Collection of EDO impressions: Difference between revisions

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== [[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.

== [[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.

== [[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.

: '''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.

== [[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.

== [[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.

: '''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: [https://www.youtube.com/watch?v=rPmuKUm2kJg ''Sevish - Fifteen (15 tone microtonal music) - YouTube'']

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: '''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.

== [[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.

: '''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.

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: '''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.

== [[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.

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: '''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.

: '''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.

: '''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".

== [[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.

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: '''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".

== [[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~~.

: '''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.

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: '''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".

== [[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.

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: '''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.

: '''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.

: '''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".

== [[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.

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: '''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".

== [[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.

: '''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.

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: '''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 wah for two reasons: it works with an impressively wide variety of timbres, and it avoids [[wolf interval]]s better than any larger tuning. I believe this elegant simplicity is the reason for its popularity.

== [[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.

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: '''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".

== [[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.

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: '''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.

: '''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".

== [[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.

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: '''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]].

== [[16edo]] ==

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

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

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

== [[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.

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

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

== [[18edo]] ==

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: '''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".

== [[19edo]] ==

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: '''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.

== [[20edo]] ==

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: '''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 greatly, ideal for composers looking for a wild world of new microtonal colours, without sounding as "sour" as some smaller EDOs do.

== [[21edo]] ==

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: '''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]] ==

: '''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.

: '''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.

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: '''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.

: '''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 interval]]s which can scare 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.

== [[23edo]] ==

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: '''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.

== [[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 a good chunk of what I know about the 11-limit.

: '''Aura:''' This EDO served as my first personal foray into the world of microtonality- namely through my song "[[:File:Folly of a Drunk.mp3|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.

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: '''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.

== [[25edo]] ==

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: '''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.

== [[26edo]] ==

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: '''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.

== [[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.

: '''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.

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: '''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. B-tier.

== [[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.

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

== [[29edo]] ==

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: '''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.

: '''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.

== [[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.

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

== [[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.

: '''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 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. 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.

: '''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.

== [[32edo]] ==

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: '''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]] ==

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: '''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!

== [[34edo]] ==

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: '''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.

: '''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, commonly cited as poor in this edo, are convincing enough to me, since when I worked with modus I never felt the out-of-tune intonation at all, unlike with porcupine. A-tier.

== [[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.

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

: '''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.

== [[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. 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.

== [[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.

== [[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 being similar to 27edo in many ways. B-tier.

== [[40edo]] ==

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== [[41edo]] ==

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

: '''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.

== [[42edo]] ==

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: '''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.

== [[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.

== [[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]] ==

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: '''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.

== [[47edo]] ==

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: '''Bozu:''' 12edo eighth-tones.

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

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

== [[49edo]] ==

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: '''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.

== [[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]] ==

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== [[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.

: '''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. 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 [[13/8|13<sup>th</sup> harmonic]] (which 31 does only an okay job at and 22 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 ~~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~~.

: '''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.

== [[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.

: '''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.

== [[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]] ==

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== [[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.

== [[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.

== [[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.

: '''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.

== [[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.

== [[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.

== [[79edo]] ==

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

== [[84edo]] ==

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== [[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.

: '''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 serious inconsistency in the 3-limit, and it was at that point that I realized that inconsistency in the 3-limit was a problem.

: '''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.

== [[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~~ "[[:File:Space Tour.mp3|Space Tour]]" ~~and "[[:File:Welcome to Dystopia~~.~~mp3|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 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.

: '''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 "[[:File:Space Tour.mp3|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.

== Sources ==

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* [[User:Aura/Aura's EDO Impressions|Aura's EDO Impressions]]

* [[Bozu's opinions of various edos]]

* [[User:CritDeathX/Sam's EDO Impressions|Nicolai's EDO Impressions]]

* [[User:Flirora/EDO_impressions]]

* [[User:FloraC/Fumica's edo impressions|Fumica's edo impressions]]

* [[Keenan's EDO impressions]]

* [[Mike's EDO impressions]]

* [[User:CritDeathX/Sam's EDO Impressions|Nicolai's EDO Impressions]]

* [https://sevish.com/2022/sevishs-scale-impressions/ Sevish's scale impressions] (''external site, Sevish.com'')

* [[Yourmusic Productions' opinion of various edos]]

[[Category:Impression]]

@@ Line 2: / Line 2: @@
 == [[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.
+: '''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.
 == [[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.
+: '''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.
 == [[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.
+: '''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.
 == [[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.
+: '''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.
 == [[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.
+: '''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: [https://www.youtube.com/watch?v=rPmuKUm2kJg ''Sevish &#45; Fifteen (15 tone microtonal music) &#45; YouTube'']
@@ Line 45: / Line 57: @@
 : '''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.
 == [[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.
+: '''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.
@@ Line 56: / Line 70: @@
 : '''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.
 == [[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.
+: '''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.
@@ Line 69: / Line 86: @@
 : '''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.
-: '''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.
+: '''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".
 == [[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.
+: '''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.
@@ Line 82: / Line 101: @@
 : '''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".
 == [[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.
+: '''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.
@@ Line 93: / Line 114: @@
 : '''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".
 == [[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.
@@ Line 106: / Line 130: @@
 : '''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.
-: '''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.
+: '''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".
 == [[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.
@@ Line 120: / Line 147: @@
 : '''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".
 == [[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.
+: '''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.
@@ Line 131: / Line 160: @@
 : '''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 wah for two reasons: it works with an impressively wide variety of timbres, and it avoids [[wolf interval]]s better than any larger tuning. I believe this elegant simplicity is the reason for its popularity.
 == [[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.
@@ Line 143: / Line 175: @@
 : '''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".
 == [[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.
+: '''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.
@@ Line 155: / Line 189: @@
 : '''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.
+: '''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".
 == [[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.
@@ Line 164: / Line 201: @@
 : '''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]].
 == [[16edo]] ==
@@ Line 174: / Line 213: @@
 : '''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. Besides that, it has armodue, basically an extremely flat fifth that doesn't sound like the 3rd harmonic at all. "Fifthiness" is useless if not for approximating the 3rd harmonic, so I'm afraid I don't consider this approach to have much value. D-tier.
 : '''Vector:''' Definitive proof that a fifth doesn't need to be a 3/2. (TBA)
+: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to timbre to prevent it sounding "out of tune".
 == [[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.
+: '''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.
@@ Line 185: / Line 226: @@
 : '''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 contains an impressive diatonic scale which is nice for both melody and harmony. Semiquartal harmony, that is using the contrast between 7/4 and 12/7 as the basis of tonality, works exceptionally well in this system. S-tier.
+: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to timbre to prevent it sounding "out of tune".
 == [[18edo]] ==
@@ Line 194: / Line 237: @@
 : '''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".
 == [[19edo]] ==
@@ Line 205: / Line 250: @@
 : '''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.
 == [[20edo]] ==
@@ Line 213: / Line 260: @@
 : '''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 greatly, ideal for composers looking for a wild world of new microtonal colours, without sounding as "sour" as some smaller EDOs do.
 == [[21edo]] ==
@@ Line 221: / Line 270: @@
 : '''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]] ==
-: '''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.
+: '''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.
@@ Line 231: / Line 283: @@
 : '''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.
+: '''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 interval]]s which can scare 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.
 == [[23edo]] ==
@@ Line 240: / Line 294: @@
 : '''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.
 == [[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 a good chunk of what I know about the 11-limit.
+: '''Aura:''' This EDO served as my first personal foray into the world of microtonality- namely through my song "[[:File:Folly of a Drunk.mp3|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.
@@ Line 251: / Line 307: @@
 : '''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.
 == [[25edo]] ==
@@ Line 259: / Line 317: @@
 : '''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.
 == [[26edo]] ==
@@ Line 267: / Line 326: @@
 : '''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.
 == [[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.
+: '''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.
+: '''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.
@@ Line 276: / Line 336: @@
 : '''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. B-tier.
 == [[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.
+: '''Fumica:''' Potentially useful as every other step of 56edo. D-tier.
 == [[29edo]] ==
@@ Line 285: / Line 347: @@
 : '''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.
+: '''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.
 == [[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.
+: '''Fumica:''' Potentially useful as every other step of 60edo. D-tier.
 == [[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.
+: '''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 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. 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.
+: '''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.
 == [[32edo]] ==
@@ Line 301: / Line 366: @@
 : '''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]] ==
@@ Line 307: / Line 373: @@
 : '''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!
 == [[34edo]] ==
@@ Line 312: / Line 380: @@
 : '''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.
+: '''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, commonly cited as poor in this edo, are convincing enough to me, since when I worked with modus I never felt the out-of-tune intonation at all, unlike with porcupine. A-tier.
 == [[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...
+: '''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.
 == [[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 third tones to plain 12edo music is interesting, but none of my attempts have been successful as I generally find them to sound forced. I think this edo is more difficult to use than it appears. C-tier.
+: '''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.
 == [[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. 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.
 == [[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.
 == [[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 being similar to 27edo in many ways. B-tier.
 == [[40edo]] ==
@@ Line 340: / Line 416: @@
 == [[41edo]] ==
-: '''Aura:''' Using Ultralocrian mode in this EDO is a challenge, but apparently quite well worth it.
+: '''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.
 == [[42edo]] ==
@@ Line 352: / Line 429: @@
 : '''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.
 == [[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.
 == [[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]] ==
@@ Line 363: / Line 443: @@
 : '''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.
 == [[47edo]] ==
@@ Line 371: / Line 452: @@
 : '''Bozu:''' 12edo eighth-tones.
 : '''Nicolai:''' 12EDO, but more fancy.
+: '''Fumica:''' More appropriate as an interval category scheme than anything else. C-tier.
 == [[49edo]] ==
@@ Line 379: / Line 461: @@
 : '''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.
 == [[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]] ==
@@ Line 387: / Line 471: @@
 == [[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.
+: '''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. 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 [[13/8|13<sup>th</sup> harmonic]] (which 31 does only an okay job at and 22 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 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.
+: '''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.
 == [[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.
+: '''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.
+== [[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]] ==
@@ Line 400: / Line 492: @@
 == [[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.
+== [[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.
+== [[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.
+: '''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.
+== [[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.
+== [[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.
+== [[79edo]] ==
+: '''Fumica:''' A disastrous non-meantone tuning. F-tier.
 == [[84edo]] ==
@@ Line 414: / Line 542: @@
 == [[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.
+: '''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 serious inconsistency in the 3-limit, and it was at that point that I realized that inconsistency in the 3-limit was a problem.
+: '''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.
 == [[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 "[[:File:Space Tour.mp3|Space Tour]]" and "[[:File:Welcome to Dystopia.mp3|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 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.
+: '''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 "[[:File:Space Tour.mp3|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.
 == Sources ==
@@ Line 426: / Line 554: @@
 * [[User:Aura/Aura's EDO Impressions|Aura's EDO Impressions]]
 * [[Bozu's opinions of various edos]]
-* [[User:CritDeathX/Sam's EDO Impressions|Nicolai's EDO Impressions]]
 * [[User:Flirora/EDO_impressions]]
+* [[User:FloraC/Fumica's edo impressions|Fumica's edo impressions]]
 * [[Keenan's EDO impressions]]
 * [[Mike's EDO impressions]]
+* [[User:CritDeathX/Sam's EDO Impressions|Nicolai's EDO Impressions]]
+* [https://sevish.com/2022/sevishs-scale-impressions/ Sevish's scale impressions] (''external site, Sevish.com'')
 * [[Yourmusic Productions' opinion of various edos]]
 [[Category:Impression]]