Collection of EDO impressions: Difference between revisions

: '''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 interval|wolf fifth]] flat enough that it merges with the concordant 11th [[subharmonic]], thereby solving the main problem that zarlino itself has.

: '''Budjarn Lambeth:''' Offers exciting melodic shapes. Still requires careful attention to [[timbre]], but it's more forgiving on that front than most similar sized tunings. The smallest equal tuning that approximates the entire [[11-limit]], so it's a great starting point for exploring new consonances which can't be found in 12.

== [[16edo]] ==

: '''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.

: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".

== [[18edo]] ==

: '''Fumica:''' Potentially useful as every other step of 36edo. D-tier.  

: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".

== [[19edo]] ==

: '''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. Octave stretch solves the intonational problem to a large extent. S-tier.

: '''Budjarn Lambeth:''' The smallest equal tuning that approximates the entire [[43-limit]]. Its melodic similarity to 12edo makes it easier to find your bearings, but harder to break out of that diatonic comfort zone and explore all those intricate high limit harmonies it has to offer.

== [[20edo]] ==

: '''Fumica:''' [[15edo]] but worse. F-tier.  

: '''Budjarn Lambeth:''' It has a lot of [[consonant]] intervals available, but they're mostly all very different to anything in 12edo. This makes it intimidating at first, but rewards exploration, ideal for composers looking for a wild world of new microtonal colours, without sounding as "sour" as some smaller EDOs do.

== [[21edo]] ==

: '''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.  

: '''Budjarn Lambeth:''' It is the first EDO bigger than 12 which sounds equally as "in-tune" as 12, in my opinion.  Though it does have some [[wolf interval]]s which can startle new composers; with experience one learns how to approach those. Its [[superpyth]] and [[pajara]] scales offer a familiar-but-not-too-familiar melodic structure where prior 12edo training is useful, but where exploration beyond it is rewarded with gorgeous new colours. In this sense, it offers the strengths of both 19 and 20 without the drawbacks of either.

== [[23edo]] ==

: '''Fumica:''' Potentially useful as every other step of [[46edo]]. D-tier.  

: '''Budjarn Lambeth:''' A great EDO to begin experimenting with [[octave stretching]] and squishing. With pure octaves, it sounds out of tune, but stretch it by about 10 [[cents]], and you get access to the full array of pretty no-13s [[59-limit]] harmonies. ''Compress'' it by about 10 cents, and you instead get access to the full array of no-19s [[37-limit]] harmonies. Both tunings punch far above their weight by having lots of consonances in only 23 notes. Experiment with both the stretched and squished versions of 23edo, to get a feeling for how stretching or squishing a scale can shift its underlying harmonies dramatically while preserving its melodic shape.

== [[24edo]] ==

: '''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.

: '''Budjarn Lambeth:''' Along with [[36edo]], it is one of the two possible ways to extend 12edo while preserving equal spacing, and keeping the number of notes somewhat manageable. 36edo is ideal if you want to add intervals involving the 7th harmonic into 12edo, while 24edo is ideal if you want to add intervals involving the 11th harmonic. Comparing and contrasting 24edo and 36edo can help you get a feel for the difference between the "vibe" of the 11th harmonic, and the "vibe" of the 7th harmonic. I recommend dipping your toes into each of the two. — Try using familar 12edo intervals in lower registers of your instrument(s)/mix, while mixing in some of the strange new 24edo intervals in the higher registers. Thus will mimic the shape of the [[harmonic series]] and sound nice and glittery.

== [[25edo]] ==

: '''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 [[flattertone|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]] ==

: '''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 {{EDOs|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 [[5/4]]s 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 [[harmonic]]s 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!

== [[28edo]] ==

: '''Yourmusic Productions:''' [[14edo]], 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]] ==

: '''Yourmusic Productions:''' [[12edo]]'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 [[24edo]] 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 (temperament)]]. The [[patent val|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]] ==

: '''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. Too great it's a little unfun to work with. It has a tuning profile close to what I consider the [[optimal tuning]] of meantone, and [[migration]], the [[meantone]] [[extension]] that maps harmonic 11 to the semi-augmented fourth, works almost perfectly in this system. [[Octave stretch]] gives better intonation. A-tier.  

== [[32edo]] ==

: '''Yourmusic Productions:''' Even better for [[5-limit]] music than [[31edo]], 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 [[harmonic]]s 7 and 11, commonly cited as poor in this edo, are convincing enough to me, since when I worked with [[modus]] I never had a problem with the intonation at all, unlike with [[porcupine]]. The sound is better than the structure. B-tier.  

== [[35edo]] ==

: '''Fumica:''' Potentially useful as every other step of [[70edo]]. D-tier.  

: '''Budjarn Lambeth:''' A very good [[dual-fifth]] edo.

== [[36edo]] ==

: '''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.

: '''Budjarn Lambeth:''' Along with 24edo, it is one of the two possible ways to extend 12edo while preserving equal spacing, and keeping the number of notes somewhat manageable. 36edo is ideal if you want to add intervals involving the 7th harmonic into 12edo, while 24edo is ideal if you want to add intervals involving the 11th harmonic. Comparing and contrasting 24edo and 36edo can help you get a feel for the difference between the "vibe" of the 11th harmonic, and the "vibe" of the 7th harmonic. I recommend dipping your toes into each of the two. — Try using familar 12edo intervals in lower registers of your instrument(s)/mix, while mixing in some of the strange new 36edo intervals in the higher registers. Thus will mimic the shape of the [[harmonic series]] and sound nice and glittery.

== [[37edo]] ==

: '''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.  

: '''Budjarn Lambeth:''' A very good [[dual-fifth]] edo.

== [[38edo]] ==

: '''Bozu:''' [[19edo]] slashed into halves.

: '''Fumica:''' This is to 19edo what [[24edo]] is to [[12edo]]. On paper it adds decent approximation to [[harmonic]]s 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]] ==

: '''Nicolai:''' Smaller version of [[53edo|53EDO]].

: '''Fumica:''' The first of the five essential comma-level edos, and the first edo to achieve [[9-odd-limit]] [[distinction]] and [[consistency]]. This is most significant for providing three flavors for each [[chromatic]] category: classical, Pythagorean, and septimal. In this case it is a [[schismic]] and [[garischismic]] system, so that all three kinds are separated by the same [[comma]] step and can be found on a stack of fifths. The comma step is somewhat larger than just, making the differences more pronounced, which is part of why I think this edo is pretty deep – the step isn't only a comma, but many things at once, including but not limited to the septimal dieses, as well as the chroma of the [[archaeotonic]] scale, the scale of [[Tetracot]][7]. The best [[subgroup]] of this edo is, actually, 2.3.5.7.11.19. [[Prime]] 13 is certainly plausible, but prime 19 fits way better. There's a unique uniform tuning for the [[harmonic segment]] 18::22, a fact related to the vanish of s10 = 100/99 and s9/s11 = 243/242. The beauty of this edo goes even beyond the structure, but also to the intonation: it has a very slightly sharp 3 and a more noticeably flat 5, making a flat, more stable 15; that is ideal for my music. Finally, it's an ideal tuning for the [[magic]] temperament. I can't compliment it enough. S-tier.  

== [[42edo]] ==

: '''Nicolai:''' You either get [[5edo|5EDO]] or [[7edo|7EDO]], but there is a middle.

: '''Fumica:''' The second essential comma-level edo. Five more notes than [[41edo]], offering the distinction of two types of [[neutral]] intervals at the cost of a narrower [[septimal diesis]]. As an eighth-tone system, it has a true [[quartertone]]. With that and all the accurate approximations, the expressive possibilities are endless. Best as a 2.3.5.7.11.17.23-[[subgroup]] temperament. A-tier.  

== [[47edo]] ==

: '''Nicolai:''' I consider this an optimal meantone EDO, due to a wealthy collection of notes here.

: '''Fumica:''' Close to [[2/7-comma meantone]] so it has a niche. Has the same problem as [[45edo]], though less severe. C-tier.  

== [[51edo]] ==

: '''Nicolai:''' [[JI]]: The Book.

: '''Fumica:''' The third essential comma-level edo. This one is kinda overrated. The best thing about it is the distinction of [[15/13]] and [[13/10]] from nearby [[7-limit|septimal]] intervals, which neither 41- nor 46edo does. What bugs me is that the fifth feels undertempered for pretty much every purpose, and while the 5-limit approximation is praiseworthy the rest deserves more love. Compared to [[41edo|41-]] or [[46edo]], it feels slack and doesn't convey a sense of tightly packed well-compromisedness. B-tier.  

== [[55edo]] ==

: '''Bozu:''' There are so many tonal options, but many of them are very useful. Maybe this could rival [[53edo]] for versatility. There are some limitations, though.

: '''Fumica:''' As every other step of [[130edo]], this edo is excellent in the 2.3.5.11.19.23-[[subgroup]], but the contrast between that and the poor approximations to 7 and 13 is fatal. Still, it allows a [[dual-n|dual-7 dual-13]] approach, not very satisfying at this level but better than nothing. C-tier.  

== [[67edo]] ==

: '''Aura:''' While I don't recall making many songs with this EDO, I did compile a private list of [[JI|Just Intervals]], and I was quite fascinated with it for a time, as this EDO has better [[5-limit]] and [[7-limit]] approximations than both [[12edo]] and [[24edo]], with the latter being inherited from [[36edo]].  However, the fifth is not [[telic]], which is a problem for me in its own right.

: '''Fumica:''' The last essential comma-level edo. Has the same problem as [[60edo]]. Even tho it approximates [[JI]] way better and thus qualifies for an essential comma-level edo, most of its structural features have been provided by 41- and 58edo. B-tier.  

== [[73edo]] ==

== [[74edo]] ==

: '''Fumica:''' A good [[meantone]] tuning. Not much else to offer. D-tier.  

== [[75edo]] ==

== [[77edo]] ==

: '''Fumica:''' This edo is very sophisticated and hard to evaluate. It's an ideal tuning for the [[valentine]] temperament, obviously. It also seems to be capable of somewhat approximating the full [[23-limit]]. Overall, the structure is a tight fit, with lots of quirks, but that's not too troublesome – they may as well be turned into advantages in the right circumstances. B-tier.  

== [[79edo]] ==

: '''Fumica:''' A disastrous non-[[meantone]] tuning. F-tier.  

== [[84edo]] ==

== [[87edo]] ==

: '''Bozu:''' [[29edo]] with each interval sliced into three. You can do some nifty stuff with it, but the number of notes is too crazy to cover much with midi unless you choose a subset. Pushing a continuum beyond this.

== [[94edo]] ==

: '''Aura:''' Surprisingly, I have attempted to use this EDO before, and it is the first EDO I've attempted to use that wasn't some kind of superset of [[12edo]].  I've noticed just from working out the [[JI]] intervals that this EDO approximates that the [[7-limit]] for this EDO is really good- better than what this EDO has to offer in the [[5-limit]].  Furthermore, all of the pitches in this EDO are connected by a single, complicated circle of fifths.  It is from working with this EDO that I learned the ways that the [[paradiatonic]] prime-limits (that would be the [[7-limit]], the [[11-limit]], and the [[13-limit]]) are connected with each other.

== [[120edo]] ==

== [[159edo]] ==

: '''Aura:''' This is the main system I use in writing [[microtonal]] music.  After finishing the list of [[JI]] equivalents of the various steps of this EDO, I have since found that not only is 159edo very good for those who like to make more just versions of the [[quartertone|quartertone-based intervals]] you see in [[24edo]], but is also very capable of approximating the steps of many lower EDOs within five [[cents]], making for some decent retunings of some of the more commonly used EDOs such as {{EDOs|22edo, 31edo, and even 41edo}}, which was part of the premise of "[[:File:Space Tour.mp3|Space Tour]]".  Based on this discovery alone, I'd have to say that 159edo is not just a superset of [[53edo]], but rather, an EDO that is quite full of potential.  However, the fact is that this EDO is [[consistent]] all the way up to the [[17-limit]], and has a good 23-[[prime]], and, should you skip the 17-prime, you have access to a decent 19-prime and 29-prime.  This, and the fact that one has access to a bunch of [[microtemperament]]s in this EDO, all for a step-size that's slightly above the average [[JND]], means I can also perform other tricks in composition.  I imagine at this point that some would ask me why I don't just use JI, and the answer is that even an EDO in the hundreds like 159edo is considerably more simple than JI, as you have to account for a lot of [[unnoticeable comma]]s in JI- a near-pointless endeavor as virtually nobody can hear such small differences in pitch.

== Sources ==

* [https://sevish.com/2022/sevishs-scale-impressions/ Sevish's scale impressions] (''external site, Sevish.com'')

* [[Yourmusic Productions' opinion of various edos]]

== Notes ==

[[Category:Impression]]