I asked my brother, Dean Wallraff, what he thought about your question. He has written wonderful music over the years. He wrote back:
Sorry, I don’t have any good ideas. Some talk about “serious” music, but that sounds too serious. An interesting comparison with “classical” music is “modern” dance, which is regarded by the dance community as pretty classical and old-school now.
“Classical music” does sound old; “new music” is indeed too vague and all-encompassing; “serious music” does sound joyless. And cute, showy coinages tend not to be adopted in actual use—so you don’t need one of those. “Modernist music” and “post-modernist music” are too specific. Does “modern music” have the right connotations, or close enough? Or possibly “new classical music”?
Barbara Wallraff, a senior editor and the back-page Word Court and Word Fugitives columnist for The Atlantic, is the author of Word Court and Your Own Words, published in 2004 as well as the editor in chief of the newsletter Copy Editor: Language News for the Publishing Profession. She is a member of the American Heritage Dictionary Usage Panel, the American Copy Editors Society, the American Dialect Society, and the Modern Language Association.