The evolutionary origins of music are much debated. One theory holds that the ability to produce complex musical sounds might reflect qualities that are relevant in mate choice contexts and hence, that music is functionally analogous to the sexually-selected acoustic displays of some animals. If so, women may be expected to show heightened preferences for more complex music when they are most fertile. Here, we used computer-generated musical pieces and ovulation predictor kits to test this hypothesis. Our results indicate that women prefer more complex music in general; however, we found no evidence that their preference for more complex music increased around ovulation. Consequently, our findings are not consistent with the hypothesis that a heightened preference/bias in women for more complex music around ovulation could have played a role in the evolution of music. We go on to suggest future studies that could further investigate whether sexual selection played a role in the evolution of this universal aspect of human culture.