I don't know much about 5e and only know D&D from other CRPGs using 3rd edition rules. So I looked up harpies:
https://roll20.net/compendium/dnd5e/Harpy#contentThe monster description doesn't say that Silence can stop the song. Harpies could be sui generis, not spellcasters as such, although it has a spell-like effect.
At any rate, I don't think Silence should work on them because that encounter, even at a lower level, just isn't that difficult. The song lure just forces your party member to get closer to the harpy if they fail the save roll, and that's not a bad thing unless it's your squishy mage.