Popular music offers a rich source of data that provides insights into long-term cultural evolutionary dynamics. One major trend in popular music, as well as other cultural products such as literary fiction, is an increase over time in negatively valenced emotional content, and a decrease in positively valenced emotional content. Here we use two large datasets containing lyrics from n=4,913 and n=159,015 pop songs respectively and spanning 1965-2015, to test whether cultural transmission biases derived from the cultural evolution literature can explain this trend towards emotional negativity. We find some evidence of content bias (negative lyrics do better in the charts), prestige bias (best-selling artists are copied) and success bias (best-selling songs are copied) in the proliferation of negative lyrics. However, the effects of prestige and success bias largely disappear when unbiased transmission is included in the models, which assumes that the occurrence of negative lyrics is predicted by their past frequency. We conclude that the proliferation of negative song lyrics may be explained partly by content bias, and partly by undirected, unbiased cultural transmission.