c. 1400, "A wind instrument made of wood and provided with six finger holes" [Middle English Dictionary], from Old French cornet (14c.) "a small horn," diminutive of corn "a horn," from Latin cornu "horn of an animal," also "a bugle horn," from PIE root *ker- (1) "horn; head."
Modern use in reference to a brass instrument with valves is short for cornet-à-pistons "cornet with pistons" (1836, from French).
The quality of the tone is penetrating and unsympathetic, by no means equal to that of the trumpet, for which it is commonly substituted. [Century Dictionary, 1897]