This thesis centers around a certain twentieth-century compositionaI device, the method of composition with twelve tones. There are many terms to designate this device, for example: "basic set," "tone-row," "note-series," "serialism," "serial technique," "twelve-note series," "twelve-tone technique" or "twelve-tone method." TI is thesis is a methodical research demonstrating the contemporary conventional way of scientifically and artfully manipulating twelve equal tempered degrees of the chromatic scale to produce a desirable system. In order to arrive at any substantial conclusions, it is necessary to make a critical examination and evaluation of known twelve-tone compositional procedures from as many angles as possible, so as virtually to exhaust every practical and speculative potentiality included in the technique, that is, within the range and limits of our present needs. This examination and evaluation will also involve a comparative investigation of various uses of the device, in order to produce and suggest ideas for further theoretical insights. The ultimate purpose of this thesis is to pinpoint the "hows" and "whys" of Rochberg's use of the twelve equal tones in Sonata-Fantasia.