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 F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.|thumb|[OUTDATED, ~~soon to~~ be updated] Ebooone's tier list of ~~EDOs~~ 5-72~~, available at https://tiermaker.com/list/personal/numbers-0-100-15569788/3966935.~~]]

[[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 F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.|thumb|['''''OUTDATED''', will be updated when I'm finished with this page''] Ebooone's tier list of edos 5-72]]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 also has its own tier list and 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 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 most cases, 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.

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 most cases (especially 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.

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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~~''', 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, 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.

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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''Tier: '''S-'''''

[[File:15edo demo.mp3|none|thumb|15edo rhythm section groove in G minor]]

~~placeholder~~

This is probably the most popular 5n-edo, and for good reason. It's like 12edo from an alternate universe; it has two flavors of thirds and a reasonable fifth, yet it also has decent approximations of 7/4 and 11/8 and it doesn't support the diatonic scale. It also doesn't really have what I would call a whole-tone. Instead, it has the interseptimal second-third from 5edo, along with a neutral second and a small semitone. These three step sizes provide a vast array of melodic possibilities, allowing you to create powerful melodies that have no analog in the diatonic scale.

The minor third is only 4.36¢ sharp of 6/5, meaning this edo has a better approximation of this ratio than every smaller edo, and it really shines when paired with the sharp fifth. It's a very pure sound, even though the fifth is pretty far off of 3/2. The major third is the same as in 12edo, but the major seventh is sharp thanks to the fifth. This means major seventh chords have a very bright quality that really accentuates the uplifting nature of the fifth. Overall, the minor and major thirds have very different vibes, and they both react with the fifth in unique ways.

15edo supports the '''[[porcupine]]''' and [[Limmic temperaments#5-limit%20.28blackwood.29|'''blackwood''']] temperaments, with the '''[[pine]]''' and '''[[pentawood]]''' mosses being present in their basic forms. Both of these mosses are rather interesting, but I prefer to work freely of any particular scale. The three vastly different step sizes really shine when used in conjunction. The second-third especially brings a lot to the table, since it can function either as a second or a third. ''[https://www.youtube.com/watch?v=0PczKDrOdUA Xênerie]'' by [https://www.youtube.com/@woyten Woyten] illustrates this quite well, using it to create an inframinor sound as well as using it as a supermajor second in the melody.

''[https://www.youtube.com/watch?v=xBqXc4PTuLw Like Satie]'' by Hideya is another great piece in this edo, illustrating the characteristic "out of tune" vibe very well. Incidentally, 15edo works great in a lofi environment. Anyway, I just went with a simple groove for this one. I wanted to accentuate the bass melody, so you can really hear how the different step sizes work together. It uses all three step sizes, as well as the undecimal superfourth approximation, which really adds a layer of grit to the end of the loop. The superfourth honestly feels totally different from everything else in the edo, but perhaps that's just the nature of it.

Overall, this is a stellar edo. It is the next smallest edo after 12edo that I am confident placing in S tier, albeit in the lower half. The sheer amount of possibilities with this few notes is honestly amazing.

=== [[16edo]] ===

''2⁴, 1° = 75¢, Fifth = 675¢ (9\16)''

''Tier: '''A'''''

''Tier: '''A+'''''

[[File:16edo demo.mp3|none|thumb|16edo wind quintet in G anti-dorian]]

~~placeholder~~

This edo is often said to be the optimal tuning for mavila temperament, and I agree. It is one of three edos that natively support it in the patent val, and I do honestly believe it does it better than the other two. Mavila is a very interesting temperament, pushing the fifth so flat that harmony is literally flipped on its head. It can create some intriguing harmonic effects, sounding like the diatonic scale until suddenly it totally doesn't. I illustrated this in the demo with a shocking E minor chord (sounding E♭ major ish) in the 6th bar, resolving to a totally different key. It never really deviates from the antidiatonic scale, at least not in a way that I would note as significant.

Anyway, the intervals in this edo are quite nice. The minor third is the same as in 12edo, but the major third is 11.31¢ flat of 5/4, giving the temperament a distinct somber quality. There is also a fairly good approximation of 7/4, being only 6.17¢ sharp. I've never heard a piece in this edo that I would describe as "joyous" or any other discrete happy adjective. There's always a tinge of solemnity, especially in the [https://www.youtube.com/watch?v=AwL95c4PlDs&list=PLblcTr4RQqwJR8klOuKHdV_QSZQVoLwgH&index=2 andantino] of ''Twelve Microtonal Etudes for Electronic Music Media''. It's an unmistakable sound.

16edo is the basis of [[Armodue theory|'''Armodue theory''']], which I don't really know much about, but it is based on the [[7L 2s|'''mavila superdiatonic''']] scale. The superdiatonic scale is an enneatonic mos that behaves somewhat similarly to oneirotonic, in that it has two fifths and a flat major third. Having two fifths is pretty cool, but in the case of 16edo, the dual sharp fifth is so sharp that I wouldn't even consider it a fifth.

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.

=== [[17edo]] ===

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 {{DISPLAYTITLE:Ebooone's EDO Impressions}}
-[[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, soon to be updated] Ebooone's tier list of EDOs 5-72, available at https://tiermaker.com/list/personal/numbers-0-100-15569788/3966935.]]
+[[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 also has its own tier list and recap.
@@ Line 89: / Line 89: @@
 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 in most cases, 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.
+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 most cases (especially 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.
@@ Line 141: / Line 141: @@
 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''', 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, 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.
 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.
@@ Line 247: / Line 247: @@
 ''Tier: '''S-'''''
 [[File:15edo demo.mp3|none|thumb|15edo rhythm section groove in G minor]]
-placeholder
+This is probably the most popular 5n-edo, and for good reason. It's like 12edo from an alternate universe; it has two flavors of thirds and a reasonable fifth, yet it also has decent approximations of 7/4 and 11/8 and it doesn't support the diatonic scale. It also doesn't really have what I would call a whole-tone. Instead, it has the interseptimal second-third from 5edo, along with a neutral second and a small semitone. These three step sizes provide a vast array of melodic possibilities, allowing you to create powerful melodies that have no analog in the diatonic scale.
+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]]''' and '''[[pentawood]]''' mosses being present in their basic forms. Both of these mosses are rather interesting, but I prefer to work freely of any particular scale. The three vastly different step sizes really shine when used in conjunction. The second-third especially brings a lot to the table, since it can function either as a second or a third. ''[https://www.youtube.com/watch?v=0PczKDrOdUA Xênerie]'' by [https://www.youtube.com/@woyten Woyten] illustrates this quite well, using it to create an inframinor sound as well as using it as a supermajor second in the melody.
+''[https://www.youtube.com/watch?v=xBqXc4PTuLw Like Satie]'' by Hideya is another great piece in this edo, illustrating the characteristic "out of tune" vibe very well. Incidentally, 15edo works great in a lofi environment. Anyway, I just went with a simple groove for this one. I wanted to accentuate the bass melody, so you can really hear how the different step sizes work together. It uses all three step sizes, as well as the undecimal superfourth approximation, which really adds a layer of grit to the end of the loop. The superfourth honestly feels totally different from everything else in the edo, but perhaps that's just the nature of it.
+Overall, this is a stellar edo. It is the next smallest edo after 12edo that I am confident placing in S tier, albeit in the lower half. The sheer amount of possibilities with this few notes is honestly amazing.
 === [[16edo]] ===
 ''2⁴, 1° = 75¢, Fifth = 675¢ (9\16)''
-''Tier: '''A'''''
+''Tier: '''A+'''''
 [[File:16edo demo.mp3|none|thumb|16edo wind quintet in G anti-dorian]]
-placeholder
+This edo is often said to be the optimal tuning for mavila temperament, and I agree. It is one of three edos that natively support it in the patent val, and I do honestly believe it does it better than the other two. Mavila is a very interesting temperament, pushing the fifth so flat that harmony is literally flipped on its head. It can create some intriguing harmonic effects, sounding like the diatonic scale until suddenly it totally doesn't. I illustrated this in the demo with a shocking E minor chord (sounding E♭ major ish) in the 6th bar, resolving to a totally different key. It never really deviates from the antidiatonic scale, at least not in a way that I would note as significant.
+Anyway, the intervals in this edo are quite nice. The minor third is the same as in 12edo, but the major third is 11.31¢ flat of 5/4, giving the temperament a distinct somber quality. There is also a fairly good approximation of 7/4, being only 6.17¢ sharp. I've never heard a piece in this edo that I would describe as "joyous" or any other discrete happy adjective. There's always a tinge of solemnity, especially in the [https://www.youtube.com/watch?v=AwL95c4PlDs&list=PLblcTr4RQqwJR8klOuKHdV_QSZQVoLwgH&index=2 andantino] of ''Twelve Microtonal Etudes for Electronic Music Media''. It's an unmistakable sound.
+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''']] 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.
+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.
 === [[17edo]] ===