“The aim of this study was to provide a better understanding of why people engage with sad music,” said Liila Taruffi and Stephan Koelsch, creators of the survey.

Discussing the results, the authors said that, surprisingly, “nostalgia rather than sadness is the most frequent emotion evoked by sad music. Correspondingly, memory was rated as the most important principle through which sadness is evoked. Finally, the trait empathy contributes to the evocation of sadness via contagion, appraisal, and by engaging social functions. The present findings indicate that emotional responses to sad music are multifaceted, are modulated by empathy, and are linked with a multidimensional experience of pleasure revealing that listening to sad music can lead to beneficial emotional effects such as regulation of negative emotion and mood as well as consolation. Such beneficial emotional effects constitute the prime motivations for engaging with sad music in everyday life.”
http://medicalxpress.com/news/2014-11-sad-music-positive-emotional-rewards.html