I think the insights and interpretations of bar1scorpio, Crocodilian, and jiBeckett are all pretty compatible. I really like Crocodilian's classing of this as a "dream story," and it makes the "shaggy dog" ending a little more palatable. So, our narrator crosses over to this "dream street," where Erich Zann is desperately trying to cancel out the sound of this intelligent "Music Out of Space," and our narrator never figures out how the story ends because he's come out of the "dream" and can't access that world again.
I'll even add my own twist on the ending: the street wasn't destroyed, or erased, or anything like that. Maybe the Sentient Hyper-Music From Beyond wanted
our narrator gone, because he didn't belong there. Maybe it was trying to close the door between its world and the real world, and Erich Zann was battling it to keep that door open. When the music wins(?) the final battle, it drives our narrator out, and closes the door so that no more pesky outsiders can intrude on its business.
...Not that I think HPL had any of this in mind. I don't think he knew any better than we do what was going on in the Rue D'Auseil (or however you spell it). I think he really just wanted to build up a bizarre event, dangle an illusory explanation in front of the reader, and then make us watch him throw it away. The fact that we get no hint at all of what's really going on makes me think he didn't have anything particularly in mind. This has the delightful side-effect of making all possible interpretations valid.