English composer, theorist, and viola da gamba player. He fought on the Royalist side in the English Civil War (1643-44), and later was employed by Sir Robert Bolles. His tutoring of Sir Robert's son John (b. 1641) occasioned the writing of The Division-Violist (London, 1659; 2nd ed. 1665), praised by Jenkins, Coleman, and Locke; its practical approach to instruction is reflected in the titles of its three sections: "Of the Viol it self, with Instructions how to Play upon it," "Use of the Concords, or a Compendium of Descant," and "The Method of ordering Division to a Ground." About 1663 he bought an estate near Egton. Another of Simpson's pupils, Sir John St. Barbe, inspired The Principles of Practical Musick (London, 1665), which became the Compendium of Practical Musick (London, 1667). Simpson's instrumental works are all for viol, with or without other instruments, and vary in difficulty.