User:Eufalesio/EDO impressions: Difference between revisions
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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. | 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. I'm not a strict octave purist, so I can tolerate tempering the octave to achieve a better harmonic palette. | ||
== EDOS I have things to talk about (and it's good) == | == EDOS I have things to talk about (and it's good) == | ||
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=== 17edo === | === 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 | 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 === | === 19edo === | ||
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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. | 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 | 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 === | === 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 | 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 | ||
=== 34edo === | |||
17edo, but good. By splitting the edo in two, we get a great 5-limit, the best so far. Fails at 7 and 11, which is sad, but at least is a very good 2.3.5.13, as it also supports kleismic. And diaschismic. I've used this to retune some classical pieces. It's good for its grain, but it's not the best. B+ | |||
=== 41edo === | === 41edo === | ||
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=== 46edo === | === 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 | The best diaschismic in my opinion. 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 === | === 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. The meantone chain of fifths already hits its apex with 31edo. | 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. The meantone chain of fifths already hits its apex with 31edo. | ||
For finer edos in this range, meantone ceases to do it for me, but I respect it. C | For finer edos in this range, meantone ceases to do it for me, but I respect it. C- | ||
=== 53edo === | === 53edo === | ||
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=== 80edo === | === 80edo === | ||
Ultimate diaschismic. Extremely surprising that this "coarse" edo can be used all the way up to the 29-odd-limit. I ran some tests on it once, and while the monotone approximations are definitely interesting, the diaschismic framework is not one I'm too comfortable with, and its approximations are a tad sharp, requiring octave compression for a better otonal result. Despite that, I can recognize and appreciate the power of this edo. | Ultimate diaschismic. Extremely surprising that this "coarse" edo can be used all the way up to the 29-odd-limit. I ran some tests on it once, and while the monotone approximations are definitely interesting, the diaschismic framework is not one I'm too comfortable with, and its approximations are a tad sharp, requiring octave compression for a better otonal result. Despite that, I can recognize and appreciate the power of this edo. C+ | ||
=== 84edo === | === 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 | 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- | ||
=== 87edo === | === 87edo === | ||
Theory says that it is a really strong 13-limit edo. So much so, that it is the first edo with distinct consistency and pure consistency in the 13-odd-limit, and normal consistency in the 15-odd-limit, and for that, I give it my respects. However, I like my fifths to have minimal error, and being a subset of 29edo, the fifths are good, but not as good. C | Theory says that it is a really strong 13-limit edo. So much so, that it is the first edo with distinct consistency and pure consistency in the 13-odd-limit, and normal consistency in the 15-odd-limit, and for that, I give it my respects. However, I like my fifths to have minimal error, and being a subset of 29edo, the fifths are good, but not as good. C+ | ||
=== 94edo === | === 94edo === | ||
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=== 130edo === | === 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 | 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 === | === 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), on which it is worse than other alternatives, as primes 7 and 13 are relatively innacurate. I've composed stuff with it, and it isn't as easy to do as in other edos, but the result is still decent. SS | 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), on which it is worse than other alternatives, as primes 7 and 13 are relatively innacurate. I've composed stuff with it, and it isn't as easy to do as in other edos, but the result is still decent. SS- | ||
=== 171edo === | === 171edo === | ||
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=== 217edo === | === 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 | 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 === | === 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 | 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 === | === 270edo === | ||
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=== 1600edo === | === 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 | 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, for ''boggling''. | ||
=== 2460edo === | === 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. | 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 === | === 8539edo === | ||
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=== 0edo === | === 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. | 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. FFF | ||
=== 1edo === | === 1edo === | ||
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=== 2,3,4,6edo === | === 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 | 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 (D+ for 3edo) | ||
=== 26edo === | === 26edo === | ||
I respect that this edo can moderately deal with the 13-limit, as it is the smallest edo that is consistent in such. However, its | The ultimate flattone. I respect that this edo can moderately deal with the 13-limit, as it is the smallest edo that is consistent in such. However, its intonation is too out of wack for my taste. Interesting as it simplifies the 13-limit a lot, potentially useful to those who are interested in meantone, but this is a very extreme meantone. C- | ||
=== 29edo === | === 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. | 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 fact that it's consistent in the 15-odd-limit is useless to me in this instance. The supersets 58 and 87 are decent, but I think there are better alternatives. E | ||
=== 43edo === | === 43edo === | ||
This meantone edo may have a seemingly good val to approximate higher limits, but doing so from a meantone framework is dumb. Apart from that, the lower limits, ones that I hold to high standards, are worsely tuned than in 31edo. In my opinion, the best meantones are the golden meantones, and from 31edo on, the peak has already been reached. | This meantone edo may have a seemingly good val to approximate higher limits, but doing so from a meantone framework is dumb. Apart from that, the lower limits, ones that I hold to high standards, are worsely tuned than in 31edo. In my opinion, the best meantones are the golden meantones, and from 31edo on, the peak has already been reached. E | ||
=== 81, 131... very fine edos that support golden meantone === | === 81, 131... very fine edos that support golden meantone === | ||
81edo is already the absolute maximum for golden meantone, as anything finer and the patent val fifth stops supporting it. If 50edo was already a bit too much, 81edo and beyond are definitely too much. At that point, it's better to not buy the entire gamut and just use rank-2 golden meantone. D | 81edo is already the absolute maximum for golden meantone, as anything finer and the patent val fifth stops supporting it. If 50edo was already a bit too much, 81edo and beyond are definitely too much. At that point, it's better to not buy the entire gamut and just use rank-2 golden meantone. D | ||
=== 55edo and other fine very sharp | === 55edo and other fine very sharp meantonoid edos === | ||
Even worse than 43edo. In fact, it's a zeta valley edo, which means that it does a bad job at approximating JI, and that in my eyes is a failed edo. I don't know what the Mozarts were on while they suggested a meantone this sharp... it's not good at all! FF | |||
== EDOS I don't have much to talk about == | == EDOS I don't have much to talk about == | ||
I'm just going to say they are useless because they have very relatively poor low prime JI approximations. {{EDOs|8,11,13,14,18,20,21,23,25,30,35,40,42,45,47}}. | I'm just going to say they are useless because they have very relatively very poor low prime JI approximations, which often means that they have horribly tuned fifths. {{EDOs|8,11,13,14,18,20,21,23,25,30,35,40,42,45,47}}. FFF | ||
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. | 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. | ||