The primary characteristic of a siren in Greek mythology is their enchanting singing. Sirens are often depicted as alluring creatures, usually with the upper body of a woman and the lower body of a bird, who lured sailors to their doom with their beautiful voices. This captivating music would entice sailors to steer their ships toward treacherous reefs, leading to shipwrecks. The sirens symbolize danger disguised as beauty, representing the perilous nature of temptation and the struggle between desire and caution in mythological narratives.