The speech-to-song illusion is a robust psychological phenomenon whereby a spoken sentence sounds increasingly more musical as it is repeated. Despite decades of research, a complete formal account of this transformation is still lacking, and some of its nuanced characteristics, namely, that certain phrases appear to transform while others do not, is not well understood. Here we provide a formal account of this phenomenon, by recasting it as a statistical inference whereby a rational agent attempts to decide whether a sequence of utterances is more likely to have been produced in a song or speech. Using this approach and analyzing song and speech corpora, we further introduce a novel prose-to-lyrics illusion that is purely text-based. In this illusion, simply duplicating written sentences makes them appear more like song lyrics. We provide robust evidence for this new illusion in both human participants and large language models.