Keenan's EDO impressions
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[[1edo|1]] - People ought to write more 2-limit music. (Or not.) [[2edo|2]] - Boring [[3edo|3]] - Boring [[4edo|4]] - Boring [[5edo|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. [[6edo|6]] - Boring as a subset of 12edo, but useful as a very simple 2.9.5.7 temperament. Most of the good 2.9.... scales have 6-note MOSes for this reason. [[7edo|7]] (aka [[11edt]]) - Cool in many of the ways that 5 is. Regular temperament model of a scale used in Thai music. [[8edo|8]] - A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2). [[9edo|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. [[10edo|10]] (aka [[16edt]]) - Like [[Blackwood|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"). [[11edo|11]] - Every other note of [[22edo|22]]. This makes it a great 2.9.7.11 temperament. Includes [[machine]], [[orgone]], [[http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11]] and [[http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11]] [[12edo|12]] (aka [[19edt]]) - 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. [[13edo|13]] - Every other note of [[26edo|26]]. This makes it a good temperament for a large 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]]. [[14edo|14]] - [[Jamesbond]], [[bug]]/[[semiphore]], etc. (Not whitewood.) 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*). [[15edo|15]] (aka 24edt) - Very interesting for [[blackwood]], [[porcupine]], and others. A good all-around EDO. If you want to internalize [[Porcupine intervals|porcupine interval categories]], use 15edo. [[16edo|16]] (aka 25edt) - [[Mavila]]/armodue; those Italians love it. 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]].) [[17edo|17]] (aka [[27edt]]) - Really good no-5's system; [[Supra|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. [[18edo|18]] - Almost totally useless. [[19edo|19]] (aka 30edt) - 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. [[20edo|20]] - 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. [[21edo|21]] - First (sub-optimal) [[whitewood]] EDO, not much else. [[22edo|22]] (aka 35edt) - Amazing and mind-blowing; many great [[22edo#Theory-Properties%20of%2022%20equal%20temperament-Linear%20Temperaments|temperaments]]. Not much reason to use more notes per octave than this, if you ask me. [[23edo|23]] - Mavila system similar to 16, but has [[superpelog]] in addition. Nothing to write home about. [[24edo|24]] (aka 38edt) - 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.x
Original HTML content:
<html><head><title>Keenan's EDO impressions</title></head><body><a class="wiki_link" href="/1edo">1</a> - People ought to write more 2-limit music. (Or not.)<br /> <a class="wiki_link" href="/2edo">2</a> - Boring<br /> <a class="wiki_link" href="/3edo">3</a> - Boring<br /> <a class="wiki_link" href="/4edo">4</a> - Boring<br /> <a class="wiki_link" href="/5edo">5</a> (aka <a class="wiki_link" href="/8edt">8edt</a>) - 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.<br /> <a class="wiki_link" href="/6edo">6</a> - Boring as a subset of 12edo, but useful as a very simple 2.9.5.7 temperament. Most of the good 2.9.... scales have 6-note MOSes for this reason.<br /> <a class="wiki_link" href="/7edo">7</a> (aka <a class="wiki_link" href="/11edt">11edt</a>) - Cool in many of the ways that 5 is. Regular temperament model of a scale used in Thai music.<br /> <a class="wiki_link" href="/8edo">8</a> - A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2).<br /> <a class="wiki_link" href="/9edo">9</a> (aka <a class="wiki_link" href="/14edt">14edt</a>) - On the one hand you can treat the 667 cent intervals as 3/2, yielding an extreme version of <a class="wiki_link" href="/mavila">mavila</a> (or 7-limit <a class="wiki_link" href="/armodue">armodue</a>) 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 <strong>recognizable</strong> "major" and "minor" chords.<br /> <a class="wiki_link" href="/10edo">10</a> (aka <a class="wiki_link" href="/16edt">16edt</a>) - Like <a class="wiki_link" href="/Blackwood">blackwood</a>, except with neutral thirds. Or, blackwood intersects <a class="wiki_link" href="/dicot">dicot</a>. 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 <a class="wiki_link" href="/decimal">decimal</a> MODMOSes are the familiar "blues scale" (and for that matter, that 0 360 960 cents is a "dominant seventh").<br /> <a class="wiki_link" href="/11edo">11</a> - Every other note of <a class="wiki_link" href="/22edo">22</a>. This makes it a great 2.9.7.11 temperament. Includes <a class="wiki_link" href="/machine">machine</a>, <a class="wiki_link" href="/orgone">orgone</a>, <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11" rel="nofollow">http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11</a> and <a class="wiki_link_ext" href="http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11" rel="nofollow">http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11</a><br /> <a class="wiki_link" href="/12edo">12</a> (aka <a class="wiki_link" href="/19edt">19edt</a>) - Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular <a class="wiki_link" href="/dominant">dominant</a> temperament. Also <a class="wiki_link" href="/augmented">augmented</a> and <a class="wiki_link" href="/diminished">diminished</a>. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.<br /> <a class="wiki_link" href="/13edo">13</a> - Every other note of <a class="wiki_link" href="/26edo">26</a>. This makes it a good temperament for a large 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 <a class="wiki_link" href="/uncle">uncle</a> and <a class="wiki_link" href="/dicot">dicot</a>.<br /> <a class="wiki_link" href="/14edo">14</a> - <a class="wiki_link" href="/Jamesbond">Jamesbond</a>, <a class="wiki_link" href="/bug">bug</a>/<a class="wiki_link" href="/semiphore">semiphore</a>, etc. (Not whitewood.) 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*).<br /> <a class="wiki_link" href="/15edo">15</a> (aka 24edt) - Very interesting for <a class="wiki_link" href="/blackwood">blackwood</a>, <a class="wiki_link" href="/porcupine">porcupine</a>, and others. A good all-around EDO. If you want to internalize <a class="wiki_link" href="/Porcupine%20intervals">porcupine interval categories</a>, use 15edo.<br /> <a class="wiki_link" href="/16edo">16</a> (aka 25edt) - <a class="wiki_link" href="/Mavila">Mavila</a>/armodue; those Italians love it. 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, <a class="wiki_link" href="/gorgo">gorgo</a>.)<br /> <a class="wiki_link" href="/17edo">17</a> (aka <a class="wiki_link" href="/27edt">27edt</a>) - Really good no-5's system; <a class="wiki_link" href="/Supra">supra</a>, <a class="wiki_link" href="/bleu">bleu</a>, 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.<br /> <a class="wiki_link" href="/18edo">18</a> - Almost totally useless.<br /> <a class="wiki_link" href="/19edo">19</a> (aka 30edt) - First EDO with a meantone diatonic scale (5L2s proper), but not only meantone! <a class="wiki_link" href="/Negri">Negri</a> is awesome, <a class="wiki_link" href="/godzilla">godzilla</a> is awesome, <a class="wiki_link" href="/sensi">sensi</a> is awesome, and <a class="wiki_link" href="/keemun">keemun</a> and <a class="wiki_link" href="/magic">magic</a> 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.<br /> <a class="wiki_link" href="/20edo">20</a> - More-complicated version of <a class="wiki_link" href="/blackwood">blackwood</a>, 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.<br /> <a class="wiki_link" href="/21edo">21</a> - First (sub-optimal) <a class="wiki_link" href="/whitewood">whitewood</a> EDO, not much else.<br /> <a class="wiki_link" href="/22edo">22</a> (aka 35edt) - Amazing and mind-blowing; many great <a class="wiki_link" href="/22edo#Theory-Properties%20of%2022%20equal%20temperament-Linear%20Temperaments">temperaments</a>. Not much reason to use more notes per octave than this, if you ask me.<br /> <a class="wiki_link" href="/23edo">23</a> - Mavila system similar to 16, but has <a class="wiki_link" href="/superpelog">superpelog</a> in addition. Nothing to write home about.<br /> <a class="wiki_link" href="/24edo">24</a> (aka 38edt) - 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.x</body></html>