Analyzing and formalizing the intricate mechanisms of music is a very challenging goal for Artificial Intelligence. Dealing with real audio recordings requires the ability to handle both uncertainty and complex relational structure at multiple levels of representation. Until now, these two aspects have been generally treated separately, probability being the standard way to represent uncertainty in knowledge, while logical representation being the standard way to represent knowledge and complex relational information. Several approaches attempting a unification of logic and probability have recently been proposed. In particular, Markov logic networks (MLNs), which combine first-order logic and probabilistic graphical models, have attracted increasing attention in recent years in many domains. This paper introduces MLNs as a highly flexible and expressive formalism for the analysis of music that encompasses most of the commonly used probabilistic and logic-based models. We first review and discuss existing approaches for music analysis. We then introduce MLNs in the context of music signal processing by providing a deep understanding of how they specifically relate to traditional models, specifically hidden Markov models and conditional random fields. We then present a detailed application of MLNs for tonal harmony music analysis that illustrates the potential of this framework for music processing.