Hi. It is a difficult question, but composed music is pretty inadequate. Dolly Parton has composed almost 1000 songs. The same can be said with Queen, Billy Joel, Paul Simon, and hundreds of composers writing songs for popular musicians. Not to mention that there is a lot of “classical music” that is improvised rather than formally composed.When someone talks about Popular Music, we have a good idea what that means. Given the decline in attendance, etc. at classical music events, we could call it Unpopular Music. The term “Art Music” has been used for a long time, and it even has its own Wiki site. One of the problems is that music is having less presence in high schools, so students don’t have as much exposure as in the past. In closing, I would suggest considering Art Music as the (already existing) term to use.