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 Just Intervals, 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 contortion in the 3-limit, and it was at that point that I realized that contortion in the 3-limit was a problem.

159edo

Aura: This is the best EDO I've worked with, hands down. 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 more familiar kinds of things 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. Based on this discovery alone, and the fact that I managed to pull off multiple songs that people really seem to like- namely "Space Tour" and "Welcome to Dystopia"- I'd have to say that 159edo is not just a superset of 53edo, but rather, an EDO that is quite full of surprises. I imagine at this point that some would ask me why I don't just use JI, and the answer is that even a Mega-EDO 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.

Sources

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

• Aura's EDO Impressions
• Bozu's opinions of various edos
• Nicolai's EDO Impressions
• User:Flirora/EDO_impressions
• Keenan's EDO impressions
• Mike's EDO impressions
• Yourmusic Productions' opinion of various edos