The paradox of enjoying listening to music that evokes sadness is yet to be fully understood. Unlike prior studies that have explored potential explanations related to lyrics, memories, and mood regulation, we investigated the types of emotions induced by unfamiliar, instrumental sad music, and whether these responses are consistently associated with certain individual difference variables. One hundred and two participants were drawn from a representative sample to minimize self-selection bias. The results suggest that the emotional responses induced by unfamiliar sad music could be characterized in terms of three underlying factors: Relaxing sadness, Moving sadness, and Nervous sadness. Relaxing sadness was characterized by felt and perceived peacefulness and positive valence. Moving sadness captured an intense experience that involved feelings of sadness and being moved. Nervous sadness was associated with felt anxiety, perceived scariness and negative valence. These interpretations were supported by indirect measures of felt emotion. Experiences of Moving sadness were strongly associated with high trait empathy and emotional contagion, but not with other previously suggested traits such as absorption or nostalgia-proneness. Relaxing sadness and Nervous sadness were not significantly predicted by any of the individual difference variables. The findings are interpreted within a theoretical framework of embodied emotions.