Collection of EDO impressions: Difference between revisions

: '''Bozu:''' 0th order [[diminished]]. Nothing interesting, too constrained.

: '''Glitchydarkness:''' [[Diminished]] harmony without the thirds, It's interesting, but there's not enough notes yet.

: '''Bozu:''' Elemental [[augmented] type tuning. Fun for a minute or two, boring after that. Sounds augmented no matter what you play.

: '''Bozu:''' Elemental [[diminished]] type tuning. Fun for a minute or two, boring after that. Sounds diminished no matter what you play.

: '''Keenan:''' Smallest useful EDO, and it's really cool. Basically [[2.3.7]] limit (no hint of the [[5/1|5th harmonic at all]]), and a great candidate for a scale people can just bang away on. Regular temperament model of [[slendro]].

: '''Mike:''' the whole tone scale. But, if you [[Octave shrinking|flatten the octaves]], you can get almost perfect [[4:5:7:11]] chords, which is worth noting.

:: 1. next-smallest EDO that has something resembling [[3/2]]. This sounds like an "equalized" diatonic scale, so that there are no more "major" or "minor" thirds, but just "thirds." 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, [[mohajira]]/maqamic[7] and its [[MODMOS]]'s, [[porcupine]][7], [[tetracot]][7], and [[mavila]][7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you [[octave stretching|stretch the octaves]] to about 1230 [[cents]], you get something which is like every other step of the popular nonoctave [[88cET]], and which can also be thought of as a nonoctave version of [[Tetracot family|tetracot temperament]], with really good [[2:3:5]] chords.

: '''Bozu:''' kind of a cool [[diminished]] scale, but it suffers from the same problems as other drone-like edo's, in terms of options and constraints.

: '''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 [[17-limit|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!

: '''Bozu:''' 3rd order [[augmented]] scale. I want to like this tuning, but I can't see any value in it beyond noodling.

: '''Keenan:''' On the one hand you can treat the 667 [[cent]] intervals as 3/2, yielding an extreme version of [[mavila]] (or 7-limit [[armodue]]) which is a very acceptable tuning for [[pelog|pelog selisir]]. On the other hand you can treat it has having no 3rd harmonics, as something like a [[subgroup|2.5.7/3 temperament]]. (Treating it as a super-accurate 2.27/25.7/3 temperament makes no sense to me.) First EDO with '''recognizable''' "major" and "minor" chords.

:: 1. If we're considering the 667 cent intervals to be 3/2, then this is the first EDO that doesn't [[temper]] out [[25/24]] in the [[5-limit]], and as such distinguishes between [[4:5:6]] and [[10:12:15]]. However you want to view it, it's definitely the first EDO to my ears where I can hear distinct "major" and "minor" chords, as detuned as they may be. This is also the first EDO that supports [[Pelogic family|mavila]] and [[Pelogic family|pelogic]] temperament, and the 7-note [[MOS]]'s are of prime interest here. Because of that, it's the first EDO I know how to create something like "functional harmony" in, although it sounds detuned (which I can get used to; it's not the end of the world). Example here: <nowiki>http://www.youtube.com/watch?v=KV_MzdtU2WQ</nowiki>. Also, like mavila in general, it also allows for common practice music to be translated into this tuning, where major chords become minor and vice versa; however, this experience can be unpleasant if one uses a harsh [[timbre]] or isn't prepared for the more discordant harmonies. Examples of that here: <nowiki>http://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo/</nowiki>. Random other things: it has a great [[7/6]] and can also be viewed as an equalized version of [[superpelog]][9] and [[orwell]][9] and [[augmented]][9], contains an interesting augmented[6] where the "minor thirds" are 7/6, and has been used to tune the mavila pelog scale (albeit with stretched octaves).

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

: '''Aura:''' With the discovery that this EDO [[temper]]s out the [[punctisma]], and that it creates part of the structure that [[24edo]] inherits, I'm interested in finding ways to put an approximation of this EDO to use.

:: 1. A neutral triad version of [[blackwood]], or a "neutral tetrad" version of [[pajara]], or a neutral [[negri]], or a neutral [[lemba]]. Elaine Walker's written some great stuff in this. I have the feeling that this is a great base scale for "diatonic"-style melodies, but haven't explored it as much yet. Also an equalized [[Trienstonic clan|octokaidecal]][10]. Need to play more

: '''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 [[13/1|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 [[7-limit|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|major third range]], and as [[5/4]] is on the flatter end of major thirds, it's just enough to latch on.

: '''Keenan:''' Every other note of [[22edo]]. This makes it a great [[2.9.7.11]] temperament. Includes [[machine]], [[orgone]], [http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11&#x20;and&#x20;http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 <nowiki>http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11</nowiki> and <nowiki>http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11</nowiki>]

:: 1. Amazing and totally underrated EDO. It supports excellent [[4:7:9:11]] chords, as well as 4:7:9:11:15:17:19 chords if you're into [[harmonic series|that thing]]. Was once thought to be mostly "atonal" for lacking 3/2, but revealed as a low-numbered EDO of prime interest after the Great [[Subgroup]] Revolution Of 2011. Giving you decently accurate [[tetrad|tetradic]] harmony for only 11 notes is almost a miracle. Supports [[machine]] temperament, of which the 2 2 1 2 2 2 [[MOS]] is of interest for being stable and sounding like a "[[warped diatonic]]". Example here that loosely uses it:

: '''ArrowHead:''' The smallest one that does [[5-limit]] well, and is right on the midpoint of the regular [[diatonic tuning spectrum]], separating [[meantone]] from [[Parapythagorean]] and [[Superpythagorean]]. Has the largest possible contrast between major and minor for a meantone tuning, though since the wide major thirds and narrow minor thirds can sound quite sludgy on certain timbres such as organs I feel like 12 is far from optimal tuning for many areas of Western music. While I do feel that Western music education should cover the mathematics of tuning before college, and talk about Pythagorean tuning and other meantones to encourage Western musicians to explore other tunings and prevent people from thinking that 12 is the only correct way to tune, I do admit that these should come ''after'' people get familiar with the common practice chords and scales, and 12edo is without a doubt the best starting point for introducing stuff.

: '''Bozu:''' Honestly, the best edo. Not too many notes, not too few. What notes are there sound great. It's the lowest composite [[hypopent]], as well as the lowest composite of [[augmented]] and [[diminished]]. You can use it to affect major, minor, augmented, and diminished tonalities very well. The only place it truly falls short is anything beyond that. It's not too great at approximating higher order [[harmonic]]s, nor does it offer any [[neutral]] intervals. It'd be sort of silly to think of a beginner musician starting with anything other than this or some form of [[meantone]] or [[JI]] that 12edo approximates.

: '''Keenan:''' Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant (temperament)|dominant]] temperament. Also [[augmented (temperament)|augmented]] and [[diminished (temperament)|diminished]]. Currently used as a basis for [[adaptive tuning]], as well as directly, by a huge number of "non-xenharmonic" ensembles.

: '''Mike''': If all things are considered, and any personal boredom with it is ignored, it's a really frickin good temperament. For its size, it supports remarkable [[5-limit]] harmony, has a debatably passable representation of the [[7-limit]], and can sort of "hint" at [[11-limit|11], as in the string of ascending dom9#11 chords in the beginning of this Art Tatum video: [https://www.youtube.com/watch?v=CaPeks0H3_s http://www.youtube.com/watch?v=CaPeks0H3_s]. Our theory places "12-EDO" and "[[meantone]]" as one example of an infinite series of musical tunings, all of which are of potential interest - however, care must be taken to not unfairly diminish 12-EDO's value in a mathematical sense because one may simply be bored with it. Many feel that everything in it "has already been done"; I have a different perspective as a jazz musician in NYC, where people do new and interesting things with 12-EDO every time I go to Smalls'. (Be more creative!!)

: '''Deja Igliashon:''' why is no one talking about how good the [[harmonic series|8:9:10:12:15:17:19]] chords are in this tuning? You can even sneak a [[14/1|14th harmonic]] in there at [[cents|1000¢]] and it won't harsh the sound very noticeably.

: '''Keenan:''' Every other note of [[26edo]]. This makes it a good temperament for a [[subgroup]] containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as [[3/2]], giving a few [[error|high-error]] 5-limit temperaments, including [[uncle]] and [[dicot]].

:: 1. [[13edo]] is insane. I can't get my head wrapped around it, but I love it at the same time. 13 wreaks havoc on my brain because it constantly sends crazy signals about my 12-EDO categories which misfire in fantastic ways. 11-EDO does the same thing, but 13-EDO is worse for no particular reason. You can use this to a particular effect by coming up with [[warped diatonic]] scales which have the pattern 2212221, but in which the "octave" now becomes more like a major 7th. Other than that, 13 is also notable for having a bunch of exceedingly beautiful scales which can generate some of the most [[xenharmonic|far out]] harmonies you've ever heard, and is also simultaneously notable for being totally ignored in this capacity because a long time ago it got a reputation for being harmonically inaccurate and that reputation stuck. The crown jewel in the 13, uh, crown, is [[father]][8], which is an amazingly vivid and bright scale, which for me evokes the imagery of galaxies in deep space and underwater coral reefs and stuff, but it's been largely ignored because it has an interval which is 30 cents off from 3/2 and which sounds bad if you expect it to be 3/2. Despite all that, I like the 738 cent interval for just being the color it is - treat it with caution but use it as an "extension" in chords and such. You can also treat it as [[32/21]], which means you're treating the inverse as [[21/16]], at which point you'll probably realize that this scale isn't bad at all - it's just the [[subgroup|2.9.7/3]] version of [[mothra]] temperament, which Igs has called "[[A-team]]". Other nice scales include 2222212, which is [[glacial]][7], and some other stuff. Oh yeah, and also the 738 cent interval is an augmented fifth in [[26edo|26-EDO]], which is twice 13. No comment. It also has good [[13/8]] and [[11/8]], and a good [[7/6]], and a decent [[9/8]], and a bunch of other random stuff. The [[circle of fifths|circle]] of not-quite-3/2's hits a ton of those intervals.

: '''Aura:''' I have to admit that I was surprised to learn from others that one can replicate dialtones in this EDO, and it was that knowledge that made me want to incorporate a [[159edo]]-based [[well temperament|approximation]] of it.  Suffice to say that based on my work with said approximation, this is a pretty strange EDO overall as you don't have as much of the familiar to rely on.

:: 2. has the whole "[[kloog]]" slash "[[kleeg]]" thing going on, and also has touch tone noises as intervals for you to try and categorize

: '''Bozu:''' 3rd order [[hyperpent]], also with the [[augmented]] tonalities pasted in. Perhaps one of the most user-friendly edo's, it has a lot to offer, but also makes composers accustomed to [[12edo]] think outside of the box.

: '''Yourmusic Productions:''' Like 14, not as good at [[5-limit|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.

: '''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 [[11-limit|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 interval]]s, but like...have you seen [[Triforce]][9]? It has three 8:10:11:12:14:15 [[hexad]]s! 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 [[temper]]s 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]]

: '''Bozu:''' [[diminished]] mayhem with extra mayhem. Check out Last Sacrament to see what this bad boy can do. It's not super user-friendly, in my experience, but it has a distinct sound that seems to pervade everything you can put together within its constraints.

: '''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.

: '''Keenan:''' Really good [[2.3.7.11|no-5's]] system; [[supra]], [[bleu]], etc. The lack of [[5-limit]] harmony forces you to think [[xenharmonic|xenharmonically]], but the nice accurate 3/2s form a solid familiar backbone you can depend on when things get too crazy. Also, [[neutral third scales]] are awesome. Compatible (not perfectly, of course) with a large number of [[maqam|maqamat]].

: '''Deja Igliashon:''' Another one of my all-time favorite and most-used tunings! You literally cannot find a better temperament for the [[subgroup|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 [[maqam|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.

: '''ArrowHead294:''' Basically the opposite of [[meantone]] (specifically [[31edo]]) when it comes to 5 vs. 7, since you find 7/6 [[subminor third]]s in places where you'd normally expect 6/5 minor thirds and 9/7 [[supermajor third]]s where you'd expect 5/4 major thirds. A great way to break out of the meantone way of thinking for most people, and probably the most optimal and practical tuning for [[superpythagorean]] temperament. Minor sevenths being [[7/4]] makes [[7-limit|septimal harmony]] easy to reach and is a really cool effect IMO. However, although the 5-limit minor and major thirds are tuned closer to JI than in 12edo, the minor third is sharp instead of flat and the major third is flat instead of sharp, which gives 5-limit chords a lot of "zonk" to them.

: '''Keenan:''' Amazing and mind-blowing; [[22edo#Theory-Properties of 22 equal temperament-Linear Temperaments|many great temperaments]]. Not much reason to use more notes per octave than this, if you ask me.

: '''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 [[subgroup|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.

: '''Keenan:''' Can be treated in two different ways ([[blackwood]] or mavila/[[armodue]]) depending on which interval you consider "the fifth" or "[[3/2]]". Too many notes for either one of them - why not use 15 or 16 instead?

: '''Yourmusic Productions:''' The whole-tone version of [[50edo|50]]EDO'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]].

: '''Keenan:''' The forgotten [[meantone]] EDO, and the first true [[flattone]] EDO. Flattone is amazing because [[8/7]] and [[7/6]] are swapped from their roles in [[septimal meantone|7-limit meantone temperament]], and because [[Flattone12|flattone[12]]] is much easier to hear as unequal than meantone[12]. Also has [[injera]] and [[cynder]]/[[mothra]].

: '''ArrowHead:''' Similar to [[22edo]], 27 is basically [[superpyth|the opposite of meantone]] (specifically [[19edo]]) when it comes to 5 vs. 7, with subminor and supermajor thirds and sixths in places where minor and major thirds and sixths usually are. Criminally underrated and underutilised for what it is. Fifths are very bright and shimmery but not [[wolf interval|wolf-sounding]] like [[5edo]] is. Its [[5-limit]] minor and major thirds are more familiar and forgiving than 22edo, and it has a very good [[13-limit|13th harmonic]]. Overall a great place to explore [[xenharmonic|xenharmony]] with temperaments like [[Tetracot]].

: '''Nicolai:''' Amazing approximations of intervals like [[7/6]], [[6/5]], [[5/4]], but its the same as 12EDO), [[3/2]], [[5/3], and [[7/4]]. Its weird how it manages to work this much with being a power of 3.

: '''Bozu:''' [[Hypopent]] and [[diminished]], I'm not really sure what else this has to offer other than some funky [[neutral|neutralish]] intervals and diminished mayhem.

: '''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]] interpretation is underwhelming. Otherwise it's a good framework as every other step of [[58edo]] and every third step of [[87edo]]. C-tier.  

: '''Bozu:''' [[Hyperpent]]. [[Augmented]]. Meh, too many seemingly useless intervals.

: '''ArrowHead:''' The second alternative tuning I knew about after [[24edo]], I got interested in it through [[historical temperaments|Baroque and Renaissance music]] due to it being an excellent representation of [[quarter-comma meantone]] that offers good approximations to all [[11-limit|intervals of 11]] (and even a [[13-limit|few involving 13]]). Personally, I think this is the best alternative tuning for most non-classical Western musicians to use. Since everything sounds more mellow and calm compared to [[12edo]], I think that many, if not most, contemporary worship songs would sound better in 31 compared to 12. I also think it's a better tuning for songs with largely pentatonic melodies, such as Hillsong's ''Highlands'', than 12edo is, since the pentatonic scale is noticeably tighter. The number of notes is not overly unwieldy (though it is pushing the limits of practicality on guitars and basses, it's still doable for chords), and the differences between its sound and 12edo's sound are big enough that people will notice (and therefore they might actually care) but not so big that it sounds jarring like [[19edo]] can be (and often is). It also allows many interesting symmetry breaks and comma pumps over 12 that to me are an extremely interesting effect. If A is still 440 Hz, to me, keys from A major and F♯ minor onwards among the sharps sound noticeably darker in 31 and more energetic in 12, D and G major and their relative minor keys sound similar, while flat keys sound noticeably brighter in 31 and more "serious" in 12. Great for temperaments like [[Orwell]] that allow for easy exploration of more exotic harmonies.

: '''Bozu:''' This is sort of the gold standard of [[meantone]] tuning. Composite [[hypopent]]. Great thirds and fifths and everything else used to make western-esque music, and also some really nifty other spicier options. Very user-friendly. If you start with 12edo and go to [[19edo]] and like it, this would be the obvious next recommendation. My only complaint here is that we are starting to get into the territory of having too many notes to easily perform on a [[guitar]] or standard black-and-white-key two row keyboard. Going with [[31edo modes|subsets]] at this point is beneficial, but those provide new challenges.

: '''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 family|meantone extension]] that maps harmonic 11 to the semi-augmented fourth, works almost perfectly in this system. [[Octave stretch]] gives better intonation. A-tier.  

: '''Bozu:''' Composite [[hyperpent]]. [[Diminished]]. Kind of user-antagonistic on first impression. Not picking up anything of striking value.

: '''Bozu:''' Composite [[hypopent]]. [[Augmented]]. Same impression as [[32edo]], except maybe even less valuable.

: '''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 felt the out-of-tune intonation at all, unlike with [[porcupine]]. A-tier.  

: '''Bozu:''' [[Hyperpent]] [[augmented]] with a lot of notes.

: '''Bozu:''' [[Amphipent]] [[diminished]]. Can't really find a good use for this one.

: '''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.  

: '''Bozu:''' [[Amphipent]] [[augmented]].

: '''ArrowHead:''' By far my favourite alternative tuning for post-Mediæval Western music where [[12edo]]'s [[enharmonic]]s aren't critical, and perhaps the most optimal [[meantone]] tuning. It has the fifths tuned flat and major thirds tuned sharp with almost exactly the same deviation from just intonation on both of them and the minor third is tuned flat by twice that amount. It's also good for [[microtonal|microtonality]] involving [[limit|higher-order]] harmonic complexes since it approximates most of the intervals [[13-limit|involving 7, ''and'' 11, ''and'' 13]] well, and has a somewhat better approximation of the first 16 harmonics of the [[harmonic series]] than [[31edo]]. However, with so many notes, in practice it's best suited for keyboards (Lumatone ''et al''). For guitar and bass players, I don't even think it's practical to put 87 frets on any real-world [[guitar]] or bass of reasonable size; at this point I think most guitar or bass players who want to use 43 would go [[fretless]].

: '''Bozu:''' [[Amphipent]] [[diminished]].

: '''Fumica:''' This edo adds decent approximation to [[13-limit|harmonic 13]] on top of 22edo's [[11-limit]], which is pretty tense to start with. At this point it just all breaks down. D-tier.  

: '''Bozu:''' [[Amphipent]] [[augmented]].

: '''Bozu:''' [[Hyperpent]] [[composite]]. Same thing where it looks great on paper, but I feel underwhelmed noodling around with it.

: '''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 [[quarter tone|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.  

: '''Bozu:''' [[Amphipent]] [[augmented]].

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

: '''Fumica:''' [[17edo]] with a major third from the [[augmented|augmented temperament]], which can be a useful combo. Otherwise it has little [[badness|tone efficiency]]. C-tier.  

: '''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 [[87edo#Scales|subset]]. Pushing a continuum beyond this.

: '''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 [[quarter tone|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.