pop music is "commercially recorded music, often oriented toward a youth market, usually consisting of relatively short, simple songs"
classical music big definiton is "Serious or conventional music following long-established principles rather than a folk, jazz, or popular tradition."
I am in the middle, so its like pseudo-classical. Its not pop because I don't write songs and I don't write in song format. Its more like classical but I don't follow the long-established principles directly, because I don't know them perfectly.
I don't think it has anything to do with notation. You are wrong about that, Dr. M. But you are right about genres not being as defined in reailty as they are in people's heads. This is big definition classical, the only difference is that I am writing for synthesizer, specifically. I am not writing for orchestra and then just using a synthesizer as a temporary recording until (a lot of student composers do that).
Art music is medieval music, baroque, classical, romantic era, modern experimental stuff. It is anything where the focus is "serious" and "implying advanced structural and theoretical considerations". My music is not classical art musics. its just some kind of bobo art music.
I think it likes a sliding scale between pop music, art music, and folk music. folk music being like traditional common people music, not like bob dylan folk music. the original kinds of music. hoedowns and bagpipes and african drumming, that sort of thing. popular music is for the most part a recent invention that is halfway in between and then there is serious music that tries too hard, like nikmis
take jazz for example. some of it is definitly just pop music with some syncopation. but some of it is very serious complex stuff, its own variety of art music.
here is my rough and probably very innacurate map of how I think it is http://i.imgur.com/mbEIh.png