Not to dominate this thread, but I literally just remembered something I've often thought about, and I thought it was apt.
Music completely defies classification. It encompasses so many things, that the only word that adequately and completely describes it is itself. Music is music. So, what does it encompass?
Mathematics. Music is essentially the mathematical applications of sounds. The entire idea of music theory is that you have a system based on numbers that helps lay out and explain the structure of what's being played. For instance, Western music is based on the idea of having 12 notes. If you choose 7 of those notes, you have a mode. Whatever those 7 notes are dictates what kind of mode you have. For instance: 1234567 is your essential Major scale (the Ionian mode). Whereas 12b345b6b7 is your standard Minor scale (the Aeolian mode). And if you put 12b3456b7, you get the Dorian mode. And that's not even looking at chords. Put a 1 and a 5 together, and you've got a simple 5 chord. Put a 3 in there as well, and you've got a Major chord. Put a 7 in there too, and you've got a Major7 chord. It's using the principles of mathematics to construct pleasing sounds.
Except that it's also physics too. Mathematics without sound to be applies to is only maths, whereas if you introduce physics, all of a sudden you've got music. For some reason, we as a species have decided that a certain sound that rings at a certain frequency should be called 'C'. Not only that, but we've also decided that a sound with a certain higher frequency should be called 'C#'. And beyond that, a certain frequency dictates the name 'D'. And so on, until we discover a new frequency that is higher than the original 'C', yet is fundamentally the same. And thus we get the 'Octave': a note that rings at a different frequency yet is fundamentally the same as a note lower down. And you can get multiple octaves, so that there is a range of dozens and dozens of notes that musicians can choose from. Even more fascinating, the fact that if you play two similar frequencies at the same time, they'll oscillate with each other until they're both made the same. In essence, the process of tuning up is the process of cancelling out oscillations between frequencies. And that sounds like something out of a science lab.
Except that music isn't a science, it's an art. As in, it's a manifestation of the artists desire to create. Which is completely against the idea of science. Science is about using logic and reason in order to learn more about the truth behind the universe. Whereas music is a personal creation that utilises emotion over reason, and seeks not to discover the truth, but to preach it as the artist sees it. It uses scientific principles to create something inherently un-scientific, which is a beautiful contradiction.
Which isn't the only contradiction either. Music is structured, it has form and 'rules' behind the theory... and yet it is fundamentally abstract. When you listen to a chord progression, there's no 'set' meaning that you're supposed to take away from it. You can apply lyrics to it, and therefore give it a literal meaning that the listener can take away, but without words music is simply an arrangement of sounds that we enjoy for their aesthetic value, and which can move us all in different ways. A highly structured art-form which nevertheless is abstract enough to allow different emotional reactions from different listeners.
Goddamn it, the more I (over)think about it, the more awesome music really is. OP, you need to get on that.