User:Eboone/EDO Impressions: Difference between revisions

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This edo is just an '''augmented triad''', but specifically one that is derived by stacking three 400¢ major thirds. This means it closes the octave and, as such, is its own inversion. So, once again, the melodic and harmonic capabilities of this triad in isolation are pretty slim compared to, say, one derived by stacking 5/4. Yet, the symmetrical nature of this chord allows for quite a "sturdy" sound that helps to keep the temperament together.

The major third itself is 13.79¢ sharp of 5/4, enough for noticeable inharmonicity to occasionally take place in timbres with a prominent 5th harmonic (such as a piano). This contributes to the "foggy" sound of the temperament, as the demo illustrates. I could say a lot more about this particular major third, but that's really all that matters in the context of 3edo.

The major third itself is 13.79¢ sharp of 5/4, enough for noticeable '''inharmonicity''' to occasionally take place in timbres with a prominent 5th harmonic (such as a piano). This contributes to the "foggy" sound of the temperament, as the demo illustrates. I could say a lot more about this particular major third, but that's really all that matters in the context of 3edo.

The uninvertible nature of the augmented triad is illustrated in the synth, as it oscillates between two inversions of the triad yet the quality of the chord remains utterly identical. If it were any other type of augmented triad, the inversions would still sound quite similar but they would each have a different vibe.

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=== Trivial EDO Recap ===

[[File:Trivial EDO Tier List.png|thumb|Tier list of edos 1-4]]These first four edos are honestly just memes, so no amount of good things I say about them can eke them out of F tier. I can't really hear them as anything other than subsets of 12edo, which really makes them seem pointless. They work best as additional colors in larger edos that contain them, not as temperaments on their own.

Also, about the whole symmetry thing. EDOs 2-4 are notable for their symmetrical nature, which I pass off as a mere gimmick. The reason I don't find this more interesting is because symmetry in music tends to be boring, especially in terms of form. I prefer music that wanders off into its own realm, rather than music that remains stagnant the entire time. Essentially, if I were to listen to a piece in 4edo, I would get really sick of hearing the same exact diminished chord.

== Macrotonal ==

Now we're getting into edos that people actually care about. 2 new prime edos are introduced here, and they both have unique sounds that carry over into their multiples, making them unmistakable. We also see the introduction of scales here, as the trivial edos have step sizes too wide to be considered scales, in my opinion.

There is still one subset of 12edo left to cover here, and it is unfortunately extremely situational. The rest of the edos, on the other hand, may surprise you with their versatility.

=== [[5edo]] ===

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''Tier: '''B'''''

[[File:5edo groove.mp3|none|thumb|5edo tribal groove in A equipentatonic]]

This is the first edo with a '''perfect fifth''', coming in 18.04¢ sharp of [[3/2]]. Because of how sharp the fifth is, 5edo works best in timbres with quick decay (like a marimba), so that the dissonance of the fifth is softened. ~~Although, the sharp fifth when used melodically~~ has quite a desirable "uplifting" quality that brings it out amidst the texture of the rest of the scale.

This is the first edo with a '''perfect fifth''', coming in 18.04¢ sharp of [[3/2]]. Because of how sharp the fifth is, 5edo works best in timbres with quick decay (like a marimba), so that the dissonance of the fifth is softened. It has quite a desirable "uplifting" quality that brings it out amidst the texture of the rest of the scale.

This edo also features [[Interseptimal interval|'''interseptimal intervals''']], a very interesting class of intervals characterized by toeing the lines between extreme septimal intervals. There's the 240¢ "second-third," which lies between [[8/7]] and [[7/6]], and the 960¢ "seventh-sixth," which lies between [[7/4]] and [[12/7]]. I'd say 240¢ definitely sounds more like a supermajor second than an inframinor third in this edo, and I find it almost impossible to hear 960¢ as a sixth since it's so close to the '''7th harmonic''', but it is interesting how these intervals are technically ambiguous.

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Oh yeah, did I just mention it has a decent approximation of the 7th harmonic? It's only 8.83¢ flat of 7/4, which is cool because this approximation extends to all 5n-edos. Anyway, the '''equipentatonic scale''' that this edo sports is a bit reminiscent of the minor pentatonic scale of 12edo (or, dare I say, the dorian pentatonic scale), making it quite familiar to unaccustomed ears, but still with a tang of xen. In many cases, it is rather difficult to notice if a piece is in this edo if you aren't familiar with it. Because of this, I'd say 5edo is a good starting edo when venturing into xen territory.

Overall, this is pretty fun edo to work in. ~~It is fairly limiting harmonically, but the melodies~~ always have a really fun sound no matter how hard you may try to make something sinister. Plus, the fact that this is the only edo with a scale but no convincing thirds is a rather interesting property. It forces you to hone in on nontonal musical factors such as rhythm, dynamics, and form, which I find quite valuable considering how easy it is to hyperfocus on harmony in larger edos. With all that being said, however, I really can't put this edo any higher than B tier because of how non-versatile it is.

The problem with this edo is the lack of harmonic expression. There really aren't any triads to work with, since there isn't a convincing third. Instead, everything is secundal or quartal (or their inversions). This means 5edo is not very versatile in the slightest, but does provide an intriguing color to use in larger 5n-edos.

Overall, this is pretty fun edo to work in. Melodies here always have a really fun sound no matter how hard you may try to make something sinister. Plus, the fact that this is the only edo with a scale but no convincing thirds is a rather interesting property. It forces you to hone in on nontonal musical factors such as rhythm, dynamics, and form, which I find quite valuable considering how easy it is to hyperfocus on harmony in larger edos. With all that being said, however, I really can't put this edo any higher than B tier because of how non-versatile it is.

=== [[6edo]] ===

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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.

Anyway, it's just the whole-tone scale. I can't reasonably put it in F tier with the rest of the 12edo subsets, since it is an actual scale rather than just an interval or chord, but there's still only one sound I find this edo to be useful for. ~~Not very versatile in~~ the ~~slightest, especially~~ in ~~isolation~~.

Anyway, it's just the whole-tone scale. I can't reasonably put it in F tier with the rest of the 12edo subsets, since it is an actual scale rather than just an interval or chord, but there's still only one sound I find this edo to be useful for. Plus, there are other edos that do the dream sound much better in my opinion.

=== [[7edo]] ===

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The '''equiheptatonic scale''' that this edo sports is a bit reminiscent of the dorian scale of 12edo, but not really. The 2nd, 3rd, 6th, and 7th are all neutral, so this edo has a very distinct xen sound. These neutral intervals, along with the rather sour fourth and fifth, have a very intense sound on an acoustic piano, which is why I elected to use electric piano and synth pads in the demo. 7edo also works very well in tinky percussive timbres, like handpan or kalimba. These sorts of sounds are heard in [[Fuschiamarine]] by [[Sevish]], a very high quality example of what this edo is capable of.

~~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~~.

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.

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 ~~any~~ other non-7n-~~edo~~. A very nice blend of xen, ease of use, and ethereality. It's also trivially easy to notate, which is always a bonus.

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.

=== [[8edo]] ===

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''Tier: '''B'''''

[[File:8edo demo 3.mp3|none|thumb|8edo march in E minor (?)]]

This is... an interesting one. Honestly, I really didn't used to like 8edo, but eventually I came to see how powerful it is when used in certain contexts. It doesn't have a perfect fifth or a whole tone, but it is extremely close to '''[[12/11]] equal step tuning'''. It also features a good approximation of [[13/10]], a rather ambiguous "third-fourth" that can either be used as an ultramajor third or a very flat fourth.

This is... an interesting one. Honestly, I really didn't used to like 8edo, but eventually I came to see how powerful it is when used in certain contexts. It doesn't have a perfect fifth or a whole tone, but it is extremely close to '''[[12/11]] equal step tuning''', meaning it responds well to '''[[octave stretching]]'''. It also features a good approximation of [[13/10]], a rather ambiguous "third-fourth" that can either be used as an ultramajor third or a very flat fourth.

Octave stretching is a technique commonly employed in edos with intervals that consistently undershoot certain desirable intervals. In the case of 8edo, 1 degree falls flat of 12/11 by 0.64¢, so by stretching the octave by 5.1¢, you can achieve perfect 12/11 equal step tuning. Of course, this will cause noticeable inharmonicity to occur with octaves, but you could argue that such an effect serves the temperament quite well.

Cadences in this temperament are relatively satisfying, but not in a traditional sense. The 150¢ neutral second can function cadentially either as a wide semitone or a narrow whole tone, meaning cadences tend to feel a bit obtuse or acute, if you will. It's an intriguing motion that sets the harmony of this edo apart from pretty much any other edo, even other 8n-edos. It's a very foreboding motion that of course must be accentuated by a pipe organ and battle-ready percussion.

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9edo is the first edo with 2 '''flavors of thirds'''. It is notable for its uncanny approximations of '''septimal intervals''' down to a fraction of a cent. These intervals have an almost ghostly quality to them, giving this edo an incredibly unique, resonant sound that other edos of this scale simply cannot match. For example, the juxtaposition of the 266.67¢ subminor third (nearly exactly 7/6) and the 400¢ major third (the one from 3edo) is totally jarring. The incredibly acrid fifth also contributes to the general vibe of resonant septimal consonances battling against sour dissonances. It's an ineffable combination of opposing stimuli, giving this edo an unmistakable sound.

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 ~~mavila temperament~~, but making the fifth any sharper would get rid of the septimal consonances, so this particular way of approaching mavila is truly unique.

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.

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[[File:Macrotonal EDO Tier List.png|thumb|Tier list of edos 5-9]]These edos are very cool and interesting. Just because they don't have very many notes doesn't necessarily mean they are limiting. Even 5edo, the most limiting of them all, has much room for expression through its interseptimal intervals. 9edo is especially intriguing to me, as it is the smallest edo with 2 flavors of thirds, making it the first edo to allow for any sort of complex chord movement. It is a beautiful edo that ends up being more versatile than you'd think, along with 7edo and even 8edo.

If you're in the market for edos that approximate simple ratios very well, you won't find much here~~. Sure, 5edo has a decent 7th harmonic and~~ 9edo ~~has spookily accurate approximations of [[27/25]] and 7/6 among other septimal intervals, but these edos shine in their simplicity~~. The main appeal here is how compact these edos are, and it's just really neat to think that you don't even need 12 notes to make awesome music.

If you're in the market for edos that approximate simple ratios very well, you won't find much here unless you're looking for something like 9edo. The main appeal here is how compact these edos are, and it's just really neat to think that you don't even need 12 notes to make awesome music.

Oh, and I just realized I have barely talked about '''notation'''! Fortunately, all five of these edos are relatively easy to notate. 5edo and 9edo are notable in this regard; 5edo can be notated pentatonic-wise on a 5-line staff by skipping B and F, and 9edo can be notated with either harmonic or melodic mavila accidentals. I prefer to preserve the harmonic integrity in mavila systems; I embrace the quirk of having reversed sharps and flats so I don't have to deal with F♭ being a perfect fifth above B. 6edo can be notated as a subset of 12edo, 7edo can be notated by simply using all seven naturals, and 8edo can be notated as a subset of 24edo with quarter-tone accidentals. As you will see with future edos, however, things may not be as simple.

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 This edo is just an '''augmented triad''', but specifically one that is derived by stacking three 400¢ major thirds. This means it closes the octave and, as such, is its own inversion. So, once again, the melodic and harmonic capabilities of this triad in isolation are pretty slim compared to, say, one derived by stacking 5/4. Yet, the symmetrical nature of this chord allows for quite a "sturdy" sound that helps to keep the temperament together.
-The major third itself is 13.79¢ sharp of 5/4, enough for noticeable inharmonicity to occasionally take place in timbres with a prominent 5th harmonic (such as a piano). This contributes to the "foggy" sound of the temperament, as the demo illustrates. I could say a lot more about this particular major third, but that's really all that matters in the context of 3edo.
+The major third itself is 13.79¢ sharp of 5/4, enough for noticeable '''inharmonicity''' to occasionally take place in timbres with a prominent 5th harmonic (such as a piano). This contributes to the "foggy" sound of the temperament, as the demo illustrates. I could say a lot more about this particular major third, but that's really all that matters in the context of 3edo.
 The uninvertible nature of the augmented triad is illustrated in the synth, as it oscillates between two inversions of the triad yet the quality of the chord remains utterly identical. If it were any other type of augmented triad, the inversions would still sound quite similar but they would each have a different vibe.
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 === Trivial EDO Recap ===
 [[File:Trivial EDO Tier List.png|thumb|Tier list of edos 1-4]]These first four edos are honestly just memes, so no amount of good things I say about them can eke them out of F tier. I can't really hear them as anything other than subsets of 12edo, which really makes them seem pointless. They work best as additional colors in larger edos that contain them, not as temperaments on their own.
+Also, about the whole symmetry thing. EDOs 2-4 are notable for their symmetrical nature, which I pass off as a mere gimmick. The reason I don't find this more interesting is because symmetry in music tends to be boring, especially in terms of form. I prefer music that wanders off into its own realm, rather than music that remains stagnant the entire time. Essentially, if I were to listen to a piece in 4edo, I would get really sick of hearing the same exact diminished chord.
 == Macrotonal ==
+Now we're getting into edos that people actually care about. 2 new prime edos are introduced here, and they both have unique sounds that carry over into their multiples, making them unmistakable. We also see the introduction of scales here, as the trivial edos have step sizes too wide to be considered scales, in my opinion.
+There is still one subset of 12edo left to cover here, and it is unfortunately extremely situational. The rest of the edos, on the other hand, may surprise you with their versatility.
 === [[5edo]] ===
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 ''Tier: '''B'''''
 [[File:5edo groove.mp3|none|thumb|5edo tribal groove in A equipentatonic]]
-This is the first edo with a '''perfect fifth''', coming in 18.04¢ sharp of [[3/2]]. Because of how sharp the fifth is, 5edo works best in timbres with quick decay (like a marimba), so that the dissonance of the fifth is softened. Although, the sharp fifth when used melodically has quite a desirable "uplifting" quality that brings it out amidst the texture of the rest of the scale.
+This is the first edo with a '''perfect fifth''', coming in 18.04¢ sharp of [[3/2]]. Because of how sharp the fifth is, 5edo works best in timbres with quick decay (like a marimba), so that the dissonance of the fifth is softened. It has quite a desirable "uplifting" quality that brings it out amidst the texture of the rest of the scale.
 This edo also features [[Interseptimal interval|'''interseptimal intervals''']], a very interesting class of intervals characterized by toeing the lines between extreme septimal intervals. There's the 240¢ "second-third," which lies between [[8/7]] and [[7/6]], and the 960¢ "seventh-sixth," which lies between [[7/4]] and [[12/7]]. I'd say 240¢ definitely sounds more like a supermajor second than an inframinor third in this edo, and I find it almost impossible to hear 960¢ as a sixth since it's so close to the '''7th harmonic''', but it is interesting how these intervals are technically ambiguous.
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 Oh yeah, did I just mention it has a decent approximation of the 7th harmonic? It's only 8.83¢ flat of 7/4, which is cool because this approximation extends to all 5n-edos. Anyway, the '''equipentatonic scale''' that this edo sports is a bit reminiscent of the minor pentatonic scale of 12edo (or, dare I say, the dorian pentatonic scale), making it quite familiar to unaccustomed ears, but still with a tang of xen. In many cases, it is rather difficult to notice if a piece is in this edo if you aren't familiar with it. Because of this, I'd say 5edo is a good starting edo when venturing into xen territory.
-Overall, this is pretty fun edo to work in. It is fairly limiting harmonically, but the melodies always have a really fun sound no matter how hard you may try to make something sinister. Plus, the fact that this is the only edo with a scale but no convincing thirds is a rather interesting property. It forces you to hone in on nontonal musical factors such as rhythm, dynamics, and form, which I find quite valuable considering how easy it is to hyperfocus on harmony in larger edos. With all that being said, however, I really can't put this edo any higher than B tier because of how non-versatile it is.
+The problem with this edo is the lack of harmonic expression. There really aren't any triads to work with, since there isn't a convincing third. Instead, everything is secundal or quartal (or their inversions). This means 5edo is not very versatile in the slightest, but does provide an intriguing color to use in larger 5n-edos.
+Overall, this is pretty fun edo to work in. Melodies here always have a really fun sound no matter how hard you may try to make something sinister. Plus, the fact that this is the only edo with a scale but no convincing thirds is a rather interesting property. It forces you to hone in on nontonal musical factors such as rhythm, dynamics, and form, which I find quite valuable considering how easy it is to hyperfocus on harmony in larger edos. With all that being said, however, I really can't put this edo any higher than B tier because of how non-versatile it is.
 === [[6edo]] ===
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 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.
-Anyway, it's just the whole-tone scale. I can't reasonably put it in F tier with the rest of the 12edo subsets, since it is an actual scale rather than just an interval or chord, but there's still only one sound I find this edo to be useful for. Not very versatile in the slightest, especially in isolation.
+Anyway, it's just the whole-tone scale. I can't reasonably put it in F tier with the rest of the 12edo subsets, since it is an actual scale rather than just an interval or chord, but there's still only one sound I find this edo to be useful for. Plus, there are other edos that do the dream sound much better in my opinion.
 === [[7edo]] ===
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 The '''equiheptatonic scale''' that this edo sports is a bit reminiscent of the dorian scale of 12edo, but not really. The 2nd, 3rd, 6th, and 7th are all neutral, so this edo has a very distinct xen sound. These neutral intervals, along with the rather sour fourth and fifth, have a very intense sound on an acoustic piano, which is why I elected to use electric piano and synth pads in the demo. 7edo also works very well in tinky percussive timbres, like handpan or kalimba. These sorts of sounds are heard in [[Fuschiamarine]] by [[Sevish]], a very high quality example of what this edo is capable of.
-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.
+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.
-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 any other non-7n-edo. A very nice blend of xen, ease of use, and ethereality. It's also trivially easy to notate, which is always a bonus.
+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.
 === [[8edo]] ===
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 ''Tier: '''B'''''
 [[File:8edo demo 3.mp3|none|thumb|8edo march in E minor (?)]]
-This is... an interesting one. Honestly, I really didn't used to like 8edo, but eventually I came to see how powerful it is when used in certain contexts. It doesn't have a perfect fifth or a whole tone, but it is extremely close to '''[[12/11]] equal step tuning'''. It also features a good approximation of [[13/10]], a rather ambiguous "third-fourth" that can either be used as an ultramajor third or a very flat fourth.
+This is... an interesting one. Honestly, I really didn't used to like 8edo, but eventually I came to see how powerful it is when used in certain contexts. It doesn't have a perfect fifth or a whole tone, but it is extremely close to '''[[12/11]] equal step tuning''', meaning it responds well to '''[[octave stretching]]'''. It also features a good approximation of [[13/10]], a rather ambiguous "third-fourth" that can either be used as an ultramajor third or a very flat fourth.
+Octave stretching is a technique commonly employed in edos with intervals that consistently undershoot certain desirable intervals. In the case of 8edo, 1 degree falls flat of 12/11 by 0.64¢, so by stretching the octave by 5.1¢, you can achieve perfect 12/11 equal step tuning. Of course, this will cause noticeable inharmonicity to occur with octaves, but you could argue that such an effect serves the temperament quite well.
 Cadences in this temperament are relatively satisfying, but not in a traditional sense. The 150¢ neutral second can function cadentially either as a wide semitone or a narrow whole tone, meaning cadences tend to feel a bit obtuse or acute, if you will. It's an intriguing motion that sets the harmony of this edo apart from pretty much any other edo, even other 8n-edos. It's a very foreboding motion that of course must be accentuated by a pipe organ and battle-ready percussion.
@@ Line 203: / Line 214: @@
 edo is the first edo with 2 '''flavors of thirds'''. It is notable for its uncanny approximations of '''septimal intervals''' down to a fraction of a cent. These intervals have an almost ghostly quality to them, giving this edo an incredibly unique, resonant sound that other edos of this scale simply cannot match. For example, the juxtaposition of the 266.67¢ subminor third (nearly exactly 7/6) and the 400¢ major third (the one from 3edo) is totally jarring. The incredibly acrid fifth also contributes to the general vibe of resonant septimal consonances battling against sour dissonances. It's an ineffable combination of opposing stimuli, giving this edo an unmistakable sound.
-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 mavila temperament, but making the fifth any sharper would get rid of the septimal consonances, so this particular way of approaching mavila is truly unique.
+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.
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 [[File:Macrotonal EDO Tier List.png|thumb|Tier list of edos 5-9]]These edos are very cool and interesting. Just because they don't have very many notes doesn't necessarily mean they are limiting. Even 5edo, the most limiting of them all, has much room for expression through its interseptimal intervals. 9edo is especially intriguing to me, as it is the smallest edo with 2 flavors of thirds, making it the first edo to allow for any sort of complex chord movement. It is a beautiful edo that ends up being more versatile than you'd think, along with 7edo and even 8edo.
-If you're in the market for edos that approximate simple ratios very well, you won't find much here. Sure, 5edo has a decent 7th harmonic and 9edo has spookily accurate approximations of [[27/25]] and 7/6 among other septimal intervals, but these edos shine in their simplicity. The main appeal here is how compact these edos are, and it's just really neat to think that you don't even need 12 notes to make awesome music.
+If you're in the market for edos that approximate simple ratios very well, you won't find much here unless you're looking for something like 9edo. The main appeal here is how compact these edos are, and it's just really neat to think that you don't even need 12 notes to make awesome music.
 Oh, and I just realized I have barely talked about '''notation'''! Fortunately, all five of these edos are relatively easy to notate. 5edo and 9edo are notable in this regard; 5edo can be notated pentatonic-wise on a 5-line staff by skipping B and F, and 9edo can be notated with either harmonic or melodic mavila accidentals. I prefer to preserve the harmonic integrity in mavila systems; I embrace the quirk of having reversed sharps and flats so I don't have to deal with F♭ being a perfect fifth above B. 6edo can be notated as a subset of 12edo, 7edo can be notated by simply using all seven naturals, and 8edo can be notated as a subset of 24edo with quarter-tone accidentals. As you will see with future edos, however, things may not be as simple.