Q.E.D. for piano, violin, and cello
Q.E.D. is a composition for piano, violin, and cello that was composed between August of 2011 and October of 2012. It is unified through the use of various transformations of a principal motive, which is presented by the violin in the first two measures of the piece. This motive was created to provide variety in rhythm and melody. The rhythmic content is generated from fragments inherent in the principal motive, with many rhythmic events being projected in triple and quintuple groupings. Pitch and interval content used throughout the piece also borrows fragments from the principal motive. This primary motive reappears throughout the piece to initiate or conclude important structural regions. However, material that is not part of a complete statement of the motive still consists largely of fragments from the motive. The transformations of the principal motive provide a variety of moods and styles in both tonal and atonal contexts. For instance the principal motive includes scale degrees 1, 2, 3, 5, 6§, 6#, and 7# in the key of E minor. The counterpoint and harmony supporting this motive can either exploit these tonal tendencies or avoid them. The changes in style and aesthetic roughly divide the piece into three main parts: (1) a frenetic opening, (2) a slow and tranquil middle section, and (3) an explosive ending that returns to the faster tempo of the opening. Though each section includes the motive in various guises, the middle section does not contain any explicit statements of the motive, thus creating a contrast to the outer sections. The return of the motive is used to mark the beginning of the final section. The title of the piece is "Q.E.D." ("quod erat demonstrandum" or "which was to be demonstrated"). This initialism is commonly used in mathematics and philosophy to signal the completion of a proof or argument. This title serves as an emblem of my compositional endeavors and completion of my graduate studies at the Master's level.