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, 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've already have my suite of edos that are perfect, supported [[User:Eufalesio/Ultimate|Ultimate]], [[olympic]], and beyond that. | ||
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. 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 | 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. 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 19-limit, with more emphasis on the 13-limit. | ||
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. 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 ''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. 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. | ||
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=== 5edo === | === 5edo === | ||
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 | 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 fine 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 | 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 fine 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. Rank: A | 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. Rank: A | ||
=== 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 | 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 narrow 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. Rank: 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 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. Rank: S | 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. It's also part of my Ultimate sequence (as 12e val)! Rank: S | ||
=== 17edo === | === 17edo === | ||
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=== 41edo === | === 41edo === | ||
The first usable | The first usable cassandra 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. It's also part of my Ultimate sequence! | ||
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. Rank: AC, not for air conditioner, but for ''accuracy'' and ''cool''. | 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. Rank: AC, not for air conditioner, but for ''accuracy'' and ''cool''. | ||
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For finer edos in this range, meantone ceases to do it for me, but I respect this one. Rank: C- | For finer edos in this range, meantone ceases to do it for me, but I respect this one. Rank: C- | ||
=== 53edo === | |||
Pythagorean tuning incarnate, and astounding ya. yathana is especially potent, but the -zatwetha is still very much usable, even the yazalatha! It feels less tempered than 41edo, so it feels like a less compromised system, but I feel bad for the rest of the edos near this one, because there is nothing like it. But what can I say? Suck it losers! It's also part of my Ultimate sequence! Rank: SSS | |||
=== 62edo === | === 62edo === | ||
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 only because it's a multiple of 31edo. Rank: C- | 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 only because it's a multiple of 31edo. Rank: C- | ||
=== 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 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! Rank: | 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! Rank: SS | ||
=== 80edo === | === 80edo === | ||
Srutal personified. 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. Rank: 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 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. Rank: 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 yazatha here is instead a great subgroup, which is a good selling point for me. It also supports olympic, unlike 72edo, which is also a great selling point. Had I known about it, I could have probably used this instead of 72edo, but I'm now not that interested in compton anymore. Rank: A- | ||
=== 87edo === | === 87edo === | ||
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=== 94edo === | === 94edo === | ||
GOAT. The combination of the two | GOAT. The combination of the two coarsest 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. It's also part of my Ultimate sequence, the cassandra optimum! | ||
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 | 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 those wider minor thirds. I really only use it for the 19-limit, but the 23-limit goodness is no joke. Rank: '''Perfect.''' | ||
=== 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 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. Rank: 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 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. At least it's olympic. Rank: 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 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. | 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. I wouldn't use it again tho. Rank: SS- | ||
=== 171edo === | === 171edo === | ||
Ennealimmal, personified. I haven't composed in it directly, but since I did compose in yaza JI, it | Ennealimmal, personified. I haven't composed in it directly, but since I did compose in yaza JI, it bet it would sound basically 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. Rank: : 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'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. | 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. It's also part of my Ultimate sequence! Rank: S+ | ||
=== 224edo === | === 224edo === | ||
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=== 270edo === | === 270edo === | ||
Ultimate low complexity JIoid edo. Though a tad | Ultimate low complexity JIoid edo. Though a tad fine 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 basically 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)). It's also part of my Ultimate sequence, the best Ultimate edo! Rank: '''Perfect'''. | ||
=== 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. 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. Rank: SS | 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. It's also part of my Ultimate sequence! Rank: SS | ||
=== 665edo === | === 665edo === | ||
Pythagorean tuning. 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 | However, this is not why you would use 665edo, as this is pythagorean tuning that works as another olympic temperament. 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. Part of that may be due to it supporting olympic... Rank: A- | ||
=== | === 935edo === | ||
Basically optimal olympic. Manages to overcome the shortcomings of 665edo and result in possibly the best patent val for olympic and metaolympic. Somehow, usable. Not by me, still, But usable nontheless. Rank: C | |||
=== 8539edo === | === 8539edo === | ||
ULTRAOLYMPIC. The precision of this behemoth is unfathomable, yet somehow usable Rank: H (Hot sauce) | |||
=== 20203edo === | |||
ULTRAOLYMPIC end. Even unfathomable-er precision, yet somehow usable. Rank: BI (Batshit Insane) | |||
== EDOS I have things to talk about (and it's bad) == | == EDOS I have things to talk about (and it's bad) == | ||
=== 1edo === | === 1edo === | ||
Octaves | Octaves. Ligeti pulled them off. I won't care to try. Rank: F | ||
=== 2,3,4,6edo === | === 2,3,4,6edo === | ||
Only ever good as subsets of other edos such as 12edo | Only ever good as subsets of other edos such as 12edo or compton. Anywhere else, they stand out, and not positively, though 3edo has a surprisingly accurate 5. Rank: D (D+ for 3edo) | ||
=== 9edo === | === 9edo === | ||
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=== 16edo === | === 16edo === | ||
Supposedly, it would be one of the best antidiatonic systems, next to 9edo, but if an edo does not have diatonic, I consider it useless. Unlike 9edo which forms the basis for ennealimmal, I don't know of any good temperaments with a 1/16 octave period. 2^n edos suck in general. Rank: D | Supposedly, it would be one of the best antidiatonic systems, next to 9edo, but if an edo does not have diatonic, I consider it useless. Unlike 9edo which forms the basis for ennealimmal, I don't know of any good temperaments with a 1/16 octave period. 2^n edos suck ass in general. Rank: D | ||
=== 26edo === | === 26edo === | ||
The ultimate flattone. I respect that this edo can moderately deal with the yazalatha, as it is the | The ultimate flattone. I respect that this edo can moderately deal with the yazalatha, as it is the coarsest 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. Rank: C- | ||
=== 29edo === | === 29edo === | ||
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=== 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. Rank: E | 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. The only saving grace of this edo is that it supports olympic... which would be a great feature, if it wasn't also meantone, as the two don't exactly synergize. In my opinion, the best meantones are the golden meantones, and from 31edo on, the peak has already been reached. Rank: E | ||
=== 81, 131... very fine edos that support golden meantone === | === 81, 131... very fine edos that support golden meantone === | ||
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=== 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 | 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 fucking sucks! Rank: FF | ||
=== 282edo === | === 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 | 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 finer 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. Rank: D | ||
=== 190537edo === | === 190537edo === | ||
This is the next edo in the list of record k-strong telicity, and music had stopped being a priority this far, this fine along the list of edos. This is '''cosmic horror''' disguised as math in the 3-limit, forget about the rest of primes. The beat period of this fifth is 984 572 779 224.54 s*Hz with two sawtooth waves in perfect sync, which would be around 70 years and 331 days at f=440. This edo has a fifth that is accurate to a level that is quite possibly beyond the scope of a human lifetime. Think about it. There is a chance you'll die before listening to 190537edo's fifth beat even once at f=440, that is, if you hadn't become insane by then. | This is the next edo in the list of record k-strong telicity, and music had stopped being a priority this far, this fine along the list of edos. This is '''cosmic horror''' disguised as math in the 3-limit, forget about the rest of primes. The beat period of this fifth is 984 572 779 224.54 s*Hz with two sawtooth waves in perfect sync, which would be around 70 years and 331 days at f=440. This edo has a fifth that is accurate to a level that is quite possibly beyond the scope of a human lifetime. Think about it. There is a chance you'll die before listening to 190537edo's fifth beat even once at f=440, that is, if you hadn't become insane by then. | ||
If you say that you need accuracy to this precision to do any semblance of a musical work, I am, beyond a reasonable doubt, wholly confident that you are joking | If you say that you need accuracy to this precision to do any semblance of a musical work, I am, beyond a reasonable doubt, wholly confident that you are joking, neck deep in bullshit, or engaging in some wild mathematical fetish. And if for some god-removed reason you aren't... you are literally not human, or not anymore. Perhaps in a couple centuries, posthumanity will be able to comprehend this near-perfection, but as we stand right now, it is impossible to comprehend. Rank: Unrankable. | ||
== 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 horrible fifths. {{EDOs|8,11,13,14,18,20,21,23,25,30,35,40,42,45,47}}. Rank: FFF | I'm just going to say they are useless because they have horrible fifths. {{EDOs|8,11,13,14,18,20,21,23,25,30,35,40,42,45,47}}. Rank: FFF | ||
If an edo is not anywhere in this article is because I believe there are better options, or | If an edo is not anywhere in this article is because I believe there are better options, I don't know, or I don't care. | ||