A new study by Japanese researchers concludes that listening to sad music may actually induce positive emotions.
Music that is perceived as sad actually induces romantic emotion as well as sad emotion. And people, regardless of their musical training, experience this ambivalent emotion to listen to the sad music.
Also, unlike sadness in daily life, sadness experienced through art actually feels pleasant, possibly because the latter does not pose an actual threat to our safety. This could help people to deal with their negative emotions in daily life.
Emotion experienced by music has no direct danger or harm unlike the emotion experienced in everyday life. Therefore, we can even enjoy unpleasant emotion such as sadness. If we suffer from unpleasant emotion evoked through daily life, sad music might be helpful to alleviate negative emotion.
Source: http://psychcentral.com/news/2013/07/12/sad-music-helps-us-deal-with-negative-emotions/57114.html