In this paper I intend to provide a more precise pragmatic foundation (based on Sperber and Wilson's relevance theory) for a number of fairly recent linguistic accounts of how tone movement can be used by a communicator to express a certain pragmatic meaning, viz. that related to the speaker's manipulation of her message with regard to the addressee's background. Thus rephrasing the theory of discourse intonation in terms of a pragmatic framework will yield two important insights: not only tonicity but also tone may be said to contribute to the correct interpretation of the focus of a message, i.e. both may have a cognitive function, and secondly, tones themselves may be said to be responsible for utterances entailing contextual effects. In a second part, I attempt to give this cognitive function a place within a summarizing account of all pragmatic meanings conveyed by tone. Five broad domains of meaning are distinguished and integrated within Lindsey's continuum scale, which represents some universal relations between tonal structure and meaning. The modified scheme by no means simple but it may reflect the complexity of the listener's interpreting task more accurately: he does not merely have to translate a set of symbols (tones) into meanings, but he will also have to invoke inferential procedures which obey the principle of relevance.