Collection of EDO impressions: Difference between revisions

Line 2:

|-

|[[edo]]

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

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

|[[Keenan's EDO impressions]]

Line 9:

Line 10:

|-

|[[1edo]]

|LOL

|The harmony of the cavemen.

|People ought to write more 2-limit music. (Or not.)

Line 16:

Line 18:

|-

|[[2edo]]

|0th order diminished. Nothing interesting, too constrained.

|The worse harmony of the cavemen.

|Boring

Line 23:

Line 26:

|-

|[[3edo]]

|Elemental augmented type tuning. Fun for a minute or two, boring after that. Sounds augmented no matter what you play.

|Augmented chord.

|Boring

Line 30:

Line 34:

|-

|[[4edo]]

|Elemental diminished type tuning. Fun for a minute or two, boring after that. Sounds diminished no matter what you play.

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

|Boring

Line 37:

Line 42:

|-

|[[5edo]]

|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.

|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.

Line 46:

Line 52:

|-

|[[6edo]]

|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.

|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.

Line 53:

Line 60:

|-

|[[7edo]]

|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.

|Equiheptatonic. Again, nothing too original.

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

Line 62:

Line 70:

|-

|[[8edo]]

|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.

|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).

Line 71:

Line 80:

|-

|[[9edo]]

|3rd order augmented scale. I want to like this tuning, but I can't see any value in it beyond noodling.

|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.

Line 80:

Line 90:

|-

|[[10edo]]

|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.

|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").

Line 89:

Line 100:

|-

|[[11edo]]

|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.

|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>

Line 101:

Line 113:

|-

|[[12edo]]

|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.

|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.

Line 108:

Line 121:

|-

|[[13edo]]

|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.

|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]].

Line 117:

Line 131:

|-

|[[14edo]]

|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.

|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!

Line 126:

Line 141:

|-

|[[15edo]]

|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.

|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.

Line 133:

Line 149:

|-

|[[16edo]]

|diminished mayhem with extra mayhem. Check out Last Sacrament to see what this bad boy can do. It's not super user-friendly, in my experience, but it has a distinct sound that seems to pervade everything you can put together within its constraints.

|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]].)

Line 140:

Line 157:

|-

|[[17edo]]

|Totally awesome composite hyperpent. Great fifths, it can sound maqam-ish or western-ish, depending on how you use it. So many possibilities.

|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.

Line 147:

Line 165:

|-

|[[18edo]]

|Augmented scale sliced into thirds. Doesn't really offer any sort of semblance of a perfect fourth or fifth, but doesn't seem to be a one-trick pony, either. I'm just not sure what to do with it.

|Nothing particularly interesting in this.

|Almost totally useless.

Line 154:

Line 173:

|-

|[[19edo]]

|This is my personal favourite. Composite hypopent, awesome thirds and sixths and a decent fourth and fifth. Kind of leaves somethign to be desired with sevenths and seconds/ninths. Can play well within the western music idiom, and has plenty of tonal options outside of that, but doesn't really offer any of the cool maqam-esque tones of 17edo or any of the weird spacey tones of 14edo. I really think this should be the intermediate step between "standard tuning" (whatever you consider that to be) and "xenharmonic tuning" (whatever you consider that to be). This really sits between those two ideas for me.

|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.

Line 161:

Line 181:

|-

|[[20edo]]

|Hyperpent. On paper, it looks okay, but seems really difficult to use musically.

|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.

Line 168:

Line 189:

|-

|[[21edo]]

|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.

|Its cool, but again, nothing particularly interesting.

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

Line 175:

Line 197:

|-

|[[22edo]]

|This one defies my categorization as well as 11edo and 13edo, but with so many options for notes, maybe there is something there. I haven't really deemed this one worth much time investigating. To my ears, after playing with it for a couple of minutes, everything just sounds off, but not weird enough to pique my interest.

|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.

Line 182:

Line 205:

|-

|[[23edo]]

|This one defies my categorization as well as 11edo and 13edo, but with so many options for notes, maybe there is something there. I haven't really deemed this one worth much time investigating. To my ears, after playing with it for a couple of minutes, everything just sounds off, but not weird enough to pique my interest.

|Hyperchromatic version of 9EDO's mavila.

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

Line 189:

Line 213:

|-

|[[24edo]]

|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.

|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).

Line 196:

Line 221:

|-

|[[25edo]]

|Hyperpent. Not really sure what to do with it, honestly. I'd rather use 22edo.

|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?

Line 203:

Line 229:

|-

|[[26edo]]

|Composite hypopent. This has some really cool possibilities and some pretty good consonant intervals, but doesn't seem (in my experience) to get too much love from xenharmonic composers. Dave Trombly has done some text-to-music stuff with it that shows how even randomly-generated notes and intervals sound quite musical, but other than that, I haven't really come across any in-depth projects exploring it. My own noodling around with it makes me think that it'd be pretty easy to use. Maybe there are better options for many specific approaches, though.

|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]].

Line 210:

Line 237:

|-

|[[27edo]]

|Comte hyperpent. Another one with tons of usable tonal possibilities that seems to get little actual use.

|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.

Line 217:

Line 245:

|-

|[[28edo]]

|Hypopent and diminished, I'm not really sure what else this has to offer other than some funky neutralish intervals and diminished mayhem.

|Meh.

|

Line 224:

Line 253:

|-

|[[29edo]]

|Awesome fifths and great overall set of usable tones with some really unstable-sounding ones in between. I think this is a great intermediate-difficulty not-too-many-notes-but-kind-of-a-lot tuning set.

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

|

Line 231:

Line 261:

|-

|[[30edo]]

|Hyperpent. Augmented. Meh, too many seemingly useless intervals.

|Meh.

|

Line 238:

Line 269:

|-

|[[31edo]]

|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.

|Meantone quarter tones.

|

Line 245:

Line 277:

|-

|[[32edo]]

|Composite hyperpent. Diminished. Kind of user-antagonistic on first impression. Not picking up anything of striking value.

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

|

Line 252:

Line 285:

|-

|[[33edo]]

|Composite hypopent. Augmented. Same impression as 32edo, except maybe even less valuable.

|11EDO, but with a better fifth.

|

Line 259:

Line 293:

|-

|[[34edo]]

|Composite hyperpent. Offers the same as 17edo, except more stable modal tones. This one is a gem. I have no idea how to handle notation, though, but it's one of the most useful.

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

|

Line 266:

Line 301:

|-

|[[35edo]]

|Smallest amphipent edo (both hyperpent and hypopent).

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

|

Line 273:

Line 309:

|-

|[[36edo]]

|12edo slashed into thirds.

|12EDO, but better.

|

Line 280:

Line 317:

|-

|[[37edo]]

|Amphipent with a lot of notes.

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

|

Line 287:

Line 325:

|-

|[[38edo]]

|19edo slashed into halves.

|Meh.

|

Line 294:

Line 333:

|-

|[[39edo]]

|Hyperpent augmented with a lot of notes.

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

|

Line 301:

Line 341:

|-

|[[40edo]]

|Amphipent diminished. Can't really find a good use for this one.

|Meh.

|

Line 308:

Line 349:

|-

|[[41edo]]

|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.

|Smaller version of 53EDO.

|

Line 315:

Line 357:

|-

|[[42edo]]

|Amphipent augmented.

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

|

Line 322:

Line 365:

|-

|[[43edo]]

|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.

|The other step-sibling of meantone.

|

Line 329:

Line 373:

|-

|[[44edo]]

|Amphipent diminished.

|Meh.

|

Line 336:

Line 381:

|-

|[[45edo]]

|Amphipent augmented.

|Meh.

|

Line 342:

Line 388:

|

|-

|46edo

|[[46edo]]

|Hyperpent composite. Same thing where it looks great on paper, but I feel underwhelmed noodling around with it.

|You either get 5EDO or 7EDO, but there is a middle.

|

Line 350:

Line 397:

|-

|[[47edo]]

|Amphipent augmented.

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

|

Line 357:

Line 405:

|-

|[[48edo]]

|12edo eighth-tones.

|12EDO, but more fancy.

|

Line 364:

Line 413:

|-

|[[49edo]]

|Amphipent with two different choices of crummy fifths. Not really obviously useful, in my opinion.

|Meh.

|

Line 371:

Line 421:

|-

|[[50edo]]

|This is a great option for meantone. Notations seems to be less of a pain, but 53edo is almost better in every way.

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

|

Line 378:

Line 429:

|-

|[[51edo]]

|Not as versatile as 50edo.

|Meh.

|

Line 385:

Line 437:

|-

|[[52edo]]

|Not as versatile as 51edo.

|Meh.

|

Line 392:

Line 445:

|-

|[[53edo]]

|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.

|JI: The Book.

|

|-

|[[59edo]]

|Seems to have some interesting options, but it's a lot of notes, and other neighbouring edo's can do some more versatile things.

|

|-

|[[60edo]]

|12edo, with each note sliced into five pieces. Not a bad option, except for the myriad of notes to navigate.

|

|-

|[[65edo]]

|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.

|

Line 399:

Line 477:

|-

|[[84edo]]

|

Line 404:

Line 483:

|

|12, only each note is split into a full rainbow, which makes for awesome looking yet still easily comprehensible notation. The best multiple of 12 for 5 limit music and my personal holy grail of edos to find a way to make playable.

|-

|[[87edo]]

|29edo with each interval sliced into three. You can do some nifty stuff with it, but the number of notes is too crazy to cover much with midi unless you choose a subset. Pushing a continuum beyond this.

|

|}

@@ Line 2: / Line 2: @@
 |-
 |[[edo]]
+|[[Bozu's opinions of various edos]]
 |[[User:CritDeathX/Sam's EDO Impressions|Sam's EDO Impressions]]
 |[[Keenan's EDO impressions]]
@@ Line 9: / Line 10: @@
 |-
 |[[1edo]]
+|LOL
 |The harmony of the cavemen.
 |People ought to write more 2-limit music. (Or not.)
@@ Line 16: / Line 18: @@
 |-
 |[[2edo]]
+|0th order diminished.  Nothing interesting, too constrained.
 |The worse harmony of the cavemen.
 |Boring
@@ Line 23: / Line 26: @@
 |-
 |[[3edo]]
+|Elemental augmented type tuning.  Fun for a minute or two, boring after that.  Sounds augmented no matter what you play.
 |Augmented chord.
 |Boring
@@ Line 30: / Line 34: @@
 |-
 |[[4edo]]
+|Elemental diminished type tuning.  Fun for a minute or two, boring after that.  Sounds diminished no matter what you play.
 |Diminished chord. It, surprisingly, has interesting melodic movement despite only being four notes.
 |Boring
@@ Line 37: / Line 42: @@
 |-
 |[[5edo]]
+|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.
 |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.
@@ Line 46: / Line 52: @@
 |-
 |[[6edo]]
+|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.
 |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.
@@ Line 53: / Line 60: @@
 |-
 |[[7edo]]
+|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.
 |Equiheptatonic. Again, nothing too original.
 |Cool in many of the ways that 5 is. Regular temperament model of a scale used in Thai music.
@@ Line 62: / Line 70: @@
 |-
 |[[8edo]]
+|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.
 |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).
@@ Line 71: / Line 80: @@
 |-
 |[[9edo]]
+|3rd order augmented scale.  I want to like this tuning, but I can't see any value in it beyond noodling.
 |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.
@@ Line 80: / Line 90: @@
 |-
 |[[10edo]]
+|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.
 |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").
@@ Line 89: / Line 100: @@
 |-
 |[[11edo]]
+|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.
 |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>
@@ Line 101: / Line 113: @@
 |-
 |[[12edo]]
+|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.
 |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.
@@ Line 108: / Line 121: @@
 |-
 |[[13edo]]
+|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.
 |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]].
@@ Line 117: / Line 131: @@
 |-
 |[[14edo]]
+|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.
 |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!
@@ Line 126: / Line 141: @@
 |-
 |[[15edo]]
+|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.
 |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.
@@ Line 133: / Line 149: @@
 |-
 |[[16edo]]
+|diminished mayhem with extra mayhem.  Check out Last Sacrament to see what this bad boy can do.  It's not super user-friendly, in my experience, but it has a distinct sound that seems to pervade everything you can put together within its constraints.
 |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]].)
@@ Line 140: / Line 157: @@
 |-
 |[[17edo]]
+|Totally awesome composite hyperpent.  Great fifths, it can sound maqam-ish or western-ish, depending on how you use it.  So many possibilities.
 |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.
@@ Line 147: / Line 165: @@
 |-
 |[[18edo]]
+|Augmented scale sliced into thirds.  Doesn't really offer any sort of semblance of a perfect fourth or fifth, but doesn't seem to be a one-trick pony, either.  I'm just not sure what to do with it.
 |Nothing particularly interesting in this.
 |Almost totally useless.
@@ Line 154: / Line 173: @@
 |-
 |[[19edo]]
+|This is my personal favourite.  Composite hypopent, awesome thirds and sixths and a decent fourth and fifth.  Kind of leaves somethign to be desired with sevenths and seconds/ninths.  Can play well within the western music idiom, and has plenty of tonal options outside of that, but doesn't really offer any of the cool maqam-esque tones of 17edo or any of the weird spacey tones of 14edo.  I really think this should be the intermediate step between "standard tuning" (whatever you consider that to be) and "xenharmonic tuning" (whatever you consider that to be).  This really sits between those two ideas for me.
 |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.
@@ Line 161: / Line 181: @@
 |-
 |[[20edo]]
+|Hyperpent.  On paper, it looks okay, but seems really difficult to use musically.
 |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.
@@ Line 168: / Line 189: @@
 |-
 |[[21edo]]
+|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.
 |Its cool, but again, nothing particularly interesting.
 |First usable (sub-optimal) [[whitewood]] EDO, not much else.
@@ Line 175: / Line 197: @@
 |-
 |[[22edo]]
+|This one defies my categorization as well as 11edo and 13edo, but with so many options for notes, maybe there is something there.  I haven't really deemed this one worth much time investigating.  To my ears, after playing with it for a couple of minutes, everything just sounds off, but not weird enough to pique my interest.
 |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.
@@ Line 182: / Line 205: @@
 |-
 |[[23edo]]
+|This one defies my categorization as well as 11edo and 13edo, but with so many options for notes, maybe there is something there.  I haven't really deemed this one worth much time investigating.  To my ears, after playing with it for a couple of minutes, everything just sounds off, but not weird enough to pique my interest.
 |Hyperchromatic version of 9EDO's mavila.
 |Mavila system similar to 16, but has [[superpelog]] in addition. Nothing to write home about.
@@ Line 189: / Line 213: @@
 |-
 |[[24edo]]
+|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.
 |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).
@@ Line 196: / Line 221: @@
 |-
 |[[25edo]]
+|Hyperpent.  Not really sure what to do with it, honestly.  I'd rather use 22edo.
 |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?
@@ Line 203: / Line 229: @@
 |-
 |[[26edo]]
+|Composite hypopent.  This has some really cool possibilities and some pretty good consonant intervals, but doesn't seem (in my experience) to get too much love from xenharmonic composers.  Dave Trombly has done some text-to-music stuff with it that shows how even randomly-generated notes and intervals sound quite musical, but other than that, I haven't really come across any in-depth projects exploring it.  My own noodling around with it makes me think that it'd be pretty easy to use.  Maybe there are better options for many specific approaches, though.
 |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]].
@@ Line 210: / Line 237: @@
 |-
 |[[27edo]]
+|Comte hyperpent.  Another one with tons of usable tonal possibilities that seems to get little actual use.
 |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.
@@ Line 217: / Line 245: @@
 |-
 |[[28edo]]
+|Hypopent and diminished, I'm not really sure what else this has to offer other than some funky neutralish intervals and diminished mayhem.
 |Meh.
 |
@@ Line 224: / Line 253: @@
 |-
 |[[29edo]]
+|Awesome fifths and great overall set of usable tones with some really unstable-sounding ones in between.  I think this is a great intermediate-difficulty not-too-many-notes-but-kind-of-a-lot tuning set.
 |Similar to 27EDO, but this is a bit better since the fifth is a little bit better compared to 27EDO.
 |
@@ Line 231: / Line 261: @@
 |-
 |[[30edo]]
+|Hyperpent.  Augmented.  Meh, too many seemingly useless intervals.
 |Meh.
 |
@@ Line 238: / Line 269: @@
 |-
 |[[31edo]]
+|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.
 |Meantone quarter tones.
 |
@@ Line 245: / Line 277: @@
 |-
 |[[32edo]]
+|Composite hyperpent.  Diminished.  Kind of user-antagonistic on first impression.  Not picking up anything of striking value.
 |Same as 27 & 29EDO, but the fifth now is sharper than 27EDO.
 |
@@ Line 252: / Line 285: @@
 |-
 |[[33edo]]
+|Composite hypopent.  Augmented.  Same impression as 32edo, except maybe even less valuable.
 |11EDO, but with a better fifth.
 |
@@ Line 259: / Line 293: @@
 |-
 |[[34edo]]
+|Composite hyperpent.  Offers the same as 17edo, except more stable modal tones.  This one is a gem.  I have no idea how to handle notation, though, but it's one of the most useful.
 |17EDO, but now there's a good third.
 |
@@ Line 266: / Line 301: @@
 |-
 |[[35edo]]
+|Smallest amphipent edo (both hyperpent and hypopent).
 |You either get 5EDO or 7EDO, there is no middle.
 |
@@ Line 273: / Line 309: @@
 |-
 |[[36edo]]
+|12edo slashed into thirds.
 |12EDO, but better.
 |
@@ Line 280: / Line 317: @@
 |-
 |[[37edo]]
+|Amphipent with a lot of notes.
 |Same situation as 35EDO, but the 5EDO fifth is now just a superpyth fifth. Also good approximations of intervals.
 |
@@ Line 287: / Line 325: @@
 |-
 |[[38edo]]
+|19edo slashed into halves.
 |Meh.
 |
@@ Line 294: / Line 333: @@
 |-
 |[[39edo]]
+|Hyperpent augmented with a lot of notes.
 |You either get mavila or superpyth, there is no middle.
 |
@@ Line 301: / Line 341: @@
 |-
 |[[40edo]]
+|Amphipent diminished.  Can't really find a good use for this one.
 |Meh.
 |
@@ Line 308: / Line 349: @@
 |-
 |[[41edo]]
+|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.
 |Smaller version of 53EDO.
 |
@@ Line 315: / Line 357: @@
 |-
 |[[42edo]]
+|Amphipent augmented.
 |You either get 7EDO or superpyth, there is no middle.
 |
@@ Line 322: / Line 365: @@
 |-
 |[[43edo]]
+|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.
 |The other step-sibling of meantone.
 |
@@ Line 329: / Line 373: @@
 |-
 |[[44edo]]
+|Amphipent diminished.
 |Meh.
 |
@@ Line 336: / Line 381: @@
 |-
 |[[45edo]]
+|Amphipent augmented.
 |Meh.
 |
@@ Line 342: / Line 388: @@
 |
 |-
-|46edo
+|[[46edo]]
+|Hyperpent composite.  Same thing where it looks great on paper, but I feel underwhelmed noodling around with it.
 |You either get 5EDO or 7EDO, but there is a middle.
 |
@@ Line 350: / Line 397: @@
 |-
 |[[47edo]]
+|Amphipent augmented.
 |You either get 7EDO or superpyth, but there's a nice third.
 |
@@ Line 357: / Line 405: @@
 |-
 |[[48edo]]
+|12edo eighth-tones.
 |12EDO, but more fancy.
 |
@@ Line 364: / Line 413: @@
 |-
 |[[49edo]]
+|Amphipent with two different choices of crummy fifths.  Not really obviously useful, in my opinion.
 |Meh.
 |
@@ Line 371: / Line 421: @@
 |-
 |[[50edo]]
+|This is a great option for meantone.  Notations seems to be less of a pain, but 53edo is almost better in every way.
 |I consider this an optimal meantone EDO, due to a wealthy collection of notes here.
 |
@@ Line 378: / Line 429: @@
 |-
 |[[51edo]]
+|Not as versatile as 50edo.
 |Meh.
 |
@@ Line 385: / Line 437: @@
 |-
 |[[52edo]]
+|Not as versatile as 51edo.
 |Meh.
 |
@@ Line 392: / Line 445: @@
 |-
 |[[53edo]]
+|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.
 |JI: The Book.
+|
+|
+|
+|
+|-
+|[[59edo]]
+|Seems to have some interesting options, but it's a lot of notes, and other neighbouring edo's can do some more versatile things.
+|
+|
+|
+|
+|
+|-
+|[[60edo]]
+|12edo, with each note sliced into five pieces.  Not a bad option, except for the myriad of notes to navigate.
+|
+|
+|
+|
+|
+|-
+|[[65edo]]
+|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.
+|
 |
 |
@@ Line 399: / Line 477: @@
 |-
 |[[84edo]]
+|
 |
 |
@@ Line 404: / Line 483: @@
 |
 |12, only each note is split into a full rainbow, which makes for awesome looking yet still easily comprehensible notation. The best multiple of 12 for 5 limit music and my personal holy grail of edos to find a way to make playable.
+|-
+|[[87edo]]
+|29edo with each interval sliced into three.  You can do some nifty stuff with it, but the number of notes is too crazy to cover much with midi unless you choose a subset.  Pushing a continuum beyond this.
+|
+|
+|
+|
+|
 |}