User:Eufalesio/EDO impressions

My main reason to use edos is to "buy" the entire gamut and be able to do JIoid stuff in it with the most accuracy, and the most conceptualization ease. I thus value edos that have a manageable grain, approximate a lot of stuff, It's easier for me to think in tempered commas. I care about the 5-limit, 7-limit, 2.3.5.13, 2.3.5.7.13, and 2.3.5.7.11.13.19(.29) JI subgroups, liking my error to be balanced across primes, but the error on 3 to be minimal.

EDOS I have things to talk about (and it's good)

5edo

The first usable edo and the first edo to have any semblance of a perfect fifth. It features an extremely simplified 2.3.7, forming a consistent circle of 8/7 and 3/2. Due to its extremely coarse grain, it is extremely simple to use, as each step is large enough that no cluttering will ever occur. It is horrible in all other limits... well... except... 2.3.7.37, but who here cares about that?

Also due to its extremely coarse grain, you can play anything, short of bashing keys and sitting on the keyboard, and it will sound good. This is because the edostep is so large that it doesn't cause audible cluttering... unless you're playing too low. The sonic profile of this edo is immediately recognizable.

It greatly benefits from non-harmonic timbres, or bell-like sounds, much like that of slendro. Its melodic capabilities are basically the same as that of all pentatonic scales, which is to say: great! It would be wrong to only call 5edo innacurate. A better descriptor would be: coarse. The coarsest, in fact. And due to the fact that it is so coarse, but it is still quite relatively accurate, it is a great edo. A

7edo

The second usable edo. Its fifth is a tad flat, but usable, and it is also the first edo to feature a heptatonic scale, obviously... an equalized diatonic. The edostep is now small enough so that cluttering can occur, but still somewhat bashable. The sonic profile is also immediately recognizable. While the 5-limit is not there, the melodic coolness you can pull of with this coarse edo are nothing to scoff at. C, not for accuracy, but for cool.

12edo

It's easily one of the best edos. 12edo is many, many things all at once, and I would say that its place in mainstream music is well earned. It's the first edo that can deal with the 5-limit at all, and it also has an incredibly accurate fifth for its size, making it the only temperament that is both meantone and pythagorean at the same time... Super practical, and very easy to conceptualize. S

17edo

Despite being the next edo with a usable fifth, the fact that it tempers the interval whose edostep best approximates it is the ultimate irony. I like the slightly sharp fifths and neo-gothic feel, but the lack of 5-limit is a hole I can't easily live without, and no matter how good it is on other limits (and it is great), the lack of 5 is sad. C

19edo

The next most easily accessible edo, and one that offers a change in perspective. It is meantone just like 12edo, but it has a completely different sonic profile, due to the flatter 5-limit, which I find very enjoyable. The near just minor thirds are definitely something to remark, though not as discernible as it is in its supersets. Great stuff! A

22edo

While the change in perspective that 19edo offers is mixed with familiarity, 22edo is an entirely different beast. It features a very exaggerated non-meantone 5-limit, making it the ultimate porcupine, which is not a temperament known for its accuracy, but it's cool! It also supports magic, featuring a flatter 5, which I enjoy, though the incredibly sharp 6/5 is a tad excessive.

The 7-limit structure inside the diatonic scale is something very sui generis, though it's 11-limit is kinda meh, but what can I say, it's the first edo to be consistent in the 11-odd-limit! C, not for accuracy, but for cool.

24edo

Entry-level xenharmonic edo. A huge improvement to the 2.3.5.11, but nothing much more to remark. Probably the most common xenharmonic edo among non xen spaces, and for good reason. We've all used it. It's trivial to build it.

Still, some ensembles fail at playing quartertones accurately (singers are the worst, some can even fail to sing 12edo accurately, which is a feat...) C

31edo

The best meantone edo. Manageable grain, incredible 11-limit. You can't get more juice out of meantone without diminishing returns. From this point on, it becomes hard to justify using a finer meantone gamut. SSS

41edo

The first usable schismic edo (29edo and 17edo don't count because their 5/4's are wack). Still manageable grain, hyperaccurate fifths and the non-meantoneness is definitely welcome. It is the first edo to introduce a comma accidental framework, which in my opinion is one of the best frameworks for composition. The 11-limit is marvelous (pun intended) but the 13-limit is... lacking. However, since it tempers so many things together, it is extremely useful.

Still, even if the 5-limit is not that accurate, since the innacuracy is flatwards, I think it's much more enjoyable, as I like wide minor thirds. Also supports Bohlen Pierce, which is also incredibly cool. AC, not for air conditioner, but for accuracy and cool.

46edo

The best diaschismic. 13-limit stuff, though a bit sharp and not as accurate as 41-edo, it is good. I haven't composed anything with it, however, as I think diaschismic is kinda hard to conceptualize, and the sharpness of the 5 is something that I find less desirable. B

50edo

Still a good meantone edo, and though it is a much better approximant for golden meantone, I prefer using golden meantone as a rank-2, and not buying the entire gamut. The 19-limit usability is surprising, still. However, having all those new intervals inside a meantone edo feels in my opinion strangely unnatural, as we're stretching the meantone chain-of-fifths beyond what's supposed to.

For bigger edos in this range, meantone ceases to do it for me, but I respect it. C

53edo

Pythagorean tuning incarnate, and astounding 5-limit. 2.3.5.13.19 is especially potent, but the .7.23 is still very much usable, even the .11! It doesn't temper as many things together as 41edo, so it feels like a less compromised system, still, I feel bad for the rest of the edos near this one, because this trumps a lot of the competition. But what can I say? Suck it losers! SS

72edo

The first compton edo that achieves any semblance of JIoid goodness. This was one of the first finer edos I've composed in. It has an astounding 11-limit, and decent 19-limit! It's also a multiple of 12, so it is very transposing-friendly and building it is trivial! It's a miracle, and it also supports it! SSS

84edo

I haven't composed anything in it, but theory tells me that it's a really good compton edo. The bad tuning of the 11 is a bit sad, but it can be useful all the way up to the 31-limit. The 2.3.5.7.13 here is instead a great subgroup, which is a good selling point for me. Had I known about it, I could have probably used this instead of 72edo, but I'm now not that interested in compton anymore. A

94edo

GOAT. The combination of the two smallest schismic edos, which are both incredibly solid choices, into one neatly rounded package that is very optimized. I am heavily biased towards this, as it represents the ultimate cassandra, and a chain-of-fifths framework that I find extremely easy to work with. It also tempers a lot of things together, much like 41edo,

Naturals for prime 3 or 19. ±1 for 17 or 23. ∓2 for 5 or 7. ±4 for 11 or 13. Throughout many different peer-reviewed experiments and in many on my compositions, I've found that this edo is good enough for most xen purposes. Still a tiny smidge innacurate in the 5-limit, but since it is flat and not sharp, I find it much more palatable, as I like wide minor thirds. I really only use it for the 2.3.5.7.11.13.19, but the 23-limit goodness is no joke. SSS

130edo

I haven't composed in it, but theory screams to me that this edo is a beast. I like to think of it as 65edo, but good. It has an extremely accurate 13-limit, and a schismic chain-of-fifths framework? Count me in! S

159edo

Aura's favorite tuning. He does have a point, it takes an extremely good edo, and tripling it makes it even better! 29-limit goodness! I don't care as much for the insanely accurate 2.3.11, as I care for the entirety of the 2.3.5.7.11.13.19(.29). It really is that good. I've composed stuff with it, and it isn't as easy to do as in other edos, but the result is still worth it. SS

171edo

Ennealimmal, personified. I haven't composed in it directly, but since I did compose in 7-limit JI, it'd sound the same. It features a dead-accurate 7-limit that I cannot distinguish from just. It's that good. The great innacuracy of the 11 is a bit sad, though it still has a usable 13, which has that going for it. A

217edo

It's the septuple of 31edo, and that is nothing less than a miracle (though it doesn't support miracle). I've done some tests on it, and it's 31-limit is incredible. It introduces an unfamiliar and slightly tedious gari-vulture-esque framework in which you have to use schisma-function steps apart from pythcommas, but apart from that, it's still within the realms of manageability. Also, it has an incredible 2.3.5.13, which I really respect. Also important to remark, from this point onward, edos start to sound more or less the same, as the absolute error gets lower and lower, and the difference between edosteps becomes harder to reliably hear. S

224edo

A cousin to 217edo which is still schismic, dare I say the ultimate schismic edo, though still harder to conceptualize. Theory tells me that the 13-limit is extremely accurate, even more than the 217edo, and for that I think it deseves. But 217edo is smaller, and it contains 31edo, so... I think I'll stick with the other one. B

270edo

Ultimate low complexity JIoid edo. Though a tad large now, consistency within its 2.3.5.7.11.13.19 is insane. This trumps a lot of the competition. Using a finer gamut in the same subgroup becomes hard to justify. SSS

311edo

Ultimate ultra-high-limit JI. Absolute error is a smidge worse than 270edo, but it makes up by being consistent to the goddamn 41-odd-limit. Serendipity personified. Very hard to justify using anything else other than this, as the difference between edosteps from this point on is definitely nigh impossible to hear. I see it as an ultimate tuning of sorts for practicality's sake. SSS

1600edo

Now we've gone far tooo big. But... you know... 43-odd-limit... ah... round number... ah! It tickles special parts of my brain, even if it's not really practical to use it. I don't really know why I like it, I'm probably not going to use anything above the 29-limit... but what if...? B

2460edo

The only reason I've put this one here is because it is a 12n edo, and that makes it slightly easier to work with, and very transposing friendly. It's astonishingly accurate, though dividing the semitone into 205ths is reasonably excessive. C

8539edo

This level of fineness is at the bleeding edge of insanity. The precision of this behemoth is astounding. I firmly believe no sane person would compose anything requiring a tuning precision higher than what this offers. And I'm one to oogle at impossibly gargantuan edos, I'll admit, but that oogling is only theoretical. Beyond here... there be monsters... and hot sauce. C

EDOS I have things to talk about (and it's bad)

0edo

Rhythm personified. As an edo, it is horrible. There is nothing. Everything is tempered out. To an extent, it not only is useless, it's also ontologically terrifying. The end of pitch. However, going back to the real world, this is just glorified rhythm, and so useless from a tuning standpoint. F

1edo

Octaves. Extremely boring to use still, as octaves are hyperconsonant, so there is no inertia. You really have to get creative to make something cool in this. Ligeti pulled it off. But I won't care to try. F

2,3,4,6edo

Only ever good as subsets of other edos such as 12edo. Basically just compton. Anywhere else, they stand out, and not positively, though 3edo has a surprisingly accurate 5. D

29edo

It's the next edo which has a fifth that's better than 12edo's... and that's it? It's worse everywhere else! By itself, it's really only a slightly worse Pythagorean tuning, which to me is a bad selling point. The supersets 58 and 87 are decent, but I think there are better alternatives. D

EDOS I don't have much to talk about

I'm just going to sort them all into wastebaskets.

• Interesting, but unjustifiably inaccurate for me: 26,81 (D)
• Potentially useful, but I don't really like them 9,16 (D)
• Useless: 8,11,13,14,18,20,21,23,25,30,35,40,42,45,47 (FF)

If an edo is not anywhere in this article is because I believe there are better options, or that I haven't even thought about it.