Here's a little bit:
Mario Attie-Picker, a philosopher at Loyola University Chicago who helped lead the research, found the results compelling. After considering the data, he proposed a relatively simple idea: Maybe we listen to music not for an emotional reaction — many subjects reported that sad music, albeit artistic, was not particularly enjoyable — but for the sense of connection to others. Applied to the paradox of sad music: Our love of the music is not a direct appreciation of sadness, it’s an appreciation of connection.
I was thinking it's because we can empathize with the artist. Life is not always fun or happy and we recognize what the artist is feeling. Also, we may not even notice the sadness, we just like the way the song sounds.