User:Eboone/EDO Impressions: Difference between revisions
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'''PROGESS REPORT, so you don't have to scroll:''' | '''PROGESS REPORT, so you don't have to scroll:''' | ||
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 Tier placements of 20-29edo are also accurate, and all tier placements after that are outdated. | |||
I | I will next create pages for 10edo and 19edo, which are linked but currently do not have any text. | ||
''Start date: May 13, 2024. Most recent update: June 10, 2024. '''28 days''' have been spent.'' | ''Start date: May 13, 2024. Most recent update: June 10, 2024. '''28 days''' have been spent.'' | ||
—————————[[File:EDO Tier List.png|alt=A tier list of EDOs. S Tier - 12, 34, 31, 53, 72, 50, 22, 17, 15, 26, 19. A Tier - 27, 10, 46, 21, 20, 7, 16, 41, 55. B Tier - 18, 24, 36, 48, 65, 58, 25, 63, 13, 11, 56, 29, 23, 9, 5, 8. C Tier - 40, 43, 28, 14, 70, 68, 57, 37, 30, 60, 54, 49, 47, 44, 38, 67, 59, 35, 6. F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.|thumb|['''''OUTDATED''', will be updated when I'm finished with this page''] Ebooone's tier list of edos 5-72]] | —————————[[File:EDO Tier List.png|alt=A tier list of EDOs. S Tier - 12, 34, 31, 53, 72, 50, 22, 17, 15, 26, 19. A Tier - 27, 10, 46, 21, 20, 7, 16, 41, 55. B Tier - 18, 24, 36, 48, 65, 58, 25, 63, 13, 11, 56, 29, 23, 9, 5, 8. C Tier - 40, 43, 28, 14, 70, 68, 57, 37, 30, 60, 54, 49, 47, 44, 38, 67, 59, 35, 6. F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.|thumb|['''''OUTDATED''', will be updated when I'm finished with this page''] Ebooone's tier list of edos 5-72]] | ||
I, at least currently, work strictly in [[EDO|'''edos''']]. I | I, at least currently, work strictly in [[EDO|'''edos''']]. I tend not to venture higher than 53edo in my own works, and for reasons that are explained in Overarching Points > Multiples of EDOs, I consider '''72edo''' to be the largest edo that interests me. So, this page will go over my general thoughts regarding every positive integer edo up to that point. There are also a few '''smackdowns''' between edos that I consider "arch rivals," with the first being between 17edo and 19edo. | ||
A few edos on this page are so intriguing that I have entirely separate pages talking about them. These pages are linked directly below the headings of these edos. | |||
Of course, all tier lists and impressions on this page are subject to change in the future. | Of course, all tier lists and impressions on this page are subject to change in the future. | ||
All demos are short loops at 120bpm created by me in [[MuseScore|'''MuseScore 3''']]. | All '''demos''' are short loops at 120bpm created by me in [[MuseScore|'''MuseScore 3''']]. | ||
== Overarching Points == | == 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'''. | 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'''. | ||
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== Macro-Semitonal == | == Macro-Semitonal == | ||
These are the first edos with what I would consider '''semitones''', meaning voice leading possibilities are about to blow wide open. 12edo is also here, but I won't be saying much about it. | |||
=== [[10edo]] === | === [[10edo]] === | ||
'''[[User:Eboone/10edo]]''' | |||
''2×5, 1° = 120¢, Fifth = 720¢ (3\5)'' | ''2×5, 1° = 120¢, Fifth = 720¢ (3\5)'' | ||
''Tier: '''A+'''''[[File:10edo groove.mp3|none|thumb|10edo heist theme in <sup>⌄</sup><nowiki>A bish (3|3 mode of 3L 4s)</nowiki>]] | ''Tier: '''A+'''''[[File:10edo groove.mp3|none|thumb|10edo heist theme in <sup>⌄</sup><nowiki>A bish (3|3 mode of 3L 4s)</nowiki>]] | ||
Ah yes, the homeland of [[Mosh|'''mosh''']]. 10edo is actually my favorite of the edos less than 12, | Ah yes, the homeland of [[Mosh|'''mosh''']] (3L 4s). 10edo is actually my favorite of the edos less than 12, though 9edo does come pretty close. This edo is the largest one with a singular third, that being the 360¢ submajor third which is extremely close to [[16/13]]. That means this temperament also features a stunning approximation of the [[13/8|'''13th harmonic''']], coming in just 0.53¢ sharp. It also features all of the interseptimal intervals from 5edo, meaning it includes the same approximation of the 7th harmonic, as well as a relatively stable fifth (especially compared to 9edo). | ||
10edo is a very xen tuning — more so than even 7edo in my opinion — because it doesn't even pretend to represent the diatonic scale | 10edo is a very xen tuning — more so than even 7edo in my opinion — because it doesn't even pretend to represent the diatonic scale. Instead, as mentioned previously, the heptatonic mos of 10edo is 3L 4s, or mosh. This is an incredibly intriguing mos that can be difficult to wrap your head around, but the sounds it produces are quite beautiful. [https://www.youtube.com/watch?v=uOsrbFEC6bQ ''Apartment in the Sky''] by [[HEHEHE I AM A SUPAHSTAR SAGA]] is an example of the brightest mode of mosh, dril. | ||
The demo I wrote for this edo is in the middle mode, bish. It oscilates between "tonic" and "dominant," and it sounds quite reminiscent of such movement in the diatonic mos, until you realize it's totally different. This mode of mosh could be mapped to the [[wikipedia:Double_harmonic_scale|double harmonic major scale]] in a diatonic system, yet doing that results in a very different sound. I was incredibly surprised when I retuned the demo to be in A♭ double harmonic major, only to be subjected to something the original could only dream of being as weird as. Of course, I probably only say that because I wasn't used to it. | The demo I wrote for this edo is in the middle mode, bish. It oscilates between "tonic" and "dominant," and it sounds quite reminiscent of such movement in the diatonic mos, until you realize it's totally different. This mode of mosh could be mapped to the [[wikipedia:Double_harmonic_scale|double harmonic major scale]] in a diatonic system, yet doing that results in a very different sound. I was incredibly surprised when I retuned the demo to be in A♭ double harmonic major, only to be subjected to something the original could only dream of being as weird as. Of course, I probably only say that because I wasn't used to it. | ||
Being the first edo with what I would consider a | Being the first edo with what I would consider a semitone, chromatic movement in this edo is relatively familiar, yet with a tang of xen. In fact, that's a fairly apt way of describing this temperament as a whole. The third feels like a major third sometimes, especially when combined with the 1080¢ major seventh, yet other times it feels totally neutral or even minor. It certainly doesn't feel minor in isolation, but it kinda does at some points in the demo. This supposed submajor third is even more ambiguous than the 240¢ second-third, which is literally ambiguous by definition. | ||
Notating this edo is an interesting challenge. I choose to notate it with the seven naturals assigned to mosh, with A dril lying on the naturals, but this certainly isn't standard. The "standard" (if you can call it that) is to notate this edo pentatonic-wise, using [[Ups and downs|'''ups and downs''']] to reach the notes in between. I, however, am not a particular fan of ups and downs. I prefer [[Sagittal|'''sagittal''']], but even that looks a bit clunky in this edo. The problem is the fact that B and F are skipped when using this method, or that B=C and E=F. I just think that looks and feels weird to read because it's based on the diatonic mos which 10edo doesn't have.* | Notating this edo is an interesting challenge. I choose to notate it with the seven naturals assigned to mosh, with A dril lying on the naturals, but this certainly isn't standard. The "standard" (if you can call it that) is to notate this edo pentatonic-wise, using [[Ups and downs|'''ups and downs''']] to reach the notes in between. I, however, am not a particular fan of ups and downs. I prefer [[Sagittal|'''sagittal''']], but even that looks a bit clunky in this edo. The problem is the fact that B and F are skipped when using this method, or that B=C and E=F. I just think that looks and feels weird to read because it's based on the diatonic mos which 10edo doesn't have.* | ||
Instead, it makes much more sense to assign the naturals to mosh and use sharps and flats to reach the notes in between. Or, you could use [[Diamond-mos notation|''' | Instead, it makes much more sense to assign the naturals to mosh and use sharps and flats to reach the notes in between. Or, you could use [[Diamond-mos notation|'''diamond-mos notation''']], which is what ''Apartment in the Sky'' is notated in. My problem with this system is how difficult it is to actually implement, plus the idea of transposing a score instead of using key signatures is not my style. I'd rather just write in the accidentals manually than transpose the entire score, unless it's an extreme case. | ||
Anyway, notation aside, this edo has such an amazing sound. Every 5n-edo (especially those up to 30edo) has a particular 5n-edo sound, yet this edo stands out even among that group. Being the largest edo with a singular third, it really cant help but sound totally xen, even though its semitone step-size tends to make it sound almost like 12edo in certain cases. Mosh is a super cool landscape, but as [https://youtube.com/@adamneely?si=w8Hhclj4OZUJEd_N Adam Neely] shows in [https://youtu.be/H4KIwA8O9LU?si=RZ3DxiC_9sl_famK&t=295 How to make Microtonal Lo-Fi Hip Hop], you can just as easily stick to the 2 interlocked equipentatonic scales and produce some great music. | Anyway, notation aside, this edo has such an amazing sound. Every 5n-edo (especially those up to 30edo) has a particular 5n-edo sound, yet this edo stands out even among that group. Being the largest edo with a singular third, it really cant help but sound totally xen, even though its semitone step-size tends to make it sound almost like 12edo in certain cases. Mosh is a super cool landscape, but as [https://youtube.com/@adamneely?si=w8Hhclj4OZUJEd_N Adam Neely] shows in [https://youtu.be/H4KIwA8O9LU?si=RZ3DxiC_9sl_famK&t=295 How to make Microtonal Lo-Fi Hip Hop], you can just as easily stick to the 2 interlocked equipentatonic scales and produce some great music. | ||
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=== [[11edo]] === | === [[11edo]] === | ||
''Prime, 1° = 109.09¢, | ''Prime, 1° = 109.09¢, Fifth = 654.55¢ (6\11)'' | ||
''Tier: '''C''''' | ''Tier: '''C''''' | ||
[[File:11edo demo.mp3|none|thumb|11edo casino swing in A altered lydian (?)]] | [[File:11edo demo.mp3|none|thumb|11edo casino swing in A altered lydian (?)]] | ||
This is a... fun one. It suffers from being almost 12edo, giving it a somewhat similar vibe to 9edo, but without the whole "battle between consonance and dissonance" thing since nearly everything here is dissonant. The fifth is more like [[16/11]] than anything close to 3/2, meaning it actually has the worst fifth since 6edo, | This is a... fun one. It suffers from being '''almost 12edo''', giving it a somewhat similar vibe to 9edo, but without the whole "battle between consonance and dissonance" thing since nearly everything here is dissonant. The fifth is more like [[16/11]] than anything close to 3/2, meaning it actually has the worst fifth since 6edo, though 8edo comes close. This edo is notable for its approximation of [[9/7]], being just 1.28¢ sharp, making it the first edo with a '''supermajor third'''. It also has a pretty good approximation of the '''[[11/8|11th harmonic]]''', being 5.87¢ flat. | ||
While 10edo is the home of mosh, 11edo is the home of '''[[smitonic]]'''. I don't really like it as much as mosh | While 10edo is the home of mosh, 11edo is the home of '''[[smitonic]]''' (4L 3s). I don't really like it as much as mosh, but it has its uses. Anyway, I don't really dabble with smitonic in this edo. I prefer to write free of any scale, since this edo is already pretty limiting as it is. That's why the demo is full of jazz chords. | ||
As always, The Equal Tempered Keyboard has some good examples of this edo. They're rather beautiful for what they are, but I find myself wishing they were in a different edo. ''[https://www.youtube.com/watch?v=28SOTJvT6sw&list=PLLZE7hMjEXRaVKJD8IPyiNFxFIVspBv6q Tostadosto]'' by [[Francium]] and ''[[Longwayaway People]]'' by Sevish are other great examples of what this edo is capable of. | As always, The Equal Tempered Keyboard has some good examples of this edo. They're rather beautiful for what they are, but I find myself wishing they were in a different edo. ''[https://www.youtube.com/watch?v=28SOTJvT6sw&list=PLLZE7hMjEXRaVKJD8IPyiNFxFIVspBv6q Tostadosto]'' by [[Francium]] and ''[[Longwayaway People]]'' by Sevish are other great examples of what this edo is capable of. | ||
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I could say many things about 12edo, but I don't think you need to hear it. It's the first edo with the '''diatonic mos''', the first edo with a decent approximation of 3/2 (1.96¢ flat), and the first edo that can claim to be a '''5-limit system'''. It's a '''[[meantone temperament]]''', but only a little. This means the thirds are closer to pure 5-limit ratios, but not enough to sacrifice the edo's ability to support '''Pythagorean''' melodies. It contains symmetrical augmented and diminished structures, as well as the whole-tone scale. It's essentially a perfect temperament that works well in basically any style, so I cannot honestly put it anywhere but the top of the tier list. | I could say many things about 12edo, but I don't think you need to hear it. It's the first edo with the '''diatonic mos''', the first edo with a decent approximation of 3/2 (1.96¢ flat), and the first edo that can claim to be a '''5-limit system'''. It's a '''[[meantone temperament]]''', but only a little. This means the thirds are closer to pure 5-limit ratios, but not enough to sacrifice the edo's ability to support '''Pythagorean''' melodies. It contains symmetrical augmented and diminished structures, as well as the whole-tone scale. It's essentially a perfect temperament that works well in basically any style, so I cannot honestly put it anywhere but the top of the tier list. | ||
Yeah, that's all I'm going to say about 12edo. The purpose of this page is to | Yeah, that's all I'm going to say about 12edo. The purpose of this page is to really to delve into the other 71 edos. | ||
=== [[13edo]] === | === [[13edo]] === | ||
''Prime, 1° = 92.31¢, | ''Prime, 1° = 92.31¢, Dual Fifths = 738.46¢ (7\13), 646.15¢ (6\13)'' | ||
''Tier: '''B''''' | ''Tier: '''B''''' | ||
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This is just a better 11edo. It has a better approximation of 11/8 (2.53¢ sharp), and is honestly much better at pulling off the "almost 12edo" effect. It also has 2 fifths, and even though they're both terrible it's still better than having whatever 11edo has. | This is just a better 11edo. It has a better approximation of 11/8 (2.53¢ sharp), and is honestly much better at pulling off the "almost 12edo" effect. It also has 2 fifths, and even though they're both terrible it's still better than having whatever 11edo has. | ||
13edo features 3 very nice mosses in their basic forms. '''[[Gramitonic]]''' (4L 5s) is an absolutely amazing enneatonic mos that makes use of dual fifths. '''[[Oneirotonic]]''' (5L 3s) is an octatonic mos that also takes advantage of the dual fifths, and can be seen as an extension of the diatonic scale. '''[[Archaeotonic]]''' (6L 1s) is a heptatonic mos that resembles 7edo if the small step is large enough. The support for these really good mosses in their basic forms is amazing. | |||
The [https://www.youtube.com/watch?v=gA6m6DW83SM sostenuto] of [[Easley Blackwood Jr.]]'s ''Twelve Microtonal Etudes for Electronic Music Media'' illustrates the vibe of the "almost 12edo" effect very well, evoking a "sinking" quality. I've also heard 13edo described as having a "jealous" sound, which is fairly apt. The intervals themselves contribute to these traits as well. The minor third is only slightly sharp of 7/6, and the major third is actually submajor with how flat it is of 5/4. These two thirds have such a unique aura that I cannot describe. They, along with the two fifths as well as the 11/8 (and 13/8) come together to create a truly profound temperament. | The [https://www.youtube.com/watch?v=gA6m6DW83SM sostenuto] of [[Easley Blackwood Jr.]]'s ''Twelve Microtonal Etudes for Electronic Music Media'' illustrates the vibe of the "almost 12edo" effect very well, evoking a "sinking" quality. I've also heard 13edo described as having a "jealous" sound, which is fairly apt. The intervals themselves contribute to these traits as well. The minor third is only slightly sharp of 7/6, and the major third is actually submajor with how flat it is of 5/4. These two thirds have such a unique aura that I cannot describe. They, along with the two fifths as well as the 11/8 (and 13/8) come together to create a truly profound temperament. | ||
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This is the first edo with 3 flavors of thirds. The neutral third is the same one from 7edo, the minor third is a rather flat subminor third (almost inframinor), and the major third is a nice supermajor third that comes in just a few cents flat of 9/7. This is a pretty wide spread, allowing for great contrast between different chord qualities. | This is the first edo with 3 flavors of thirds. The neutral third is the same one from 7edo, the minor third is a rather flat subminor third (almost inframinor), and the major third is a nice supermajor third that comes in just a few cents flat of 9/7. This is a pretty wide spread, allowing for great contrast between different chord qualities. | ||
Being a low 7n-edo, the '''[[apotome]]''' is tempered out. This makes sense in 7edo, since there simply aren't enough notes for there to be anything close to a semitone, but in the case of 14edo, it's quite intriguing. You could create a "diatonic" scale, but it would either end up equalized or with more than 2 step sizes. In fact, this edo doesn't have any heptatonic mosses. Instead, it features the likes of '''[[semiquartal]]''' and [[4L 6s|'''lime''']], both in their basic forms. These mosses are rather interesting, with semiquartal being somewhat popular. The one example of lime in 14edo that I could find is [https://www.youtube.com/watch?v=EhjSEUaBXxU&list=PLLZE7hMjEXRaVKJD8IPyiNFxFIVspBv6q&index=3 ''Rexasaurus''] by Francium. | Being a low 7n-edo, the '''[[apotome]]''' is tempered out. This makes sense in 7edo, since there simply aren't enough notes for there to be anything close to a semitone, but in the case of 14edo, it's quite intriguing. You could create a "diatonic" scale, but it would either end up equalized or with more than 2 step sizes. In fact, this edo doesn't have any heptatonic mosses. Instead, it features the likes of '''[[semiquartal]]''' (5L 4s) and [[4L 6s|'''lime''']] (4L 6s), both in their basic forms. These mosses are rather interesting, with semiquartal being somewhat popular (especially in 19edo). The one example of lime in 14edo that I could find is [https://www.youtube.com/watch?v=EhjSEUaBXxU&list=PLLZE7hMjEXRaVKJD8IPyiNFxFIVspBv6q&index=3 ''Rexasaurus''] by Francium. | ||
Notating 14edo presents similar problems to that of 10edo. Instead of having to battle the whole B=C and E=F thing, now the issue is the fact that sharps and flats have no meaning. Since the apotome is tempered out, G♯ is literally the same pitch as G. To get around this, most people would just use ups and downs, but I already said I don't really like ups and downs. So, I prefer sagittal. It's a bit clunky since this edo officially uses the Athenian [[55/54]] symbol | Notating 14edo presents similar problems to that of 10edo. Instead of having to battle the whole B=C and E=F thing, now the issue is the fact that sharps and flats have no meaning. Since the apotome is tempered out, G♯ is literally the same pitch as G. To get around this, most people would just use ups and downs, but I already said I don't really like ups and downs. So, I prefer sagittal. It's a bit clunky since this edo officially uses the Athenian [[55/54]] symbol instead of something from the Spartan set, but it works well enough. | ||
Anyway, this edo is underappreciated in my opinion. It inherits the xen quality of 7edo and places it in an environment with many more opportunities. My favorite piece in this edo is the prelude from The Equal Tempered Keyboard, and I don't think it would've sounded any better in a different temperament. The watery fifth when paired with the extremely flat subminor third has such a bittersweet sound, and when paired with the supermajor third it has a particular nostalgic vibe. And, of course, the neutral third has its own character that is completely separate from the other two thirds. To think that such a breadth of emotions can be achieved with so few notes is honestly beautiful ( | Anyway, this edo is underappreciated in my opinion. It inherits the xen quality of 7edo and places it in an environment with many more opportunities. My favorite piece in this edo is the prelude from The Equal Tempered Keyboard, and I don't think it would've sounded any better in a different temperament. The watery fifth when paired with the extremely flat subminor third has such a bittersweet sound, and when paired with the supermajor third it has a particular nostalgic vibe. And, of course, the neutral third has its own character that is completely separate from the other two thirds. To think that such a breadth of emotions can be achieved with so few notes is honestly beautiful (ignoring 12edo). | ||
I wish I could say more about 14edo, but I really don't have that much experience in it. On the surface, it seems like a pretty weird tuning since it does a horrible job of approximating pretty much any prime harmonics, which is why I haven't used it much. But, in the future, I do wish to use it in a variety of styles to see what it is truly capable of. | I wish I could say more about 14edo, but I really don't have that much experience in it. On the surface, it seems like a pretty weird tuning since it does a horrible job of approximating pretty much any prime harmonics, which is why I haven't used it much. But, in the future, I do wish to use it in a variety of styles to see what it is truly capable of. | ||
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Anyway, those two are clearly not my favorites. 14edo is, as I said, totally underappreciated and underexplored. It can create some truly ethereal sounds on par with 9edo, which is why I put them right next to each other on the tier list. I don't like saying xen temperaments are good for "alien" music, but 14edo really does hit the mark in this regard (as is seen in the glorious thumbnail of ''[https://www.youtube.com/watch?v=2BzDOibAJO8 Warp Drive]'' by [[JUMBLE]]). | Anyway, those two are clearly not my favorites. 14edo is, as I said, totally underappreciated and underexplored. It can create some truly ethereal sounds on par with 9edo, which is why I put them right next to each other on the tier list. I don't like saying xen temperaments are good for "alien" music, but 14edo really does hit the mark in this regard (as is seen in the glorious thumbnail of ''[https://www.youtube.com/watch?v=2BzDOibAJO8 Warp Drive]'' by [[JUMBLE]]). | ||
10edo is one of my favorite edos. I'd like to have a custom 10edo marimba, if that's even a feasible project. It's a great edo for tuning your ears to the world of xenharmony without just being a 5-limit system like 19edo or 31edo, because of its familiar semitone size | 10edo is one of my favorite edos. I'd like to have a custom 10edo marimba, if that's even a feasible project. It's a great edo for tuning your ears to the world of xenharmony without just being a 5-limit system like 19edo or 31edo, because of its familiar semitone size. It's honestly one of the most underrated edos in existence, since even 5edo gets more attention than it. | ||
And then there's 12edo. Pretty good, I'd say. | And then there's 12edo. Pretty good, I'd say. | ||
== Micro-Semitonal == | == Micro-Semitonal == | ||
All 5 of these edos are amazing. Even 18edo ended up growing on me and climbing its way into A tier, putting every single edo here above B tier. | |||
A few of these are very popular, and a few of these are criminally underexplored. You've probably already seen your fair share of music in 17edo and 19edo, but the other 3 are absolutely incredible as well. | |||
=== [[15edo]] === | === [[15edo]] === | ||
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The minor third is only 4.36¢ sharp of 6/5, meaning this edo has a better approximation of this ratio than every smaller edo, and it really shines when paired with the sharp fifth. It's a very pure sound, even though the fifth is pretty far off of 3/2. The major third is the same as in 12edo, but the major seventh is sharp thanks to the fifth. This means major seventh chords have a very bright quality that really accentuates the uplifting nature of the fifth. Overall, the minor and major thirds have very different vibes, and they both react with the fifth in unique ways. | The minor third is only 4.36¢ sharp of 6/5, meaning this edo has a better approximation of this ratio than every smaller edo, and it really shines when paired with the sharp fifth. It's a very pure sound, even though the fifth is pretty far off of 3/2. The major third is the same as in 12edo, but the major seventh is sharp thanks to the fifth. This means major seventh chords have a very bright quality that really accentuates the uplifting nature of the fifth. Overall, the minor and major thirds have very different vibes, and they both react with the fifth in unique ways. | ||
15edo supports the '''[[porcupine]]''' and [[Limmic temperaments#5-limit%20.28blackwood.29|'''blackwood''']] temperaments, with the '''[[pine]]''' and '''[[pentawood]]''' mosses being present in their basic forms. Both of these mosses are rather interesting, but I prefer to work freely of any particular scale. The three vastly different step sizes really shine when used in conjunction. The second-third especially brings a lot to the table, since it can function either as a second or a third. ''[https://www.youtube.com/watch?v=0PczKDrOdUA Xênerie]'' by [https://www.youtube.com/@woyten Woyten] illustrates this quite well, using it to create an inframinor sound as well as using it as a supermajor second in the melody. | 15edo supports the '''[[porcupine]]''' and [[Limmic temperaments#5-limit%20.28blackwood.29|'''blackwood''']] temperaments, with the '''[[pine]]''' (7L 1s) and '''[[pentawood]]''' (5L 5s) mosses being present in their basic forms. Both of these mosses are rather interesting, but I prefer to work freely of any particular scale. The three vastly different step sizes really shine when used in conjunction. The second-third especially brings a lot to the table, since it can function either as a second or a third. ''[https://www.youtube.com/watch?v=0PczKDrOdUA Xênerie]'' by [https://www.youtube.com/@woyten Woyten] illustrates this quite well, using it to create an inframinor sound as well as using it as a supermajor second in the melody. | ||
''[https://www.youtube.com/watch?v=xBqXc4PTuLw Like Satie]'' by Hideya is another great piece in this edo, illustrating the characteristic "out of tune" vibe very well. Incidentally, 15edo works great in a lofi environment. Anyway, I just went with a simple groove for this one. I wanted to accentuate the bass melody, so you can really hear how the different step sizes work together. It uses all three step sizes, as well as the undecimal superfourth approximation, which really adds a layer of grit to the end of the loop. The superfourth honestly feels totally different from everything else in the edo, but perhaps that's just the nature of it. | ''[https://www.youtube.com/watch?v=xBqXc4PTuLw Like Satie]'' by Hideya is another great piece in this edo, illustrating the characteristic "out of tune" vibe very well. Incidentally, 15edo works great in a lofi environment. Anyway, I just went with a simple groove for this one. I wanted to accentuate the bass melody, so you can really hear how the different step sizes work together. It uses all three step sizes, as well as the undecimal superfourth approximation, which really adds a layer of grit to the end of the loop. The superfourth honestly feels totally different from everything else in the edo, but perhaps that's just the nature of it. | ||
Overall, this is a stellar edo. It is the next smallest edo after 12edo that I am confident placing in S tier, albeit in the lower half. The sheer amount of possibilities with this few notes is honestly amazing. | ''[https://www.youtube.com/watch?v=YJQsR-Z5aDc Suite for Guitar in 15-Note Equal Tuning]'' by Easley Blackwood is probably my favorite piece in this edo. I have nothing to say about it, I just thought I'd mention it. Overall, this is a stellar edo. It is the next smallest edo after 12edo that I am confident placing in S tier, albeit in the lower half. The sheer amount of possibilities with this few notes is honestly amazing. | ||
=== [[16edo]] === | === [[16edo]] === | ||
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This edo is often said to be the optimal tuning for mavila temperament, and I agree. It is one of three edos that natively support it in the patent val, and I do honestly believe it does it better than the other two. Mavila is a very interesting temperament, pushing the fifth so flat that harmony is literally flipped on its head. It can create some intriguing harmonic effects, sounding like the diatonic scale until suddenly it totally doesn't. I illustrated this in the demo with a shocking E minor chord (sounding E♭ major ish) in the 6th bar, resolving to a totally different key. It never really deviates from the antidiatonic scale, at least not in a way that I would note as significant. | This edo is often said to be the optimal tuning for mavila temperament, and I agree. It is one of three edos that natively support it in the patent val, and I do honestly believe it does it better than the other two. Mavila is a very interesting temperament, pushing the fifth so flat that harmony is literally flipped on its head. It can create some intriguing harmonic effects, sounding like the diatonic scale until suddenly it totally doesn't. I illustrated this in the demo with a shocking E minor chord (sounding E♭ major ish) in the 6th bar, resolving to a totally different key. It never really deviates from the antidiatonic scale, at least not in a way that I would note as significant. | ||
Anyway, the intervals in this edo are | Anyway, the intervals in this edo are very nice. The minor third is the same as in 12edo, but the major third is 11.31¢ flat of 5/4, giving the temperament a distinct somber quality. There is also a fairly good approximation of 7/4, being only 6.17¢ sharp. I've never heard a piece in this edo that I would describe as "joyous" or any other discrete happy adjective. There's always a tinge of solemnity, especially in the [https://www.youtube.com/watch?v=AwL95c4PlDs&list=PLblcTr4RQqwJR8klOuKHdV_QSZQVoLwgH&index=2 andantino] of ''Twelve Microtonal Etudes for Electronic Music Media''. It's an unmistakable sound. | ||
16edo is the basis of [[Armodue theory|'''Armodue theory''']], which I don't really know much about, but it is based on the [[7L 2s|'''mavila superdiatonic''']] scale. The superdiatonic scale is an enneatonic mos that behaves somewhat similarly to oneirotonic, in that it has two fifths and a flat major third. Having two fifths is pretty cool, but in the case of 16edo, the dual sharp fifth is so sharp that I wouldn't even consider it a fifth. | 16edo is the basis of [[Armodue theory|'''Armodue theory''']], which I don't really know much about, but it is based on the [[7L 2s|'''mavila superdiatonic''']] (7L 2s) scale. The superdiatonic scale is an enneatonic mos that behaves somewhat similarly to oneirotonic, in that it has two fifths and a flat major third. Having two fifths is pretty cool, but in the case of 16edo, the dual sharp fifth is so sharp that I wouldn't even consider it a fifth. | ||
This edo also works well in a blues context, somewhat surprisingly. ''[https://www.youtube.com/watch?v=LLgClI8pyNw Don't Take Five]'' by Woyten is a prime example of this, being one of the coolest pieces I've heard in this edo behind the Blackwood etude. 16edo is honestly underexplored; it has so much potential in a ton of different genres, yet I feel that people are deterred by the fifth and other dissonant intervals. The antidiatonic scale works amazingly in its soft form, which is why I think this is the best tuning for mavila. It's like 9edo, but in exchange for the profound war between consonance and dissonance, you get a somewhat nicer fifth and a somber vibe that is difficult to emulate in other edos. That may not seem like a fair trade since I hyped up 9edo so much, but it makes 16edo much more versatile and interesting. | This edo also works well in a blues context, somewhat surprisingly. ''[https://www.youtube.com/watch?v=LLgClI8pyNw Don't Take Five]'' by Woyten is a prime example of this, being one of the coolest pieces I've heard in this edo behind the Blackwood etude. 16edo is honestly underexplored; it has so much potential in a ton of different genres, yet I feel that people are deterred by the fifth and other dissonant intervals. The antidiatonic scale works amazingly in its soft form, which is why I think this is the best tuning for mavila. It's like 9edo, but in exchange for the profound war between consonance and dissonance, you get a somewhat nicer fifth and a somber vibe that is difficult to emulate in other edos. That may not seem like a fair trade since I hyped up 9edo so much, but it makes 16edo much more versatile and interesting. | ||
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17edo features mosh in its soft form and gramitonic in its hard form. This means 17edo features my entire top 3 favorite mosses, which is absolutely fabulous. I do prefer softer forms of gramitonic (particularly those found in 22edo, 31edo, and 53edo), but it's still great that it's here. Plus, it's always great to experiment with hard and soft forms of mosses. | 17edo features mosh in its soft form and gramitonic in its hard form. This means 17edo features my entire top 3 favorite mosses, which is absolutely fabulous. I do prefer softer forms of gramitonic (particularly those found in 22edo, 31edo, and 53edo), but it's still great that it's here. Plus, it's always great to experiment with hard and soft forms of mosses. | ||
The first time I encountered this edo, it was placed next to its arch rival | The first time I encountered this edo, it was placed next to its arch rival in the same style. I thought it was pretty obvious that 17edo sounded worse, but that's because it was played in a piano timbre. Sure, it can sound quite beautiful in a piano timbre, as shown in [https://www.youtube.com/watch?v=gaYvK9OBHK0 ''The Bedoginning''] by Woyten (one of my favorite pieces), but have a listen to the acoustic version of the [https://www.youtube.com/watch?v=WCedVC3Sl04 con moto] of ''Twelve Microtonal Etudes for Electronic Music Media'', arranged by Matthew Sheeran. When I showed this to my fellow musician brother who had little experience with microtonal music, he literally thought it was in 12edo even after I told him it wasn't. Even I had a hard time telling until the middle section (1:42 in the video) began and I heard that diatonic semitone. | ||
This edo really lends itself well to music that I can only describe as "bouncy," like the Blackwood etude. I feel that meantone temperaments suffer in this regard, while pythagorean and superpyth temperaments thrive. Overall, this is one of my absolute favorite edos, and one that I will surely continue to use in the future. But will it win against its meantone rival in a smackdown?! | This edo really lends itself well to music that I can only describe as "bouncy," like the Blackwood etude. I feel that meantone temperaments suffer in this regard, while pythagorean and superpyth temperaments thrive. Overall, this is one of my absolute favorite edos, and one that I will surely continue to use in the future. But will it win against its meantone rival in a smackdown?! | ||
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''2×3², 1° = 66.67¢, Dual Fifths = 733.33¢ (11\18), 666.67¢ (5\9)'' | ''2×3², 1° = 66.67¢, Dual Fifths = 733.33¢ (11\18), 666.67¢ (5\9)'' | ||
''Tier: ''' | ''Tier: '''A''''' | ||
[[File:18edo demo 2.mp3|none|thumb|18edo brass quintet in B♭]] | [[File:18edo demo 2.mp3|none|thumb|18edo brass quintet in B♭]] | ||
18edo is also known as the '''third-tone system''' because one step is exactly equal to one third of a whole-tone in 12edo. It sits in an interesting position, not being too similar to any edos around it. It inherits the subminor and major thirds from 9edo, along with a supraminor third. It also has two fifths that are almost | 18edo is also known as the '''third-tone system''' because one step is exactly equal to one third of a whole-tone in 12edo. It sits in an interesting position, not being too similar to any edos around it. It inherits the subminor and major thirds from 9edo, along with a supraminor third. It also has two fifths that are almost equidistant from 3/2, making it a much more convincing dual fifth system than 13edo. | ||
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... | 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... | ||
... | ...this is a segment that was edited at a future time. What I originally explained here is that I feel 9edo is superior to 18edo because of the idea that fewer notes is better. I believed this until I heard Supahstar Saga's arrangement of ''[https://www.youtube.com/watch?v=mkSlVrpC7HI&t=437s Aquatic Ambience]'' from Donkey Kong Country. The tight voicings in the electric piano at bar 27 made me realize just how much the in-between notes really add to this edo. I also rediscovered my love for oneirotonic upon hearing this, certainly placing it among my top 5 favorite mosses. | ||
So yeah, it's better than 9edo, but only marginally. In fact, they are positioned right next to each other in A tier, where they will likely remain for the foreseeable future. Whereas 9edo is perfect for creating a sort of "ghostly" sonic landscape, 18edo seems to be perfect for dissonance in general. I realize that's a bit of a bold, sweeping claim, but I suppose that's just because I'm not articulating myself correctly. This edo has such a distinct aura that just gives it a wonderful dissonant sound that I cannot really put into words. | |||
Anyway, 18edo is really cool. 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. | |||
===[[19edo]]=== | ===[[19edo]]=== | ||
'''[[User:Eboone/19edo]]''' | |||
''Prime, 1° = 63.16¢, Fifth = 694.74¢ (11\19)'' | ''Prime, 1° = 63.16¢, Fifth = 694.74¢ (11\19)'' | ||
''Tier: '''S''''' | ''Tier: '''S''''' | ||
[[File:19edo demo 2.mp3|none|thumb|19edo lofi in C major]] | [[File:19edo demo 2.mp3|none|thumb|19edo lofi in C major]] | ||
19edo is the next edo after 17edo to have the diatonic scale, and it is the first that really demonstrates meantone. Specifically, it is very close to '''1/3-comma meantone''' with [[eigenmonzo]] 6/5, so the minor third of this edo is only 0.15¢ flat of 6/5. This is the best approximation of 6/5 among all edos on this page. The approximation of 5/4 is also relatively decent, coming in 7.36¢ flat. This particular flat major third has a marvelous quality (pun intended), as it comes extremely close to '''[[56/45]]'''. It's a very distinct and beautiful major third that really makes this edo shine. | 19edo is the next edo after 17edo to have the diatonic scale, and it is the first that really demonstrates meantone. Specifically, it is very close to '''1/3-comma meantone''' with [[eigenmonzo]] 6/5, so the minor third of this edo is only 0.15¢ flat of 6/5. This is the best approximation of 6/5 among all non-19n-edos on this page. The approximation of 5/4 is also relatively decent, coming in 7.36¢ flat. This particular flat major third has a marvelous quality (pun intended), as it comes extremely close to '''[[56/45]]'''. It's a very distinct and beautiful major third that really makes this edo shine. | ||
The fifth is also quite marvelous (pun still intended), as it comes extremely close to '''[[112/75]]'''. These "marvelous" intervals truly define how this edo feels in the 5-limit, giving it a sound that, in a way, feels even purer than 5-limit just intonation. The soft diatonic scale also melds very well with these slightly flat intervals, giving the temperament a nostalgic quality. | The fifth is also quite marvelous (pun still intended), as it comes extremely close to '''[[112/75]]'''. These "marvelous" intervals truly define how this edo feels in the 5-limit, giving it a sound that, in a way, feels even purer than 5-limit just intonation. The soft diatonic scale also melds very well with these slightly flat intervals, giving the temperament a nostalgic quality. | ||
Now.. the septimal intervals. If you just look at 19edo as a 5-limit system, then it is absolutely amazing and certainly rivals 12edo and 31edo. But that isn't all we have here. There are septimal intervals too, and they are... intriguing. It took a while for them to grow on me, but if you stop trying to hear them as perfect approximations of 7/6, 9/7, 7/4 etc. (which they absolutely aren't), their true beauty begins to shine through. | Now.. the septimal intervals. If you just look at 19edo as a 5-limit system, then it is absolutely amazing and certainly rivals 12edo and 31edo. But that isn't all we have here. There are septimal intervals too, and they are... intriguing. It took a while for them to grow on me, but if you stop trying to hear them as perfect approximations of 7/6, 9/7, 7/4 etc. (which they absolutely aren't), their true beauty begins to shine through. To put it generally, you must hear this edo for what it is, rather than for what it is not. | ||
Anyway, the subminor third is even flatter than the one in 14edo, landing right in the middle of the interseptimal region between 9/7 and 7/6. In fact, I'd say it's an inframinor third. Likewise, the supermajor third lands right in the interseptimal region between 9/7 and 21/16, albeit closer to 9/7. The inframinor third really doesn't have a septimal sound at all, and neither does the abysmal approximation of the 7th harmonic (21.46¢ flat), but the supermajor third does come close enough to 9/7 for it to have a septimal quality. The thing is, it's even sharper than the septimal supermajor third, which is already a bit of an extreme sound to get used to, so it ends up being a harsh sound in certain contexts. | Anyway, the subminor third is even flatter than the one in 14edo, landing right in the middle of the interseptimal region between 9/7 and 7/6. In fact, I'd say it's an inframinor third. Likewise, the supermajor third lands right in the interseptimal region between 9/7 and 21/16, albeit closer to 9/7. The inframinor third really doesn't have a septimal sound at all, and neither does the abysmal approximation of the 7th harmonic (21.46¢ flat), but the supermajor third does come close enough to 9/7 for it to have a septimal quality. The thing is, it's even sharper than the septimal supermajor third, which is already a bit of an extreme sound to get used to, so it ends up being a harsh sound in certain contexts. | ||
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====Verdict==== | ====Verdict==== | ||
Of course, retuning two 8-bar loops isn't going to decide which edo is better. This is just a fun experiment I thought I'd do, and I must say that ''' | Of course, retuning two 8-bar loops isn't going to decide which edo is better. This is just a fun experiment I thought I'd do, and I must say that '''19edo wins this showdown!''' While the lack of neutral intervals is certainly a bit of a tank, the utter beauty and ethereality of 19edo is something that is truly unique. Not even 31edo can sound like it, thanks to the interseptimal intervals. Anyway, there really isn't a way to compare these in any objective sense because they're so different. They are both absolutely amazing edos considering their size! | ||
By the way, this isn't the only showdown. Stay tuned... (pun intended) | By the way, this isn't the only showdown. Stay tuned... (pun intended) | ||
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===Micro-Semitonal EDO Recap=== | ===Micro-Semitonal EDO Recap=== | ||
[[File:Micro-Semitonal EDO Tier List.png|thumb|Tier list of edos 15-19]] | [[File:Micro-Semitonal EDO Tier List.png|thumb|Tier list of edos 15-19]] | ||
Three S tier edos in one category! All five of these edos are amazing for their own reasons. 15edo has a particular "living" quality that makes it great for lofi and Gymnopédie-style pieces. ''[https://www.youtube.com/watch?v=xBqXc4PTuLw Like Satie]'' by Hideya illustrates this quality quite well, and I will likely experiment with this sort of sound myself. 16edo is just amazing, evoking beautiful solemnity and bittersweetness that I cannot overstate. 18edo is its own thing entirely, sounding similar to 9edo but with more options for complex harmony. It's an incredibly potent edo that works extremely well in | Three S tier edos in one category! All five of these edos are amazing for their own reasons. 15edo has a particular "living" quality that makes it great for lofi and Gymnopédie-style pieces. ''[https://www.youtube.com/watch?v=xBqXc4PTuLw Like Satie]'' by Hideya illustrates this quality quite well, and I will likely experiment with this sort of sound myself. 16edo is just amazing, evoking beautiful solemnity and bittersweetness that I cannot overstate. 18edo is its own thing entirely, sounding similar to 9edo but with more options for complex harmony. It's an incredibly potent edo that works extremely well in contexts that you would never expect. | ||
Then there's 17edo and 19edo, two of the most common edos to get people introduced into xenharmony. Supahstar Saga's "[https://www.youtube.com/watch?v=-R9DX_-2JH0&list=PLha3CFvr8SzwlDpGL9MrJcoN8xOHyowsw Exploring 19-TET]" series is a brilliant introduction to 19edo that I would honestly recommend for anyone just getting into the realm of xenharmonic edos. I'm almost tempted to make my own series talking about various edos (if you're from the future and I have already done this, hi), sort of like this page you're reading but in video form so it's easier to digest. | Then there's 17edo and 19edo, two of the most common edos to get people introduced into xenharmony. Supahstar Saga's "[https://www.youtube.com/watch?v=-R9DX_-2JH0&list=PLha3CFvr8SzwlDpGL9MrJcoN8xOHyowsw Exploring 19-TET]" series is a brilliant introduction to 19edo that I would honestly recommend for anyone just getting into the realm of xenharmonic edos. I'm almost tempted to make my own series talking about various edos (if you're from the future and I have already done this, hi), sort of like this page you're reading but in video form so it's easier to digest. | ||
I absolutely love the way 17edo's superpyth/parapyth hybrid flavor affects melodies. I generally prefer harder forms of the diatonic scale, so 19edo often feels too soft for me, but 17edo is just perfect. It lends itself very well to more extreme modes, like lydian and phrygian. | I absolutely love the way 17edo's superpyth/parapyth hybrid flavor affects melodies. I generally prefer harder forms of the diatonic scale, so 19edo often feels too soft for me, but 17edo is just perfect. It lends itself very well to more extreme modes, like lydian and phrygian. | ||
19edo on the other hand, while softer than 17edo, is absolutely amazing in the 5-limit. The interseptimal intervals add so much on top of it as well, making it an absolutely fascinating edo that even 31edo struggles to emulate. | |||
==Macro-Diesitonal== | ==Macro-Diesitonal== | ||