User:Eboone/EDO Impressions: Difference between revisions

Line 1:

'''PROGESS REPORT, so you don't have to scroll:'''

~~Everything~~ up to 20edo is now complete, with the 20edo and 22edo demos currently available. Tier placements of 20-29edo are also accurate~~. All~~ tier placements after that are outdated.

The first draft of everything up to 20edo is now complete, with the 20edo and 22edo demos also currently available. Tier placements of 20-29edo are also accurate, and all tier placements after that are outdated.

~~Keep in mind~~, I ~~may~~ go back and ~~change stuff that I say is complete.~~ I ~~want this page to be as comprehensive as possible, so if I feel that my earlier work doesn~~'~~t meet my current standards~~, ~~I will fix it~~.

There is currently only one overarching point, and my next task is to add more. I will then go back and edit what I've already written thus far, making sure to maximize the efficiency of the reading experience.

''Start date: May 13, 2024. Most recent update: June 8, 2024. '''26 days''' have been spent.''

Line 29:

=== Why Categorize EDOs? ===

The main reason I wanted to split these edos into categories was so that this wiki page wouldn't be an absolutely mammoth wall of text on mobile. Plus, it just felt like a fun challenge.

The main reason I wanted to split these edos into categories was so that this wiki page wouldn't be an absolutely mammoth wall of text on mobile (which ended up happening anyway, but oh well). Plus, it just felt like a fun challenge.

But why by step size? EDOs are generally distinguished by their intervals, so wouldn't it make sense to group edos by similar interval content? Sure, but how would you actually do that? There would be so much overlap that any and all meaningful distinction between categories would be lost. 29edo, 41edo, and 53edo would be grouped together as [[3-limit|Pythagorean]] systems, but 41edo and 53edo would also be grouped with 31edo and 50edo as [[5-limit]] systems, and 31edo and 50edo would be grouped with 36edo and 72edo as [[7-limit|septimal]] systems, and 72edo would be grouped with 24edo and 26edo as [[11-limit|undecimal]] systems...

Line 35:

As you can see, that falls apart quickly (as does attempting to group edos by factors or [[MOS scale|mosses]] or anything else, for the same reason), meaning the only other option is to categorize edos by step size. This is a great option because the size of an edo's step is what dictates its voice leading capabilities. For example, chromatic motion in 12edo is limited to semitones, whereas 31edo allows for movement by diesis. Also, no more extreme overlap between categories; 12 is similar to 11 and 13, and 31 is similar to 30 and 32. The borders between categories may be fuzzy, but that's to be expected when categorizing tuning systems anyway, since harmony itself is fuzzy by nature.

In terms of the actual categories themselves, I essentially divided them by significantly different [[Interval region|'''interval regions''']], and then into smaller subcategories. There are ~~really~~ 4 overarching categories: macrotonal, semitonal, diesitonal, and syntonic, but these still feel too large and contain vastly different edos within themselves. So, I basically just split each category down the middle.

In terms of the actual categories themselves, I essentially divided them by significantly different [[Interval region|'''interval regions''']], and then into smaller subcategories. There are 4 overarching categories: macrotonal, semitonal, diesitonal, and syntonic, but these still feel too large and contain vastly different edos within themselves. So, I basically just split each category down the middle.

== Overarching Points ==

After working on this project for about a month, I realized there were many points I found myself repeating. This isn't inherently an issue, but I thought it would make more sense if I sectioned off a few points that apply to multiple edos. I will be referencing these points directly in the descriptions of many edos, so it may be wise to '''read them before continuing'''.

=== Multiples of EDOs ===

Looking at the tier list, you may wonder why 12edo is at the top if its multiples are simply the same temperament but with more options. There are a few reasons for this, and it all comes down to the appeals of using smaller edos in general. Here are some of those appeals.

==== Fewer Notes, Easier ====

This isn't always the case, but it generally is. One of the primary appeals of edos in general is their convenience and versatility, especially in comparison to just intonation. The extreme end of this is very small edos, and as you venture into larger edos, their compactness becomes less important as they strive to be closer to [[just intonation]]. Essentially, a small edo that works very well in a certain JI subset (such as 12edo) gains less from being multiplied, as the amount of new notes isn't justified by a newfound ability to approximate JI.

For example, 72edo does a much better job in the 2.3.5.7.11 subgroup than 12edo, but now you have to deal with 72 notes. At that point, why not just use just intonation?* Smaller examples include 9edo and and 10edo being placed above 18edo and 20edo respectively.

''*I understand the rationale behind using very large edos instead of just intonation. It isn't just about approximating ratios; there are also things like mosses to consider. I, however, am not in the crowd that uses very large edos. At a certain point (72edo to be exact), the sheer amount of notes is enough to tank any other possible advantages of using a particular edo. This segues nicely into the next point:''

==== The Novelty of Fewer ====

Yeah, I'm literally just saying smaller edos are cooler (unless they're too small; see F tier). I mean, think about it. Equally dividing the octave seems to clash with the logarithmic nature of the [[harmonic series]], so the fact that this even works at all is already cool enough. Yet, all you need are 12 equal partitions to completely dominate the music industry. Sure, your ears may not care about the novelty factor of using a small number of notes within the uncountably infinite realm of pitch, but conceptually I find it incredibly neat.

5edo is a great example. Like, really? Only 5? But it sounds so cute! Then there's 7edo, a surprisingly versatile temperament that often gets me thinking "wait... there's only 7 notes here?" It's kind of like my brain is drawing parallels from the idea of simple ratios being consonant. In a way, small edos are "consonant" and large edos are "dissonant" in terms of their conception.

==== All You Need ====

At the end of the day, use whatever tuning you need to achieve your musical vision. It just happens that I basically never consider very large edos to be necessary. If all I need is 12, then all I need is 12. No need to use 24 or 36 or whatever if those extra notes won't help me hone in on the emotions I plan to engender in the listener.

== Trivial ==

These edos are characterized by the fact that they are all '''subsets of 12edo'''. This means that, along with being incredibly situational, they also aren't xenharmonic. 1edo in particular raises the question of what a tuning system even is, since it only has one note (assuming octave equivalence).

All 4 of these edos are best used sparingly, as they do not provide much in the way of melodic/harmonic capabilities.

=== [[1edo]] ===

Line 44:

Line 68:

''Tier: '''F'''''

[[File:1edo demo.mp3|none|thumb|1edo metal on E]]

Honestly, can this one even be called an edo? I mean, "equal divisions of the octave" implies that the octave is divided. Anyway, this edo is pretty lame because the whole point of using different temperaments is to access different melodic and harmonic opportunities, and this edo doesn't allow any of that. The only way to make this edo musical is through rhythm, dynamics, form, etc... stuff that isn't related to tuning.

Honestly, can this one even be called an edo? I mean, "equal divisions of the octave" implies that the octave is divided. On top of that, since '''octave equivalence''' is almost always assumed, this "temperament" literally only has '''one note'''. Anyway, this edo is pretty lame because the whole point of using different temperaments is to access different melodic and harmonic opportunities, and this edo doesn't allow any of that. The only way to make this edo musical is through rhythm, dynamics, form, etc... stuff that isn't related to tuning.

~~Although~~, ~~technically~~ there is some room for "melodic" expression if you allow yourself to use devices such as pitch bend. Or, perhaps you could use timbres that don't exactly settle on one pitch but clearly aren't unpitched either, like an old guitar string with wobbly harmonics. These "cheat codes" are partially what make one-note jazz solos so interesting, but of course the rest of the interest comes from the novelty of playing only one note amidst an electron cloud of dissonance. On its own, there really isn't much this ~~temperament~~ offers.

These factors alone make this edo terrible, but that doesn't mean you can't make it work. Technically, there is some room for "melodic" expression if you allow yourself to use devices such as pitch bend. Or, perhaps you could use timbres that don't exactly settle on one pitch but clearly aren't unpitched either, like an old guitar string with wobbly harmonics. These "cheat codes" are partially what make one-note jazz solos so interesting, but of course the rest of the interest comes from the novelty of playing only one note amidst an electron cloud of dissonance. On its own, there really isn't much this edo offers.

At least it's better than '''[[0edo]]'''.

Line 306:

Line 330:

The acoustic version of the [https://www.youtube.com/watch?v=b-fTC2y7o_U allegro] of ''Twelve Microtonal Etudes for Electronic Music Media'' is one of my favorite pieces in 18edo. It's a very hectic piece that really taps into the dissonant nature of the temperament. ''[https://www.youtube.com/watch?v=pEvT2oyWEuo 3 Bagatelles]'' by [[norokusi]] is another absolutely beautiful piece (pieces?) that demonstrates this temperament wonderfully. It's honestly haunting, almost to the degree of 9edo...

...why is 9edo above 18edo on the tier list if it's a subset? Well, let's think back to a statement I made about 2edo. "In theory, there should be no reason to choose 1edo over 2edo, but how much does that one extra note really add in practice?" I believe the same thing applies here. 18edo seems to evoke the same emotions as 9edo, in my opinion. It's all about the dissonant fifths battling against the extremely consonant septimal intervals, and if 9edo can do it with half as many notes, that's all I need. I absolutely love using edos with ~~less~~ notes if they are able to convey the emotions that I am going for, even if that means I technically have ~~less~~ options.

...why is 9edo above 18edo on the tier list if it's a subset? Well, let's think back to a statement I made about 2edo. "In theory, there should be no reason to choose 1edo over 2edo, but how much does that one extra note really add in practice?" I believe the same thing applies here. 18edo seems to evoke the same emotions as 9edo, in my opinion. It's all about the dissonant fifths battling against the extremely consonant septimal intervals, and if 9edo can do it with half as many notes, that's all I need. I absolutely love using edos with fewer notes if they are able to convey the emotions that I am going for, even if that means I technically have fewer options.

Anyway, 18edo is actually really cool. In fact, I'm placing it right at the top of B tier, where it will remain unmoving. It's kind of like a mix of 12edo and 13edo, if that makes sense. It's like 13edo in that it supports oneirotonic and has a similar dissonant vibe, but it contains many structures found in 12edo due to their shared factors. This edo certainly has a lot of potential.

@@ Line 1: / Line 1: @@
 '''PROGESS REPORT, so you don't have to scroll:'''
-Everything up to 20edo is now complete, with the 20edo and 22edo demos currently available. Tier placements of 20-29edo are also accurate. All tier placements after that are outdated.
+The first draft of everything up to 20edo is now complete, with the 20edo and 22edo demos also currently available. Tier placements of 20-29edo are also accurate, and all tier placements after that are outdated.
-Keep in mind, I may go back and change stuff that I say is complete. I want this page to be as comprehensive as possible, so if I feel that my earlier work doesn't meet my current standards, I will fix it.
+There is currently only one overarching point, and my next task is to add more. I will then go back and edit what I've already written thus far, making sure to maximize the efficiency of the reading experience.
 ''Start date: May 13, 2024. Most recent update: June 8, 2024. '''26 days''' have been spent.''
@@ Line 29: / Line 29: @@
 === Why Categorize EDOs? ===
-The main reason I wanted to split these edos into categories was so that this wiki page wouldn't be an absolutely mammoth wall of text on mobile. Plus, it just felt like a fun challenge.
+The main reason I wanted to split these edos into categories was so that this wiki page wouldn't be an absolutely mammoth wall of text on mobile (which ended up happening anyway, but oh well). Plus, it just felt like a fun challenge.
 But why by step size? EDOs are generally distinguished by their intervals, so wouldn't it make sense to group edos by similar interval content? Sure, but how would you actually do that? There would be so much overlap that any and all meaningful distinction between categories would be lost. 29edo, 41edo, and 53edo would be grouped together as [[3-limit|Pythagorean]] systems, but 41edo and 53edo would also be grouped with 31edo and 50edo as [[5-limit]] systems, and 31edo and 50edo would be grouped with 36edo and 72edo as [[7-limit|septimal]] systems, and 72edo would be grouped with 24edo and 26edo as [[11-limit|undecimal]] systems...
@@ Line 35: / Line 35: @@
 As you can see, that falls apart quickly (as does attempting to group edos by factors or [[MOS scale|mosses]] or anything else, for the same reason), meaning the only other option is to categorize edos by step size. This is a great option because the size of an edo's step is what dictates its voice leading capabilities. For example, chromatic motion in 12edo is limited to semitones, whereas 31edo allows for movement by diesis. Also, no more extreme overlap between categories; 12 is similar to 11 and 13, and 31 is similar to 30 and 32. The borders between categories may be fuzzy, but that's to be expected when categorizing tuning systems anyway, since harmony itself is fuzzy by nature.
-In terms of the actual categories themselves, I essentially divided them by significantly different [[Interval region|'''interval regions''']], and then into smaller subcategories. There are really 4 overarching categories: macrotonal, semitonal, diesitonal, and syntonic, but these still feel too large and contain vastly different edos within themselves. So, I basically just split each category down the middle.
+In terms of the actual categories themselves, I essentially divided them by significantly different [[Interval region|'''interval regions''']], and then into smaller subcategories. There are 4 overarching categories: macrotonal, semitonal, diesitonal, and syntonic, but these still feel too large and contain vastly different edos within themselves. So, I basically just split each category down the middle.
+== Overarching Points ==
+After working on this project for about a month, I realized there were many points I found myself repeating. This isn't inherently an issue, but I thought it would make more sense if I sectioned off a few points that apply to multiple edos. I will be referencing these points directly in the descriptions of many edos, so it may be wise to '''read them before continuing'''.
+=== Multiples of EDOs ===
+Looking at the tier list, you may wonder why 12edo is at the top if its multiples are simply the same temperament but with more options. There are a few reasons for this, and it all comes down to the appeals of using smaller edos in general. Here are some of those appeals.
+==== Fewer Notes, Easier ====
+This isn't always the case, but it generally is. One of the primary appeals of edos in general is their convenience and versatility, especially in comparison to just intonation. The extreme end of this is very small edos, and as you venture into larger edos, their compactness becomes less important as they strive to be closer to [[just intonation]]. Essentially, a small edo that works very well in a certain JI subset (such as 12edo) gains less from being multiplied, as the amount of new notes isn't justified by a newfound ability to approximate JI.
+For example, 72edo does a much better job in the 2.3.5.7.11 subgroup than 12edo, but now you have to deal with 72 notes. At that point, why not just use just intonation?* Smaller examples include 9edo and and 10edo being placed above 18edo and 20edo respectively.
+''*I understand the rationale behind using very large edos instead of just intonation. It isn't just about approximating ratios; there are also things like mosses to consider. I, however, am not in the crowd that uses very large edos. At a certain point (72edo to be exact), the sheer amount of notes is enough to tank any other possible advantages of using a particular edo. This segues nicely into the next point:''
+==== The Novelty of Fewer ====
+Yeah, I'm literally just saying smaller edos are cooler (unless they're too small; see F tier). I mean, think about it. Equally dividing the octave seems to clash with the logarithmic nature of the [[harmonic series]], so the fact that this even works at all is already cool enough. Yet, all you need are 12 equal partitions to completely dominate the music industry. Sure, your ears may not care about the novelty factor of using a small number of notes within the uncountably infinite realm of pitch, but conceptually I find it incredibly neat.
+edo is a great example. Like, really? Only 5? But it sounds so cute! Then there's 7edo, a surprisingly versatile temperament that often gets me thinking "wait... there's only 7 notes here?" It's kind of like my brain is drawing parallels from the idea of simple ratios being consonant. In a way, small edos are "consonant" and large edos are "dissonant" in terms of their conception.
+==== All You Need ====
+At the end of the day, use whatever tuning you need to achieve your musical vision. It just happens that I basically never consider very large edos to be necessary. If all I need is 12, then all I need is 12. No need to use 24 or 36 or whatever if those extra notes won't help me hone in on the emotions I plan to engender in the listener.
 == Trivial ==
+These edos are characterized by the fact that they are all '''subsets of 12edo'''. This means that, along with being incredibly situational, they also aren't xenharmonic. 1edo in particular raises the question of what a tuning system even is, since it only has one note (assuming octave equivalence).
+All 4 of these edos are best used sparingly, as they do not provide much in the way of melodic/harmonic capabilities.
 === [[1edo]] ===
@@ Line 44: / Line 68: @@
 ''Tier: '''F'''''
 [[File:1edo demo.mp3|none|thumb|1edo metal on E]]
-Honestly, can this one even be called an edo? I mean, "equal divisions of the octave" implies that the octave is divided. Anyway, this edo is pretty lame because the whole point of using different temperaments is to access different melodic and harmonic opportunities, and this edo doesn't allow any of that. The only way to make this edo musical is through rhythm, dynamics, form, etc... stuff that isn't related to tuning.
+Honestly, can this one even be called an edo? I mean, "equal divisions of the octave" implies that the octave is divided. On top of that, since '''octave equivalence''' is almost always assumed, this "temperament" literally only has '''one note'''. Anyway, this edo is pretty lame because the whole point of using different temperaments is to access different melodic and harmonic opportunities, and this edo doesn't allow any of that. The only way to make this edo musical is through rhythm, dynamics, form, etc... stuff that isn't related to tuning.
-Although, technically there is some room for "melodic" expression if you allow yourself to use devices such as pitch bend. Or, perhaps you could use timbres that don't exactly settle on one pitch but clearly aren't unpitched either, like an old guitar string with wobbly harmonics. These "cheat codes" are partially what make one-note jazz solos so interesting, but of course the rest of the interest comes from the novelty of playing only one note amidst an electron cloud of dissonance. On its own, there really isn't much this temperament offers.
+These factors alone make this edo terrible, but that doesn't mean you can't make it work. Technically, there is some room for "melodic" expression if you allow yourself to use devices such as pitch bend. Or, perhaps you could use timbres that don't exactly settle on one pitch but clearly aren't unpitched either, like an old guitar string with wobbly harmonics. These "cheat codes" are partially what make one-note jazz solos so interesting, but of course the rest of the interest comes from the novelty of playing only one note amidst an electron cloud of dissonance. On its own, there really isn't much this edo offers.
 At least it's better than '''[[0edo]]'''.
@@ Line 306: / Line 330: @@
 The acoustic version of the [https://www.youtube.com/watch?v=b-fTC2y7o_U allegro] of ''Twelve Microtonal Etudes for Electronic Music Media'' is one of my favorite pieces in 18edo. It's a very hectic piece that really taps into the dissonant nature of the temperament. ''[https://www.youtube.com/watch?v=pEvT2oyWEuo 3 Bagatelles]'' by [[norokusi]] is another absolutely beautiful piece (pieces?) that demonstrates this temperament wonderfully. It's honestly haunting, almost to the degree of 9edo...
-...why is 9edo above 18edo on the tier list if it's a subset? Well, let's think back to a statement I made about 2edo. "In theory, there should be no reason to choose 1edo over 2edo, but how much does that one extra note really add in practice?" I believe the same thing applies here. 18edo seems to evoke the same emotions as 9edo, in my opinion. It's all about the dissonant fifths battling against the extremely consonant septimal intervals, and if 9edo can do it with half as many notes, that's all I need. I absolutely love using edos with less notes if they are able to convey the emotions that I am going for, even if that means I technically have less options.
+...why is 9edo above 18edo on the tier list if it's a subset? Well, let's think back to a statement I made about 2edo. "In theory, there should be no reason to choose 1edo over 2edo, but how much does that one extra note really add in practice?" I believe the same thing applies here. 18edo seems to evoke the same emotions as 9edo, in my opinion. It's all about the dissonant fifths battling against the extremely consonant septimal intervals, and if 9edo can do it with half as many notes, that's all I need. I absolutely love using edos with fewer notes if they are able to convey the emotions that I am going for, even if that means I technically have fewer options.
 Anyway, 18edo is actually really cool. In fact, I'm placing it right at the top of B tier, where it will remain unmoving. It's kind of like a mix of 12edo and 13edo, if that makes sense. It's like 13edo in that it supports oneirotonic and has a similar dissonant vibe, but it contains many structures found in 12edo due to their shared factors. This edo certainly has a lot of potential.