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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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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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! | 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. Rank | 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 === | ||
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=== 270edo === | === 270edo === | ||
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 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'''. | 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 === | ||
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=== 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) == | ||
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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 === | ||