Collection of EDO impressions: Difference between revisions

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: '''Yourmusic Productions''': The opposite of 10 - recognisable, but distorted so there's three types of 3rd and 6th with exaggerated expressive qualities. Even though it's best intervals aren't as in tune as 12, it sounds much less dissonant when playing all the notes at once, so it seems a natural home for Schoenberg influenced serialism and extended chords.

: '''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.

== [[15edo]] ==

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: '''Yourmusic Productions''': Like 14, not as good at simple harmonies as 12, but some glorious extended blackwood chords that combine more notes than you can in 12 and still sound good. Porcupine looks simpler, but I actually find it more of a struggle than blackwood to use.

: '''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

== [[16edo]] ==

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: '''Yourmusic Productions''': 12's evil twin. Scales are recognisable but inverted and everything but the mellowest of timbres or simplest of harmonies sounds horrible once you start combining notes.

: '''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.

== [[17edo]] ==

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: '''Yourmusic Productions''': Interestingly alien, but with good 2nd's, 4ths & 5ths to retreat too when you're not sure what to do next.

: '''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.

== [[18edo]] ==

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: '''Yourmusic Productions''': A universe in monochrome, but with extended dynamic range. There's enough complexity in other areas to keep it interesting, but I'm still aware in the back of my mind that something's missing.

: '''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.

== [[19edo]] ==

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: '''Yourmusic Productions''': The more I study it, the more I love how elegantly everything fits together, how you can use standard notation, but things that are equivalent in 12 actually have proper meaning here, how familiar tunes are transferable and recognisable but the emphasis on intervals is subtly shifted to making minor chords and melodies sound more stable and consonant than major ones. It still has it's limitations, power chord based heavy rock in particular suffers from the weaker 5ths, but just works so much better than 12 in general.

: '''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.

== [[20edo]] ==

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: '''Yourmusic Productions''': Looking at the math on paper, it should be possible to create pleasant music in this one, but nothing I've heard has actually managed it yet.

: '''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.

== [[21edo]] ==

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: '''Yourmusic Productions''': Like 14 but moreso. Dramatically exaggerated harmonic expressiveness, shares the relatively nice major 3rd with 12 rather than the horrible tritone, and the highest edo that works with standard notation without having to add more letters or learn new kinds of accidental. Not as good as 19 for familiar sounding intervals, but still really rather nice.

: '''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.

== [[22edo]] ==

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 : '''Yourmusic Productions''': The opposite of 10 - recognisable, but distorted so there's three types of 3rd and 6th with exaggerated expressive qualities. Even though it's best intervals aren't as in tune as 12, it sounds much less dissonant when playing all the notes at once, so it seems a natural home for Schoenberg influenced serialism and extended chords.
 : '''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.
 == [[15edo]] ==
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 : '''Yourmusic Productions''': Like 14, not as good at simple harmonies as 12, but some glorious extended blackwood chords that combine more notes than you can in 12 and still sound good. Porcupine looks simpler, but I actually find it more of a struggle than blackwood to use.
 : '''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
 == [[16edo]] ==
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 : '''Yourmusic Productions''': 12's evil twin. Scales are recognisable but inverted and everything but the mellowest of timbres or simplest of harmonies sounds horrible once you start combining notes.
 : '''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.
 == [[17edo]] ==
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 : '''Yourmusic Productions''': Interestingly alien, but with good 2nd's, 4ths & 5ths to retreat too when you're not sure what to do next.
 : '''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.
 == [[18edo]] ==
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 : '''Yourmusic Productions''': A universe in monochrome, but with extended dynamic range. There's enough complexity in other areas to keep it interesting, but I'm still aware in the back of my mind that something's missing.
 : '''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.
 == [[19edo]] ==
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 : '''Yourmusic Productions''': The more I study it, the more I love how elegantly everything fits together, how you can use standard notation, but things that are equivalent in 12 actually have proper meaning here, how familiar tunes are transferable and recognisable but the emphasis on intervals is subtly shifted to making minor chords and melodies sound more stable and consonant than major ones. It still has it's limitations, power chord based heavy rock in particular suffers from the weaker 5ths, but just works so much better than 12 in general.
 : '''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.
 == [[20edo]] ==
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 : '''Yourmusic Productions''': Looking at the math on paper, it should be possible to create pleasant music in this one, but nothing I've heard has actually managed it yet.
 : '''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.
 == [[21edo]] ==
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 : '''Yourmusic Productions''': Like 14 but moreso. Dramatically exaggerated harmonic expressiveness, shares the relatively nice major 3rd with 12 rather than the horrible tritone, and the highest edo that works with standard notation without having to add more letters or learn new kinds of accidental. Not as good as 19 for familiar sounding intervals, but still really rather nice.
 : '''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.
 == [[22edo]] ==