 Greatorex did much to advance the standard of sacred music in the United States in the days when country singing-school teachers imposed their trivial melodies and the convivial measures of foreign composers on the texts of the hymn books at hand.He published a "Collection of Psalm and Hymn Tunes, Chants, Anthems, and Sentences" (Boston, 1851).One of Greatorex's best-known compositions is a setting of the Gloria Patri, widely used in Protestant denominations for the singing of the doxology in services to this day.