"That sounds like fireworks?"
Indeed it was.
Turns out the end of the 2016 Edinburgh International Festival was being celebrated with a Virgin Money Fireworks Concert on Calton Hill...which is right up the hill from our flat. This was our view. We got to see the whole thing. The ball of light on the left side of 'our tree' is the moon. The ball of light on the right is the fireworks show getting going.