What do you think separates Art music(erudite, classical, traditional) and pop music?

This is gonna be an extra-credit short essay thing on my history final...but I think the topic is interesting enough to talk about. My view is that the separation is strictly a westernized take on older and newer...like it has to be Bach vs. Coltrane or something. But it's weird to see the loose definitions of "art" music as traditional, or even simply notated music...and pop music as music based on improv that lacks form and/or tradition...which is stupid and dated.

The original essay-style question is as follows: Some have claimed that "art" or "Classical" music is in effect, museum music. How is this an inflammatory view? How does function affect musical style? Why is there such a pronounced gulf between "popular" and "art" music.
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It's usually connected to Duke, but I agree, and it's not his, or anybody's:

There's only one division in music, the good and the bad, and even that's not too clear.

Anyway some quick thoughts on the topic:

First you have to look at the motivations to create a distinction. All I can see is to give airs, to perpetuate an elitism, which should receive contempt itself. I don't like the term "art music" and I try not to use it. Various schools of music have been connected with the bourgeois and with the aristocracy: some use these labels to try to connect or distance themselves from those classes. Also silly. The art world is getting hung up about this distancing: the artists and their in-crowd, and "public" (bad word, but ... I can't think of anything better) who are resentful (how many have you met who proudly proclaim their distaste with "modern art", whatever they mean by that) are at odds, and neither side is ever going to concede, it seems. And so if we as artists mistakenly hold ourselves enlightened it should be us then who begin to erase any notion of high / low art and simply create.
It's not opinion based. Those terms are given to categorize them for use in communication. How you name it as music genre doesn't exclusively say how ur music sounds, it's based on what it sounds like the most, and/or which audience it draws the most.

Classical music however is a true genre, cause all of the traditional classical pieces are based on the same theory and frameworks, thus it can be classified on something concrete rather then opinion.

The names given to Art and Pop are already based on a perspective, and trying to opinionate what they define is trying to rewrite the musical accepted language.

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the distinctions between classical and pop are a grey area at best. remember, in its height what we consider classical now was pop then (pop of course being the abbreviation for popular, which has come to mean something different now of course but the root definition has remained the same)
It depends entirely how you define art.

For simplicity's sake, I'll use that old aestheticism definition 'art for art's sake' which I'm sure most of us are familiar with. Under those kind of parameters the distinction becomes clear. Music as commodity is 'pop', music that is created for it's own sake is art; a very simple and understandable argument I think, but superficial at best, and utterly useless in all practicality.

I must admit, I have used the term 'art music' before, and in the aforementioned taste, but only for the reason that I personally believe that art, being so inseparable from its motive, is not a ***** and will always violently revolt from any purely monetary motive and turn itself into a hideous thing.

Frankly, to argue from the practical standpoint, I agree with nick that obviously a distinction is made to distinguish something and therefore there is some kind of class or socio-economic dissension amongst a group of people. In this case, between artist and audience. But there isn't much more to say on that except that it is and that it should be recognized.
The artist - audience divide isn't the norm outside of Western tradition.

Art for art's sake was the romantic era, "bohemian" ideal - while it isn't dead, it's been reconsidered, passed, and can be thought of as dated. Nowadays the idea of the artist aloof from his society is pretentious and futile. Absurdly extended, at its limit, art for its own sake cannot have any audience, which is silly. It can be argued that any art which turns out to have had any commercial appeal, was able to exist outside of an artist, was a result of the artist's whoring of it, conscious or not, to the expectations he'd been created with.
Interesting thread, I think I'll just point out the obvious before going back to lurking...

Art music is music created for aethetics with respect to the influences of the past

Pop music is music created for a commercial purpose with respect to the image that's popular