State-of-the-art spoken dialogue models (Défossez et al. 2024; Schalkwyk et al. 2025) use neural audio codecs to "tokenize" audio signals into a lower-frequency stream of vectorial latent representations, each quantized using a hierarchy of vector codebooks. A transformer layer allows these representations to reflect some time- and context-dependent patterns. We train probes on labeled audio data from Cole et al. (2023) to test whether the pitch trajectories that characterize English phrase-final (nuclear) intonational tunes are among these patterns. Results: Linear probes trained on the unquantized latents or some of the associated codewords yield above-chance accuracy in distinguishing eight phonologically specified nuclear tunes with monotonal pitch accents (top average test accuracy (TATA): 0.31) and the five clusters of these tunes that are robust in human speech production and perception (TATA: 0.45). Greater accuracy (TATAs: 0.74-0.89) is attained for binary distinctions between classes of rising vs. falling tunes, respectively used for questions and assertions. Information about tunes is spread among all codebooks, which calls into question a distinction between 'semantic' and 'acoustic' codebooks found in the literature. Accuracies improve with nonlinear probes, but discrimination among the five clusters remains far from human performance, suggesting a fundamental limitation of current codecs.