Interactional approaches to prosody have seen an enormous growth in the last decades. One crucial assumption common to these approaches is that prosodic devices may serve as resources for structuring and organizing an interaction. Methodologically, interactionally informed research of prosody rests upon ethnomethodological conversation analysis and contextualization theory. In this paper, a case study of the Cologne German rising-falling intonation contour serves to illuminate the prevalent methods in the field. The results are discussed with respect to their implications for basic theoretical assumptions about prosody and intonation. Consistent with core assumptions of Interactional Linguistics, they point to the variable and gradient nature of intonational functions that can best be captured in a grammar model that allows for holistic descriptions of linguistic structures.