User:Eboone/EDO Impressions: Difference between revisions
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—————————[[File:EDO Tier List.png|alt=A tier list of EDOs. S Tier - 12, 34, 31, 53, 72, 50, 22, 17, 15, 26, 19. A Tier - 27, 10, 46, 21, 20, 7, 16, 41, 55. B Tier - 18, 24, 36, 48, 65, 58, 25, 63, 13, 11, 56, 29, 23, 9, 5, 8. C Tier - 40, 43, 28, 14, 70, 68, 57, 37, 30, 60, 54, 49, 47, 44, 38, 67, 59, 35, 6. F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.|thumb|['''''OUTDATED''', will be updated when I'm finished with this page''] Ebooone's tier list of edos 5-72]] | —————————[[File:EDO Tier List.png|alt=A tier list of EDOs. S Tier - 12, 34, 31, 53, 72, 50, 22, 17, 15, 26, 19. A Tier - 27, 10, 46, 21, 20, 7, 16, 41, 55. B Tier - 18, 24, 36, 48, 65, 58, 25, 63, 13, 11, 56, 29, 23, 9, 5, 8. C Tier - 40, 43, 28, 14, 70, 68, 57, 37, 30, 60, 54, 49, 47, 44, 38, 67, 59, 35, 6. F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.|thumb|['''''OUTDATED''', will be updated when I'm finished with this page''] Ebooone's tier list of edos 5-72]] | ||
I, at least currently, work strictly in [[EDO|'''edos''']]. I don't tend to go any higher than 72edo in my own works, so here are my impressions of all the positive integer edos up to 72. This page is designed to be read wholly from top to bottom, but you can still read specific entries in isolation. Additionally, each edo category | I, at least currently, work strictly in [[EDO|'''edos''']]. I don't tend to go any higher than 72edo in my own works, so here are my impressions of all the positive integer edos up to 72. This page is designed to be read wholly from top to bottom, but you can still read specific entries in isolation. Additionally, each edo category has its own tier list and recap. | ||
Of course, all tier lists and impressions on this page are subject to change in the future. | Of course, all tier lists and impressions on this page are subject to change in the future. | ||
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# '''Unique''' | # '''Unique''' | ||
These are just guidelines that I tend to follow, and they in no way provide a concrete method of objectifying edos. However, | These are just guidelines that I tend to follow, and they in no way provide a concrete method of objectifying edos. However, knowing what I'm looking for will greatly aid in understanding why I place certain edos where I do. For example, 53edo is certainly on the larger side, yet it still resides in S tier because it's just so consonant. It really puts into perspective just how consonant it is if I'm willing to place it that high in spite of the amount of notes. | ||
Plus, these aren't the only guidelines. '''[[MOS scales]]''' are also considered, especially if they are scales that I find interesting. This is largely subjective, as I really have no way of classifying mosses in any sort of objective way. Certain intervals that are technically dissonant may also greatly contribute to an edo's high rating, such as the major third in 17edo (foreshadowing). At the end of the day, everything on this page is based on my own recreational research and opinions, so I'm sorry if your favorite edo is in D tier simply because it doesn't meet my criteria for what makes an edo desirable. | Plus, these aren't the only guidelines. '''[[MOS scales]]''' are also considered, especially if they are scales that I find particularly interesting. This is largely subjective, as I really have no way of classifying mosses in any sort of objective way. '''Factors''' are also considered, as the factors of an edo determine a lot about its structure. Certain intervals that are technically dissonant may also greatly contribute to an edo's high rating, such as the major third in 17edo (foreshadowing). At the end of the day, everything on this page is based on my own recreational research and opinions, so I'm sorry if your favorite edo is in D tier simply because it doesn't meet my criteria for what makes an edo desirable. | ||
In terms of the actual ranks, I think of B tier as the default, meaning I automatically assume that any given edo is going to be good before I experiment with it. If it turns out to be totally outclassed by edos that are obviously better, it goes in F tier or D tier. If it's pretty useful every once in a while, it goes in C tier. If it has exceptional ethereality, versatility, uniqueness, etc., it goes in A tier or S tier. | |||
== Categorization == | == Categorization == | ||
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Honestly, can this one even be called an edo? I mean, "equal divisions of the octave" implies that the octave is divided. On top of that, since '''octave equivalence''' is almost always assumed, this "temperament" literally only has '''one note'''. Anyway, this edo is pretty lame because the whole point of using different temperaments is to access different melodic and harmonic opportunities, and this edo doesn't allow any of that. The only way to make this edo musical is through rhythm, dynamics, form, etc... stuff that isn't related to tuning. | Honestly, can this one even be called an edo? I mean, "equal divisions of the octave" implies that the octave is divided. On top of that, since '''octave equivalence''' is almost always assumed, this "temperament" literally only has '''one note'''. Anyway, this edo is pretty lame because the whole point of using different temperaments is to access different melodic and harmonic opportunities, and this edo doesn't allow any of that. The only way to make this edo musical is through rhythm, dynamics, form, etc... stuff that isn't related to tuning. | ||
These factors alone make this edo terrible, but that doesn't mean you can't make it work. Technically, there is some room for "melodic" expression if you allow yourself to use devices such as pitch bend. Or, perhaps you could use timbres that don't exactly settle on one pitch but clearly aren't unpitched either, like an old guitar string with wobbly harmonics. These "cheat codes" are partially what make one-note jazz solos so interesting, but of course the rest of the interest comes from the novelty of playing only one note amidst an electron cloud of dissonance | These factors alone make this edo terrible, but that doesn't mean you can't make it work. Technically, there is some room for "melodic" expression if you allow yourself to use devices such as pitch bend. Or, perhaps you could use timbres that don't exactly settle on one pitch but clearly aren't unpitched either, like an old guitar string with wobbly harmonics. These "cheat codes" are partially what make one-note jazz solos so interesting, but of course the rest of the interest comes from the novelty of playing only one note amidst an electron cloud of dissonance. | ||
At least it's better than '''[[0edo]]'''. | If we were to view this edo as being the first in the set of all positive integer edos, we could say it "introduces" the idea of pitch classes, thus establishing octave equivalence for all edos to come. While it is somewhat neat to view edos as entries in a sequence, it's probably more useful to view them in isolation, which leaves this edo with essentially nothing. At least it's better than '''[[0edo]]'''. | ||
=== [[2edo]] === | === [[2edo]] === | ||
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''Tier: '''F''''' | ''Tier: '''F''''' | ||
[[File:2edo groove.mp3|none|thumb|2edo mischievous theme on E and B♭]] | [[File:2edo groove.mp3|none|thumb|2edo mischievous theme on E and B♭]] | ||
This edo is literally just a '''tritone''' | This edo is literally just a '''tritone''', but in this case it's a rather interesting one. It's the 600¢ '''hemioctave''' tritone, the only one that is its own [[octave complement|'''octave complement''']]. So, while its melodic and harmonic capabilities in isolation are pretty bare, its symmetrical nature allows for some cool gimmicks. If instead it were, say, [[11/8]], that would open the possibility of using both 11/8 and [[16/11]], its octave complement. This would allow for greater melodic and harmonic expression, but at the expense of having a neat symmetrical tritone. | ||
To illustrate this tritone's nature, the demo for this edo is completely flipped on its head. If you listen carefully, you will notice that the pizzicato violins and celli play each other's parts upside down in the second half of the loop. The gimmick is that this only affects contour, not the harmony. So yeah, that's pretty cool. | To illustrate this tritone's nature, the demo for this edo is completely flipped on its head. If you listen carefully, you will notice that the pizzicato violins and celli play each other's parts upside down in the second half of the loop. The gimmick is that this only affects contour, not the harmony. So yeah, that's pretty cool. | ||
One interesting property of this edo that cannot be overlooked is the fact that it is '''prime'''. The fundamental theorem of arithmetic states that all integers greater than 1 can be represented as a unique product of prime numbers, which applies in this context because we're dealing with positive integer edos. EDOs with lots of prime factors have more opportunities for symmetry within the octave. In this case, 2edo's symmetrical tritone is inherited by all 2n-edos, essentially splitting them down the middle. | |||
Anyway, it's just a tritone. And in fact, I can't honestly say this edo is any better than 1edo. In theory, there should be no reason to choose 1edo over 2edo, but how much does that one extra note really add in practice? At the end of the day, both edos are mere novelties. | |||
=== [[3edo]] === | === [[3edo]] === | ||
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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. | 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. | 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. | 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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The minor third is sat between 6/5 and [[32/27]], giving it a mildly dark sound that is quite apt for the diminished tetrad. It's a powerful minor third, but without the 5-limit resonance of 6/5. Overall, a great minor third. | The minor third is sat between 6/5 and [[32/27]], giving it a mildly dark sound that is quite apt for the diminished tetrad. It's a powerful minor third, but without the 5-limit resonance of 6/5. Overall, a great minor third. | ||
I'd say this edo is on equal footing with 3edo, maybe slightly behind. You could certainly argue that it's better than 3edo, considering it contains 2 interlocked instances of 2edo, as well as an extra note. | I'd say this edo is on equal footing with 3edo, maybe slightly behind. You could certainly argue that it's better than 3edo, considering it contains 2 interlocked instances of 2edo, as well as an extra note. I, however, think augmented triads are more interesting than diminished tetrads in isolation. It's really all about taste, as is everything in the world of music. | ||
=== Trivial EDO Recap === | === Trivial EDO Recap === | ||
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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. 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 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 | 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. | ||
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. | 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 | 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. | ||
=== [[6edo]] === | === [[6edo]] === | ||
''2×3, 1° = 200¢, No fifth'' | ''2×3, 1° = 200¢, No fifth'' | ||
''Tier: ''' | ''Tier: '''D''''' | ||
[[File:6edo demo.mp3|none|thumb|6edo dream sequence in F whole-tone]] | [[File:6edo demo.mp3|none|thumb|6edo dream sequence in F whole-tone]] | ||
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. | 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 | 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 | 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. Not very versatile in the slightest, especially in isolation. | ||
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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. | 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. | |||
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. | |||
=== [[8edo]] === | === [[8edo]] === | ||
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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 | 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. | ||
=== [[9edo]] === | === [[9edo]] === | ||
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''Tier: '''A'''''[[File:9edo groove.mp3|none|thumb|9edo tango in A [[2L 5s|anti-minor]]]] | ''Tier: '''A'''''[[File:9edo groove.mp3|none|thumb|9edo tango in A [[2L 5s|anti-minor]]]] | ||
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. | 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. | ||
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 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. | ||
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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 | 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. | ||
=== Macrotonal EDO Recap === | === Macrotonal EDO Recap === | ||
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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. 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. | ||
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 | 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. | ||
== Macro-Semitonal == | == Macro-Semitonal == | ||