Bozu's opinions of various edos

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I see edo's as fitting into one or more of four different elemental makeups:

1. Augmented. If X is divisible by three, X edo is "augmented type". The elemental basis of augmented type edo's is 3edo. 2. Diminished. If X is divisible by four, X edo is "diminished type". The elemental basis of diminished type edo is 4edo. 3. Hyperpent. If X is divisible by five, X edo is "hyperpent". The elemental basis of hyperpent is 5edo. 4. Hypopent. If X is divisible by seven, X edo is "hypopent". The elemental basis of hypopent is 7edo.

If X is not divisible by three, four, five, or seven, then X edo is a composite type. However, if X can be expressed as X = 5A + 7B, where A and B are natural numbers, X edo will be a composite hyperpent (if A>B) or composite hypopent (otherwise, i.e. A>B AND C<=D or A<=B AND C>D, with A, B, C, and D being non-negative integers.

There are also a couple of cases in which X edo has no relation to any of these elements. One special case is 2edo, which I classify as 0th order diminished type. The other cases are 11edo, 13edo, and 23edo, which are not divisible by 3, 4, 5, nor 7, and cannot be expressed as 5A + 7B with any non-negative integers A and B.


Sizes of edo's

Any X edo X<5 is terribly uninteresting, in my opinion. These offer only drones with very few harmonies. There isn't really enough room to provide any sort of harmonic motion.

Any X edo X>=5 but X<9 is overconstrained. Harmonies are possible, different tonics are possible, but the possibilities are so limited that the differences between melodies are trivial. These tuning sets are what I have been personally calling "drone-like."

When X>=9, but X<31, we are working beyond the basic elements of edo framework, and there are different colour palettes available, so that melodies can take distinct forms, and pedal motion is possible. These are tuning sets that I have historically called "chromatic-like." Chroma- being the prefix that describes something that has colour and -matic being something with mechanical function of such.

When X>=31, but X<56, scales begin to open up to multiple options for some tonalities. I historically had categorized those tunings as "Supercommas."

When X>55, the step size between adjacent tones is less than a syntonic comma, and the possibilities open up a lot more. I had historically categorized those tunings as "Subcomma."

List of edo's


1edo - LOL

2edo - 0th order diminished. Nothing interesting, too constrained.

3edo - Elemental augmented type tuning. Fun for a minute or two, boring after that. Sounds augmented no matter what you play.

4edo - Elemental diminished type tuning. Fun for a minute or two, boring after that. Sounds diminished no matter what you play.

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.

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.

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.

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.


9edo - 3rd order augmented scale. I want to like this tuning, but I can't see any value in it beyond noodling.

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.

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.

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.

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.

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.

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.

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.

17edo - Totally awesome composite hyperpent. Great fifths, it can sound maqam-ish or western-ish, depending on how you use it. So many possibilities.

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.

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.

20edo - Hyperpent. On paper, it looks okay, but seems really difficult to use musically.

21edo - Hypopent. Like 20edo, it just seems difficult to use.

22edo - 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.

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.

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.

25edo - Hyperpent. Not really sure what to do with it, honestly. I'd rather use 22edo.

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.

27edo - Comte hyperpent. Another one with tons of usable tonal possibilities that seems to get little actual use.

28edo - Hypopent and diminished, I'm not really sure what else this has to offer other than some funky neutralish intervals and diminished mayhem.

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.

30edo - Hyperpent. Augmented. Meh, too many seemingly useless intervals.


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.

32edo - Composite hyperpent. Diminished. Kind of user-antagonistic on first impression. Not picking up anything of striking value.

33edo - Composite hypopent. Augmented. Same impression as 32edo, except maybe even less valuable.

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.

35edo - Smallest amphipent edo (both hyperpent and hypopent).

36edo - 12edo slashed into thirds.

37edo - Amphipent with a lot of notes.

38edo - 19edo slashed into halves.

39edo - Hyperpent augmented with a lot of notes.

40edo - Amphipent diminished. Can't really find a good use for this one.

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.

42edo - Amphipent augmented.

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.

44edo - Amphipent diminished.

45edo - Amphipent augmented.

46edo - Hyperpent composite. Same thing where it looks great on paper, but I feel underwhelmed noodling around with it.

47edo - Amphipent augmented.

48edo - 12edo eighth-tones.

49edo - Amphipent with two different choices of crummy fifths. Not really obviously useful, in my opinion.

50edo - This is a great option for meantone. Notations seems to be less of a pain, but 53edo is almost better in every way.

51edo - Not as versatile as 50edo.

52edo - Not as versatile as 51edo.

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.


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.

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.