One of the questions with which the emperor Tiberius notoriously plagued his scholarly companions on Capri was Quid Sirenes cantare sint solitae, ‘What did the Sirens usually sing?1 Like the other such questions he asked (Who was Hecuba’s mother? What name did Achilles take when he was draft-dodging on Scyros?) the form and content of the Sirens’ song were clearly things that investigation of extant Greek literature left obscure: the grammatici in Tiberius’ entourage were baffled despite, presumably, access to the libraries of Rome and, through their personal connections, Athens, Pergamum and Alexandria. ‘The song the sirens sang’ is thus an appropriate constituent of the title of an investigation into Alcman’s Louvre Partheneion: for it too has continued to baffle modern grammatici since its discovery in 1855 and its first publication in 1863. I would be combining the foolhardiness of Odysseus with the insensitivity of Tiberius if I pretended to have privileged access to this particular Sirens’ song. But in many years of discussing the poem with pupils and colleagues I have formed some views on the limits within which our interpretations should be confined, and risking these views in print is long overdue. Nor is the title’s reference to the Sirens’ song simply a meretricious attempt to sugar a scholarly pill: its presence there is not merely a symbol, but (as I hope to show) the nature of the song the Sirens sang has a particular relevance to Alcman’s Partheneion.