There's an interesting discussion of the symbolism of music on the following page:

http://www.enotes.com/where-are/q-and-a/discuss-symbolic-importance-music-story-17105

In addition to this important symbol, I think there is another set of symbols that makes it clear how much of an imposter Arnold Friend is. Whether he is a satanic figure or just an older predatory man (the story has been read both ways by critics), there are several things that make it clear that things are not as they seem. His car is "a convertible jalopy painted gold," his crazy hair looks like a wig, he is dressed like a rock star, but at the same time he moves carefully and stands "in a strange way," as if his boots do not fit him. Oates tells us that "his feet [do] not go all the way down" in his boots," suggesting that perhaps Arnold may not have human feet, but wobbly hooves instead. He "pretend[s] to be relaxed," he looks like he has makeup on his eyelashes, and he has a face of a "forty-year-old baby." He does not speak in a normal voice, but rather with "the voice of the man on the radio" and in meaningless cliches with a "stage voice." He is not a person, only a disguise.

The disguise works, however. Connie, a sexually experienced girl who has given her body away plenty of times, allows Arnold to take over her mind as well.