Ha! I am actually laughing. That very broad definition includes everything you claim it doesn't. Of course music hall, pop songs and modern amplified non narrative music are all literally part of the people's culture. Of course they are. That is exactly what they are. What they are separate from is classical music and church music (often the only kind of music you see discussed my so-called music historians). Where they fall into the picture is: music that you arbitrarily don't like and so exclude from your personal definition.