If you think YOUR neighbour has a problem, I highly recommend watching
The 4th Floor.
I suppose I'm luck because my nearest neigbour is about 1/2 mile away.
I do remember moving into a new flat once though and the people downstairs had a dog (prohibited in the building!) which would bark almost non-stop
when they went out. We had a hard time convincing them we were telling the truth until we invited them for a drink one evening with us upstairs. They
were very embaressed and the dog was rehoused elsewhere.
Maybe the really social approach would work. Be overly nice and friendly until she would feel rude complaining. Get her loaded on Gin

and play
her some of your "sweet" tunes until the bottle is empty.
She probably just needs a hug!