Linguistic communication takes place across multiple channels, including segmental information, prosody, co-speech gestures, and facial expressions. Often, each channel conveys its own unique information; however, channels are sometimes redundant with each other. In this talk, I present a series of collaborative studies seeking to quantify and characterize this redundancy and to explore its implications for linguistic and psycholinguistic theories. I focus on the redundancy between segmental information (operationalized as text) and various prosodic features, including pitch, duration, pause, energy, and a composite measure of prosodic prominence. The talk is divided into three parts. In the first part, we propose that redundancy between linguistic channels can be operationalized as their mutual information (MI), a measure from information theory that quantifies the amount of information one variable contains about another. I present a computational pipeline for estimating the MI between text and prosody, using large language models to capture the information carried in text. Applying the pipeline to an English audiobook corpus, we find significant redundancy for all prosodic features with both past and future textual information. In the second part, I extend this method to investigate linguistic typology by using these methods to provide a theory-neutral, principled way of estimating the degree to which a language is tonal. We predict that the mutual information between word identity and pitch should be higher in tonal languages, where lexical distinctions are made on pitch. We show that this is, indeed, the case, across ten languages from six different language families. In part three, I investigate the time scale of the prosody-text redundancy. In a corpus of English audiobooks, we show an asymmetric relationship, where prosody and past textual context display longer-scale informational overlap than prosody and future textual context. This suggests that prosody is more useful for recall, as opposed to prediction. I close by highlighting several limitations and future directions for this work. All research reported in this talk is collaborative, and conducted jointly with (but not limited to!) Alex Warstadt (UCSD), Tiago Pimentel (ETH Zürich), and Tamar Regev (MIT).