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Template shamelessly stolen from Keenan's EDO impressions. I reserve the right to change this at any time if I missed something.

(Everyone should make one of these!)

1 - lol

2 - lol

3 - lol

4 - lol

5 (aka 8edt) - 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: http://www.youtube.com/watch?v=rPmuKUm2kJg

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

7 (aka 11edt) - next-smallest EDO that has something resembling 3/2. This sounds like an "equalized" diatonic scale, so that there are no more "major" or "minor" thirds, but just "thirds." 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, mohajira/maqamic[7] and its MODMOS's, porcupine[7], tetracot[7], and mavila[7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you stretch the octaves to about 1230 cents, you get something which is like every other step of the popular nonoctave 88cET, and which can also be thought of as a nonoctave version of tetracot temperament, with really good 2:3:5 chords.

8 - An EDO that's often dismissed as an equalized diminished[8] scale, yet contains a lot more. For starters, it's also an equalized sensi[8] (especially if viewed as existing in the 2.9/7.5/3 subgroup, and has, for its size, excellent approximations to the tempered 1/1-9/7-5/3 sensamagic chord), made of two 450 cent "supermajor thirds" on top of one another. This chord provides a great contrast to the usual diminished chord, as it's much less intense and "evil" sounding, and much more floaty and abstract. I also tend to enjoy huge stacks of 450 cent intervals, which I think are beautiful. Stacks of 750 cent intervals can also be very beautiful: I don't know whether they "approximate 3/2 poorly" or "approximate 14/9 well" or whatever it is, but they sound really good. They're two things that categorically sound to me like sharp fifths mixed with minor sixths, and two of them gets you a minor tenth; this is another way to get away from making it sound "diminished." Lastly, I also note that 8-EDO is an equalized porcupine[8], so for those who are used to porcupine, 2 1 1 1 1 1 1 may trip you out as being sort of like porcupine but with 4:5:6 replaced with 7:9:11. With sensamagic chords, diminished chords, and 7:9:11 chords - all of which differ in consonance - there's no reason why you can't use this tuning to make beautiful, programmatic, and to my ears somewhat "spacy" sounding music.

9 (aka 14edt) - If we're considering the 667 cent intervals to be 3/2, then this is the first EDO that doesn't temper out 25/24 in the 5-limit, and as such distinguishes between 4:5:6 and 10:12:15. However you want to view it, it's definitely the first EDO to my ears where I can hear distinct "major" and "minor" chords, as detuned as they may be. This is also the first EDO that supports mavila and pelogic temperament, and the 7-note MOS's are of prime interest here. Because of that, it's the first EDO I know how to create something like "functional harmony" in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: http://www.youtube.com/watch?v=KV_MzdtU2WQ. Also, like mavila in general, it also allows for common practice music to be translated into this tuning, where major chords become minor and vice versa; however, this experience can be unpleasant if one uses a harsh timbre or isn't prepared for the more discordant harmonies. Examples of that here: http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/. Random other things: it has a great 7/6 and can also be viewed as an equalized version of superpelog[9] and orwell[9] and augmented[9], contains an interesting augmented[6] where the "minor thirds" are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).

10 (aka 16edt, "blackwood semitones") - A neutral triad version of blackwood, or a "neutral tetrad" version of pajara, or a neutral negri, or a neutral lemba. Elaine Walker's written some great stuff in this. I have the feeling that this is a great base scale for "diatonic"-style melodies, but haven't explored it as much yet. Also an equalized octokaidecal[10]. Need to play more

11 - Amazing and totally underrated EDO. It supports excellent 4:7:9:11 chords, as well as 4:7:9:11:15:17:19 chords if you're into that thing. Was once thought to be mostly "atonal" for lacking 3/2, but revealed as a low-numbered EDO of prime interest after the Great Subgroup Revolution Of 2011. Giving you decently accurate tetradic harmony for only 11 notes is almost a miracle. Supports machine temperament, of which the 2 2 1 2 2 2 MOS is of interest for being stable and sounding like a "warped diatonic." Example here that loosely uses it:
http://www.youtube.com/watch?v=AhPjsCoMy-Q. Also supports orgone[7], or 2 2 1 2 1 2 1, which is another "warped diatonic" scale. An example of this:
http://soundcloud.com/mikebattagliaexperiments/sets/tonal-study-in-orgone-temperament/. Also, much like 8-EDO supports the excellent and underrated 2.9/7.5/3 version of sensi temperament.

12 (aka 19edt, "standard semitones") - If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable 5-limit harmony, has a debatably passable representation of the 7-limit, and can sort of "hint" at 11, as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: http://www.youtube.com/watch?v=CaPeks0H3_s. Our theory places "12-EDO" and "meantone" as one example of an infinite series of musical tunings, all of which are of potential interest - however, care must be taken to not unfairly diminish 12-EDO's value in a mathematical sense because one may simply be bored with it. Many feel that everything in it "has already been done"; I have a different perspective as a jazz musician in NYC, where people do new and interesting things with 12-EDO every time I go to Smalls'. (Be more creative!!)

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

14-EDO has frickin touch tone noises! Holy shit! Just play two 7-EDO chains a b9 apart and you'll hear it! It's also interesting for not having 5/4 or 6/5 in any real capacity, but having 11/9 and 9/7 and a passable 7/6. So if you think about the way a 14-EDO native listener would hear the harmonic series, instead of hearing the sequence of intervals like octave-fifth-fourth-major third-minor third-smaller minor third, they'd probably hear octave-fifth-fourth-large neutral third-small neutral third-large subminor third-small subminor third-etc. Note that they'd probably not use names like "neutral" and "subminor" though, since those are just our names for those things. It also has a really interesting version of hedgehog temperament which makes the 5:6 in 5:6:7 out to be a neutral third; this is great for categories and then when you move into hedgehog[8] in 22-EDO, the scalar structure remains intelligible despite the intonation shifting under it. A great tuning I also wish I knew more about.

15-EDO is the first EDO in what I call the "Holy Trinity" of low-numbered xenharmonic EDOs. It's the first EDO after 12 to give you a halfway decent representation of the 5-limit, although it does it worse than 12. It also gives you some 7-limit and 11-limit stuff. Now that I've said the obligatory ratio crap, what's really interesting is the fact that V/V/V/V/V in this tuning is the same as I. This is because the circle of fifths is only 5 notes long - in fact it's 5-EDO - and as such closes in on itself much sooner than you'd expect. The things recognizable as major thirds are "outside of" the circle of fifths and independent of it. If you take two circles of fifths offset by 400 cents, you get the 10 note Blackwood scale, which is LsLsLsLsLs. Everyone should know this scale and use it a lot. It also has porcupine[7], and is the first EDO to support it to any decent capacity - it's also great for building porcupine categories if you want, which will then be evoked when you play porcupine[15] in things like 22-EDO later. Most notably, 15-EDO even sort of hits the 11-limit - not perfectly, but well enough to make some trippy effects! This suggests that 15-note circulating temperaments are of interest.

5-EDO - equipentatonic, which is trippy
7-EDO - equidiatonic, which is trippy
8-EDO is a great tuning but I dunno if it has a ton of specifically categorically interesting stuff
9-EDO - has a lot of what 16-EDO does but with less notes. However, 3/2 is weaker. comparing 9-EDO to 16-EDO can let you compare less notes + easier categorization vs more notes + better accuracy. Smallest EDO with major and minor chords (unless you count 8-EDO but that's kind of out there)
10-EDO - don't know a lot about it, but 10-note scales are interesting for also being something in which major and minor can share a triad class, which may be of semi-categorical relevance
11-EDO - has machine[6] which is a key warped diatonic scale, and orgone[7]. I'd say 11-EDO is way up there in terms of key things to learn for categories because it's small, has great 4:7:9:11 triads, and has warped diatonic scales.

13-EDO and 11-EDO both have warped diatonic scales with stretched/compressed octaves
14-EDO - has the whole "kloog" slash "kleeg" thing going on, and also has touch tone noises as intervals for you to try and categorize
15-EDO - has 5-limit harmony plus a 5 note circle of 3/2's, which is crazy in terms of "tonality," which would seem to be peripherally relevant
16-EDO - is notable for being the first EDO (to me) where the 3 step interval can sound like "a step" instead of "a leap." Example is machine: 3 3 1 3 3 3. Much like 3 3 1 3 3 3 1 in 17-EDO, machine[6] in 16-EDO has L/s = 3/1 but the 3-step interval still sounds like "a second." It sounds like 16-EDO is an "enharmonic" scale for machine[11], which I (sort of) perceive as the true "background" for 331333, much like I perceive 19-EDO as an enharmonic underpinning for meantone[12] or whatever.

17-EDO - superpyth machine blah blah
18-EDO - has a really useful 10 note scale called "supersharp" which is 2 2 2 2 1 2 2 2 2 1, which has major/minor/diminished chords which are a bit sharp
19-EDO - needs to be in there for the above reason about enharmonic-sized EDOs in general, but also because learning to differentiate things like #4's and b5's is easy and attainable and a good "first step." I hear A# and Bb as different notes in 19-EDO now - the first fits into things like E lydian, the second fits into things like E diminished, etc. Then you can experiment with melodic diesis movements
22-EDO - in keeping with the above note about enharmonic EDOs, can be thought of as an enharmonic scale for something like porcupine, so that you can perceive a 15-note background but have better intonation - the same way you can perceive a 12-note background in 19 (meantone[12]) but have better intonation than 12. You can do the same with orwell and perceive an orwell[13]-note background, but have much better intonation for orwell than 13-EDO itself. There's other stuff too. Also has superpyth[7] which is good for revealing the diatonic scale in a different intonational context.
23-EDO - same as the above but with mavila and 16-EDO and some other stuff too.
24-EDO - allows you to take a sound you all intuitively know (the blues) and make it "real" and "tangible" and manipulate it to see what comes of it
25-EDO, dunno
26-EDO - has meantone but the intonation is bad. However, the minor sixths are really good 13/8's. Also, the half steps are 138 cents, which is pretty big - but they still function as leading tones and all that. This behavior is exacerbated in 33-EDO. Good for messing with your head and also revealing the diatonic scale in a different intonational context.