In that both 'I like music' and 'i like the music' are accepted as answers, could someone explain to me how one would go about differentiating the two in Greek? In English, they are vastly different sentences with vastly different meanings. How do I express 'I like music' (generally it is something i like) from 'I like the music' (that is currently playing) ?
This sentence is a bit tricky. To me, the difference could be much more visible if the pronoun αυτή wasn't omitted. Let's just say:
Μου αρέσει η μουσική (without another sentence following) - I like music (in general)
exp. Μου αρέσει η μουσική - I like music.
Μου αρέσει (αυτή) η μουσική (with another sentence following, usually with that as a conjunction between the two) - I like the/this music (A certain music.)
exp. Μου αρέσει (αυτή) η μουσική - I like this music. (when it's demonstrative, sometimes Greeks omit the pronoun.)
Μου αρέσει η μουσική που παίζεις - I like the music that you're playing.
That's why this sentence is a bit unclear. If there was another sentence, you could definitely tell that you could also use a the in there. I hope I helped a bit. ^.^