Complex sentence: He may have been preceded in his use of neoclassical devices by composers such as Prokofiev and Erik Satie; by the late 1920s and 1930s, the use by composers of neoclassicism had become widespread.
Split into simpler sentences: He may have been preceded in his use of neoclassical devices by composers such as Prokofiev and Erik Satie. By the late 1920s and 1930s, the use by composers of neoclassicism had become widespread.