I think it's interesting that the 20th century saw a shift in attention from musical periods to music of particular generations. I do wonder though, if that is changing. Music is of course, still something teens latch on to as a way of defining themselves, but for non-teens, it certainly seems like people are freely selecting music from any and all generations and periods. In fact, a lot of new music seems to take that as a given, as styles are mixed and altered in any number of configurations. It almost seems like there is a desire to move beyond the concept of musical style. As to the question "is music representative or not?" well, I don't know. I certainly think that a lot can be inferred about the people who created that music, but inferences are not necessarily representations. I guess I'm not so clear on what is meant by "representative" in this context.
That ends up being a crux of the debate as well: how does one define 'representative'. One of the oft sited arguments for representation in music is Handel's Messiah. Without expressly stating in lyrics what is happening, you can stil understand the intention, depict scenes, etc., etc., but the other side is that any representation given is given based on what is wanted to be portrayed by the listener or who assigns the scene, not that it inherently has that meaning. For example, if someone called Messiah Richard III, people would still find correlations, and the rebuttal for that is that representation is still there, but more ethereal. It continues on likewise. On top of that there are those that argue that evne without specific scenes or concepts, the mere conveyance of emotion through music is itself a form of representation; a musical measure or piece isn't inherently sad or happy, and yet you can hear a singer in Portuguese and know exactly what she wants you to without hearing a single word.