Well, we do research on nearly any topic you can think of in the orbit of music's technical elements, history, interaction with culture, and interaction with individual people. There is a slowly-eroding bias toward working on "classical" music, i.e. music of the Western European "art music" tradition, although musics from outside that tradition are (as of the last couple of decades) now entirely accepted as legitimate at least in principle, and have attracted quite a bit of scholarship since they were under-studied until recently.

A few examples of the kinds of things music scholars might do:

• Examine documents in an archive in order to elucidate some episode in music history (pretty much exactly what many "regular" historians do)
• Use primary-source research (often conducted by others) to spin a broader narrative about the trajectory of music history in some time or place -- often bringing together historical, cultural, and technical elements
• Visit some unfamiliar music-culture and document its social and technical elements -- in the old days, this always meant some far-flung part of the globe, increasingly these days is done anywhere a distinctive social practice around some kind of music exists (this approach in all its incarnations is known as "ethnomusicology")
• Construct a controlled experiment to test some aspect of what is going on in people's brains when they hear, perform, or otherwise participate in music
• Examine anywhere from one to thousands of musical compositions in order to describe or analyze their features or structure. When one or a few pieces are involved, this will tend to focus on what is distinctive about the composition(s); when many are involved, it will tend to generalize about broad tendencies and similarities. The actual method of analysis varies extremely widely depending on the repertoire and the analyst's interests and orientations.

The field has largely moved on from its 1990s-era infatuation with postmodernism and a reasonably high level of scholarly rigor is present -- this is not to say that no junk gets published or that music scholarship ever does (or should) resemble an exact science.

A few things that distinguish the best professional music scholarship from crankery:

• While pretty much all professional music scholars do really like at least some music, we tend to be aesthetic relativists at least enough to avoid this kind of trainwreck (it's a website whose author suggests some metrics by which we might determine that some chord progressions, melodies, etc., simply are better than others). Music scholarship has enough robust results to be quite sure that nothing like that could possibly be the case. Like most modern linguistics scholars, our basic orientation is descriptive rather than prescriptive, which is strikingly infrequently the case among cranks. (Of course, since music is nearly always in part an aesthetic object, music scholars can and do express aesthetic judgments, we just know better than to confuse them with any "absolute" notion of correctness.)
• We're very comfortable with the fact that music is a cultural product, and not metaphysically special in any way -- although it is a very, very complex phenomenon and frequently harder to discuss in very concrete terms than some other kinds of cultural products seem to be.
• We rely on painstakingly gathered data wherever possible.
• We maintain a professional expectation that we know not only the history of music but the history of our discipline, which helps us avoid rehashing the same problems others were struggling with in past centuries. Cranks often reinvent various square wheels that were long ago either dispensed with or refined into usable ideas.
• We have good peer review and few enough journals that most published work has been vetted for glaring problems and does meet certain minimum standards.

I don't claim that these standards are met in every published piece of music scholarship, but they are what the profession aspires to and usually attains. I don't think music scholarship is as difficult as science assuming the necessary preparation, but the fact is that the necessary preparation in terms of gaining fluency with music notation, music theory, and music history takes a long time and is a high bar to clear for most people who aren't professionals.

To generalize from my own experience, most people with graduate level education don't have the passion to really learn how to think.

We are the weirdest of the weirdos in this respect. A mental model that neglects this fact will be punished by reality.

I was just trying to raise points for discussion...If you guys don't like my method, what do you suggest to do?

Hold off on proposing solutions during the first stages of discussion.

It's not that easy to convince average (lazy!) teens to try to think

I disagree.

They were talking about the Lottery. Winston looked back when he had gone thirty metres. They were still arguing, with vivid passionate faces. The Lottery, with its weekly payout of enormous prizes, was the one public event to which the proles paid serious attention. It was probable that there were some millions of proles for whom the Lottery was the principal if not the only reason for remaining alive. It was their delight, their folly, their anodyne, their intellectual stimulant. Where the Lottery was concerned, even people who could barely read and write seemed capable of intricate calculations and staggering feats of memory. There was a whole tribe of men who made a living simply by selling systems, forecasts and lucky amulets.

--George Orwell, 1984

Where isn't math useful?

Literature, most of the humanities, the social sciences except at high levels of abstraction

Statistics aren't useful in social sciences???

The mains fields listed on Wikipedia are: anthropology, economics, education, geography, history, law, linguistics, political science, psychology and sociology. I'd say statistics are probably useful in around half of those.

I'd like to know of a science - any science, social or otherwise - that can be optimally useful without utilizing mathematical analysis.

I'm surprised you don't think there could be any more to art history/criticism than either "Look, it's a picture of a duck" or postmodern babble.

I am perhaps a bit oversensitive to the word "understanding", which was what I was mainly pointing at. Every time I met this word in connection with art or literature, it was someone trying to impose her aesthetic preferences on me while signalling her superior cultural sophistication. I am not completely ignorant about history of art, I paint as a hobby and usually spend more than fifteen minutes in a gallery. But all my school experiences with learning to understand art or literature or music - as opposed to learning how to draw or write or sing - was a boring exercise in snobbery.

Even with the uniformly blue canvas, looking at it can be an interesting opportunity to learn about who painted it and why they thought they were doing it (even if you don't agree with their rationale or take it at face value), and maybe spend ten seconds trying to see it through their eyes. Even if you ultimately conclude that it sucks and that the painter was stupid and wrong about everything, it's not less enjoyable than just seeing the blue canvas and spending ten seconds being baffled or bored by it and then moving on.

This can be said about almost anything. Look at a chair, a railroad track or a dog's leash and ponder about the maker's intentions and motives. Almost any product of human effort is worth ten seconds of thought, usually more interesting than with a blue canvas. Singling out paintings for such an argument is privileging the hypothesis. And remember, modern art advocates even don't tell us to think ten seconds about any object we happen to look at. They tell us to spend much longer time thinking about objects classified within the quite arbitrary category "art", pretending that those are especially interesting or important. They aren't. Rothko's thoughts about colour fields on one of his paintings are no more interesting than my neighbour's thoughts about the shape of his new flowerbed; after all, both are of comparable complexity and take about the same time to complete. I have had discussions about the blue canvas (I remember neither the author nor the name of the painting) when my friend said that I can't pronounce the canvas worthless - perhaps the choice of the exact colour was the unique act of creativity and the precise uniformity reflects the author's genius. It's silly.

I'm surprised you don't think there could be any more to art history/criticism than either "Look, it's a picture of a duck" or postmodern babble. There is less postmodern babble in nearly all fields in the humanistic disciplines than most people around here seem to think.

My knowledge of art history specifically is limited to a single college course, but I've been exposed to literary criticism in a little more depth. At least in that field, the predominant failure mode seems not to be postmodern babble (there's some of that in a lot of contemporary work, but it seems more in the nature of a stylistic tic than an actual fixture of thought) but what I might call promiscuous application: that is, readings of a work are decoupled from the needs of readers and writers generally and selected according to what looks fresh and interesting to the literary criticism community. This produces a lot of entertainingly hyperspecialized but ultimately sterile interpretations, a lot of ingroup pandering, and a lot of political grandstanding, but not -- as a fraction of the whole -- much insight into the actual mechanics of literature.

That's not to say that I've gotten nothing out of it; I have. But it tends to take a lot of digging.

shend, shimux. I am not questioning the overall thesis of the post. Just reacting to:

"I think the problem here is that people can’t understand what is really important. Calculus, mechanical physics, chemistry, microiology, etc. are interesting to learn, perhaps. But, they are relatively advanced topics. People don’t use them in daily life unless they are professionals. Why not learn things that we think about every day instead of those that will frankly be useless to most? "