User:Eboone/EDO Impressions: Difference between revisions

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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 Tier placements of 20-29edo are also accurate, and all tier placements after that are outdated.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 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 13, 2024. '''31 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 F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.|thumb|['''''OUTDATED''', will be updated when I'm finished with this page''] Ebooone's tier list of edos 5-72]]

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.

A few edos on this page are so intriguing that I (will soon) 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.

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Of the subsets of 12edo, I'd say this is the most interesting because it contains a '''whole tone''', and it's the only one that isn't just a meme. 6edo contains 2 interlocked instances of 3edo, meaning it has the same echoey major third, and it also contains 3 interlocked instances of 2edo, meaning it has the same uninvertible tritone. The combination of these intervals really contributes to the infamous dreamy quality of this edo, better known as the whole-tone scale.

There are many pieces that make use of the whole-tone scale, but very few that exist strictly in 6edo. [[wikipedia:Claude_Debussy|Claude Debussy]] is well known for his use of the scale, and it's a very interesting color to use while working in 6n-edos, but a very limiting scale to use in isolation. The best 6edo pieces I could find are the prelude and invention from [[Aaron Andrew Hunt]]'s "[https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard The Equal Tempered Keyboard]," and they are pretty interesting for what they are. They don't really sound dreamy, which is the sound that I feel is most well suited for this edo, but they are actually able to guide the listener on a comprehensive harmonic journey which is certainly no easy task.

There are many pieces that make use of the whole-tone scale, but very few that exist strictly in 6edo. [[wikipedia:Claude_Debussy|Claude Debussy]] is well known for his use of the scale, and it's a very interesting color to use while working in 6n-edos, but a very limiting scale to use in isolation. The best 6edo pieces I could find are the prelude and invention from [[Aaron Andrew Hunt]]'s [https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard ''The Equal Tempered Keyboard''], and they are pretty interesting for what they are. They don't really sound dreamy, which is the sound that I feel is most well suited for this edo, but they are actually able to guide the listener on a comprehensive harmonic journey which is certainly no easy task.

6edo is the first edo to contain a '''dominant 7th chord''', which would be more interesting if there were a perfect fifth, but at least you can resolve it through the back door (up a whole step). In fact, that's really one of the only ways to make satisfying chord progressions in this edo. The arguably more infamous Mario cadence (♭VI-♭VII-I) is ever-present here, as it is, in my opinion, the most satisfying progression that exists in this edo. So, if you really wanted to, you could create a Mario-style fanfare using just the whole-tone scale, but deliberately avoiding the perfect fifth in such a style would be uncharacteristic.

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This is also the first edo that contains multiple different meaningful scales (ones with at least 5 notes). It contains the basic form of '''[[pentic]]''' (2L 3s), as well as the hard form of '''[[1L 4s]]'''. The basic form of '''[[1L 5s|antimachinoid]]''' (1L 5s) is also present here, which can be seen as a rather crude tempering of [[Tetracot]][6]. This is a pretty interesting scale, in that it's essentially a compressed whole-tone scale where one of the steps is larger than the others. The equiheptatonic scale itself can be seen as an equal-tempered Tetracot[7], which is surely a bonus for the tetracot fans out there.

It's honestly incredible what this edo can do with so few notes. I often find myself hearing more notes than there actually are, as its very easy for my brain to hear major and minor even when everything is neutralized. 7edo has a tendency to sound like a joke, but has the ability to be extremely powerful. ''[https://www.youtube.com/watch?v=kFoXuN_gkJM Toccata for Organ]'' by [https://www.youtube.com/@neilthornock Neil Thornock] is another fantastical specimen of this temperament.

It's honestly incredible what this edo can do with so few notes. I often find myself hearing more notes than there actually are, as its very easy for my brain to hear major and minor even when everything is neutralized. 7edo has a tendency to sound like a joke, but has the ability to be extremely powerful. [https://www.youtube.com/watch?v=kFoXuN_gkJM Toccata for Organ] by [https://www.youtube.com/@neilthornock Neil Thornock] is another fantastical specimen of this temperament.

Overall, this edo may not be very versatile harmonically, but its sound is truly something to behold, and a sound that cannot be easily replicated in other non-7n-edos. A very nice blend of xen, ease of use, and ethereality. It's also trivially easy to notate, which is always a bonus.

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8edo contains 2 interlocked instances of 4edo, meaning it houses the familiar diminished tetrad. And, just like in 4edo, the diminished/minor sound is what tends to sound the most appealing here since the 450¢ Barbados third really isn't a stable point of rest. This is mainly why I used to think 8edo wasn't very good, since the room for harmonic expression without the major/minor third dichotomy just seemed bland. Plus, the only stable sounds being a minor chord with an omitted fifth and a diminished chord just didn't seem very appealing.

But, as you can hopefully hear in the demo, I believe to have found the perfect sound for this temperament. It was somewhat inspired by Aaron Andrew Hunt's ''Fantasia & Fugue a4 in 8ET'', once again from The Equal Tempered Keyboard, another piece I find quite fascinating. Other neat environments for 8edo include, as always, the percussive style characteristic of [[Hideya]]'s music, another one of my favorite xen composers. ''[https://www.youtube.com/watch?v=h75K1KOb5is Like Ensor's paintings]'' is a very cool example of what 8edo sounds like in a strictly melodic context. It's, as Hideya says, an unpleasant experience that really gets you thinking for some reason.

But, as you can hopefully hear in the demo, I believe to have found the perfect sound for this temperament. It was somewhat inspired by Aaron Andrew Hunt's "Fantasia & Fugue a4 in 8ET", once again from ''The Equal Tempered Keyboard'', another piece I find quite fascinating. Other neat environments for 8edo include, as always, the percussive style characteristic of [[Hideya]]'s music, another one of my favorite xen composers. [https://www.youtube.com/watch?v=h75K1KOb5is Like Ensor's paintings] is a very cool example of what 8edo sounds like in a strictly melodic context. It's, as Hideya says, an unpleasant experience that really gets you thinking for some reason.

Overall, a bit of a niche edo, but the sounds it produces are ineffable. I found myself struggling to place 8edo on the tier list, because the utter absence of a perfect fifth isn't something to just gloss over, yet its inquisitive properties certainly warrant a placement above 6edo and the melodic nature of the neutral second puts it on par with 7edo. So, I just placed it in B tier, above 5edo.

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9edo is also the first edo to support [[Mavila temperament|'''mavila temperament''']], being one of 3 that support it natively in the [[patent val|'''patent val''']]. It's certainly an extreme tempering, but making the fifth any sharper would get rid of the septimal consonances, so this particular way of approaching mavila is truly unique.

As this edo is right on the border of what I consider to be the macrotonal edos, 1 degree of 9edo has a particular quality to it that makes it sound like a semitone in some contexts and a neutral second in other contexts. My piece ''[https://www.youtube.com/watch?v=1D2_6LsRsPM Elegy of the Willow]'' illustrates this by including many chromaticisms, sometimes in the context of a chromatic scale and sometimes in the context of cadential motion.

As this edo is right on the border of what I consider to be the macrotonal edos, 1 degree of 9edo has a particular quality to it that makes it sound like a semitone in some contexts and a neutral second in other contexts. My piece [https://www.youtube.com/watch?v=1D2_6LsRsPM Elegy of the Willow] illustrates this by including many chromaticisms, sometimes in the context of a chromatic scale and sometimes in the context of cadential motion.

Other inspiring works in this temperament include [https://youtu.be/O9fJnq-WkqQ?si=3tIsJpfrOHkWZLt2 ''Buttered Cat Paradox''] by Xolta and [https://youtu.be/oXe1mSIMrho?si=_dX7MiN3AgVPPnXm ''Caelum''] by miaxia. ''Caelum'' especially illustrates the nature that I've described, leading me to believe 9edo works best in such a style. The demo I wrote for this edo, however, is nowhere near the style of any of these pieces, yet I think it works quite well. The aforementioned "ghostly" quality of 9edo, particularly in the fifth, gives the tango an "abandoned" quality that would fit well in a old lost town, like the Hidden Village from The Legend of Zelda: Twilight Princess.

Other inspiring works in this temperament include [https://youtu.be/O9fJnq-WkqQ?si=3tIsJpfrOHkWZLt2 Buttered Cat Paradox] by Xolta and [https://youtu.be/oXe1mSIMrho?si=_dX7MiN3AgVPPnXm Caelum] by miaxia. ''Caelum'' especially illustrates the nature that I've described, leading me to believe 9edo works best in such a style. The demo I wrote for this edo, however, is nowhere near the style of any of these pieces, yet I think it works quite well. The aforementioned "ghostly" quality of 9edo, particularly in the fifth, gives the tango an "abandoned" quality that would fit well in a old lost town, like the Hidden Village from The Legend of Zelda: Twilight Princess.

Overall, a very unique edo. You can choose to avoid the dissonant fifth or embrace it, with both approaches leading to an incredible sound. It's surprisingly versatile, more so than any edo smaller than it, putting it above 7edo.

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=== [[10edo]] ===

~~'''[[User:Eboone/10edo]]'''~~

''2×5, 1° = 120¢, Fifth = 720¢ (3\5)''

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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. 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.

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.

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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|'''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.

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.

Overall, a very unique and awesome edo that stands atop the macrotonal podium as the best edo smaller than 12edo (in my opinion).

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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.

The best way to notate this edo is as a subset of 22edo, which also isn't doing it any favors. Overall, a niche edo with an alien sound that I just cannot find myself wanting to use very often. Its approximation of the 11th harmonic is somewhat appealing, and the "almost 12edo" quality can make for some interesting effects, but there are better edos for both of these things (spoiler alert).

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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.

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.

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 instead of something from the Spartan set, but it works well enough.

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=== Macro-Semitonal EDO Recap ===

[[File:Macro-Semitonal EDO Tier List.png|thumb|Tier list of edos 10-14]]

A mix of really good and... decent... edos. I'd say 11edo is a bit of an outlier here, even though it is quite similar to 13edo, since I see it as being totally outclassed. Although, perhaps you could use both 11edo and 13edo in conjunction to create some cool effects, as [[Claudi Meneghin]] did in his ''[https://www.youtube.com/shorts/KqjNRqCQqro Micropiece in 11edo & 13edo]''. Either way, a pretty niche use case for two pretty niche edos.

A mix of really good and... decent... edos. I'd say 11edo is a bit of an outlier here, even though it is quite similar to 13edo, since I see it as being totally outclassed. Although, perhaps you could use both 11edo and 13edo in conjunction to create some cool effects, as [[Claudi Meneghin]] did in his [https://www.youtube.com/shorts/KqjNRqCQqro Micropiece in 11edo & 13edo]. Either way, a pretty niche use case for two pretty niche edos.

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. It's honestly one of the most underrated edos in existence, since even 5edo gets more attention than it.

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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.

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.

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.

''[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.

[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]] ===

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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.

Overall, an incredible edo deserving of high A tier. I wouldn't say it's better than 10edo, but I know that's just my personal taste holding it back.

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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.

...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.

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===[[19edo]]===

~~'''[[User:Eboone/19edo]]'''~~

''Prime, 1° = 63.16¢, Fifth = 694.74¢ (11\19)''

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With that being said, these intervals are still beautiful. This is technically the first edo with a '''harmonic 7th chord''', and even though it really doesn't sound a whole lot like 4:5:6:7 because of how bad the approximation of the 7th harmonic is, it still has a unique and interesting sound with a warm quality. Plus, it still works better than the native dominant 7th chord in terms of voice leading. The inframinor third is a bit reminiscent of the interseptimal second-third in 5n-edos, but without nearly as much ambiguity about whether it's a second or a third.

Also, something that is easily overlooked in meantone temperaments is how they soften dissonant intervals. ''[https://www.youtube.com/watch?v=Vfj39Fc6X8w Sunrise]'' by HEHEHE I AM A SUPAHSTAR SAGA (an absolutely beautiful piece) illustrates this in the 2nd bar with a spicy B♭maj7(♯11,♯15) chord, yet it doesn't sound spicy at all (to me) because the augmented fifteenth is stretched compared to, say, 12edo. ''[https://www.youtube.com/watch?v=Xpujgr-0QTc Prelude for playing No. 1]'' by Tapeworm Saga also shows many of the capabilities of 19edo, even implementing some undecimal harmony.

Also, something that is easily overlooked in meantone temperaments is how they soften dissonant intervals. [https://www.youtube.com/watch?v=Vfj39Fc6X8w Sunrise] by HEHEHE I AM A SUPAHSTAR SAGA (an absolutely beautiful piece) illustrates this in the 2nd bar with a spicy B♭maj7(♯11,♯15) chord, yet it doesn't sound spicy at all (to me) because the augmented fifteenth is stretched compared to, say, 12edo. [https://www.youtube.com/watch?v=Xpujgr-0QTc Prelude for playing No. 1] by Tapeworm Saga also shows many of the capabilities of 19edo, even implementing some undecimal harmony.

Oh, and this edo doesn't just feature the diatonic mos. It also features semiquartal in its hard form, a rather popular mos (especially in this edo). I don't really mess with it, but it is there. Anyway, this edo is absolutely amazing for lofi. It doesn't have the same sort of "out of tune" vibe as 15edo, but the unique way this edo handles the 5-limit works very well in the style.

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===Micro-Semitonal EDO Recap===

[[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 contexts that you would never expect.

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. 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.

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 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 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 13, 2024. '''31 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]]
 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.
+A few edos on this page are so intriguing that I (will soon) 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.
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 Of the subsets of 12edo, I'd say this is the most interesting because it contains a '''whole tone''', and it's the only one that isn't just a meme. 6edo contains 2 interlocked instances of 3edo, meaning it has the same echoey major third, and it also contains 3 interlocked instances of 2edo, meaning it has the same uninvertible tritone. The combination of these intervals really contributes to the infamous dreamy quality of this edo, better known as the whole-tone scale.
-There are many pieces that make use of the whole-tone scale, but very few that exist strictly in 6edo. [[wikipedia:Claude_Debussy|Claude Debussy]] is well known for his use of the scale, and it's a very interesting color to use while working in 6n-edos, but a very limiting scale to use in isolation. The best 6edo pieces I could find are the prelude and invention from [[Aaron Andrew Hunt]]'s "[https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard The Equal Tempered Keyboard]," and they are pretty interesting for what they are. They don't really sound dreamy, which is the sound that I feel is most well suited for this edo, but they are actually able to guide the listener on a comprehensive harmonic journey which is certainly no easy task.
+There are many pieces that make use of the whole-tone scale, but very few that exist strictly in 6edo. [[wikipedia:Claude_Debussy|Claude Debussy]] is well known for his use of the scale, and it's a very interesting color to use while working in 6n-edos, but a very limiting scale to use in isolation. The best 6edo pieces I could find are the prelude and invention from [[Aaron Andrew Hunt]]'s [https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard ''The Equal Tempered Keyboard''], and they are pretty interesting for what they are. They don't really sound dreamy, which is the sound that I feel is most well suited for this edo, but they are actually able to guide the listener on a comprehensive harmonic journey which is certainly no easy task.
 edo is the first edo to contain a '''dominant 7th chord''', which would be more interesting if there were a perfect fifth, but at least you can resolve it through the back door (up a whole step). In fact, that's really one of the only ways to make satisfying chord progressions in this edo. The arguably more infamous Mario cadence (♭VI-♭VII-I) is ever-present here, as it is, in my opinion, the most satisfying progression that exists in this edo. So, if you really wanted to, you could create a Mario-style fanfare using just the whole-tone scale, but deliberately avoiding the perfect fifth in such a style would be uncharacteristic.
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 This is also the first edo that contains multiple different meaningful scales (ones with at least 5 notes). It contains the basic form of '''[[pentic]]''' (2L 3s), as well as the hard form of '''[[1L 4s]]'''. The basic form of '''[[1L 5s|antimachinoid]]''' (1L 5s) is also present here, which can be seen as a rather crude tempering of [[Tetracot]][6]. This is a pretty interesting scale, in that it's essentially a compressed whole-tone scale where one of the steps is larger than the others. The equiheptatonic scale itself can be seen as an equal-tempered Tetracot[7], which is surely a bonus for the tetracot fans out there.
-It's honestly incredible what this edo can do with so few notes. I often find myself hearing more notes than there actually are, as its very easy for my brain to hear major and minor even when everything is neutralized. 7edo has a tendency to sound like a joke, but has the ability to be extremely powerful. ''[https://www.youtube.com/watch?v=kFoXuN_gkJM Toccata for Organ]'' by [https://www.youtube.com/@neilthornock Neil Thornock] is another fantastical specimen of this temperament.
+It's honestly incredible what this edo can do with so few notes. I often find myself hearing more notes than there actually are, as its very easy for my brain to hear major and minor even when everything is neutralized. 7edo has a tendency to sound like a joke, but has the ability to be extremely powerful. [https://www.youtube.com/watch?v=kFoXuN_gkJM Toccata for Organ] by [https://www.youtube.com/@neilthornock Neil Thornock] is another fantastical specimen of this temperament.
 Overall, this edo may not be very versatile harmonically, but its sound is truly something to behold, and a sound that cannot be easily replicated in other non-7n-edos. A very nice blend of xen, ease of use, and ethereality. It's also trivially easy to notate, which is always a bonus.
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 edo contains 2 interlocked instances of 4edo, meaning it houses the familiar diminished tetrad. And, just like in 4edo, the diminished/minor sound is what tends to sound the most appealing here since the 450¢ Barbados third really isn't a stable point of rest. This is mainly why I used to think 8edo wasn't very good, since the room for harmonic expression without the major/minor third dichotomy just seemed bland. Plus, the only stable sounds being a minor chord with an omitted fifth and a diminished chord just didn't seem very appealing.
-But, as you can hopefully hear in the demo, I believe to have found the perfect sound for this temperament. It was somewhat inspired by Aaron Andrew Hunt's ''Fantasia & Fugue a4 in 8ET'', once again from The Equal Tempered Keyboard, another piece I find quite fascinating. Other neat environments for 8edo include, as always, the percussive style characteristic of [[Hideya]]'s music, another one of my favorite xen composers. ''[https://www.youtube.com/watch?v=h75K1KOb5is Like Ensor's paintings]'' is a very cool example of what 8edo sounds like in a strictly melodic context. It's, as Hideya says, an unpleasant experience that really gets you thinking for some reason.
+But, as you can hopefully hear in the demo, I believe to have found the perfect sound for this temperament. It was somewhat inspired by Aaron Andrew Hunt's "Fantasia & Fugue a4 in 8ET", once again from ''The Equal Tempered Keyboard'', another piece I find quite fascinating. Other neat environments for 8edo include, as always, the percussive style characteristic of [[Hideya]]'s music, another one of my favorite xen composers. [https://www.youtube.com/watch?v=h75K1KOb5is Like Ensor's paintings] is a very cool example of what 8edo sounds like in a strictly melodic context. It's, as Hideya says, an unpleasant experience that really gets you thinking for some reason.
 Overall, a bit of a niche edo, but the sounds it produces are ineffable. I found myself struggling to place 8edo on the tier list, because the utter absence of a perfect fifth isn't something to just gloss over, yet its inquisitive properties certainly warrant a placement above 6edo and the melodic nature of the neutral second puts it on par with 7edo. So, I just placed it in B tier, above 5edo.
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 edo is also the first edo to support [[Mavila temperament|'''mavila temperament''']], being one of 3 that support it natively in the [[patent val|'''patent val''']]. It's certainly an extreme tempering, but making the fifth any sharper would get rid of the septimal consonances, so this particular way of approaching mavila is truly unique.
-As this edo is right on the border of what I consider to be the macrotonal edos, 1 degree of 9edo has a particular quality to it that makes it sound like a semitone in some contexts and a neutral second in other contexts. My piece ''[https://www.youtube.com/watch?v=1D2_6LsRsPM Elegy of the Willow]'' illustrates this by including many chromaticisms, sometimes in the context of a chromatic scale and sometimes in the context of cadential motion.
+As this edo is right on the border of what I consider to be the macrotonal edos, 1 degree of 9edo has a particular quality to it that makes it sound like a semitone in some contexts and a neutral second in other contexts. My piece [https://www.youtube.com/watch?v=1D2_6LsRsPM Elegy of the Willow] illustrates this by including many chromaticisms, sometimes in the context of a chromatic scale and sometimes in the context of cadential motion.
-Other inspiring works in this temperament include [https://youtu.be/O9fJnq-WkqQ?si=3tIsJpfrOHkWZLt2 ''Buttered Cat Paradox''] by Xolta and [https://youtu.be/oXe1mSIMrho?si=_dX7MiN3AgVPPnXm ''Caelum''] by miaxia. ''Caelum'' especially illustrates the nature that I've described, leading me to believe 9edo works best in such a style. The demo I wrote for this edo, however, is nowhere near the style of any of these pieces, yet I think it works quite well. The aforementioned "ghostly" quality of 9edo, particularly in the fifth, gives the tango an "abandoned" quality that would fit well in a old lost town, like the Hidden Village from The Legend of Zelda: Twilight Princess.
+Other inspiring works in this temperament include [https://youtu.be/O9fJnq-WkqQ?si=3tIsJpfrOHkWZLt2 Buttered Cat Paradox] by Xolta and [https://youtu.be/oXe1mSIMrho?si=_dX7MiN3AgVPPnXm Caelum] by miaxia. ''Caelum'' especially illustrates the nature that I've described, leading me to believe 9edo works best in such a style. The demo I wrote for this edo, however, is nowhere near the style of any of these pieces, yet I think it works quite well. The aforementioned "ghostly" quality of 9edo, particularly in the fifth, gives the tango an "abandoned" quality that would fit well in a old lost town, like the Hidden Village from The Legend of Zelda: Twilight Princess.
 Overall, a very unique edo. You can choose to avoid the dissonant fifth or embrace it, with both approaches leading to an incredible sound. It's surprisingly versatile, more so than any edo smaller than it, putting it above 7edo.
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 === [[10edo]] ===
-'''[[User:Eboone/10edo]]'''
 ''2×5, 1° = 120¢, Fifth = 720¢ (3\5)''
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 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).
-edo 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.
+edo 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.
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 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|'''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.
+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.
 Overall, a very unique and awesome edo that stands atop the macrotonal podium as the best edo smaller than 12edo (in my opinion).
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 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.
 The best way to notate this edo is as a subset of 22edo, which also isn't doing it any favors. Overall, a niche edo with an alien sound that I just cannot find myself wanting to use very often. Its approximation of the 11th harmonic is somewhat appealing, and the "almost 12edo" quality can make for some interesting effects, but there are better edos for both of these things (spoiler alert).
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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.
-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.
+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 instead of something from the Spartan set, but it works well enough.
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 === Macro-Semitonal EDO Recap ===
 [[File:Macro-Semitonal EDO Tier List.png|thumb|Tier list of edos 10-14]]
-A mix of really good and... decent... edos. I'd say 11edo is a bit of an outlier here, even though it is quite similar to 13edo, since I see it as being totally outclassed. Although, perhaps you could use both 11edo and 13edo in conjunction to create some cool effects, as [[Claudi Meneghin]] did in his ''[https://www.youtube.com/shorts/KqjNRqCQqro Micropiece in 11edo & 13edo]''. Either way, a pretty niche use case for two pretty niche edos.
+A mix of really good and... decent... edos. I'd say 11edo is a bit of an outlier here, even though it is quite similar to 13edo, since I see it as being totally outclassed. Although, perhaps you could use both 11edo and 13edo in conjunction to create some cool effects, as [[Claudi Meneghin]] did in his [https://www.youtube.com/shorts/KqjNRqCQqro Micropiece in 11edo & 13edo]. Either way, a pretty niche use case for two pretty niche edos.
-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]]).
 edo 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.
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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.
-edo 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.
+edo 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.
-''[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.
+[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]] ===
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 edo 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.
 Overall, an incredible edo deserving of high A tier. I wouldn't say it's better than 10edo, but I know that's just my personal taste holding it back.
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 edo 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.
+...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.
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 ===[[19edo]]===
-'''[[User:Eboone/19edo]]'''
 ''Prime, 1° = 63.16¢, Fifth = 694.74¢ (11\19)''
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 With that being said, these intervals are still beautiful. This is technically the first edo with a '''harmonic 7th chord''', and even though it really doesn't sound a whole lot like 4:5:6:7 because of how bad the approximation of the 7th harmonic is, it still has a unique and interesting sound with a warm quality. Plus, it still works better than the native dominant 7th chord in terms of voice leading. The inframinor third is a bit reminiscent of the interseptimal second-third in 5n-edos, but without nearly as much ambiguity about whether it's a second or a third.
-Also, something that is easily overlooked in meantone temperaments is how they soften dissonant intervals. ''[https://www.youtube.com/watch?v=Vfj39Fc6X8w Sunrise]'' by HEHEHE I AM A SUPAHSTAR SAGA (an absolutely beautiful piece) illustrates this in the 2nd bar with a spicy B♭maj7(♯11,♯15) chord, yet it doesn't sound spicy at all (to me) because the augmented fifteenth is stretched compared to, say, 12edo. ''[https://www.youtube.com/watch?v=Xpujgr-0QTc Prelude for playing No. 1]'' by Tapeworm Saga also shows many of the capabilities of 19edo, even implementing some undecimal harmony.
+Also, something that is easily overlooked in meantone temperaments is how they soften dissonant intervals. [https://www.youtube.com/watch?v=Vfj39Fc6X8w Sunrise] by HEHEHE I AM A SUPAHSTAR SAGA (an absolutely beautiful piece) illustrates this in the 2nd bar with a spicy B♭maj7(♯11,♯15) chord, yet it doesn't sound spicy at all (to me) because the augmented fifteenth is stretched compared to, say, 12edo. [https://www.youtube.com/watch?v=Xpujgr-0QTc Prelude for playing No. 1] by Tapeworm Saga also shows many of the capabilities of 19edo, even implementing some undecimal harmony.
 Oh, and this edo doesn't just feature the diatonic mos. It also features semiquartal in its hard form, a rather popular mos (especially in this edo). I don't really mess with it, but it is there. Anyway, this edo is absolutely amazing for lofi. It doesn't have the same sort of "out of tune" vibe as 15edo, but the unique way this edo handles the 5-limit works very well in the style.
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 ===Micro-Semitonal EDO Recap===
 [[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 contexts that you would never expect.
+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. 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.