User:Eufalesio/EDO impressions - Revision history

Eufalesio at 17:58, 4 July 2026

2026-07-04T17:58:15Z

← Older revision		Revision as of 17:58, 4 July 2026
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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. I've already have my suite of edos that are perfect, supported [[User:Eufalesio/Ultimate\|Ultimate]].		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 ~~yazalatha~~.		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-

	~~=== 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: 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 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: ~~SSS~~		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 ===
	~~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. Rank: C+		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 ~~slightly wide~~ minor thirds. I really only use it for the ~~yazalathana~~, but the 23-limit goodness is no joke. Rank: '''Perfect.'''		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 ===
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	=== 171edo ===		=== 171edo ===
	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. Rank: : A		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 ===
	~~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.		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 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 care about the chain~~ of ~~fifths as a theoretical construct, I think this is good~~. Rank: A-		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-

	=== ~~7315edo~~ ===		=== 935edo ===
	~~Undecupling 665edo results in insane precision~~. ~~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 telic backbone~~, ~~and thirteenths of a qian comma serving as nanoalterations~~. ~~For not being in my ULTRAOLYMPIC sequence~~, ~~it's alright~~. Rank: B		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 ===
	~~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. Beyond here... there be monsters... and hot sauce. It's also part of my ULTRAOLYMPIC sequence~~, ~~as an extra~~. Rank: C		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 ===

Eufalesio at 11:28, 30 June 2026

2026-06-30T11:28:45Z

← Older revision		Revision as of 11:28, 30 June 2026
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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]].

	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 yazalatha.		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 yazalatha.
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	=== 53edo ===		=== 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, ~~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! It's also part of my Ultimate sequence! Rank: SS		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: SS

	=== 72edo ===		=== 72edo ===
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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 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: : 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 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 ===

Eufalesio at 13:32, 22 June 2026

2026-06-22T13:32:29Z

Show changes

Eufalesio: things

2026-04-19T12:06:31Z

things

← Older revision		Revision as of 12:06, 19 April 2026
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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 ~~large~~ enough that no cluttering will ever occur. It is horrible in all other limits... well... except... ''zathisa'', but who here cares about that?		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 ~~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 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 ~~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. Rank: C, not for accuracy, but for ''cool''.		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 ===
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	=== 94edo ===		=== 94edo ===
	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.		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.

	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. Rank: '''Perfect.'''		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. Rank: '''Perfect.'''
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	=== 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: ~~Rank~~: 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 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: : SS-

	=== 171edo ===		=== 171edo ===
	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. Rank: ~~Rank~~: A		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. 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. Rank: ~~Rank~~: 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'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. Rank: : S+

	=== 224edo ===		=== 224edo ===
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	=== 270edo ===		=== 270edo ===
	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)). 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 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)). Rank: '''Perfect'''.

	=== 311edo ===		=== 311edo ===
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	=== 26edo ===		=== 26edo ===
	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. Rank: C-		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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	=== 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 ~~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. Rank: D		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 ===

Eufalesio: /* 7edo */

2026-04-19T11:40:18Z

7edo

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	=== 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 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''.		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. Rank: C, not for accuracy, but for ''cool''.

	=== 12edo ===		=== 12edo ===

Eufalesio: Hotfixes!

2026-04-18T21:23:12Z

Hotfixes!

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Eufalesio: Important breakthroughs

2026-04-18T21:08:05Z

Important breakthroughs

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Eufalesio at 23:03, 9 March 2026

2026-03-09T23:03:42Z

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	=== 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.		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 care about this ''theoretically''. A-		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 care about this ''theoretically''. A-
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	=== 8539edo ===		=== 8539edo ===
	This level of fineness is at the bleeding edge of insanity. 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 ~~oogle~~ at impossibly gargantuan edos, I'll admit, but that ~~oogling~~ is only theoretical. Beyond here... there be monsters... and hot sauce. C		This level of fineness is at the bleeding edge of insanity. 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) ==
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	=== 190537edo ===		=== 190537edo ===
	This is the next edo in the list of record k-strong telicity, and it starts to get scary from this point. This is '''unadulterated 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, at f=440.		This is the next edo in the list of record k-strong telicity, and it starts to get scary from this point. This is '''unadulterated 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.

	If you say that you need accuracy to this precision, I am, beyond a reasonable doubt, wholly confident you are 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. Unrankable.		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 or neck deep in bullshit. 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. Unrankable.

	== EDOS I don't have much to talk about ==		== EDOS I don't have much to talk about ==

Eufalesio at 17:56, 8 March 2026

2026-03-08T17:56:58Z

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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.		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 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 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 useless to me.		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 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 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.

	~~Despite the fifth inaccuracy,~~ I do like meantone as it is arguably one of the best 5-limit temperaments, and it is obviously the theoretical backbone of Western music theory, still today.		I will make an exception to meantone and compton; I do like meantone as it is arguably one of the best 5-limit 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.

Eufalesio at 17:49, 8 March 2026

2026-03-08T17:49:31Z

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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 (D+ for 3edo)		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)

			=== 9edo ===
			Because this system does not support diatonic, I consider it useless. On its own. However, as a subset of other edos, it absolutely rules, as it is '''the''' basis for ennealimmal. A great deal of ''nineven'' edos are top-tier, because of this. Alone, F. As a subset, A.

			=== 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. D

	=== 26edo ===		=== 26edo ===