Story generation (including interactive narrative) consists in creating a narrative experience on computer by generating narrative events. It requires building an abstract computational model that can generate a variety of narrative events from a limited set of authored content. These models implement a "story logic", as they formalize the occurrence of an event in the story according to various algorithms. At the same time, these stories aim to be expressed to an audience using digital media, which requires a "media logic". However, it is not quite clear how the logical constraints in a theory of story should impact the media representation. Reciprocally, how media constraints influence the story logic remains overlooked. As a result, projects which aim at providing a generative and appealing experience adopt a simple "pipeline" approach where the story is sent as a series of events to the media logic, and each event is separately translated to the digital media at hand. This has the advantage of simplicity but it raises two issues: - The media logic possesses limited information from the story logic and performs an "uninformed" flat representation of story events. - The story logic generates story events without fully exploiting the strengths of the available media. In this contribution, a theory describing the interrelation between story and media is sketched. After reviewing the contrasting positions concerning the media (in)dependance in narrative theories, core principles are exposed. They consider narrative as a dynamic generative process composed of a series of independent voices that negotiate with each other to fulfill their respective goals. The creation of story events, the introduction of a plot, the visual narration, the audio narration, etc. are example of voices and sub-voices. We illustrate our theory with examples drawn from our own computer-generated stories in different digital media.