Aesthetic appreciation means well-informed, skilled and close attention to a work of art, all of which can be improved by various types of education. It may be that philosophers of aesthetics tend to not use the word 'appreciation', but the constituent ideas are certainly important. Have a look at previous answers on this site under the heading of 'art': quite a few of them concern context, culture or knowledge.
I'm not sure the Moonlight Sonata is perceived as sad by every person in every culture. This is an empirical question: our perception of music's expressive features has some dependence on the musical culture(s) with which we're familiar, though I gather there's greater cross-cultural uniformity than one might think. The question of how animals or aliens might hear music is also empirical, though I gather there's little evidence that animals respond to music in the ways we do.
The philosphical question is why we perceive music as having expressive featues like sadness in the first place. This is puzzling because there's no comfortable place to situate the sadness: listeners don't always or even typically feel sad when perceiving sad music, and music isn't a phenomenon that seems capable of emotions.
I wish I had a good account to offer you. One possibility is that we hear music as having an expressive feature when it resembles in some way the vocal quality, body-language or other behavior in which humans typically express a given emotion. This might go some way towards exaplning why a slow rhythm or drooping melody can express lament or reflection. But it doesn't, in my view, go very far towards explaining the emotive properties we percieve in a minor tonality.
It is surely possible that a person's music reflects his or her personality and self, and possible that, by listening to this music, you gain insight and understanding of him or her as a person. But I would be very reluctant simply to assume that this is so. Here are three reasons why.
First, the inference from artwork to artist's personality is hardly straightforward. It is rarely true that only a very specific kind of person could possibly have produced a certain set of artworks. And there is little reason to believe that we are good at tracing whatever such connections there may be. I have often been stunned at seeing an artist I greatly admired say silly things in interviews, often including silly things about his or her own artworks.
Second, we live in a world of commerialized art, where a single popular song can pull in millions of dollars. A great deal of money is therefore spent on fine-tuning songs to fit a certain free-spending segment of the audience. To put it bluntly, many an artist is "designed" by marketing specialists who try to manage every tiny aspect of her or his public persona (including appearance, of course, but also little missteps, scandals, and all this) for maximum sales impact. Singers are (also) commercial actors, playing roles for a paying public.
Third, the claim or belief that you know and love this musician as a person is of no real value to you. Imagine, for example, that you have an opportunity to meet him. He does not know you; and for any sort of meaningful relationship (including love) to develop between you, you would need to spend time together, walking, talking, dancing, dining, and such. As he would get to know you, you would have ample opportunity to test and perhaps revise your earlier hunches about his personality. It's just so much better for two people to fall in love with each other than for one of them to do it all by herself... . -- In other words, there's no good reason to gamble on the assumption that you understand him.
There is no uncontroversial definition of a language. However, a requirement that is often cited is that there should be rules on how different elements of a language are composed together (syntax). Another requirement is that the elements of a language should have representational content (semantics).
Music arguably passes the first requirement: notes cannot be strung together in any way one likes to make music. But it appears to fail the second requirement: it is not obvious that individual musical notes represent anything at all. One might argue that sometimes there are phrases in music that do represent: for example, different instrumental lines in Prokofiev's Peter and the Wolf represent the activities of different animals. But these tend to be rather isolated cases of representation; they are not as widespread and systematic as one would expect from a language (e.g. flutes in music do not always represent birds, or indeed anything at all).
Even if music is not a language in the above sense, that does not mean that there aren't interesting connections between language and music, or that our linguistic and musical abilities aren't related.
You're right that a work of music can't literally feel sad. It's also true that we, the listeners, often (perhaps even typically) don't feel sad when we hear a sad piece of music. In fact, we might feel exhiliration or awe in the presence of a wonderful performance of a sad piece--a slow one in a minor key, for example. (If sad music typically made us sad we probably wouldn't choose to listen to as much of it as we do.) There's no reason to think that the composer or performer(s) of a sad piece of music need to feel sad. So who or what is the subject of the emotions we seem to perceive in music?
And come to think of it, unlike garden variety emotions, the emotions that we perceive in music don't have clear objects either. What is the sadness of the music about?
Even though the emotions we seem to hear in music have no clear subjects or objects, it often (though not always) seems right to describe music in emotional terms. Saying how this can be is one of the central problems--if not the central problem--in the philosophy of music. And there's still significant disagreement because sorting it out touches on broader issues such as the nature of artistic expression and interpretation, as well as the nature of emotions and moods. I won't sketch the options here, but instead recommend Peter Kivy's recent book An Introduction to a Philosophy of Music, which provides a nice account of these issues.
I'm not convinced that European music ever had the clear periodisation that you describe. 'Baroque', 'Classical' and so forth tend to be descriptions applied by historians of music after the fact. In fact, at any one time, there were thousands of composers, working to specialised markets, with different players (large, small, amateur, professional, private, or public) and publishers in mind, with regional styles, and so forth. It may well be that the music scene you describe will, a generation from now, be seen as much more simple and homogeneous than it now appears. History naturally simplifies music just as it naturally simplifies philosophy. Is there more variety now, do genres ‘fragment’ more quickly? Probably, but this may be only a matter of degree, rather than an essential change.
Nor am I convinced by the argument that the pursuit of a public, or the employment of new technology, are new phenomena. There were, and still are, ‘artists’ more concerned with making music than with having it widely heard – and there were and still are artists who judge themselves by their public. There were, and still are, artists using the latest instruments, styles, and technologies, alongside traditionalists. (A good example would be the rapid evolution of the piano, and those who did or did not take advantage of it, during the period that we now see as homogenous: the classical.)
All this is philosophically interesting for at least two reasons. First, the simplification of a historical picture seems to be a condition of innovation: one must lump the past together in order to move on. The dependency of innovation and creativity on the act of repudiating the past is a principle that might be worth investigating. Second, it suggests that the concepts that aesthetics might wish to put forth such as ‘disinterest’, 'attention' (what you term 'serious effort'), ‘communication’, or ‘tradition’ do not easily accord with the historical record.
I expect teenagers have been hearing their parents say that the music to which the teenager listens isn't "real" music for about as long as there have been teenagers, parents, and music. It's not at all clear what that is supposed to mean. Is it that the music is fake music? the way a toy car isn't a real car? Presumably not. I expect it is meant, rather, in the sense in which one might say that someone isn't a "real man". It's not that the person isn't a man, or is only pretending to be one. It's rather that, although he is a man, he doesn't meet some standard for manhood the speaker endorses; or again: He's a man, but not a very good example of one. So, in that sense, saying that something isn't "real" music means: It's music, but it doesn't meet some standard or other; it's music, but not very good music.
Of course, different people can be presumed to have different standards, but it certainly doesn't follow that there are no objective standards. What those objective standards might be is, of course, another question altogether. But I don't myself see why technical difficulty should be an appropriate standard. That music is hard to play doesn't make it good; that music is easy to play doesn't make it bad. Of course, if someone is a mediocre musician, then that will sharply limit how they can express themselves, so it's not as if technical ability isn't relevant. It's just not the end-all and be-all.
My own view is that really good music is music that is full of ideas: musical ideas, at least, and lyrical ideas if it's music with words. Such ideas may be present in the piece as written, or they may be present in the piece as performed. (With some music, there's less of a difference there than with other music.) Only music that is full of such ideas really engages me and keeps me engaged. Otherwise, I just find my mind wandering elsewhere, especially if I've heard the song a few times: It's all used up, like an empty can of soda. A really good piece of music, one full of ideas, I can listen to over and over and over again and always find something new and interesting, even surprising, in it.
You might find it interesting to engage your father here. If he's amusician, then I'm sure he could say a great deal about what makes for"real" music, and he might be interested to hear what it is about the music you like that makes you like it. (If he's just closed-minded, well, that's too bad.) You too might find it interesting to think about that question, too---what it is about the music you like that makes you like it---and you might even find that reflection leading you to become interested in music you don't appreciate now. I've been a total music junkie since I was about your age (I own about 1000 CDs and maybe 4000 records), and I know that my own musical tastes have changed and evolved over the last three decades. That isn't to say I don't still like the music I liked when I was twelve, or twenty-two, or thirty-two. Some of it I still like, some of it I don't, and sometimes I am really surprised what I don't like anymore. But I'm glad I heard it all. There's so much great music out there, and, well, sometimes you have to kiss a few frogs before you get to kiss the prince(ss).
One last thing. I think we ought also to remember that it is possible to enjoy music that one doesn't oneself think is actually very good music. It might be, for example, that a particular song has a really good groove that just makes you want to get up and dance, and yet one might also be prepared to say that a really good groove is about all that tune's got. So one enjoys it, for a while, until it gets kind of boring, which it eventually does because there's just not much to it. And that's OK.
The cultural historical moment described by Richard Heck aside, it remains that there was something that Cage was turning on its head when he offered - composed would be the wrong word - the event that is 4'33: the experience of listening to music itself. There would be no history of music if all composers had been like Cage. But there would have been no Cage without music, no content to 4'33 if people didn't know what music normally was. That it is possible to exhibit a urinal in a museum or not play anything in a concert hall and be taken entirely seriously as an artist must be considered a cultural phenomenon, worthy of interest, but not a phenomenon internal to the technical forms that developed over the centuries and that gave us symphonies, songs, paintings and sculptures.
Music can certainly bring about emotions, and I think it can also make us conscious of ones that we already have. It may bring about emotions in a variety of ways. A work of music may remind us of something and produce emotion in that way, or it may move us when we recognize its quality or expressive power, or it may encourage us to imagine certain things and--in so doing--arouse emotion. An interesting question is whether we should understood the expressive nature of certain pieces of music in terms of their tendency to arouse emotions. Simply put: Are works of music sad because they are disposed to make us sad? I think there are reasons to doubt this. For example, it seems to me that one may recognize the sadness of a piece of music w/out feeling any inclination to sadness--and that this is true even under the best listening conditions. That certainly doesn't settle the issue, but it does suggest that we should look for an account of the expressive qualities of music in some other place.