English is not my mother tongue. I once came across information that listening to music and listening to the music mean something different. Listening to the music would mean you put whole heart into it, which can be evident by dance, other similar behaviour like improvised accompaniment or changes in face expression. Is this true?
The only difference is the definite article ('the') which means the second sentence refers to some specific music.
For example, as you put your iPod headphones on you might say "I am going to listen to music", meaning no particular music.
If you were in a park, and hear a band playing in the distance you might say "I am going to listen to the music", meaning that specific music you can hear now.
Neither of them is necessarily accompanied by dancing or changes in expression.