Collection of EDO impressions: Difference between revisions

: '''Aura:''' The framework for all other EDOs. As it offers only 2-limit consonance, all notes belong to the same pitch class, and this can get boring pretty quickly, though admittedly not as boring as if you only had one note to play.

: '''Aura:''' This EDO is very simple, offering only the perfect consonance of the octave and perfect dissonance of the tritone. The brute force contrast between the antitonic (my name for the diatonic function of pitches located at or around 600 cents away from the tonic) and the tonic does make for good minimalistic harmonic progression, but to use this to its maximum potential requires some of the same techniques needed to master traditional music theory's Locrian mode, and even then, this EDO's limited note palette only ensures that it gets boring rather quickly.

: '''Aura:''' This EDO is also quite simple, and it relies on the perfect consonance of the octave to obtain resolution, with the dominant harmony consisting only of the two steps surrounding the octave. Like with 2edo, 3edo does make for good minimalistic harmonic progression, but to use it to its maximum potential requires serious skills, and its limited note palette again ensures that it gets boring rather quickly.

: '''Aura:''' This EDO is twice as complicated as 2edo, but no more than that. Again, it relies on the perfect consonance of the octave to obtain any type of resolution, and the brute force contrast between the antitonic and the tonic makes for good minimalistic harmonic progression. This time, however, the pitch directly above the tonic can be used in conjunction with the tonic and the octave to create a surprisingly decent tonic chord- more or less the exact means of obtaining resolution in the strictest forms of traditional music theory's Locrian mode. However, given that there are only two other pitch classes to work with, a chord like this is best saved for the end of a piece. Unlike 2edo, 4edo has more of a melodic structure to work with, but again, this requires skills, and this EDO is liable to get boring rather quickly in the hands of an unskilled composer.

: '''Aura:''' This EDO is the smallest one commonly used and is the first one that allows the usage of the fifth above the tonic as part of a resolved tonic harmony, though this admittedly sounds dirty, and furthermore the note a fifth above the dominant acts more like a second than a third in this case. Thankfully, this EDO doesn't take as much skill to work with as the previous three EDOs, and it is not quite as dissonant in terms of its note palette either. Beyond this, and the fact that it provides the framework for the varicant and contravaricant functions, I can't say much more about this EDO than what has already been said by others who have used it, as the only reason I know anything beyond what I've mentioned here is due to observations of others' work on this EDO.

: '''Aura:''' This EDO requires a mixture of the aforementioned techniques for 2edo and 3edo for proper harmonizing, along with knowledge of the whole tone scale from 12edo, as that scale is exactly what this EDO is. I'd really like to see someone take on this challenge, especially as there are more options for this EDO than for either 2edo or 3edo- particularly in the realm of melody.

: '''Aura:''' This EDO provides the framework for all the diatonic functions and most of the paradiatonic functions. Beyond that, the fact that all triads are essentially neutral in this EDO, and the fact that this EDO supports Amity, I have very little to comment on.

: '''Aura:''' The only things I knew for a fact about this EDO going in were from my understanding of 4edo- namely that the same techniques available in 4edo are also viable here, with the added bonus of being able to use the Locrian-style tonic harmony in other ways due to there being more available pitch contrasts. It is true that one has to omit the fifth from most chords for harmony in this EDO to be useful, but I have to say I was pleasantly surprised when I found out not only that the antitonic harmony could now be fortified with what is effectively a supermajor third rather than simply another instance of the tonic, but also that the pitch immediately above the antitonic could serve as a good set-up for the antitonic harmony thanks to also having this same supermajor third above the root in the form of the tonic itself. Suffice to say I now have a new xenharmonic trick up my sleeve.

: '''Aura:''' The only things I know for a fact about this EDO come from my understanding of 3edo, as the same techniques available in 3edo are also viable here. Listening to others' antidiatonic scales in this EDO does have my curiosity peaked, but at the same time, the lack of a good fifth is a turn-off for me.

: '''Aura:''' Finally! The EDO I have the most extensive experience with. All my direct, first-hand experience with 1edo, 2edo, 3edo, 4edo and 6edo prior to me finishing this page came about because I have access to a 12edo instrument- my grandmother's piano. It is also from here that I've taken the bulk of my ideas on tonality- including my idea for Treble-Down tonality. I still use this EDO as a basis for forming harmonic and melodic ideas, however, now that I've grown accustomed to having microtonal gestures available, I find it rather anemic in terms of its expressive potential.

: '''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 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.

: '''Aura:''' Like 14edo this EDO is pretty strange as you don't have as much of the familiar to rely on, though it does better than 12edo in some respects. Judging from my experience with the 159edo-based approximation of it, I can surmise that trying to work with Neapolitan-type scales in this EDO makes for an interesting experience.

: '''Aura:''' I have to say that judging from the 159edo-based approximation that I'm using, the pentatonic scales actually sound pretty good, but the fact that this EDO forces its users to explore unfamiliar harmonic territory is a double-edged sword, and the diatonic fifth that this system offers is more like a 128/85 than a 3/2.

: '''Aura:''' This EDO served as my first personal foray into the world of microtonality- namely through my song "[[:File:Folly of a Drunk.mp3|Folly of a Drunk]]".  It is also from here that I learned a good chunk of what I know about the 11-limit, and given its telic fifth inherited from 12edo, it still holds a place in my musical practice.  However, while its pitch-hue palette is richer than that of 12edo, and I've finally settled on an interpretation of my signature simul half cadence for this system, I still feel the need to branch out some.

: '''ArrowHead:''' Similar to 22edo, 27 is basically 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-sounding like 5edo is. Its 5-limit minor and major thirds are more familiar and forgiving than 22edo, and it has a very good 13th harmonic. Overall a great place to explore xenharmony with temperaments like Tetracot.

: '''Aura:''' Not going to lie, given how underexplored this EDO is, I felt it necessary to try working with a 159edo-based retuning of it. Judging from my experience with that, it should suffice to say that working with Superlocrian in this EDO is another interesting experience.

: '''ArrowHead:''' The second alternative tuning I knew about after 24edo, I got interested in it through Baroque and Renaissance music due to it being an excellent representation of quarter-comma meantone that offers good approximations to all intervals of 11 (and even a 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 12, 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.

: '''Aura:''' Working with Superlocrian in this EDO is again interesting, but it's easier to do with this EDO than with 27edo.  Apart from that, I'm not too thrilled with the lack of the telic fifth, nor the nature of this tuning system's approximation of the 11-prime.

: '''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.  

: '''Aura:''' Interestingly enough, this EDO has a heptatonic scale that consists of the following steps- 5\35, 7\35, 14\35, 21\35, 26\35, 30\35, 35\35. I found this scale while trying to find a good scale to use in a 159edo-based approximation of this EDO. All in all, this particular scale has a quality mostly evocative of something akin to Dorian mode despite obvious tuning differences that seem to give a sort of middle ground between the 5edo qualities and the 7edo of this EDO. So much for some of the claims of some other microtonalists about this one...

: '''Aura:''' Using Ultralocrian mode in this EDO is a challenge, but apparently quite well worth it.  It's tendencies to temper 15/11 and 27/20 together and similarly tempering their octave complements together make for giving my traditional diatonic music an unexpected edge, however, the lack of a telic fifth means this system is just not for me.

: '''ArrowHead:''' Works great as an extended Pythagorean tuning, making it well-suited for Mediæval music. Also suited for those wanting to experiment with true 5-limit JI but also having the ability to modulate. It is also perhaps the most optimal equal temperament tuning supporting [[Orwell]], due to its fifth being almost indistinguishable from just, the fact that it has a good approximation of the [[13/8|13^th harmonic]] (which 31 does only an okay job at and 22 lacks entirely), and 84edo has so many notes that it really does get unwieldy. Turkish music theory is also based on 53edo. However, this is truly near the stopping point for physical instruments and 107 frets isn't practical for almost any real-world guitar or bass.

: '''Aura:''' Most of my experience with this EDO comes from my discovery of its admirable performiance in the 5-limit, and this will likely continue to be the case, since while it has a telic fifth, the lack of good approximations other than the 2.3.5.13 subgroup- particularly its bad 11-prime- is a turn-off, and, to be honest, I wasn't sure how to get around that issue until I discovered 159edo.

: '''Aura:''' While I don't recall making many songs with this EDO, I did compile a private list of 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:''' A disastrous non-meantone tuning. F-tier.  

: '''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.

: '''Aura:''' Just like with 72edo, I don't recall making many songs with this EDO, but again, I did compile a private list of JI intervals that this system approximates, and I was quite fascinated with it for a time. However, I eventually learned that you can't make a proper diatonic scale in this EDO without dealing with serious inconsistency in the 3-limit, and it was at that point that I realized that inconsistency in the 3-limit was a problem, which ultimately led to my formulation of telicity.

: '''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-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 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 microtemperaments 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 commas in JI- a near-pointless endeavor as virtually nobody can hear such small differences in pitch.