I guess I'm unsure what differs a cover from a parody.
I only play piano and I can add some MIDI instruments on my computer. How would I do a parody in my case? A parody for me is basically changing the lyrics, but I wouldn't have any lyrics. Instead I would play the singer's melody on the piano, but I could change the melody as well. To me that is some sort of cover. Is it possible to make it a parody?
