User:Eufalesio/EDO impressions - Revision history

Eufalesio at 13:32, 22 June 2026

2026-06-22T13:32:29Z

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

← Older revision		Revision as of 11:40, 19 April 2026
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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!

Show changes

Eufalesio: Important breakthroughs

2026-04-18T21:08:05Z

Important breakthroughs

Show changes

Eufalesio at 23:03, 9 March 2026

2026-03-09T23:03:42Z

← Older revision		Revision as of 23:03, 9 March 2026
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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

← Older revision		Revision as of 17:49, 8 March 2026
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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 ===

Eufalesio at 17:29, 8 March 2026

2026-03-08T17:29:12Z

← Older revision		Revision as of 17:29, 8 March 2026
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	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.

	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''. B		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-

	=== 1600edo ===		=== 1600edo ===
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	=== 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. A		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

	=== 8539edo ===		=== 8539edo ===

Eufalesio: Added 665, 7315, 190537edo

2026-03-08T17:25:07Z

Added 665, 7315, 190537edo

← Older revision		Revision as of 17:25, 8 March 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.		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.

	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. I care about the 5-limit, 7-limit, 2.3.5.13, 2.3.5.7.13, and 2.3.5.7.11.13.19(.29) JI subgroups, liking my error to be balanced across primes, but the error on 3 to be minimal. I ''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 useless to me.

			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'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.
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	=== 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. Serendipity personified. Very hard to justify using anything else other than this, as the difference between edosteps from this point on is definitely nigh impossible to hear. I see it as an ultimate tuning of sorts for practicality's sake. SSS		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. Serendipity personified. Very hard to justify using anything else other than this, as the difference between edosteps from this point on is definitely nigh impossible to hear. I see it as an ultimate tuning of sorts for practicality's sake. SSS

			=== 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.

			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''. B

	=== 1600edo ===		=== 1600edo ===
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	=== 2460edo ===		=== 2460edo ===
	The only reason I've put this one here is because it is a 12n edo, and that makes it ''slightly'' easier to work with, and very transposing friendly. It's astonishingly accurate, though dividing the semitone into 205ths is reasonably excessive. C+		The only reason I've put this one here is because it is a 12n edo, and that makes it ''slightly'' easier to work with, and very transposing friendly. It's astonishingly accurate, though dividing the semitone into 205ths is reasonably excessive. C+

			=== 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. A

	=== 8539edo ===		=== 8539edo ===
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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'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

			=== 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.

			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.

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