This paper argues that the relationship between lexical identity and prosody—one well-studied parameter of linguistic variation—can be characterized using information theory. We predict that languages that use prosody to make lexical distinctions should exhibit a higher mutual information between word identity and prosody, compared to languages that don’t. We test this hypothesis in the domain of pitch, which is used to make lexical distinctions in tonal languages, like Cantonese. We use a dataset of speakers reading sentences aloud in ten languages across five language families to estimate the mutual information between the text and their pitch curves. We find that, across languages, pitch curves display similar amounts of entropy. However, these curves are easier to predict given their associated text in the tonal languages, compared to pitch- and stress-accent languages, and thus the mutual information is higher in these languages, supporting our hypothesis. Our results support perspectives that view linguistic typology as gradient, rather than categorical.