User:FloraC/Fumica's edo impressions

Exo

• 1 – An exposition of pitch.
• 2 – An exposition of consonance and dissonance.
• 3 – Augmented chord.
• 4 – Diminished chord.
• 5 – Neutral pentic.
• 6 – Whole tone scale.
• 7 – Neutral diatonic.
• 8 – The first nontrivial nondiatonic edo. Since neither the fifth nor the major second passes as consonance, quintal harmony isn't available, not to mention tertian harmony. From here the more complex ratios it approximate on paper generally lack the context to make them ring, so with the very sparse harmonic resource, it forces an approach that focuses on rhythm, texture – anything but harmony. Of course, some resource is there if you try hard enough, but suspending the idea of treating it as more than two diminished chords will spare you a demoralizing fight. Ultimately, I just believe music that sounds good in it sounds good despite it, not because of it; this isn't different from any of the previous edos.
• 9 – Similar to 8edo, its harmonic resource is quite sparse. Treat it as augmented chords. Good news is there are three.

Semitone-size

• 10 – The first serious edo. Expressivity in the classical and/or septimal chords are neutralized, but harmonic 13 is accurately approximated and offers a critical advantage over 12edo. Imo the best edo for serialism. A-tier.
• 11 – Every other step of 22edo. It hits harmonics 7, 9, 11, and 15, and that's quite something. The 9 allows a form of quintal harmony. The 15 has good voice-leading utility. Of course, those properties are but implications of it being next to 10- and 12edo, both of which have those and can do much more. It just happens they're enough to make 11edo my favorite strictly nondiatonic edo. B-tier.
• 12 – A no-brainer. Fully laid-back, like a good font to an article – never to get in the way, never to show itself off. It disappears. It lets you forget about it and focus on the musical contents instead. S-tier.
• 13 – Every other step of 26edo. Like 11edo, quintal harmony can be used. The intonation sucks. D-tier.
• 14 – I heard it too that this was the "most dissonant edo". The intonation surely has a lot of spice. Supports squares and godzilla, making it important in theory. Perhaps works better as an interval category scheme than as sound to be listened to. A-tier.

Subsemitone-size

• 15 – The error of the fifth is getting quite large for its step size, particularly if you compare it with 10edo. Either this or 10edo can be viewed as the opposite of 14edo, so I think of this as the direct competitor of 10edo. As for which I prefer? I have no idea. A-tier.
• 16 – 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. "Fifthness" 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.
• 17 – 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.
• 18 – Potentially useful as every other step of 36edo. D-tier.
• 19 – 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. S-tier.
• 20 – 15edo but worse. F-tier.
• 21 – 14edo but worse. F-tier.
• 22 – 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.
• 23 – Potentially useful as every other step of 46edo. D-tier.
• 24 – 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.
• 25 – Potentially useful as every other step of 50edo. D-tier.
• 26 – Just as 19edo is the point separating meantone and flattone, this is the point separating flattone and a meantone extension that implies an even flatter fifth. Therefore it shares all the advantages of 12edo and 19edo, at least theoretically, that is if not for its poor intonation in the 5-limit. C-tier.

Diesis-size

• 27 – The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 subgroup with the sole exception of harmonic 15 tuned way too sharp, for I prefer a flat tuning of 15 or at least no sharper than 12edo's to improve its stability as a consonant major seventh. Other than that it's pretty good. B-tier.
• 28 – Potentially useful as every other step of 56edo. D-tier.
• 29 – The first edo that sounds like Pythagorean tuning with distinct chromatic and diatonic semitones, by which I mean most contemporary 12edo music will sound alright if retempered to this through dominant. The patent-val interpretation is pretty underwhelming. Otherwise it's a good framework as every other step of 58edo and every third step of 87edo. C-tier.
• 30 – Potentially useful as every other step of 60edo. D-tier.
• 31 – This is a great edo, with a tuning profile close to what I consider the optimal tuning of meantone. Too great it's a little unfun to work with. A-tier.
• 32 – 27edo but worse. F-tier.
• 33 – 26edo but worse. F-tier.
• 34 – 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 harmonics 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-ness at all, unlike with porcupine. A-tier.
• 35 – Potentially useful as every other step of 70edo. D-tier.
• 36 – The idea of adding third tones to plain 12edo music is interesting, but none of my attempts have been successful as I generally find them to sound forced. I think this edo is more difficult to use than it appears. C-tier.
• 37 – 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.
• 38 – This is to 19edo what 24edo is to 12edo. On paper it adds decent approximation to harmonics 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.

Comma-size

The sense of uniqueness of each edo begins to diminish in this range. As the steps get smaller, more and more intervals start to be reasonably approximated, and the edos feel more and more like free pitch. For one thing, starting from here, all edos have at least one diatonic scale (35edo being the last nondiatonic edo). For this reason I'm only listing those which have a good fifth (relative error < 1/3). For the rest, expect

n-edo – Potentially useful as every other step of 2n-edo. D-tier.

• 39 – 1/5-comma quasisuper, most notable for tuning the minor second to 28/27 (with the 39d val) which I feel is where the tension peaks for voice leading. Such an overlooked system despite being similar to 27edo in many ways. B-tier.
• 41 – 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.
• 43 – 1/5-comma meantone, basically the optimal meantone tuning in the 5-limit. The 3 and 5 are equally off, making up a beautifully pure 15. Unfortunately the diesis is too small to achieve good septimal and undecimal harmony. B-tier.
• 44 – This edo adds decent approximation to 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.
• 45 – The only legit edo tuning for flattone. Otherwise it has little utility. It has this weird structure of 9/8~10/9~11/10 all tempered together as a characteristic of flattone, but meanwhile the septimal comma is tuned to two steps, which feels a bit ugly. D-tier.
• 46 – 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.
• 48 – More appropriate as an interval category scheme than anything else. C-tier.
• 50 – Close to 2/7-comma meantone so it has a niche. Has the same problem as 45edo, though less severe. C-tier.

…

• 53 – 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 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 41- or 46edo, it feels slack and doesn't convey a sense of tightly packed well-compromisedness. A-tier.
• 55 – This edo is out of the optimal range of meantone. Septimal meantone feels dumb here since we know 43edo is sharp enough. It can be used for mohaha, but that feels so similar to 24edo that I'd just go with the latter. D-tier.