I too have struggled with calling the genre Classical Music. I am not completely sold the title Composed Music yet. I’m going to let myself digest the idea, it could grow on me. When I try to include the 20th century and beyond as belonging to the same tradition, I find myself using the term Art Music. Now in my mind it has a specific meaning — a self awareness of the past and future of music — but, to most, the meaning is probably vague. What about Concert Music? — That is the preferred term of John Corigliano.