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1 - People ought to write more 2-limit music. (Or not.)
2 - Boring
3 - Boring
4 - Boring
5 (aka 8edt) - 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.
6 - Boring as a subset of 12edo, but useful as a very simple temperament. Most of the good 2.9.... scales have 6-note MOSes for this reason.
7 (aka 11edt) - Cool in many of the ways that 5 is. Regular temperament model of a scale used in Thai music.
8 - A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2).
9 (aka 14edt) - 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.
10 (aka 16edt, "blackwood semitones") - Like blackwood, except with neutral thirds. Or, blackwood intersects dicot. Same circle-of-3/2s structure as 5edo, but now there are 360-cent "neutral thirds" and 600-cent "tritones". It's easy to trick people into thinking that decimal MODMOSes are the familiar "blues scale" (and for that matter, that 0 360 960 cents is a "dominant seventh").
11 - Every other note of 22. This makes it a great temperament. Includes machine, orgone, http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 and http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11
12 (aka 19edt, "standard semitones") - Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular dominant temperament. Also augmented and diminished. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.
13 - Every other note of 26. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including uncle and dicot.
14 (aka "whitewood semitones") - Jamesbond, bug/semaphore, etc. (Quite bad whitewood tuning.) Pretty much misses "minor" and "major" thirds entirely, going straight from "subminor" to "neutral" to "supermajor", which makes it very xenharmonic (thought not necessarily *pleasant*). Also don't forget the presence of DTMF ("touch tone") tones. Any phone number is a two-part piece of music!
15 (aka 24edt, "blackwood 1/3-tones") - Very interesting for blackwood, porcupine, and others. A good all-around EDO. If you want to internalize porcupine interval categories, use 15edo.
16 (aka 25edt, "armodue semitones") - Mavila/armodue. Really versatile and interesting - if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, gorgo.)
17 (aka 27edt, "superpyth 1/3-tones") - Really good no-5's system; supra, bleu, etc. The lack of 5-limit harmony forces you to think xenharmonically, but the nice accurate 3/2s form a solid familiar backbone you can depend on when things get too crazy. Also, neutral third scales are awesome. Compatible (not perfectly, of course) with a large number of maqamat.
18 - Almost totally useless.
19 (aka 30edt, "meantone 1/3-tones") - First EDO with a meantone diatonic scale (5L2s proper), but not only meantone! Negri is awesome, godzilla is awesome, sensi is awesome, and keemun and magic are both quite interesting. Excellent EDO to promote to newcomers because it works beautifully with standard meantone notation and familiar meantone harmony is possible, but again, it's so much more than meantone. Xenharmonic scales and comma pumps abound.
20 (aka "blackwood 1/4-tones") - More-complicated version of blackwood, not much else. Instead of [5edo interval], minor, major, [5edo interval] it now goes [5edo interval], minor, neutral, major, [5edo interval]. Big deal. I'd choose 15 over 20 any day because it has porcupine.
21 (aka "whitewood 1/3-tones") - First usable (sub-optimal) whitewood EDO, not much else.
22 (aka 35edt, "superpyth 1/4-tones") - Amazing and mind-blowing; many great temperaments. Not much reason to use more notes per octave than this, if you ask me.
23 (aka "hornbostel 1/3-tones") - Mavila system similar to 16, but has superpelog in addition. Nothing to write home about.
24 (aka 38edt, "standard 1/4-tones") - Very worthwhile, and underrated because of its long history of "microtonal" (rather than "xenharmonic") use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones).
25 (either "blackwood 1/5-tones" or "armodue 1/3-tones") - Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider "the fifth" or "3/2". Too many notes for either one of them - why not use 15 or 16 instead?
26 (aka 41edt, "flattone 1/4-tones") - The forgotten meantone EDO, and the first true flattone EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because flattone[12] is much easier to hear as unequal than meantone[12]. Also has injera and cynder/mothra.
27 (aka 43edt, "superpyth 1/5-tones") - First true tetracot/modus EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.