In this paper, we propose an algebraic framework for organizing interactive musical systems in temporal space in a way that helps in their design. The objective is to structure this space in order to be able to represent the existing and to open the exploration of new configurations that could inspire new musical practices. To do so, we propose some properties of interactive music systems allowing to compare them in a temporal lattice. This framework should be extended to the other musical dimensions and give rise to optimizations of musical systems according to the desired performative properties.