Drawing on research by, among others, Monika Fludernik, Marie-Laure Ryan, and previous publications by the author, the present article outlines the foundations of a transmedial narratology that draws on intermediality theory, frame theory, and prototype semantics. These foundations permit the simultaneous conceptualization of narrative as a semiotic macro-mode and as a cognitive frame which enables recipients to classify given artifacts (texts, performances, etc.) as more or less narrative in accordance with the extent to which "narremes" as features of prototypical narratives can be recognized. This approach is illustrated with examples taken from three media: literary fiction, the visual arts, and instrumental music. The comparison of the different narrative potentials of these media leads to some general reflections on both the recipient's and the artifact's share in narrativization (the artifact and the medium it belongs to can be strongly narrative, more or less narrativity-inducing, or non-narrative), moreover on constitutive elements of a media-conscious narratology, and a typology of medial realization of narrativity based on transmission modes. In conclusion, benefits and problems of transmedial narratology are adumbrated.