Robust and flexible event representations are important to many core areas in language understanding. Scripts were proposed early on as a way of representing sequences of events for such understanding, and has recently attracted renewed attention. However, obtaining effective representations for modeling script-like event sequences is challenging. It requires representations that can capture event-level and scenario-level semantics. We propose a new tensor-based composition method for creating event representations. The method captures more subtle semantic interactions between an event and its entities and yields representations that are effective at multiple event-related tasks. With the continuous representations, we also devise a simple schema generation method which produces better schemas compared to a prior discrete representation based method. Our analysis shows that the tensors capture distinct usages of a predicate even when there are only subtle differences in their surface realizations.