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, and the most conceptualization ease. 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.

== EDOS I have ~~much~~ to talk about ==

== EDOS I have things to talk about (and it's good) ==

=== 5edo ===

The first usable edo and the first edo to have any semblance of a perfect fifth. It features an extremely simplified 2.3.7, 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... 2.3.7.37, 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.

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. A

=== 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 5-limit is not there, the melodic coolness you can pull of with this coarse edo are nothing to scoff at. C, not for accuracy, but for ''cool''.

=== 12edo ===

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Line 23:

=== 22edo ===

While the change in perspective that 19edo offers is mixed with familiarity, 22edo is an entirely different beast. It features a very exaggerated non-meantone 5-limit, making it the ultimate porcupine, which is not a temperament known for its accuracy, but it's cool! The 7-limit structure inside the diatonic scale is something very sui generis, though it's 11-limit is kinda meh, but what can I say, it's the first edo to be consistent in the 11-odd-limit! C, not for accuracy, but for ''cool''.

While the change in perspective that 19edo offers is mixed with familiarity, 22edo is an entirely different beast. It features a very exaggerated non-meantone 5-limit, making it the ultimate porcupine, which is not a temperament known for its accuracy, but it's cool!

The 7-limit structure inside the diatonic scale is something very sui generis, though it's 11-limit is kinda meh, but what can I say, it's the first edo to be consistent in the 11-odd-limit! C, not for accuracy, but for ''cool''.

=== 24edo ===

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=== 41edo ===

The first usable schismic edo (29edo and 17edo don't count because their 5/4's are wack). Still manageable grain, 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 11-limit is marvelous (pun intended) but the 13-limit is... lacking. Still, even if the 5-limit is not that accurate, since the innacuracy is flatwards, I think it's much more enjoyable, as I like wide minor thirds. Also supports Bohlen Pierce, which is also incredibly cool. AC, not for air conditioner, but for ''accuracy'' and ''cool''.

The first usable schismic edo (29edo and 17edo don't count because their 5/4's are wack). Still manageable grain, hyperaccurate fifths and the non-meantoneness is definitely welcome. It is the first edo to introduce a comma accidental framework, which in my opinion is one of the best frameworks for composition. The 11-limit is marvelous (pun intended) but the 13-limit is... lacking.

Still, even if the 5-limit is not that accurate, since the innacuracy is flatwards, I think it's much more enjoyable, as I like wide minor thirds. Also supports Bohlen Pierce, which is also incredibly cool. AC, not for air conditioner, but for ''accuracy'' and ''cool''.

=== 46edo ===

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=== 50edo ===

Still a good meantone edo, and though it is a much better approximant for golden meantone, I prefer using golden meantone as a rank-2, and not buying the entire gamut. The 19-limit usability is surprising, still. However, having all those new intervals inside a meantone edo feels in my opinion strangely unnatural, as we're stretching the meantone chain-of-fifths beyond what's supposed to. For bigger edos in this range, meantone ceases to do it for me, but I respect it. C

Still a good meantone edo, and though it is a much better approximant for golden meantone, I prefer using golden meantone as a rank-2, and not buying the entire gamut. The 19-limit usability is surprising, still. However, having all those new intervals inside a meantone edo feels in my opinion strangely unnatural, as we're stretching the meantone chain-of-fifths beyond what's supposed to.

For bigger edos in this range, meantone ceases to do it for me, but I respect it. C

=== 53edo ===

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=== 94edo ===

GOAT. The combination of the two smallest schismic edos, which are both incredibly solid choices, into one neatly rounded package that is very optimized. I am heavily '''biased''' towards this, as it represents the ultimate cassandra, and a chain-of-fifths framework that 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 5-limit, but since it is flat and not sharp, I find it much more palatable, as I like wide minor thirds. I really only use it for the 2.3.5.7.11.13.19, but the 23-limit goodness is no joke. SSS

GOAT. The combination of the two smallest schismic edos, which are both incredibly solid choices, into one neatly rounded package that is very optimized. I am heavily '''biased''' towards this, as it represents the ultimate cassandra, and a chain-of-fifths framework that 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 5-limit, but since it is flat and not sharp, I find it much more palatable, as I like wide minor thirds. I really only use it for the 2.3.5.7.11.13.19, but the 23-limit goodness is no joke. SSS

=== 130edo ===

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=== 171edo ===

I haven't composed in it directly, but since I did compose in 7-limit JI, it'd sound the same. It features a dead-accurate 7-limit that I cannot distinguish from just. It's that good. The great innacuracy of the 11 is a bit sad, though it still has a usable 13, which has that going for it. A

Ennealimmal, personified. I haven't composed in it directly, but since I did compose in 7-limit JI, it'd sound the same. It features a dead-accurate 7-limit that I cannot distinguish from just. It's that good. The great innacuracy of the 11 is a bit sad, though it still has a usable 13, which has that going for it. A

=== 217edo ===

It's the septuple of 31edo, and that is nothing less than a miracle (though it doesn't support miracle). I've done some tests on it, and it's 31-limit is incredible. It introduces an unfamiliar and slightly tedious gari-vulture-esque framework in which you have to use schisma-function steps apart from pythcommas, but apart from that, it's still within the realms of manageability. Also, it has an incredible 2.3.5.13, which I really respect. SS

It's the septuple of 31edo, and that is nothing less than a miracle (though it doesn't support miracle). I've done some tests on it, and it's 31-limit is incredible. It introduces an unfamiliar and slightly tedious gari-vulture-esque framework in which you have to use schisma-function steps apart from pythcommas, but apart from that, it's still within the realms of manageability. Also, it has an incredible 2.3.5.13, which I really respect. Also important to remark, from this point onward, edos start to sound more or less the same, as the absolute error gets lower and lower. S

=== 224edo ===

A cousin to 217edo, which is still schismic, though still harder to conceptualize. Theory tells me that the 13-limit is extremely accurate, even more than the 217edo. But 217edo is smaller, and it contains 31edo, so... I think I'll stick with the other one. B

A cousin to 217edo which is still schismic, dare I say the ultimate schismic edo, though still harder to conceptualize. Theory tells me that the 13-limit is extremely accurate, even more than the 217edo, and for that I think it deseves. But 217edo is smaller, and it contains 31edo, so... I think I'll stick with the other one. B

=== 270edo ===

Ultimate low complexity JIoid edo. Though a tad large now, consistency within its 2.3.5.7.11.13.19 is insane. This trumps a lot of the competition. Using a ~~larger~~ edo in the same subgroup becomes SSS

Ultimate low complexity JIoid edo. Though a tad large now, consistency within its 2.3.5.7.11.13.19 is insane. This trumps a lot of the competition. Using a finer edo in the same subgroup becomes harder to justify. SSS

=== 311edo ===

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=== 8539edo ===

This level of fineness is at the bleeding edge of insanity. The precision of this behemoth is astounding. 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

== EDOS I have things to talk about (and it's bad) ==

=== 0edo ===

Rhythm personified. As an edo, it is horrible. There is nothing. Everything is tempered out. To an extent, it not only is useless, it's also ontologically terrifying. ''The end of pitch''. However, going back to the real world, this is just glorified rhythm, and so useless from a tuning standpoint. F

=== 1edo ===

Octaves. Extremely boring to use still, as octaves are hyperconsonant, so there is no inertia. You really have to get creative to make something cool in this. Ligeti pulled it off. But I won't care to try. F

=== 2,3,4,6edo ===

Only ever good as subsets of other edos such as 12edo. And compton in general. Anywhere else, they stand out, and not positively, though 3edo has a surprisingly accurate 5. D

=== 29edo ===

It's the next edo which has a fifth that's better than 12edo's... and that's it? It's worse everywhere else! By itself, it's really only a slightly sharp Pythagorean tuning, which to me is a bad selling point. The supersets 58 and 87 are decent, but I think there are better alternatives. D

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

I'm just going to sort them all into wastebaskets.

* Important, but too coarse for me: {{EDOs|5,7,10}} (C-ish?)

* Interesting, but unjustifiably inaccurate for me: {{EDOs|26,81}} (D)

* Interesting, but unjustifiably inaccurate for me: {{EDOs|26~~,29~~,81}} (D)

* Potentially useful, but I don't really like them {{EDOs|9,16}} (D)

* Useless: {{EDOs|~~0,1,2,3,4,6,~~11,13,14,18,20,21,23,25,30,35,40,42,45,47}} (F)

* Useless: {{EDOs|11,13,14,18,20,21,23,25,30,35,40,42,45,47}} (F)

* There are better options~~: everything else~~

If an edo is not anywhere in this article is because I believe there are better options, or that I haven't even thought about it.

@@ Line 1: / Line 1: @@
 My main reason to use edos is to "buy" the entire gamut and be able to do JIoid stuff in it with the most accuracy, and the most conceptualization ease. 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.
-== EDOS I have much to talk about ==
+== EDOS I have things to talk about (and it's good) ==
+=== 5edo ===
+The first usable edo and the first edo to have any semblance of a perfect fifth. It features an extremely simplified 2.3.7, 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... 2.3.7.37, 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.
+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. A
+=== 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 5-limit is not there, the melodic coolness you can pull of with this coarse edo are nothing to scoff at. C, not for accuracy, but for ''cool''.
 === 12edo ===
@@ Line 13: / Line 23: @@
 === 22edo ===
-While the change in perspective that 19edo offers is mixed with familiarity, 22edo is an entirely different beast. It features a very exaggerated non-meantone 5-limit, making it the ultimate porcupine, which is not a temperament known for its accuracy, but it's cool! The 7-limit structure inside the diatonic scale is something very sui generis, though it's 11-limit is kinda meh, but what can I say, it's the first edo to be consistent in the 11-odd-limit! C, not for accuracy, but for ''cool''.
+While the change in perspective that 19edo offers is mixed with familiarity, 22edo is an entirely different beast. It features a very exaggerated non-meantone 5-limit, making it the ultimate porcupine, which is not a temperament known for its accuracy, but it's cool!
+The 7-limit structure inside the diatonic scale is something very sui generis, though it's 11-limit is kinda meh, but what can I say, it's the first edo to be consistent in the 11-odd-limit! C, not for accuracy, but for ''cool''.
 === 24edo ===
@@ Line 22: / Line 34: @@
 === 41edo ===
-The first usable schismic edo (29edo and 17edo don't count because their 5/4's are wack). Still manageable grain, 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 11-limit is marvelous (pun intended) but the 13-limit is... lacking. Still, even if the 5-limit is not that accurate, since the innacuracy is flatwards, I think it's much more enjoyable, as I like wide minor thirds. Also supports Bohlen Pierce, which is also incredibly cool. AC, not for air conditioner, but for ''accuracy'' and ''cool''.
+The first usable schismic edo (29edo and 17edo don't count because their 5/4's are wack). Still manageable grain, hyperaccurate fifths and the non-meantoneness is definitely welcome. It is the first edo to introduce a comma accidental framework, which in my opinion is one of the best frameworks for composition. The 11-limit is marvelous (pun intended) but the 13-limit is... lacking.
+Still, even if the 5-limit is not that accurate, since the innacuracy is flatwards, I think it's much more enjoyable, as I like wide minor thirds. Also supports Bohlen Pierce, which is also incredibly cool. AC, not for air conditioner, but for ''accuracy'' and ''cool''.
 === 46edo ===
@@ Line 28: / Line 42: @@
 === 50edo ===
-Still a good meantone edo, and though it is a much better approximant for golden meantone, I prefer using golden meantone as a rank-2, and not buying the entire gamut. The 19-limit usability is surprising, still. However, having all those new intervals inside a meantone edo feels in my opinion strangely unnatural, as we're stretching the meantone chain-of-fifths beyond what's supposed to. For bigger edos in this range, meantone ceases to do it for me, but I respect it. C
+Still a good meantone edo, and though it is a much better approximant for golden meantone, I prefer using golden meantone as a rank-2, and not buying the entire gamut. The 19-limit usability is surprising, still. However, having all those new intervals inside a meantone edo feels in my opinion strangely unnatural, as we're stretching the meantone chain-of-fifths beyond what's supposed to.
+For bigger edos in this range, meantone ceases to do it for me, but I respect it. C
 === 53edo ===
@@ Line 37: / Line 53: @@
 === 94edo ===
-GOAT. The combination of the two smallest schismic edos, which are both incredibly solid choices, into one neatly rounded package that is very optimized. I am heavily '''biased''' towards this, as it represents the ultimate cassandra, and a chain-of-fifths framework that 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 5-limit, but since it is flat and not sharp, I find it much more palatable, as I like wide minor thirds. I really only use it for the 2.3.5.7.11.13.19, but the 23-limit goodness is no joke. SSS
+GOAT. The combination of the two smallest schismic edos, which are both incredibly solid choices, into one neatly rounded package that is very optimized. I am heavily '''biased''' towards this, as it represents the ultimate cassandra, and a chain-of-fifths framework that 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 5-limit, but since it is flat and not sharp, I find it much more palatable, as I like wide minor thirds. I really only use it for the 2.3.5.7.11.13.19, but the 23-limit goodness is no joke. SSS
 === 130edo ===
@@ Line 46: / Line 64: @@
 === 171edo ===
-I haven't composed in it directly, but since I did compose in 7-limit JI, it'd sound the same. It features a dead-accurate 7-limit that I cannot distinguish from just. It's that good. The great innacuracy of the 11 is a bit sad, though it still has a usable 13, which has that going for it. A
+Ennealimmal, personified. I haven't composed in it directly, but since I did compose in 7-limit JI, it'd sound the same. It features a dead-accurate 7-limit that I cannot distinguish from just. It's that good. The great innacuracy of the 11 is a bit sad, though it still has a usable 13, which has that going for it. A
 === 217edo ===
-It's the septuple of 31edo, and that is nothing less than a miracle (though it doesn't support miracle). I've done some tests on it, and it's 31-limit is incredible. It introduces an unfamiliar and slightly tedious gari-vulture-esque framework in which you have to use schisma-function steps apart from pythcommas, but apart from that, it's still within the realms of manageability. Also, it has an incredible 2.3.5.13, which I really respect. SS
+It's the septuple of 31edo, and that is nothing less than a miracle (though it doesn't support miracle). I've done some tests on it, and it's 31-limit is incredible. It introduces an unfamiliar and slightly tedious gari-vulture-esque framework in which you have to use schisma-function steps apart from pythcommas, but apart from that, it's still within the realms of manageability. Also, it has an incredible 2.3.5.13, which I really respect. Also important to remark, from this point onward, edos start to sound more or less the same, as the absolute error gets lower and lower. S
 === 224edo ===
-A cousin to 217edo, which is still schismic, though still harder to conceptualize. Theory tells me that the 13-limit is extremely accurate, even more than the 217edo. But 217edo is smaller, and it contains 31edo, so... I think I'll stick with the other one. B
+A cousin to 217edo which is still schismic, dare I say the ultimate schismic edo, though still harder to conceptualize. Theory tells me that the 13-limit is extremely accurate, even more than the 217edo, and for that I think it deseves. But 217edo is smaller, and it contains 31edo, so... I think I'll stick with the other one. B
 === 270edo ===
-Ultimate low complexity JIoid edo. Though a tad large now, consistency within its 2.3.5.7.11.13.19 is insane. This trumps a lot of the competition. Using a larger edo in the same subgroup becomes SSS
+Ultimate low complexity JIoid edo. Though a tad large now, consistency within its 2.3.5.7.11.13.19 is insane. This trumps a lot of the competition. Using a finer edo in the same subgroup becomes harder to justify. SSS
 === 311edo ===
@@ Line 68: / Line 86: @@
 === 8539edo ===
 This level of fineness is at the bleeding edge of insanity. The precision of this behemoth is astounding. 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
+== EDOS I have things to talk about (and it's bad) ==
+=== 0edo ===
+Rhythm personified. As an edo, it is horrible. There is nothing. Everything is tempered out. To an extent, it not only is useless, it's also ontologically terrifying. ''The end of pitch''. However, going back to the real world, this is just glorified rhythm, and so useless from a tuning standpoint. F
+=== 1edo ===
+Octaves. Extremely boring to use still, as octaves are hyperconsonant, so there is no inertia. You really have to get creative to make something cool in this. Ligeti pulled it off. But I won't care to try. F
+=== 2,3,4,6edo ===
+Only ever good as subsets of other edos such as 12edo. And compton in general. Anywhere else, they stand out, and not positively, though 3edo has a surprisingly accurate 5. D
+=== 29edo ===
+It's the next edo which has a fifth that's better than 12edo's... and that's it? It's worse everywhere else! By itself, it's really only a slightly sharp Pythagorean tuning, which to me is a bad selling point. The supersets 58 and 87 are decent, but I think there are better alternatives. D
 == EDOS I don't have much to talk about ==
 I'm just going to sort them all into wastebaskets.
-* Important, but too coarse for me: {{EDOs|5,7,10}} (C-ish?)
+* Interesting, but unjustifiably inaccurate for me: {{EDOs|26,81}} (D)
-* Interesting, but unjustifiably inaccurate for me: {{EDOs|26,29,81}} (D)
 * Potentially useful, but I don't really like them {{EDOs|9,16}} (D)
-* Useless: {{EDOs|0,1,2,3,4,6,11,13,14,18,20,21,23,25,30,35,40,42,45,47}} (F)
+* Useless: {{EDOs|11,13,14,18,20,21,23,25,30,35,40,42,45,47}} (F)
-* There are better options: everything else
+If an edo is not anywhere in this article is because I believe there are better options, or that I haven't even thought about it.