In 1571 and 1581, the Ferrarese cleric-musician Don Lodovico Agostini published two books each containing, amongst other pieces, a group of madrigals cryptically notated as musical puzzles, advertised as enigmi musicali on their title pages. The enigmi are aptly named; no doubt the composer would have delighted in the doppio senso, or double entendre, inherent in the term, for they are musical riddles in both a formal and a metaphorical sense. Their content and their very existence in print pose an intriguing array of questions beyond the obvious enquiries regarding the identifying characteristics of the genre and the identity of their composer. Certainly, the enigmi musicali invite speculation about the nature of music as a pastime in late sixteenth-century courtly Italy. Agostini's enigmi musicali are secular, polyphonic vocal works, but they cannot be classed simply as madrigals, nor are they representative of so-called lighter genres of villanelle or canzonette. They exist somewhere on the fringe of the repertoire, with a specific character that reaches in towards the (to us) more familiar forms of Italian secular music, but that also reaches out to and overlaps with other spheres of play and philosophical engagement. So where may the enigmi be placed within the wider compass of early modern social recreation, and what factors might have motivated their composition and their use? Furthermore, if we accept them as evidence of some sort of collective diversion, how are they intended to amuse – are they humorous or cerebral, or both?