In particular, how I like the music from specific artists. To give a few examples (and I don't mean to misrepresent here, so if the facts are off, oh well...): Ned mostly likes Daydream Nation and Goo. Tom likes Ladies and Gentlemen We Are Floating in Space, the older stuff less so or not at all. Plenty of Stereolab fans like this album or that album, conspicuously Dots and Loops in the dislike category. And so on.
More than lots of other people whose opinions about music I respect (if not always their tastes), I seem to like more of what musicians do. Where people like songs, I like albums. Where people like albums, I like strings of albums, or everything. I don't think this can be chalked up to fandom. I don't tend to it; I don't buy bootlegs or rare mail-order stuff or $30 concert T-shirts (hi Ned, Dan), typical fan stuff. Mostly I just buy the kind of stuff you can find in a good record store - devoted, but not fanatical. I'll give up on bands; I don't see the need for more Rush, and am beginning to think the same of King Crimson, but still I have a wealth of older recordings, and still try the newer ones I don't like as much (THRAK or Power Windows, anybody?).
No, I think it's something else. I would rather not romanticize it, but it's easy to put it in terms like this:
A big problem with any artwork is that there's a divide between you and its creator. The creator, hopefully, in order to create something good, had to really live with it: whether or not it was a concerted effort or a longer-term building-up, they had to go through experiences in order to arrive at the product you're left with. But you don't have to do that, if you don't want: you can just listen, or read, etc. If you don't like what you hear, that can be that, if you like.
I learned of a few similarities between what people usually consider disparate fields, in college: a math and philosophy major, and erstwhile english major, I found myself often encountering ideas I didn't understand at first. This meant I spent a lot of time "thinking:" a word which people in my fields use a lot, and which is deceiving because it implies some sort of mental labor, when in fact it's more than that. "Thinking" about a difficult proof, or an unfamiliar new approach to aesthetics, or a poem you just don't get, goes on over a period of time. You live with the idea, whatever it is, variously approaching it directly, and just sort of letting it kick around. Some of my best ideas about ideas have happened when walking, or just sitting around doing nothing (and you thought philosophy majors were just lazy). None of this is all that surprising, for anyone who's had to do thinking-work before. Programming, writing, etc. work similarly, though there there's more intentionality, more direction (there being some kind of "product" like goal).
So of course what this means for listening is a different approach, one that's not just do-I-like-this-or-not, or even do-I-like-this-or-not after-n-days, etc., but one where the music stays with me more often, for longer. Not active listening, or even "let it play in the background to get used to it" listening, but the kind where it kicks around in my head for days.
A way to make this better is much like the ways I can understand math or philosophy or anything - immersion. Taking notes, even just mental ones, rereading frequently, you know, just paging through a text now and then, thinking about the relations to other ideas. Etc. For me, immersion with music means taking the good and bad together. The main example I have in mind lately is Sonic Youth, because the Star Chamber has been talking about them, because I've just been listening to them a lot lately, and because they have a new album out that lots of people don't like. With the way I do things, I don't look for sublime moments, great tracks, etc. exclusively. If this song is boring, I might skip it, but I might live with it, too, and wait for the next one. Make the best of it and see how it feels; obviously the band wanted it there, maybe there's more to it than I think after spending so little time with it.
Maybe I'll have a better idea how this works in 5-10 years, but right now, there's this: listening in this way seems to smooth out the "bad" spots (i.e. the parts of Sonic Youth lots of people think are boring or redundant or nothing new, or another in a succession of not all that distinctive repetitive Stereolab songs) - they become irrelevant. I don't want to say they're completely irrelevant, but they seem of less interest, at least. "Bad" spots are sort of like the hurdles I face on the road to really experiencing a musician's work. And by the time I have, they're no longer bad. Kind of. Get it?