User:Aura/Aura's EDO Impressions

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Okay, so if I say "Um..." that means I haven't messed with the EDO enough yet.

1 - 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.

2 - 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.

3 - This EDO is also quite simple, and 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.

4 - 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 of 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.

5 - 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, 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 beyond what I've mentioned here comes from observations of others' work on this EDO.

6 - This EDO requires a mixture of the aforementioned techniques for 2edo and 3edo for proper harmonizing. 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.

7 - Um...

8 - 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.

9 - 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. However, I can't say much about the other aspects of this EDO due to lack of other relevant experience on my part.

10 - Um...

11 - Um...

12 - 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.

13 - Um...

14 - 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.

15-16 - Um...

17 - 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.

18 - Um...

19 - Judging from my experience with the 159edo-based approximation of it, I can surmise that this EDO is a little easier to work with than 17edo, but again, trying to work with Neapolitan-type scales in this EDO makes for an interesting experience.

20-21 - Um...

22 - 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.

23 - Um...

24 - This EDO served as my first personal foray into the world of microtonality. It is also from here that I learned what I have about the 11-limit.

25-26 - Um...

27 - 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.

28-30 - Um...

31 - Working with Superlocrian in this EDO is again interesting, but it's easier to do with this EDO than with 27edo.

32-52 - Um...

53 - Most of my experience with this EDO comes from my current experiments with 159edo, and this will likely continue to be the case since this EDO doesn't have good approximations of the 11-limit.

54-71 - Um...

72 - 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.

73-93 - Um...

94 - 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.

95-119 - Um...

120 - Just like with 72edo, I don't recall making many songs with this EDO, but again, I did compile a private list of Just Intervals, 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 contortion in the 3-limit, and it was at that point that I realized that contortion in the 3-limit was a problem.

121-158 - Um...

159 - This is the best EDO I've worked with, hands down. 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 more familiar kinds of things 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, according to my calculations, even 41edo. 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 rather full of surprises.