Transpositional Combination of Beat-Class Sets in Steve Reich's Phase-Shifting Music

IN 1968 STEVE REICH WROTE "Music as a Gradual Process," an essay inspired by his work with the compositional technique of phaseshifting.' Reacting against both aleatoric and serial composers, who use "hidden structural devices" to disconnect "the compositional process" from "the sounding music," Reich implied that in his phase-shifting music he had discovered a way to enable musical processes to be perceived "throughout the sounding music," and thus to have achieved "a compositional process and a sounding music that are one and the same thing."2 He showed a draft of his essay-in-progress to James Tenney, who pointed out an important implication: "then the composer isn't privy to anything." Reich concurred, concluding that "I don't know any secrets of structure that you can't hear."3 Such a conclusion hardly encourages analysis. If there is nothing in the bones that is not in the skin, analysts may as well leave their surgical