The interaction between tones in a corpus is analyzed using conditional probability and mutual information, and a probabilistic model of intonation in American English is presented. The last pitch accent in the final intermediate phrase is found to be a strong predictor of boundary tone; this is modeled as a second order Markov process. The implications of these results for the compositional theory of intonational meaning of Pierrehumbert and Hirschberg (1990) are discussed. The conclusion is reached that the tones in a tune are interrelated in a way that a model that assigns separate meaning to each tone cannot capture.