in the Hobbit we are told that the elves learned their greatest magics in the West
"For most of them [Wood-elves] (together with their
scattered relations in the hills and mountains) were
descended from the ancient tribes that never
went to Faerie in the West. There the Light-
elves and the Deep-elves and the Sea-elves
went and lived for ages, and grew fairer and
wiser and more learned,
and invented their
magic and their cunning craft in the making of
beautiful and marvellous things, before some
came back into the Wide World."
Just because one source said they invented their magic in the West doesn't necessarily mean we need to use the music of Faerie, though. It was just a thought.