Collection of EDO impressions: Difference between revisions

m Move colons inside bold for consistency (not that it has to be this way)
+ the long-overdue impressions of mine, up to 38edo
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: '''Yourmusic Productions:''' Contained within 12 and so not worth talking about.
: '''Yourmusic Productions:''' Contained within 12 and so not worth talking about.
: '''Carmen14edo/Bragtime:''' It's just a single note m8, but somehow it's all we need
: '''Carmen14edo/Bragtime:''' It's just a single note m8, but somehow it's all we need
: '''Fumica:''' An exposition of pitch.
: '''Glitchydarkness:''' Perfect, but eventually it gets boring, you can only rely on timbre for so long! I'd know it's all i do
: '''Glitchydarkness:''' Perfect, but eventually it gets boring, you can only rely on timbre for so long! I'd know it's all i do
: '''Vector:''' Not as "trivial" as some people think. The 2-limit sorta forces you to think of the octave as less of an equivalence than in higher limits.  
: '''Vector:''' Not as "trivial" as some people think. The 2-limit sorta forces you to think of the octave as less of an equivalence than in higher limits.  
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: '''Yourmusic Productions:''' Contained within 12 and so not worth talking about.
: '''Yourmusic Productions:''' Contained within 12 and so not worth talking about.
: '''Carmen14edo/Bragtime:''' It's just a tritone m8, but 12edo and fellow even edos just wouldn't be the same without it
: '''Carmen14edo/Bragtime:''' It's just a tritone m8, but 12edo and fellow even edos just wouldn't be the same without it
: '''Fumica:''' An exposition of consonance and dissonance.
: '''Glitchydarkness:''' Diminished harmony without the thirds, It's interesting, but there's not enough notes yet.
: '''Glitchydarkness:''' Diminished harmony without the thirds, It's interesting, but there's not enough notes yet.


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: '''Yourmusic Productions:''' Contained within 12 and so not worth talking about.
: '''Yourmusic Productions:''' Contained within 12 and so not worth talking about.
: '''Carmen14edo/Bragtime:''' Honestly I've just never been much of a fan of this one.
: '''Carmen14edo/Bragtime:''' Honestly I've just never been much of a fan of this one.
: '''Fumica:''' Augmented chord.
: '''Glitchydarkness:''' You can make chords with this one! I'll name a few: Augmented ...  ...Augmented... Yeah you can't really do much, but it's neat! It's still the first EDO to actually have chords, and it's better than whatever 2edo was!
: '''Glitchydarkness:''' You can make chords with this one! I'll name a few: Augmented ...  ...Augmented... Yeah you can't really do much, but it's neat! It's still the first EDO to actually have chords, and it's better than whatever 2edo was!


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: '''Yourmusic Productions:''' Contained within 12 and so not worth talking about.
: '''Yourmusic Productions:''' Contained within 12 and so not worth talking about.
: '''Carmen14edo/Bragtime:''' UH OH IT'S A TRAIN A-COMING 💀
: '''Carmen14edo/Bragtime:''' UH OH IT'S A TRAIN A-COMING 💀
: '''Fumica:''' Diminished chord.
: '''Glitchydarkness:''' Has some good melodic movement for its size, and can play the diminished chord! Who cares if it's contained within 12edo, you could name any EDO and it's contained in another higher one too, it's a property of numbers!
: '''Glitchydarkness:''' Has some good melodic movement for its size, and can play the diminished chord! Who cares if it's contained within 12edo, you could name any EDO and it's contained in another higher one too, it's a property of numbers!


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: '''Yourmusic Productions:''' The emancipation from harmony. Nothing clashes with anything else, so you're free to play any combination of notes and concentrate on rhythm, arrangement and instrumentation instead. (and you really need to push those other areas to keep it from getting boring.)
: '''Yourmusic Productions:''' The emancipation from harmony. Nothing clashes with anything else, so you're free to play any combination of notes and concentrate on rhythm, arrangement and instrumentation instead. (and you really need to push those other areas to keep it from getting boring.)
: '''Carmen14edo/Bragtime:''' As the others have already explained, this one is a certified hood classic. I second what Bozu and Keenan said
: '''Carmen14edo/Bragtime:''' As the others have already explained, this one is a certified hood classic. I second what Bozu and Keenan said
: '''Fumica:''' Equalized pentic scale.
: '''Glitchydarkness:''' Really good for its size, and is the first EDO to have multiple types of chords! There are now sus2 and sus4 chords to be used, the harmony is evolving! We also get some more variety over at the melodic aspect of the scale, and overall everything is better then all previous edos. Even better, we have a perfect fifth! The key to harmony! Overall the best tiny EDO
: '''Glitchydarkness:''' Really good for its size, and is the first EDO to have multiple types of chords! There are now sus2 and sus4 chords to be used, the harmony is evolving! We also get some more variety over at the melodic aspect of the scale, and overall everything is better then all previous edos. Even better, we have a perfect fifth! The key to harmony! Overall the best tiny EDO
: '''Vector:''' This is the best 2.3.7 edo by far for its size. Other than that, it's equipentatonic, and so you get the first hint of diatonic-style melody in this edo. It's a subset of 15edo.
: '''Vector:''' This is the best 2.3.7 edo by far for its size. Other than that, it's equipentatonic, and so you get the first hint of diatonic-style melody in this edo. It's a subset of 15edo.
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: '''Yourmusic Productions:''' A universe in monochrome. You can make things out, but so much is missing.
: '''Yourmusic Productions:''' A universe in monochrome. You can make things out, but so much is missing.
: '''Carmen14edo/Bragtime:''' ''wooOO the main character's having a flashback or a dream! *always visually accompanied by a ripple effect*''
: '''Carmen14edo/Bragtime:''' ''wooOO the main character's having a flashback or a dream! *always visually accompanied by a ripple effect*''
: '''Fumica:''' Whole tone scale.
: '''Vector:''' Whole tone scale. It's interesting because it has basically all the basic consonances of 12edo except the fifths. I usually end up harmonizing with tritones; it doesn't even sound that dissonant because I'm already using the wholetone scale.
: '''Vector:''' Whole tone scale. It's interesting because it has basically all the basic consonances of 12edo except the fifths. I usually end up harmonizing with tritones; it doesn't even sound that dissonant because I'm already using the wholetone scale.


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: '''Yourmusic Productions:''' The emancipation from harmony, but now with recognisable, if bland diatonic melodies.
: '''Yourmusic Productions:''' The emancipation from harmony, but now with recognisable, if bland diatonic melodies.
: '''Carmen14edo/Bragtime:''' The basis of knowsur's melody and harmony on the 14edo album NANA WODORI, and thus one of my personal favorites.
: '''Carmen14edo/Bragtime:''' The basis of knowsur's melody and harmony on the 14edo album NANA WODORI, and thus one of my personal favorites.
: '''Fumica:''' Equalized diatonic scale.
: '''Vector:''' This... could honestly fit in as a diatonic tuning. It's the first kind of tuning where we have functional harmony, although all the chords are neutral.  
: '''Vector:''' This... could honestly fit in as a diatonic tuning. It's the first kind of tuning where we have functional harmony, although all the chords are neutral.  


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: '''Carmen14edo/Bragtime:''' I'm convinced anyone who thinks this edo legitimately sounds good are lying
: '''Carmen14edo/Bragtime:''' I'm convinced anyone who thinks this edo legitimately sounds good are lying
: '''Deja Igliashon:''' Do you like 24edo? Do you think a chord of 0-400-550-700-850-1000¢ sounds close enough to 8:10:11:12:13:14? Great! Now play just the 10:11:12:13:14 part of the chord--it's 0-150-300-450-600¢, which also happens to be five consecutive notes of 8edo. Say what?! A decently-concordant 5-note chord in an 8-note tuning that everyone thinks is awful?! Who knew?? You can even extend it to 10:11:12:13:14:17 if you like that spicy 17th-harmonic flavor: just add 900¢ to the chord, and enjoy playing 3/4 of all the notes in the tuning at once and still sounding good!
: '''Deja Igliashon:''' Do you like 24edo? Do you think a chord of 0-400-550-700-850-1000¢ sounds close enough to 8:10:11:12:13:14? Great! Now play just the 10:11:12:13:14 part of the chord--it's 0-150-300-450-600¢, which also happens to be five consecutive notes of 8edo. Say what?! A decently-concordant 5-note chord in an 8-note tuning that everyone thinks is awful?! Who knew?? You can even extend it to 10:11:12:13:14:17 if you like that spicy 17th-harmonic flavor: just add 900¢ to the chord, and enjoy playing 3/4 of all the notes in the tuning at once and still sounding good!
: '''Fumica:''' The first nontrivial nondiatonic edo. Since neither the fifth nor the major second passes as consonance, quintal harmony isn't available, not to mention tertian harmony. From here the more complex ratios it approximates on paper generally lack the context to make them ring, so with the very sparse harmonic resource, it forces an approach that focuses on rhythm, texture – anything but harmony. Of course, some resource is there if you try hard enough, but suspending the idea of treating it as more than two diminished chords will spare you a demoralizing fight. Ultimately, I just believe music that sounds good in it sounds good despite it, not because of it; this isn't different from any of the previous edos.


== [[9edo]] ==
== [[9edo]] ==
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: '''Carmen14edo/Bragtime:''' The only song I ever heard in this edo was from the video "1 to 11 tone Equal temperament songs" by 5 hideya, but it sounded like anxiety on steroids.
: '''Carmen14edo/Bragtime:''' The only song I ever heard in this edo was from the video "1 to 11 tone Equal temperament songs" by 5 hideya, but it sounded like anxiety on steroids.
: '''Deja Igliashon:''' Do you like 36edo? Do you think a chord of 0-400-567-700-833-967-1100¢ sounds close enough to 8:10:11:12:13:14:15? Rad! Now play just the 11:12:13:14:15 part of the chord--it's 0-133-267-400-533¢, which also happens to be five consecutive notes of 9edo. You can even extend it to approximate 11:12:13:14:15:19 if you're into that kinky 19-limit stuff, just add 933¢ on top!
: '''Deja Igliashon:''' Do you like 36edo? Do you think a chord of 0-400-567-700-833-967-1100¢ sounds close enough to 8:10:11:12:13:14:15? Rad! Now play just the 11:12:13:14:15 part of the chord--it's 0-133-267-400-533¢, which also happens to be five consecutive notes of 9edo. You can even extend it to approximate 11:12:13:14:15:19 if you're into that kinky 19-limit stuff, just add 933¢ on top!
: '''Fumica:''' Similar to 8edo, its harmonic resource is quite sparse. Treat it as augmented chords. Good news is there are three.
: '''Vector:''' Our first mavila edo! I'm not a huge fan of this tuning, because of all the enharmonic notes it gives in mavila.  It's the first time we have a distinction between normal major and minor chords, though.
: '''Vector:''' Our first mavila edo! I'm not a huge fan of this tuning, because of all the enharmonic notes it gives in mavila.  It's the first time we have a distinction between normal major and minor chords, though.


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: '''Bill Sethares:''' ''If God Had Intended Us To Play In Ten Tones Per Octave, Then He Would Have Given Us Ten Fingers''
: '''Bill Sethares:''' ''If God Had Intended Us To Play In Ten Tones Per Octave, Then He Would Have Given Us Ten Fingers''
: '''Deja Igliashon:''' How is nobody talking about how awesome this tuning is for 8:13:14:15 chords? Like if you understand 15-limit JI at all, and you look at the intervals of this tuning, the harmonic series implications should just be slapping you across the face with an ice-cold salmon straight from the river. Lots of big accurate EDOs like 50edo and 60edo get their approximations to the 7th, 13th, and 15th harmonics from 10edo. And jeez, give a blues guitarist a 10edo guitar and she'll absolutely shred it without thinking twice because so many blues guitar gestures work just great in 10edo.
: '''Deja Igliashon:''' How is nobody talking about how awesome this tuning is for 8:13:14:15 chords? Like if you understand 15-limit JI at all, and you look at the intervals of this tuning, the harmonic series implications should just be slapping you across the face with an ice-cold salmon straight from the river. Lots of big accurate EDOs like 50edo and 60edo get their approximations to the 7th, 13th, and 15th harmonics from 10edo. And jeez, give a blues guitarist a 10edo guitar and she'll absolutely shred it without thinking twice because so many blues guitar gestures work just great in 10edo.
: '''Fumica:''' The first serious edo. Expressivity in the classical and/or septimal chords are neutralized, but harmonic 13 is accurately approximated and offers a critical advantage over 12edo. Imo the best edo for serialism. A-tier.
: '''Vector''': This EDO is a decent 2.3.5.7 system, somehow, despite only having neutral thirds. It tunes its fifth exactly sharp enough that the neutral third just peeks into the major third range, and as 5/4 is on the flatter end of major thirds, it's just enough to latch on.  
: '''Vector''': This EDO is a decent 2.3.5.7 system, somehow, despite only having neutral thirds. It tunes its fifth exactly sharp enough that the neutral third just peeks into the major third range, and as 5/4 is on the flatter end of major thirds, it's just enough to latch on.  


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: '''Carmen14edo/Bragtime:''' One of the only ones I'll probably never explore out of sheer fear
: '''Carmen14edo/Bragtime:''' One of the only ones I'll probably never explore out of sheer fear
: '''Deja Igliashon:''' Mike mostly said it, but also: if you like 22edo's approximation to 4:5:6:7:9:11:15:17, all you gotta do is leave out the 5/4 and 3/2 and everything else is in 11edo. If ya wanna make really zonky xenharmonic music and don't care to keep the 3rd and 5th harmonics around, 11edo absolutely rules. Heck, even if you try playing tertian triads, i.e. 0-3-7 and 0-4-7, you're still more or less approximating 9:11:14 and 7:9:11, which aren't even that weird. Why are people so scared of this tuning??
: '''Deja Igliashon:''' Mike mostly said it, but also: if you like 22edo's approximation to 4:5:6:7:9:11:15:17, all you gotta do is leave out the 5/4 and 3/2 and everything else is in 11edo. If ya wanna make really zonky xenharmonic music and don't care to keep the 3rd and 5th harmonics around, 11edo absolutely rules. Heck, even if you try playing tertian triads, i.e. 0-3-7 and 0-4-7, you're still more or less approximating 9:11:14 and 7:9:11, which aren't even that weird. Why are people so scared of this tuning??
: '''Fumica:''' Every other step of 22edo. It hits harmonics 7, 9, 11, and 15, and that's quite something. The 9 allows a form of quintal harmony. The 15 has good voice-leading utility. Of course, those properties are but implications of it being next to 10- and 12edo, both of which have those and can do much more. It just happens they're enough to make 11edo my favorite strictly nondiatonic edo. B-tier.


== [[12edo]] ==
== [[12edo]] ==
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: '''Carmen14edo/Bragtime:''' For all the hate others have for 12edo, I have love and respect. I believe we microtonal musicians take it for granted, and while it's not the best edo to be the western standard regarding sheer possibilities in this tuning, it's very far from the worst choice imo, and I'd personally choose it as western culture's standard tuning over most all other edos of a similar size.
: '''Carmen14edo/Bragtime:''' For all the hate others have for 12edo, I have love and respect. I believe we microtonal musicians take it for granted, and while it's not the best edo to be the western standard regarding sheer possibilities in this tuning, it's very far from the worst choice imo, and I'd personally choose it as western culture's standard tuning over most all other edos of a similar size.
: '''Deja Igliashon:''' why is no one talking about how good the 8:9:10:12:15:17:19 chords are in this tuning? You can even sneak a 14th harmonic in there at 1000¢ and it won't harsh the sound very noticeably.
: '''Deja Igliashon:''' why is no one talking about how good the 8:9:10:12:15:17:19 chords are in this tuning? You can even sneak a 14th harmonic in there at 1000¢ and it won't harsh the sound very noticeably.
: '''Fumica:''' A no-brainer. Fully laid-back, like a good font to an article – never to get in the way, never to show itself off. It disappears. It lets you forget about it and focus on the musical contents instead. S-tier.
: '''Vector:''' The tuning I write most of my music in. It's good enough for writing the kind of music I want to write, as long as that kind of music isn't "xenharmonic". 12edo theory is my inspiration for my 15edo theory system, and my general approach to xenharmony. (It also brought with it a fair share of misconceptions: for a while, I assumed "sharp" just meant "1 edostep", and after I was corrected wtih 17edo I assumed it meant "between whatever intervals are (true) minor and major".)
: '''Vector:''' The tuning I write most of my music in. It's good enough for writing the kind of music I want to write, as long as that kind of music isn't "xenharmonic". 12edo theory is my inspiration for my 15edo theory system, and my general approach to xenharmony. (It also brought with it a fair share of misconceptions: for a while, I assumed "sharp" just meant "1 edostep", and after I was corrected wtih 17edo I assumed it meant "between whatever intervals are (true) minor and major".)


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: '''Carmen14edo/Bragtime:''' The other one I'll probably never explore out of sheer fear
: '''Carmen14edo/Bragtime:''' The other one I'll probably never explore out of sheer fear
: '''Deja Igliashon:''' I'm amazed that people are actually using the random scale names I put on the 13edo wiki page (archeotonic, oneirotonic, etc.)! That's so cool! I love 13edo and I'm happy some other folks do too. It's fantastic for approximating 8:9:10:11:13:17:21 for such a small number of notes. 13edo's approximation to 13/8 also happens to be quite close to acoustic phi, for those who are into that sort of thing--stretch the octave a few cents sharp and you can get some really interesting phi-based combination tones.
: '''Deja Igliashon:''' I'm amazed that people are actually using the random scale names I put on the 13edo wiki page (archeotonic, oneirotonic, etc.)! That's so cool! I love 13edo and I'm happy some other folks do too. It's fantastic for approximating 8:9:10:11:13:17:21 for such a small number of notes. 13edo's approximation to 13/8 also happens to be quite close to acoustic phi, for those who are into that sort of thing--stretch the octave a few cents sharp and you can get some really interesting phi-based combination tones.
: '''Fumica:''' Every other step of 26edo. Like 11edo, quintal harmony can be used. The intonation sucks. D-tier.


== [[14edo]] ==
== [[14edo]] ==
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: '''Carmen14edo/Bragtime:''' Need I say anything? It used to be my bae, and will forever have a special spot in my heart.
: '''Carmen14edo/Bragtime:''' Need I say anything? It used to be my bae, and will forever have a special spot in my heart.
: '''Deja Igliashon:''' Semaphore--the temperament where 49/48 vanishes and therefor 7/6=8/7=half of a perfect 4th--has to be one of the most underappreciated temperaments, and 14edo is my favorite tuning of it. A chain of the 257¢ intervals generates both a 5-note MOS scale and a 9-note one, and the 9-note scale is incredibly rich in subminor (6:7:9) and supermajor (14:18:21) triads! How rich, you ask? On 7 of the 9 notes, you can build either a subminor triad, supermajor triad, or BOTH--mostly both, actually. And unlike 5-limit triads where the minor 3rd and major 3rd are a semitone apart, these septimal 3rds here are a whole-tone apart, which makes moving between triad types on a single root feel less wonky-chromatic and more akin to the vibe of moving from (say) a sus2 to a major triad or a sus4 to a minor triad. The triadic lattice is so hyperconnected in this temperament that common-tone chord progressions are basically everywhere, and you can drastically alter the mood without modulating to a different key while ALSO retaining a scale that feels melodically very similar to the diatonic, rather than a chromatic scale or a diatonic scale with extra passing tones. You can even selectively omit 2 of the 9 notes to play melodic gestures that essentially sound diatonic. Not to mention that since the Semaphore generator is half of a perfect 4th, there are 2 chains of fifths/fourths in this scale that are separated by subminor 3rds, so there are lots of possible chord progressions involving root movements by 4ths or 5ths. Okay, sure, these are the same shaky 4ths and 5ths as in 7edo, but there are plenty of musical contexts where that doesn't really matter.  
: '''Deja Igliashon:''' Semaphore--the temperament where 49/48 vanishes and therefor 7/6=8/7=half of a perfect 4th--has to be one of the most underappreciated temperaments, and 14edo is my favorite tuning of it. A chain of the 257¢ intervals generates both a 5-note MOS scale and a 9-note one, and the 9-note scale is incredibly rich in subminor (6:7:9) and supermajor (14:18:21) triads! How rich, you ask? On 7 of the 9 notes, you can build either a subminor triad, supermajor triad, or BOTH--mostly both, actually. And unlike 5-limit triads where the minor 3rd and major 3rd are a semitone apart, these septimal 3rds here are a whole-tone apart, which makes moving between triad types on a single root feel less wonky-chromatic and more akin to the vibe of moving from (say) a sus2 to a major triad or a sus4 to a minor triad. The triadic lattice is so hyperconnected in this temperament that common-tone chord progressions are basically everywhere, and you can drastically alter the mood without modulating to a different key while ALSO retaining a scale that feels melodically very similar to the diatonic, rather than a chromatic scale or a diatonic scale with extra passing tones. You can even selectively omit 2 of the 9 notes to play melodic gestures that essentially sound diatonic. Not to mention that since the Semaphore generator is half of a perfect 4th, there are 2 chains of fifths/fourths in this scale that are separated by subminor 3rds, so there are lots of possible chord progressions involving root movements by 4ths or 5ths. Okay, sure, these are the same shaky 4ths and 5ths as in 7edo, but there are plenty of musical contexts where that doesn't really matter.  
: '''Fumica:''' I heard it too that this was the "most dissonant edo". The intonation surely has a lot of spice. Supports squares and godzilla, making it important in theory. Perhaps works better as an interval category scheme than as sound to be listened to. B-tier.


== [[15edo]] ==
== [[15edo]] ==
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: '''Carmen14edo/Bragtime:''' Blackwood[10] is like the coolest scale ever, change my mind (you won't)
: '''Carmen14edo/Bragtime:''' Blackwood[10] is like the coolest scale ever, change my mind (you won't)
: '''Deja Igliashon:''' One of my all-time favorite and most-used tunings. It absolutely RULES on guitar, it's so easy, it's so fun, it's so versatile, everyone should try it! Also, why is no one talking about the fact that 15edo is essentially the smallest EDO that can recognizably render harmonics 2, 3, 5, 7, and 11? Yeah, Blackwood[10] is rad AF for having an unbroken circular chain of alternating major and minor 5-limit triads with no wolf intervals, but like...have you seen Triforce[9]? It has three 8:10:11:12:14:15 hexads! That's UNHINGED. Sure they are not tuned super accurately, but you can practically just mash random combinations of pitches in that scale and end up with some recognizable 11-limit harmony. Also, 15edo supports Orgone temperament, like 11edo and 26edo, but unlike those other two, 15edo tempers out 56/55, making 5/4=14/11, and making the utonal counterpart of 8:11:14 equal to 4:5:7. That gives Orgone[7] some extra concordance  
: '''Deja Igliashon:''' One of my all-time favorite and most-used tunings. It absolutely RULES on guitar, it's so easy, it's so fun, it's so versatile, everyone should try it! Also, why is no one talking about the fact that 15edo is essentially the smallest EDO that can recognizably render harmonics 2, 3, 5, 7, and 11? Yeah, Blackwood[10] is rad AF for having an unbroken circular chain of alternating major and minor 5-limit triads with no wolf intervals, but like...have you seen Triforce[9]? It has three 8:10:11:12:14:15 hexads! That's UNHINGED. Sure they are not tuned super accurately, but you can practically just mash random combinations of pitches in that scale and end up with some recognizable 11-limit harmony. Also, 15edo supports Orgone temperament, like 11edo and 26edo, but unlike those other two, 15edo tempers out 56/55, making 5/4=14/11, and making the utonal counterpart of 8:11:14 equal to 4:5:7. That gives Orgone[7] some extra concordance  
: '''Fumica:''' The error of the fifth is getting quite large for its step size, particularly if you compare it with 10edo. Either this or 10edo can be viewed as the opposite of 14edo, so I think of this as the direct competitor of 10edo. As for which I prefer? I have no idea. A-tier.
: '''Vector:''' A shining example of why the chain of fifths is not suitable as a universal model. 15edo has a diatonic scale (the zarlino scale of 2313231) that makes for a much more familiar interpretation of the tuning than inflecting the 5edo notes up and down. In terms of just intonation, it approximates simple intervals of the 11-limit, and tempers the infamous zarlino wolf fifth flat enough that it merges with the concordant 11th subharmonic, thereby solving the main problem that zarlino itself has.
: '''Vector:''' A shining example of why the chain of fifths is not suitable as a universal model. 15edo has a diatonic scale (the zarlino scale of 2313231) that makes for a much more familiar interpretation of the tuning than inflecting the 5edo notes up and down. In terms of just intonation, it approximates simple intervals of the 11-limit, and tempers the infamous zarlino wolf fifth flat enough that it merges with the concordant 11th subharmonic, thereby solving the main problem that zarlino itself has.


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: '''Carmen14edo/Bragtime:''' I want Easley Blackwood's "16 notes: Andantino" to play at my funeral
: '''Carmen14edo/Bragtime:''' I want Easley Blackwood's "16 notes: Andantino" to play at my funeral
: '''Deja Igliashon:''' There's lots of cool stuff happening in 16edo, but a surprising amount of it is basically just inherited from 8edo. What 16edo adds to the mix is a nice 5-limit major 3rd and a nice approximation to the 7th harmonic, and also the freaky-funky Mavila[7] inside-out diatonic (where major chords become minor, minor chords become major, diminished chords become augmented, and mice chase cats). But IDK, despite my high tolerance for tunings with awful or non-existent perfect 5ths, I've yet to find anything I can do in 16edo that I don't feel like I can do better in a different tuning.
: '''Deja Igliashon:''' There's lots of cool stuff happening in 16edo, but a surprising amount of it is basically just inherited from 8edo. What 16edo adds to the mix is a nice 5-limit major 3rd and a nice approximation to the 7th harmonic, and also the freaky-funky Mavila[7] inside-out diatonic (where major chords become minor, minor chords become major, diminished chords become augmented, and mice chase cats). But IDK, despite my high tolerance for tunings with awful or non-existent perfect 5ths, I've yet to find anything I can do in 16edo that I don't feel like I can do better in a different tuning.
: '''Fumica:''' Potentially useful as every other step of 32edo. Besides that, it has armodue, basically an extremely flat fifth that doesn't sound like the 3rd harmonic at all. "Fifthiness" is useless if not for approximating the 3rd harmonic, so I'm afraid I don't consider this approach to have much value. D-tier.
: '''Vector:''' Definitive proof that a fifth doesn't need to be a 3/2. (TBA)
: '''Vector:''' Definitive proof that a fifth doesn't need to be a 3/2. (TBA)


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: '''Carmen14edo/Bragtime:''' Some people like that one guy who wrote a paper argue this is better for diatonic melody & counterpoint, but at what cost? The answer is concordant triadic harmony lol
: '''Carmen14edo/Bragtime:''' Some people like that one guy who wrote a paper argue this is better for diatonic melody & counterpoint, but at what cost? The answer is concordant triadic harmony lol
: '''Deja Igliashon:''' Another one of my all-time favorite and most-used tunings! You literally cannot find a better temperament for the no-5s 13-limit unless you give an incredibly high weight to accuracy, in which case 207edo finally edges it out. (Or so little weight to accuracy that 9edo eventually beats it). It is just so accurate AND so small that any mathematical approach to quantifying temperament badness practically cannot help but declare 17edo the true lord and savior of the 2.3.7.11.13 subgroup. And if you can stop moaning about how out-of-tune the major triads sound long enough to actually mess around with other harmonic possibilities, you'll quickly discover that practically anywhere you put your fingers, you're stumbling on something that hums and buzzes with that wonderful cold and alien 13-limit energy. Oh, and this is also the smallest EDO that can distinctly represent the rough melodic shapes of all the maqamat from Maqam World, since it is the smallest EDO that has neutral 2nds (half of a minor 3rd), neutral 3rds (half of a perfect 5th), AND good perfect 4ths and perfect 5ths.
: '''Deja Igliashon:''' Another one of my all-time favorite and most-used tunings! You literally cannot find a better temperament for the no-5s 13-limit unless you give an incredibly high weight to accuracy, in which case 207edo finally edges it out. (Or so little weight to accuracy that 9edo eventually beats it). It is just so accurate AND so small that any mathematical approach to quantifying temperament badness practically cannot help but declare 17edo the true lord and savior of the 2.3.7.11.13 subgroup. And if you can stop moaning about how out-of-tune the major triads sound long enough to actually mess around with other harmonic possibilities, you'll quickly discover that practically anywhere you put your fingers, you're stumbling on something that hums and buzzes with that wonderful cold and alien 13-limit energy. Oh, and this is also the smallest EDO that can distinctly represent the rough melodic shapes of all the maqamat from Maqam World, since it is the smallest EDO that has neutral 2nds (half of a minor 3rd), neutral 3rds (half of a perfect 5th), AND good perfect 4ths and perfect 5ths.
: '''Fumica:''' This edo contains an impressive diatonic scale which is nice for both melody and harmony. Semiquartal harmony, that is using the contrast between 7/4 and 12/7 as the basis of tonality, works exceptionally well in this system. S-tier.


== [[18edo]] ==
== [[18edo]] ==
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: '''Carmen14edo/Bragtime:''' I'll go out on a limb and guess this is one of the least used and least liked edos. I have nothing against it, but I have nothing for it.
: '''Carmen14edo/Bragtime:''' I'll go out on a limb and guess this is one of the least used and least liked edos. I have nothing against it, but I have nothing for it.
: '''Deja Igliashon:''' Of all of the EDOs I've played in or looked at, this is definitely one of them. Normally I'm able to find some compelling subset of harmonics 8-16 (or at least 16-32) that every EDO really excels at approximating better than anything else near it in size. For 18edo the best I can find is 11:12:13:14:15:17, which looks good at first until you realize the 11:12:13:14:15 part of it is all 9edo, and adding that 17 to the end just doesn't really expand the possibilities very much at all. 18edo is also really good for 16:18:20:21 chords, but 13edo is also pretty good at those AND can extend them to include the 11th, 13th, and 17th harmonics, so it's hard to make the case that 18edo is a better choice, since it is also BIGGER.
: '''Deja Igliashon:''' Of all of the EDOs I've played in or looked at, this is definitely one of them. Normally I'm able to find some compelling subset of harmonics 8-16 (or at least 16-32) that every EDO really excels at approximating better than anything else near it in size. For 18edo the best I can find is 11:12:13:14:15:17, which looks good at first until you realize the 11:12:13:14:15 part of it is all 9edo, and adding that 17 to the end just doesn't really expand the possibilities very much at all. 18edo is also really good for 16:18:20:21 chords, but 13edo is also pretty good at those AND can extend them to include the 11th, 13th, and 17th harmonics, so it's hard to make the case that 18edo is a better choice, since it is also BIGGER.
: '''Fumica:''' Potentially useful as every other step of 36edo. D-tier.


== [[19edo]] ==
== [[19edo]] ==
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: '''Carmen14edo/Bragtime:''' I'd rate it 10/10 if it didn't have such a shite approximation of 7/4, but 9.5/10 is still quite good. Sunsrise by SAGA and the cover Sunsrise v2 on YouTube have made my brain explode in the best way possible.
: '''Carmen14edo/Bragtime:''' I'd rate it 10/10 if it didn't have such a shite approximation of 7/4, but 9.5/10 is still quite good. Sunsrise by SAGA and the cover Sunsrise v2 on YouTube have made my brain explode in the best way possible.
: '''Deja Igliashon:''' I have tried SO HARD to like this tuning, but I just can't. Yeah, it's a very nice meantone and those syrupy-sweet 5-limit harmonies are delicious. It also supports Semaphore temperament, which I gushed over when talking about 14edo, and in fact it even adds a teensy bit of 5-limit grounding to Semaphore (making it Godzilla). But the fact that it's just so good at 5-limit diatonic music, and so not-so-good at most things involving the 7th, 11th, and/or 13th harmonics, makes me feel like I'm getting zapped by a shock collar any time I try to step from meantone into something more esoteric. There aren't any 7- to 10-note scales that really allow 5-limit harmony to expand to include higher primes very well...Magic[10] is probably the most rich in harmonic possibilities, but it's so melodically awkward! That said, I've heard musicians who are much better than me pull some spectacular sounds from 19edo by indulging in forms of chromaticism that are lost on my jazz-illiterate self. Then again, 19edo has so many fans and cheerleaders that I feel like it's my sacred duty to diss it and hype up the less-popular EDOs instead.
: '''Deja Igliashon:''' I have tried SO HARD to like this tuning, but I just can't. Yeah, it's a very nice meantone and those syrupy-sweet 5-limit harmonies are delicious. It also supports Semaphore temperament, which I gushed over when talking about 14edo, and in fact it even adds a teensy bit of 5-limit grounding to Semaphore (making it Godzilla). But the fact that it's just so good at 5-limit diatonic music, and so not-so-good at most things involving the 7th, 11th, and/or 13th harmonics, makes me feel like I'm getting zapped by a shock collar any time I try to step from meantone into something more esoteric. There aren't any 7- to 10-note scales that really allow 5-limit harmony to expand to include higher primes very well...Magic[10] is probably the most rich in harmonic possibilities, but it's so melodically awkward! That said, I've heard musicians who are much better than me pull some spectacular sounds from 19edo by indulging in forms of chromaticism that are lost on my jazz-illiterate self. Then again, 19edo has so many fans and cheerleaders that I feel like it's my sacred duty to diss it and hype up the less-popular EDOs instead.
: '''Fumica:''' This edo is where my microtonal journey began. Extremely versatile yet friendly to beginners. Using it as a tuning of meantone, the tuning profile is sort of opposite to 12edo, but with seven more pitch classes, the expressive possibility explodes. Presence of an exact hemitwelfth sets it apart from many other meantone edos. S-tier.


== [[20edo]] ==
== [[20edo]] ==
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: '''Carmen14edo/Bragtime:''' Once edos get this big, they no longer offer me the inherent "woah I'm a small number edo" appeal, and that's when having other redeemable qualities must kick in. I'm yet to hear of such qualities with this edo.
: '''Carmen14edo/Bragtime:''' Once edos get this big, they no longer offer me the inherent "woah I'm a small number edo" appeal, and that's when having other redeemable qualities must kick in. I'm yet to hear of such qualities with this edo.
: '''Deja Igliashon:''' People be SLEEPING on this absolute xenharmonic powerhouse! "Oh, it has terrible renditions of the 3rd and 5th harmonic, and there are smaller EDOs that have good renditions of them, so why would anyone use 20edo?" Honey. Darling. Sweetheart! You have NO IDEA! The harmonic series goes so much further, WHY are you stopping at the 5th harmonic? Does 20edo do a good 7th harmonic? Yes. 11th? Sure! 13th? Almost perfect! 15th? Less than 9 cents off! 17th? Eh, passably. 19th? You bet! 21st? Oooh yeah, 10 cents isn't that far off. 23rd? Meh, 12 cents is pushing it, but... 25th? Hell yeah! 27th? Yes ma'am! 29th? Also within 10 cents! 31st? You bet your neon tutu! Yes fam, I am telling you, 20edo does a better job at 4:7:9:11:13:15:17:19:21:23:25:27:29:31 than just about anything that is less than twice its size, and if you omit its weaker 9th, 17th, and 23rd harmonics, it is absolutely BREATHTAKING in its accuracy. So okay, you give up harmonics 3, 5, 9, 17, and 23, and in exchange you get 7, 11, 13, 15, 19, 21, 25, 27, 29, and 31? And there's still only 20 notes in the whole tuning? That's a hell of a bargain IMO, especially considering that the larger the otonal chord you are playing, the less it matters if one or two harmonics are out of tune, so realistically you can absolutely keep the 17th and 23rd harmonics in there.
: '''Deja Igliashon:''' People be SLEEPING on this absolute xenharmonic powerhouse! "Oh, it has terrible renditions of the 3rd and 5th harmonic, and there are smaller EDOs that have good renditions of them, so why would anyone use 20edo?" Honey. Darling. Sweetheart! You have NO IDEA! The harmonic series goes so much further, WHY are you stopping at the 5th harmonic? Does 20edo do a good 7th harmonic? Yes. 11th? Sure! 13th? Almost perfect! 15th? Less than 9 cents off! 17th? Eh, passably. 19th? You bet! 21st? Oooh yeah, 10 cents isn't that far off. 23rd? Meh, 12 cents is pushing it, but... 25th? Hell yeah! 27th? Yes ma'am! 29th? Also within 10 cents! 31st? You bet your neon tutu! Yes fam, I am telling you, 20edo does a better job at 4:7:9:11:13:15:17:19:21:23:25:27:29:31 than just about anything that is less than twice its size, and if you omit its weaker 9th, 17th, and 23rd harmonics, it is absolutely BREATHTAKING in its accuracy. So okay, you give up harmonics 3, 5, 9, 17, and 23, and in exchange you get 7, 11, 13, 15, 19, 21, 25, 27, 29, and 31? And there's still only 20 notes in the whole tuning? That's a hell of a bargain IMO, especially considering that the larger the otonal chord you are playing, the less it matters if one or two harmonics are out of tune, so realistically you can absolutely keep the 17th and 23rd harmonics in there.
: '''Fumica:''' 15edo but worse. F-tier.


== [[21edo]] ==
== [[21edo]] ==
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: '''Carmen14edo/Bragtime:''' Once edos get this big, they no longer offer me the inherent "woah I'm a small number edo" appeal, and that's when having other redeemable qualities must kick in. I'm yet to hear of such qualities with this edo, but I've heard inthar compose very pretty music in it. All that said, it's a multiple of 7edo so I should be a fan of it.
: '''Carmen14edo/Bragtime:''' Once edos get this big, they no longer offer me the inherent "woah I'm a small number edo" appeal, and that's when having other redeemable qualities must kick in. I'm yet to hear of such qualities with this edo, but I've heard inthar compose very pretty music in it. All that said, it's a multiple of 7edo so I should be a fan of it.
: '''Deja Igliashon:''' 21edo is an enigma to me, because I ADORE it, I think it sounds amazing and I've made some of my best music with it, but I have NO IDEA how to explain that in terms of theory. It is solidly mediocre as a 7-limit temperament, not any better or worse as an 11- or 13-limit one, starts to look better as a no-3's 13-limit temperament since its approximations to harmonics 5, 7, 11, and 13 all lean sharp. I suppose one thing it has going for it is that it really is the poster child for tempering out 36/35, thereby making 7/6=6/5 and 5/4=9/7, such that the utonal counterpart of 4:5:6 becomes 6:7:9, and that's cool. But it doesn't really have any MOS scales that grab me--I usually approach it with tetrachordal scales in mind rather than MOS scales. It kinda seems like it might maximize a lot of harmonic entropy, since most of its intervals are smack in between a pair of adjacent simple ratios. Everything is kinda blurry and washy and watery and woozy except for the 7th harmonic, and I really can't think of any other ET that is just so good at that kind of ambiguity. Which is the kind of vibe I generally aspire to, honestly.
: '''Deja Igliashon:''' 21edo is an enigma to me, because I ADORE it, I think it sounds amazing and I've made some of my best music with it, but I have NO IDEA how to explain that in terms of theory. It is solidly mediocre as a 7-limit temperament, not any better or worse as an 11- or 13-limit one, starts to look better as a no-3's 13-limit temperament since its approximations to harmonics 5, 7, 11, and 13 all lean sharp. I suppose one thing it has going for it is that it really is the poster child for tempering out 36/35, thereby making 7/6=6/5 and 5/4=9/7, such that the utonal counterpart of 4:5:6 becomes 6:7:9, and that's cool. But it doesn't really have any MOS scales that grab me--I usually approach it with tetrachordal scales in mind rather than MOS scales. It kinda seems like it might maximize a lot of harmonic entropy, since most of its intervals are smack in between a pair of adjacent simple ratios. Everything is kinda blurry and washy and watery and woozy except for the 7th harmonic, and I really can't think of any other ET that is just so good at that kind of ambiguity. Which is the kind of vibe I generally aspire to, honestly.
: '''Fumica:''' 14edo but worse. F-tier.


== [[22edo]] ==
== [[22edo]] ==
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: '''Carmen14edo/Bragtime:''' Gleam was the first microtonal song for me. I have no words to describe it other than ear candy of the future, peering into an alternate world with music better than our own. That aside, having concordant major and minor triads and a usable 11/8 approximation is really nice, but lacking a really concordant and non-septimal diatonic scale is a deal-breaker for me regarding me composing in it & exploring it.
: '''Carmen14edo/Bragtime:''' Gleam was the first microtonal song for me. I have no words to describe it other than ear candy of the future, peering into an alternate world with music better than our own. That aside, having concordant major and minor triads and a usable 11/8 approximation is really nice, but lacking a really concordant and non-septimal diatonic scale is a deal-breaker for me regarding me composing in it & exploring it.
: '''Deja Igliashon:''' 22edo not being a meantone does NOT mean you're forced into unfamiliar territory, at least not any more than pure 5-limit JI forces you into unfamiliar territory. Yes indeed 22edo OFFERS lots of fun new exciting possibilities, particularly in approximating the 11-limit with some very simple chordal/scalar structures, but you can absolutely make the most banal, trite, pedestrian music you want to as well. Don't let anyone scare you away from this tuning! Sure, certain chord progressions from popular songs written in 12edo don't work the same way, but if you're into microtonality enough to be looking at this page, you're probably not super concerned with playing faithful renditions of traditional songs.
: '''Deja Igliashon:''' 22edo not being a meantone does NOT mean you're forced into unfamiliar territory, at least not any more than pure 5-limit JI forces you into unfamiliar territory. Yes indeed 22edo OFFERS lots of fun new exciting possibilities, particularly in approximating the 11-limit with some very simple chordal/scalar structures, but you can absolutely make the most banal, trite, pedestrian music you want to as well. Don't let anyone scare you away from this tuning! Sure, certain chord progressions from popular songs written in 12edo don't work the same way, but if you're into microtonality enough to be looking at this page, you're probably not super concerned with playing faithful renditions of traditional songs.
: '''Fumica:''' The least evil solution to porcupine and less so to superpyth. I happen to have experience working with porcupine and it felt quite alright, except that I often found myself struggling to combat its out-of-tune nature. B-tier.


== [[23edo]] ==
== [[23edo]] ==
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: '''Carmen14edo/Bragtime:''' Thanks, I hate it. Eikositriophobia exists for a reason.
: '''Carmen14edo/Bragtime:''' Thanks, I hate it. Eikositriophobia exists for a reason.
: '''Deja Igliashon:''' 23edo is the first EDO I've liked enough to write two full albums in, exclusively. It is probably my favorite EDO ever, I've even thought about getting the 23edo circle of flat fifths tattooed on my lower back! At first I thought 23edo was like 21edo, i.e. "it sounds better than it looks like it should", but then I realized I just wasn't looking at it the right way. It has amazingly-accurate representations of 3:5:7:11:19:27:29 and 9:13:15:17:21:23:25:31:33 (I'm probably missing some additional harmonics TBH)...because OH YEAH it's simply half of 46edo, and 46edo is a phenomenal rank-1 temperament for super-extended JI! It's actually surprisingly easy to stumble into some really smooth near-JI harmonies in 23edo, provided you're not trying to play basic 5-limit triads. Although honestly even 23edo's version of Mavila temperament sounds unexpectedly smooth...I think there's something funky going on with those 678¢ fifths where a whole bunch of clashing partials all have nearly identical beat frequencies or something? IDK, but either way I have found 23edo to be the most inspiring, deep, and intriguing EDO I've laid hands on (and I've laid hands on a LOT).  
: '''Deja Igliashon:''' 23edo is the first EDO I've liked enough to write two full albums in, exclusively. It is probably my favorite EDO ever, I've even thought about getting the 23edo circle of flat fifths tattooed on my lower back! At first I thought 23edo was like 21edo, i.e. "it sounds better than it looks like it should", but then I realized I just wasn't looking at it the right way. It has amazingly-accurate representations of 3:5:7:11:19:27:29 and 9:13:15:17:21:23:25:31:33 (I'm probably missing some additional harmonics TBH)...because OH YEAH it's simply half of 46edo, and 46edo is a phenomenal rank-1 temperament for super-extended JI! It's actually surprisingly easy to stumble into some really smooth near-JI harmonies in 23edo, provided you're not trying to play basic 5-limit triads. Although honestly even 23edo's version of Mavila temperament sounds unexpectedly smooth...I think there's something funky going on with those 678¢ fifths where a whole bunch of clashing partials all have nearly identical beat frequencies or something? IDK, but either way I have found 23edo to be the most inspiring, deep, and intriguing EDO I've laid hands on (and I've laid hands on a LOT).  
: '''Fumica:''' Potentially useful as every other step of 46edo. D-tier.


== [[24edo]] ==
== [[24edo]] ==
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: '''Carmen14edo/Bragtime:''' Many people in the microtonal community write it off due to the notoriousness of "quarter tone music", but I'm particularly attracted to the new 12edo-polyphony key changes possible in this tuning.
: '''Carmen14edo/Bragtime:''' Many people in the microtonal community write it off due to the notoriousness of "quarter tone music", but I'm particularly attracted to the new 12edo-polyphony key changes possible in this tuning.
: '''Deja Igliashon:''' it is an absolute crime that Western academic composers got into 24edo during the period when atonality was in vogue, and approached it with no care or consideration for the wealth of concordant harmonic possibilities it presents. It is really just awesome at no-7s 19-limit JI, like just try 0-200-400-550-700-850-1100-1300-1500¢, and tell me it's not doing just as good at approximating 8:9:10:11:12:13:15:17:19, as any other EDOs of similar size or smaller are doing at whatever harmonic series approximations they're known for. 24edo just gives you all kinds of fun ways to tack the 11th and 13th harmonics onto boring ol' 12edo 12-tone harmonies, and it really deserves to be recognized for that, not for its tradition of dreadful atonal discordance.
: '''Deja Igliashon:''' it is an absolute crime that Western academic composers got into 24edo during the period when atonality was in vogue, and approached it with no care or consideration for the wealth of concordant harmonic possibilities it presents. It is really just awesome at no-7s 19-limit JI, like just try 0-200-400-550-700-850-1100-1300-1500¢, and tell me it's not doing just as good at approximating 8:9:10:11:12:13:15:17:19, as any other EDOs of similar size or smaller are doing at whatever harmonic series approximations they're known for. 24edo just gives you all kinds of fun ways to tack the 11th and 13th harmonics onto boring ol' 12edo 12-tone harmonies, and it really deserves to be recognized for that, not for its tradition of dreadful atonal discordance.
: '''Fumica:''' This is kind of a normie's edo, but also the most accessible. Quartertones in my otherwise 12edo works often go unnoticed by the audience. A natural next step of 12edo with a structurally beautiful 2.3.5.11.17.19 subgroup interpretation. A-tier.


== [[25edo]] ==
== [[25edo]] ==
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: '''Yourmusic Productions:''' The whole-tone version of 50EDO's golden meantone. Lots and lots of bad options but like 6 vs 12, missing most of the good combinations.
: '''Yourmusic Productions:''' The whole-tone version of 50EDO's golden meantone. Lots and lots of bad options but like 6 vs 12, missing most of the good combinations.
: '''Deja Igliashon:''' 25edo might be "the one that got away" for me. It bears a lot of similarities to 23edo by virtue of being half the notes of a large very-accurate ET (50edo), having half of the nice 2nds, 3rds, 6ths, and 7ths, but not the nice 4ths and 5ths. Lots of nice harmony to be had, but no 5-limit triads (or at least, none that are very nice). I've thought about having a guitar made in 25edo multiple times but always ended up going with something else for some reason. Anyway, it's really really good for 8:9:10:14:17:19:23:25 chords, as well as 11:12:13:15:21:27 chords, but you can't put the two together unless you are in 50edo.  
: '''Deja Igliashon:''' 25edo might be "the one that got away" for me. It bears a lot of similarities to 23edo by virtue of being half the notes of a large very-accurate ET (50edo), having half of the nice 2nds, 3rds, 6ths, and 7ths, but not the nice 4ths and 5ths. Lots of nice harmony to be had, but no 5-limit triads (or at least, none that are very nice). I've thought about having a guitar made in 25edo multiple times but always ended up going with something else for some reason. Anyway, it's really really good for 8:9:10:14:17:19:23:25 chords, as well as 11:12:13:15:21:27 chords, but you can't put the two together unless you are in 50edo.  
: '''Fumica:''' Potentially useful as every other step of 50edo. D-tier.


== [[26edo]] ==
== [[26edo]] ==
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: '''Yourmusic Productions:''' Definitely deserves more attention than it's got so far.
: '''Yourmusic Productions:''' Definitely deserves more attention than it's got so far.
: '''Deja Igliashon:''' I just don't have much to say about this one. It's sort of the opposite of 21edo to me: looks like it should be really cool and good on paper, but I just don't really enjoy the sound. Most of what it's good at can be done in smaller EDOs too, and that's usually what I'd rather choose.  
: '''Deja Igliashon:''' I just don't have much to say about this one. It's sort of the opposite of 21edo to me: looks like it should be really cool and good on paper, but I just don't really enjoy the sound. Most of what it's good at can be done in smaller EDOs too, and that's usually what I'd rather choose.  
: '''Fumica:''' Just as 19edo is the point separating meantone and flattone, this is the point separating flattone and a meantone extension that implies an even flatter fifth. Therefore it should share all the advantages of 12edo and 19edo, at least theoretically, that is if not for its poor intonation in the 5-limit. C-tier.


== [[27edo]] ==
== [[27edo]] ==
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: '''Yourmusic Productions:''' Like all pure powers of 3, unusually good for it's size. All the melodic coolness of 9 plus decent minor and neutral intervals and an acceptable 5th. Definitely my favourite superpyth system of manageable size.
: '''Yourmusic Productions:''' Like all pure powers of 3, unusually good for it's size. All the melodic coolness of 9 plus decent minor and neutral intervals and an acceptable 5th. Definitely my favourite superpyth system of manageable size.
: '''Deja Igliashon:''' if this EDO got as much attention as 31edo, the world would be a better place. For many EDOs, getting into the particulars of how they temper extended JI is kind of unnecessary to really appreciate them, but 27edo is just so disgustingly ELEGANT in how it tempers that it makes it SO MUCH EASIER to navigate extended JI than darn near anything that can approach it in accuracy. First, consider the unison vector 64/63: just like 5, 10, 15, 20, 22, and 25edo (and I guess 12d?), tempering this out makes it so you can divide 7/4 into two equal parts that are each equal to 4/3, so even a short chain of fifths just automagically incorporates a bunch of ratios of 7. Then you've got 128/125, aka the Augmented comma, aka the diesis or something, which makes it so three approximate 5/4s span exactly one octave--if you simply follow a chain of 5/4s, you literally can't get lost in the tuning! So far so good but also 15edo can do both of these as well, so what else do we have? How about the holy trinity of 144/143, 169/168, and 196/195, the vanishing of which make it so 12/11=13/12=14/13=15/14? This is the trinity that really gives 9edo its mojo, and in 27edo we have three parallel closed circles of 9edo, offset from one another by 1 and 2 steps of 27edo (respectively). Why is this cool? Because if you have a root note on one chain of 9edo, you have a 5/4 above it on the same chain, and then you have 11/8, 3/2, 13/8, 7/4, and 15/8 on the next chain of 9edo that's 1\27 higher. So you can just arpeggiate a bunch of harmonics using motion by a single uniform step size, and if you keep moving by that same step size, instead of getting lost or circulating through ALL THE NOTES OF THE TUNING, you end up back at familiar territory after just a few off-kilter notes. Basically 27edo just makes it really easy not to get lost in 15-odd-limit JI, because you have can find your way between harmonics with simple motions on small closed circles. Just AMAZING!
: '''Deja Igliashon:''' if this EDO got as much attention as 31edo, the world would be a better place. For many EDOs, getting into the particulars of how they temper extended JI is kind of unnecessary to really appreciate them, but 27edo is just so disgustingly ELEGANT in how it tempers that it makes it SO MUCH EASIER to navigate extended JI than darn near anything that can approach it in accuracy. First, consider the unison vector 64/63: just like 5, 10, 15, 20, 22, and 25edo (and I guess 12d?), tempering this out makes it so you can divide 7/4 into two equal parts that are each equal to 4/3, so even a short chain of fifths just automagically incorporates a bunch of ratios of 7. Then you've got 128/125, aka the Augmented comma, aka the diesis or something, which makes it so three approximate 5/4s span exactly one octave--if you simply follow a chain of 5/4s, you literally can't get lost in the tuning! So far so good but also 15edo can do both of these as well, so what else do we have? How about the holy trinity of 144/143, 169/168, and 196/195, the vanishing of which make it so 12/11=13/12=14/13=15/14? This is the trinity that really gives 9edo its mojo, and in 27edo we have three parallel closed circles of 9edo, offset from one another by 1 and 2 steps of 27edo (respectively). Why is this cool? Because if you have a root note on one chain of 9edo, you have a 5/4 above it on the same chain, and then you have 11/8, 3/2, 13/8, 7/4, and 15/8 on the next chain of 9edo that's 1\27 higher. So you can just arpeggiate a bunch of harmonics using motion by a single uniform step size, and if you keep moving by that same step size, instead of getting lost or circulating through ALL THE NOTES OF THE TUNING, you end up back at familiar territory after just a few off-kilter notes. Basically 27edo just makes it really easy not to get lost in 15-odd-limit JI, because you have can find your way between harmonics with simple motions on small closed circles. Just AMAZING!
: '''Fumica:''' The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 subgroup with the sole exception of harmonic 15 tuned way too sharp, for I prefer a flat tuning of 15 or at least no sharper than 12edo's to improve its stability as a consonant major seventh. Other than that it's pretty good. B-tier.


== [[28edo]] ==
== [[28edo]] ==
: '''Bozu:''' Hypopent and diminished, I'm not really sure what else this has to offer other than some funky neutralish intervals and diminished mayhem.
: '''Bozu:''' Hypopent and diminished, I'm not really sure what else this has to offer other than some funky neutralish intervals and diminished mayhem.
: '''Yourmusic Productions:''' 14, only with a really in tune major 3rd and lots of other really interesting extra intervals. Really want an instrument that can do this one justice, probably an 8-string guitar tuned in it's slightly stretched 5ths so the top string is 3 octaves up from the bottom, and a 28-30" fanned fret multiscale fretboard that makes all the chords isomorphic.
: '''Yourmusic Productions:''' 14, only with a really in tune major 3rd and lots of other really interesting extra intervals. Really want an instrument that can do this one justice, probably an 8-string guitar tuned in it's slightly stretched 5ths so the top string is 3 octaves up from the bottom, and a 28-30" fanned fret multiscale fretboard that makes all the chords isomorphic.
: '''Fumica:''' Potentially useful as every other step of 56edo. D-tier.


== [[29edo]] ==
== [[29edo]] ==
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: '''Nicolai:''' Similar to 27EDO, but this is a bit better since the fifth is a little bit better compared to 27EDO.
: '''Nicolai:''' Similar to 27EDO, but this is a bit better since the fifth is a little bit better compared to 27EDO.
: '''Yourmusic Productions:''' 12's evil twin, but in an awesome way. About the same amount of error but in opposite directions means similar kinds of psychoacoustic beating, majors and minors are still clearly recognisable, and everything sounds deceptively familiar right up until it does something awesome that 12 can't. When you do focus on xen intervals and chords, it still sounds much better than 24. Another definite favourite.
: '''Yourmusic Productions:''' 12's evil twin, but in an awesome way. About the same amount of error but in opposite directions means similar kinds of psychoacoustic beating, majors and minors are still clearly recognisable, and everything sounds deceptively familiar right up until it does something awesome that 12 can't. When you do focus on xen intervals and chords, it still sounds much better than 24. Another definite favourite.
: '''Fumica:''' The first edo that sounds like Pythagorean tuning with distinct chromatic and diatonic semitones, such that most contemporary 12edo music will sound alright if retempered to this through dominant. The patent-val interpretation is underwhelming. Otherwise it's a good framework as every other step of 58edo and every third step of 87edo. C-tier.


== [[30edo]] ==
== [[30edo]] ==
: '''Bozu:''' Hyperpent. Augmented. Meh, too many seemingly useless intervals.
: '''Bozu:''' Hyperpent. Augmented. Meh, too many seemingly useless intervals.
: '''Yourmusic Productions:''' Whole tone + Blackwood. Like 24, mainly just adds more ways to sound bad compared to 15 and not worth the hassle.
: '''Yourmusic Productions:''' Whole tone + Blackwood. Like 24, mainly just adds more ways to sound bad compared to 15 and not worth the hassle.
: '''Fumica:''' Potentially useful as every other step of 60edo. D-tier.


== [[31edo]] ==
== [[31edo]] ==
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: '''Nicolai:''' Meantone quarter tones.
: '''Nicolai:''' Meantone quarter tones.
: '''Yourmusic Productions:''' It definitely sounds nice, but I don't hear much actual songwriting going on in it, just people building enormous washes of harmony and luxuriating in them. Maybe it has too LITTLE tension in it, or maybe it's just past the point of complexity that the human mind can fully comprehend. In any case, it definitely hasn't been used to it's full potential yet.
: '''Yourmusic Productions:''' It definitely sounds nice, but I don't hear much actual songwriting going on in it, just people building enormous washes of harmony and luxuriating in them. Maybe it has too LITTLE tension in it, or maybe it's just past the point of complexity that the human mind can fully comprehend. In any case, it definitely hasn't been used to it's full potential yet.
: '''Fumica:''' This is a great edo, with a tuning profile close to what I consider the optimal tuning of meantone. Too great it's a little unfun to work with. A-tier.


== [[32edo]] ==
== [[32edo]] ==
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: '''Nicolai:''' Same as 27 & 29EDO, but the fifth now is sharper than 27EDO.
: '''Nicolai:''' Same as 27 & 29EDO, but the fifth now is sharper than 27EDO.
: '''Yourmusic Productions:''' Like all pure powers of 2, unusually bad for it's size.
: '''Yourmusic Productions:''' Like all pure powers of 2, unusually bad for it's size.
: '''Fumica:''' 27edo but worse. F-tier.


== [[33edo]] ==
== [[33edo]] ==
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: '''Nicolai:''' 11EDO, but with a better fifth.
: '''Nicolai:''' 11EDO, but with a better fifth.
: '''Yourmusic Productions:''' Interesting, but another one that's too big to explore properly without better equipment, and nothing I've heard yet has really managed to do it justice.
: '''Yourmusic Productions:''' Interesting, but another one that's too big to explore properly without better equipment, and nothing I've heard yet has really managed to do it justice.
: '''Fumica:''' 26edo but worse. F-tier.


== [[34edo]] ==
== [[34edo]] ==
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: '''Nicolai:''' 17EDO, but now there's a good third.
: '''Nicolai:''' 17EDO, but now there's a good third.
: '''Yourmusic Productions:''' Even better for 5-limit music than 31, with it's gorgeous thirds, actually defined different sizes of whole tone and still sour harmonic 7, yet even more underused. Definitely deserves more attention. Maybe a half-kite guitar, with full frets up to the perfect 4th or 5th, then 17edo above that point, with adjacent strings tuned so the full range of higher notes can still be played would make it feasible.
: '''Yourmusic Productions:''' Even better for 5-limit music than 31, with it's gorgeous thirds, actually defined different sizes of whole tone and still sour harmonic 7, yet even more underused. Definitely deserves more attention. Maybe a half-kite guitar, with full frets up to the perfect 4th or 5th, then 17edo above that point, with adjacent strings tuned so the full range of higher notes can still be played would make it feasible.
: '''Fumica:''' This is to 17edo what 24edo is to 12edo. While 17edo is often good enough, this offers some more sophisticated solutions such as tetracot. Even the harmonics 7 and 11, commonly cited as poor in this edo, are convincing enough to me, since when I worked with modus I never felt the out-of-tune intonation at all, unlike with porcupine. A-tier.


== [[35edo]] ==
== [[35edo]] ==
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: '''Nicolai:''' You either get 5EDO or 7EDO, there is no middle.
: '''Nicolai:''' You either get 5EDO or 7EDO, there is no middle.
: '''Yourmusic Productions:''' The highest EDO that absolutely refuses to fit into a diatonic framework and forces you to work with it on it's own terms. If you do, it's ability to combine whitewood and blackwood make it incredibly flexible, with very interesting extended harmonies. Something like a 14 string chapman stick with one side tuned in 3 octaves of stretched 4ths and the other in 2 octaves of compressed ones would properly highlight and take advantage of it's unique strengths.
: '''Yourmusic Productions:''' The highest EDO that absolutely refuses to fit into a diatonic framework and forces you to work with it on it's own terms. If you do, it's ability to combine whitewood and blackwood make it incredibly flexible, with very interesting extended harmonies. Something like a 14 string chapman stick with one side tuned in 3 octaves of stretched 4ths and the other in 2 octaves of compressed ones would properly highlight and take advantage of it's unique strengths.
: '''Fumica:''' Potentially useful as every other step of 70edo. D-tier.


== [[36edo]] ==
== [[36edo]] ==
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: '''Nicolai:''' 12EDO, but better.
: '''Nicolai:''' 12EDO, but better.
: '''Yourmusic Productions:''' 12, only with lots of extra harmonic options that actually sound good and are much easier to slip into an otherwise normal track than 24's.
: '''Yourmusic Productions:''' 12, only with lots of extra harmonic options that actually sound good and are much easier to slip into an otherwise normal track than 24's.
: '''Fumica:''' The idea of adding third tones to plain 12edo music is interesting, but none of my attempts have been successful as I generally find them to sound forced. I think this edo is more difficult to use than it appears. C-tier.


== [[37edo]] ==
== [[37edo]] ==
: '''Bozu:''' Amphipent with a lot of notes.
: '''Bozu:''' Amphipent with a lot of notes.
: '''Nicolai:''' Same situation as 35EDO, but the 5EDO fifth is now just a superpyth fifth. Also good approximations of intervals.
: '''Nicolai:''' Same situation as 35EDO, but the 5EDO fifth is now just a superpyth fifth. Also good approximations of intervals.
: '''Fumica:''' Potentially useful as every other step of 74edo. Besides that, it has a good 2.5.7.11.13 subgroup interpretation, tho I have no idea how harmony in this subgroup is supposed to work. D-tier.


== [[38edo]] ==
== [[38edo]] ==
: '''Bozu:''' 19edo slashed into halves.
: '''Bozu:''' 19edo slashed into halves.
: '''Fumica:''' This is to 19edo what 24edo is to 12edo. On paper it adds decent approximation to harmonics 11, 17, and 19, but in practice I never had a situation where I felt I needed these additional notes when working with 19edo. C-tier.


== [[39edo]] ==
== [[39edo]] ==
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* [[Mike's EDO impressions]]
* [[Mike's EDO impressions]]
* [[Yourmusic Productions' opinion of various edos]]
* [[Yourmusic Productions' opinion of various edos]]
* [[User:FloraC/Fumica's edo impressions|Fumica's edo impressions]]


[[Category:Impression]]
[[Category:Impression]]