Music and language are often so intertwined that it seems strange that Tolkien never devised alternate musical systems (at least to my knowledge) for the various races and peoples of Middle Earth. Especially considering how many songs he himself wrote for Middle Earth.
If different groups of people had different languages and different scripts, surely their systems of musical notation would be different as well. What does Elvish music notation look like?
Additionally their means of making music would be different, but across Middle Earth the same types of instruments, which are heavily inspired by if not completely borrowed from our own world, are used.