User:Eufalesio/EDO impressions: Difference between revisions
No edit summary |
Important breakthroughs |
||
| Line 1: | Line 1: | ||
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, the least amount of pitch classes, and the most conceptualization ease within a chain-of-fifths framework. | 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, the least amount of pitch classes, and the most conceptualization ease within a chain-of-fifths framework. | ||
I thus value edos that have a manageable grain, approximate a lot of stuff, and allow easy chain-of-fifths frameworks; It's easier for me to think in tempered commas along the chain of fifths. I care about the | I thus value edos that have a manageable grain, approximate a lot of stuff, and allow easy chain-of-fifths frameworks; It's easier for me to think in tempered commas along the chain of fifths. I care about the ya (ya), yaza (yaza), yatha (2.3.5.13), yazatha (2.3.5.7.13), and yazalatha (13-limit) JI subgroups, liking my error to be balanced across primes, but the error on 3 to be minimal so that I can work within a chain-of-fifths framework. I ''can't'' not have a fifth, and it can't be badly out of tune. If there is no diatonic, it's outright useless to me. How out of tune do I allow it to be? Between 24\41 and 38\65 both inclusive, including multiples. From primes 17 onwards (and specially 19) I only care about the octave-reduced harmonics, possibly up a fourth or a fifth, and ''nothing'' else. Generally though, I only do yazalatha. | ||
I will make an exception to meantone and compton; I do like meantone as it is arguably one of the best | I will make an exception to meantone and compton; I do like meantone as it is arguably one of the best ya temperaments, and it is obviously the theoretical backbone of Western music theory still today. Compton because 12edo is very powerful, and some of its supersets are arguably among the best edos. | ||
I'm not a strict octave purist; I tolerate tempering the octave to achieve a better harmonic palette, and often do so to achieve higher consistency or better intonation, sacrificing a tiny bit of error on the octave to approximate all the harmonics I care about better. I don't mind having the subharmonics being worsely tuned, as they are not mirror images of harmonics, they are their own thing. | I'm not a strict octave purist; I tolerate tempering the octave to achieve a better harmonic palette, and often do so to achieve higher consistency or better intonation, sacrificing a tiny bit of error on the octave to approximate all the harmonics I care about better. I don't mind having the subharmonics being worsely tuned, as they are not mirror images of harmonics, they are their own thing. | ||
| Line 10: | Line 10: | ||
=== 5edo === | === 5edo === | ||
The first usable edo and the first edo to have any semblance of a perfect fifth. It features an extremely simplified | The first usable edo and the first edo to have any semblance of a perfect fifth. It features an extremely simplified ''za'', 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... ''zathisa'', 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. | 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. | ||
| Line 17: | Line 17: | ||
=== 7edo === | === 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 | 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 ya 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 === | === 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 | 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 ya 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 === | === 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 | 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 ya 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 === | ||
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 | 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 ya, 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 === | === 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 | 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 ya, 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 | The yaza structure inside the diatonic scale is something very sui generis, though it's yazala 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 === | === 24edo === | ||
| Line 39: | Line 39: | ||
=== 31edo === | === 31edo === | ||
The best meantone edo. Manageable grain, incredible | The best meantone edo. Manageable grain, incredible yazala. 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 === | === 34edo === | ||
17edo, but good. By splitting the edo in two, we get a great | 17edo, but good. By splitting the edo in two, we get a great ya, the best so far. Fails at 7 and 11, which is sad, but at least is a very good yazatha, 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 === | ||
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 | 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 yazala is marvelous (pun intended) but the yazalatha is... lacking. However, since it tempers so many things together, it is extremely useful. | ||
Still, even if the | Still, even if the ya 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 === | === 46edo === | ||
The best diaschismic in my opinion. | The best diaschismic in my opinion. Yazalatha 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 === | ||
| Line 58: | Line 58: | ||
=== 62edo === | === 62edo === | ||
Keeps all the | Keeps all the yazala goodness from 31edo and greatly improves on primes from 13 and beyond. It can be used all the way to the 23-limit, with monotonic error. Interesting, but approaching higher limits from a meantone framework is dumb. Like 50edo, I still give it my respect, but mainly because it's a multiple of 31edo. C- | ||
=== 53edo === | === 53edo === | ||
Pythagorean tuning incarnate, and astounding | Pythagorean tuning incarnate, and astounding ya. yathana 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 === | === 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 | 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 yazala, 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 | ||
=== 80edo === | === 80edo === | ||
| Line 70: | Line 70: | ||
=== 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 | 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 yazatha 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 | Theory says that it is a really strong yazalatha 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 === | ||
GOAT. The combination of the two smallest schismic edos, which are both incredibly solid choices, into | GOAT. The combination of the two smallest schismic edos, which are both incredibly solid choices. However, 41edo is a tad too tempered and 53edo is a tad too untempered and too close to using pythagorean tuning as if it were yazalatha. However, 94edo is tempered ''just'' enough, into a neatly optimized cassandra package. '''I am heavily''' '''biased''' '''towards this''', as it represents the ultimate cassandra, the simplest extended chain-of-fifths framework which I find extremely easy to work with. | ||
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 | 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 ya, but since it is flat and not sharp, I find it much more palatable, as I like slightly wide minor thirds. I really only use it for the yazalathana, but the 23-limit goodness is no joke. '''Perfect score.''' | ||
=== 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 | 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 a very accurate yazalatha, and a schismic chain-of-fifths framework? Cool. Only problem... It's rastmic. Rastmic is a tad innacurate of a framework for an edo in the hundreds, but oh well. 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 | 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 ila, as I care for the entire yazalatha, 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 === | ||
Ennealimmal, personified. I haven't composed in it directly, but since I did compose in | Ennealimmal, personified. I haven't composed in it directly, but since I did compose in yaza JI, it'd sound the same. It features a dead-accurate yaza that I cannot distinguish from just. It's that good. The great innacuracy of the prime 11 is a bit sad, though it still has a usable yazatha, which has that going for it. A | ||
=== 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 | 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's a simple high-accuracy system with very useful subsets. It introduces the cassaschismic framework in which you have to use 3-5 cent steps apart from the pyth spine, but apart from that, it's still within the realms of manageability. Also, it has an incredible yazatha, which I really respect. 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 | 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 yazalatha is extremely accurate, even more than the 217edo, and for that I think it deserves praise. However, 217edo has 31edo as a subset, whilst 224edo only has powers of 2 which suck ass as subsets. B+ | ||
=== 270edo === | === 270edo === | ||
Ultimate low complexity JIoid edo. Though a tad large now, consistency within its | Ultimate low complexity JIoid edo. Though a tad large now, consistency and accuracy within its yazalathana is insane. I've done some tests with this and this is straight up unbeatable. For practically all musical purposes, this sounds like JI. There is literally no edo better than this within reason, as its step size is still discernible (by me (in mid frequency range)). Perfect score. | ||
=== 311edo === | === 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. | 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. Since its yazalathana mappings are the same as 270edo, it can be used to retune pieces for much more in tune otonality, but I'm not one to do that. This is my boundary of practicality. From this point on, edosteps begin to blend with each other and using JI is most surely a better option. SS | ||
=== 665edo === | === 665edo === | ||
Ultimate pyth. It has an unfathomably perfect 2.3, and I say that in an almost literal sense. It is very much fathomable, obviously: the beat period of 665edo's fifth is 5077906.80060 s*Hz with two sawtooth waves in perfect sync, which would be around 3 hours, 12 minutes 21 seconds at f=440. 3 fucking hours. That's what it would take you to hear the beating of 665edo. It is, for all intents and purposes, unfathomable to focused human perception. Or, you could make a 3-hour track out of this and sell it to ''connoisseurs'' disenchanted with the mainstream. | Ultimate pyth. It has an unfathomably perfect 2.3, and I say that in an almost literal sense. It is very much fathomable, obviously: the beat period of 665edo's fifth is 5077906.80060 s*Hz with two sawtooth waves in perfect sync, which would be around 3 hours, 12 minutes 21 seconds at f=440. 3 fucking hours. That's what it would take you to hear the beating of 665edo. It is, for all intents and purposes, unfathomable to focused human perception. Or, you could make a 3-hour track out of this and sell it to ''connoisseurs'' disenchanted with the mainstream. | ||
However, this is not why you would use 665edo, as this essentially allows you to extend the precision limit of the chain of fifths from very good to ''extreme,'' by adding the mercator (+53 fifths) and an equalized qian comma (+306/-359 fifths) into the mix, also working as a schisma. Yes, it has a bad prime 11, but it is surprisingly good in the rest of primes up to the 27-odd-limit, which is very surprising for a convergent. I will likely never use this, but since I do greatly care about the chain of fifths as a theoretical construct, I | However, this is not why you would use 665edo, as this essentially allows you to extend the precision limit of the chain of fifths from very good to ''extreme,'' by adding the mercator (+53 fifths) and an equalized qian comma (+306/-359 fifths) into the mix, also working as a schisma. Yes, it has a bad prime 11, but it is surprisingly good in the rest of primes up to the 27-odd-limit, which is very surprising for a convergent. I will likely never use this, but since I do greatly care about the chain of fifths as a theoretical construct, I think this is good. A- | ||
=== 7315edo === | === 7315edo === | ||
Undecupling 665edo results in what I believe to be one of the potentially theoretically most robust yet precise JI-oid systems. Splitting the equalized qian comma in 11s greatly amplifies the accuracy of this edo and allows you to keep the unfathomably accurate chain of fifths as a strong backbone, and thirteenths of a qian comma serving as nanoalterations. I will likely never use this due to the insane precision it demands, but I have nothing other than respect for this behemoth of an edo. S | Undecupling 665edo results in what I believe to be one of the potentially theoretically most robust yet precise JI-oid systems beyond practicality. Splitting the equalized qian comma in 11s greatly amplifies the accuracy of this edo and allows you to keep the unfathomably accurate chain of fifths as a strong backbone, and thirteenths of a qian comma serving as nanoalterations. I will likely never use this due to the insane precision it demands, but I have nothing other than respect for this behemoth of an edo. S | ||
=== 8539edo === | === 8539edo === | ||
If 311edo was my boundary of practicality, 8539edo is my boundary of sanity. The precision of this behemoth is unfathomable. I firmly believe no sane person would compose anything requiring a tuning precision higher than what this offers. And I'm one to ogle at impossibly gargantuan edos, I'll admit, but that ogling is only theoretical. Beyond here... there be monsters... and hot sauce. C | |||
== EDOS I have things to talk about (and it's bad) == | == EDOS I have things to talk about (and it's bad) == | ||
| Line 138: | Line 130: | ||
=== 26edo === | === 26edo === | ||
The ultimate flattone. I respect that this edo can moderately deal with the | The ultimate flattone. I respect that this edo can moderately deal with the yazalatha, 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 yazalatha a lot, potentially useful to those who are interested in meantone, but this is a very extreme meantone. C- | ||
=== 29edo === | === 29edo === | ||
| Line 151: | Line 143: | ||
=== 55edo and other fine very sharp meantonoid edos === | === 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 | 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 | ||
=== 282edo === | |||
It is surprisingly 94*3, taking all the worse mappings of 94edo and improving them to reach 29-limit consistency. However, 311edo which is only a bit larger is a ''much'' better alternative for high-limit, and 270edo is a ''way'' better choice for yazalatha. There is no reason to use this unless to improve the intonation of a fixed, non-negotiably 94edo piece. D | |||
=== 190537edo === | === 190537edo === | ||