User:FloraC/Fumica's edo impressions: Difference between revisions

* 9 – Similar to 8edo, its harmonic resource is quite sparse. Treat it as augmented chords. Good news is there are three.  

* 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.  

* 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.

* 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.  

* 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.  

* 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.  

* 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.  

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