to enchant or tempt someone using siren-like qualities, or to lure someone with an irresistible appeal.
From be- (prefix) + siren (from Greek seirēn, the mythological sea creatures whose singing lured sailors). The verb form emerged to mean enchanting someone the way sirens enchanted sailors in Homer's Odyssey.
Sirens weren't originally mermaids—ancient Greek sirens were bird-women, not fish-women! The fish-tail version came from medieval artists misreading descriptions, and now that's what everyone imagines.
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