Barnett was the eldest son of a Prussian Jew named Bernhard Beer, who changed his surname on settling in England as a jeweller.
Barnett was born at Bedford, and at the age of eleven sang at the Lyceum Theatre stage in London.
His good voice led to his being given a musical education, and he soon began writing songs and lighter pieces for the stage.
Amongst his light music is a piece for Concertina and Piano called Spare Moments composed in 1859.
Although The Mountain Sylph is all but forgotten, it inspired parts of Gilbert and Sullivan's 1882 Savoy Opera, Iolanthe.