Collection of EDO impressions: Difference between revisions

|Contained within 12 and so not worth talking about.

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|The worse harmony of the cavemen.

|Boring

|Contained within 12 and so not worth talking about.

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|Augmented chord.

|Boring

|Contained within 12 and so not worth talking about.

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|Diminished chord. It, surprisingly, has interesting melodic movement despite only being four notes.

|Boring

|Contained within 12 and so not worth talking about.

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|Equipentatonic. Nothing too original.

|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.

|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.)

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|Whole tone scale. Take out 4\6 and you have a pentatonic subset of the lydian dominant scale.

|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.

|A universe in monochrome. You can make things out, but so much is missing.

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|Equiheptatonic. Again, nothing too original.

|Cool in many of the ways that 5 is. Regular temperament model of a scale used in Thai music.

|The emancipation from harmony, but now with recognisable, if bland diatonic melodies.

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|First EDO with some kind of quarter tone interval.

|A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2).

|Any combination of more than 2 notes sounds bad, and most 2 note combinations sound bad too. Just vile.

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|Cool approximation of 7/6. I also consider it something of the parent scale of gamelan music.

|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.

|Marvellously elegant little system. More than enough room for complex melodies and fortifying them with double-stopped 3rds and 6ths sounds awesome.

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|The first ''actually'' usable EDO. Decent chords & decent melodic ideas. Sevish's ''Vidya'' is a good example of how it can sound.

|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").

|A universe that's recognisable, but everything is distorted and the people have no faces. The merging of 3rds and 6ths removes one of the primary forms of textural expressiveness in 12, leaving it disconcertingly emotionally flat.

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|This is probably a good example of where you should use secundal harmony rather than tertial harmony.

|Every other note of [[22edo|22]]. This makes it a great 2.9.7.11 temperament. Includes [[machine]], [[orgone]], <nowiki>http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11</nowiki> and <nowiki>http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11</nowiki>

|It can almost pass for 12 as long as you only play one note at at time, but more than that and it's limitations become painfully clear.

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|I probably shouldn't have listed this.

|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.

|The more I study it, the more it's flaws and limitations irritate me.

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|Extremely dissonant, but at least the major chord sounds somewhat decent. Not much decent, but its better than nothing.

|Every other note of [[26edo|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]].

|All the various kinds of 9thno5 chords work, and have interesting new flavours compared to their 12edo equivalents. Well worth getting to grips with the cluster based harmony needed to make it sound nice.

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|Cool chords. People say that its really dissonant, but I don't hear anything out of the ordinary.

|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!

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

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|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.

|Very interesting for [[blackwood]], [[porcupine]], and others. A good all-around EDO. If you want to internalize [[Porcupine intervals|porcupine interval categories]], use 15edo.

|Like 14, not as good at simple harmonies as 12, but some glorious extended blackwood chords that combine more notes than you can in 12 and still sound good. Porcupine looks simpler, but I actually find it more of a struggle than blackwood to use.

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|Chromatic version of 9EDO's mavila. Also cool approximation of 7/4.

|[[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]].)

|12's evil twin. Scales are recognisable but inverted and everything but the mellowest of timbres or simplest of harmonies sounds horrible once you start combining notes.

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|The smallest EDO with more consonant harmony than the previous ones.

|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.

|Interestingly alien, but with good 2nd's, 4ths & 5ths to retreat too when you're not sure what to do next.

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|Nothing particularly interesting in this.

|Almost totally useless.

|A universe in monochrome, but with extended dynamic range. There's enough complexity in other areas to keep it interesting, but I'm still aware in the back of my mind that something's missing.

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|The smallest EDO with a really nice meantone fifth. I consider this the smallest EDO to use if you want to make pop music into microtonal music.

|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.

|The more I study it, the more I love how elegantly everything fits together, how you can use standard notation, but things that are equivalent in 12 actually have proper meaning here, how familiar tunes are transferable and recognisable but the emphasis on intervals is subtly shifted to making minor chords and melodies sound more stable and consonant than major ones. It still has it's limitations, power chord based heavy rock in particular suffers from the weaker 5ths, but just works so much better than 12 in general.

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|Nothing particularly interesting.

|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.

|Looking at the math on paper, it should be possible to create pleasant music in this one, but nothing I've heard has actually managed it yet.

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|Its cool, but again, nothing particularly interesting.

|First usable (sub-optimal) [[whitewood]] EDO, not much else.

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

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|Smallest cool superpyth EDO. I think there's orwell in there, too, but don't quote me on that.

|Amazing and mind-blowing; many great [[22edo#Theory-Properties of 22 equal temperament-Linear Temperaments|temperaments]]. Not much reason to use more notes per octave than this, if you ask me.

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

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|Hyperchromatic version of 9EDO's mavila.

|Mavila system similar to 16, but has [[superpelog]] in addition. Nothing to write home about.

|Not enough songs using this to get a proper opinion. Definitely one of the tougher ones to get to grips with.

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|12EDO, but fancy.

|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).

|Double the complexity, but considerably less than double the number of good-sounding combinations. A lot of extra work for little extra return.

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|Great approximation of 5/4, but its another hyperchromatic version of 9EDO's mavila.

|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?

|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.

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|The step-sibling of the meantone series. Its twice of 13EDO though, so the closest approximation of 5/4 is still trash. 14/11 is cool, though, so lets use that.

|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 [[Flattone12|flattone[12]]] is much easier to hear as unequal than meantone[12]. Also has [[injera]] and [[cynder]]/[[mothra]].

|Definitely deserves more attention than it's got so far.

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|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.

|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.

|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.

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|Meh.

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|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.

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

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|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.

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|Meh.

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

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|Meantone quarter tones.

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|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.

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|Same as 27 & 29EDO, but the fifth now is sharper than 27EDO.

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|Like all pure powers of 2, unusually bad for it's size.

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|11EDO, but with a better fifth.

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|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.

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|17EDO, but now there's a good third.

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|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.

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|You either get 5EDO or 7EDO, there is no middle.

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|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.

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|12EDO, but better.

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|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.

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|Same situation as 35EDO, but the 5EDO fifth is now just a superpyth fifth. Also good approximations of intervals.

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|Meh.

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

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|Meh.

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|Smaller version of 53EDO.

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

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|The other step-sibling of meantone.

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|Meh.

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|Meh.

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

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|12EDO, but more fancy.

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|Meh.

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|I consider this an optimal meantone EDO, due to a wealthy collection of notes here.

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|Meh.

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|Meh.

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|JI: The Book.

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