major-general (n.)

military rank above captain and below lieutenant colonel, 1640s, from French major, short for sergent-major, originally a higher rank than at present, from Medieval Latin major "chief officer, magnate, superior person," from Latin maior "an elder, adult," noun use of the adjective (see major (adj.)).

His chief duties consist in superintending the exercises of his regiment or battalion, and in putting in execution the commands of his superior officer. His ordinary position in the line is behind the left wing. [Century Dictionary, 1897]

The musical sense is attested by 1797.

late 14c., "whole class of things or persons, a broad classification, a general truth," from general (adj.). Meaning "commander of an army" is 1570s, shortening of captain general, from French capitaine général. The English adjective was affixed to civic officer designations by late 14c. to indicate superior rank and extended jurisdiction.