We argue that electronic dance music (EDM) exhibits a parallel structural organization to that which has been proposed for cartoons (comics) after the model of hierarchical structure proposed in theoretical linguistics. According to this parallel, both systems are governed by general cognitive mechanisms for the narrative organization of tension and release, which are not modality-specific. We show that notions from visual narrative analysis, such as an Establisher–Initial–Peak–Release template, can be applied directly to EDM tracks as an Intro/Breakdown–Buildup–Core–Outro/Cut template. In doing so, we focus on how to formally define and operationalize relevant notions such as Breakdown, Buildup, and Core. As part of our analysis, we show that the scene-setting Establisher segments of visual narratives map onto two distinct categories in EDM: they correspond to intro sections at the beginning of a track and to breakdown sections in the middle of a track; we strengthen the analogy to visual narrative analysis by introducing refinements such as a pre-drop break that often occurs at the end of a buildup segment. To adjudicate between competing hypotheses on the hierarchical structure of a given EDM track, we demonstrate that analytical tests from linguistics and visual narrative analysis can be successfully applied. By introducing these analytical tools, this article sets the stage for further explorations in the linguistically informed analysis of the structure and meaning of EDM.