Analyzing musical influence networks, such as those formed by artist influence or sampling, has provided valuable insights into contemporary Western music. Here, computational methods like centrality rankings help identify influential artists. However, little attention has been given to how influence changes over time. In this paper, we apply Bayesian Surprise to track the evolution of musical influence networks. Using two networks -- one of artist influence and another of covers, remixes, and samples -- our results reveal significant periods of change in network structure. Additionally, we demonstrate that Bayesian Surprise is a flexible framework for testing various hypotheses on network evolution with real-world data.