The Sonata for Two Pianos, eighteen in duration, is in the form of a large arch. The arch is constructed by relating the last movement to the second and first movements by borrowing material from these movements. The resulting form is a large ABA comprising the entire composition. The arch is superimposed over a more traditional formal concept of sonata. A sonata-allegro form is distinguishable in the first movement, a fantasia-variations in the second, and a modified sonata-allegro in the final movement.

The problem of this study was to determine the emphasis placed on various science teaching practices by a random sample of high school biology, chemistry, and physics teachers in selected Texas high schools. The subproblem was to compare the emphasis placed on the practices as reported by the high school teachers with the emphasis as recommended by national science education specialists, teachers of biology, chemistry, and physics in selected Texas colleges and universities, and teachers of professional education courses in selected Texas colleges and universities.

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.