This tool assists in the creation and manipulation of a twelve-tone matrix, a structure fundamental to composition using the twelve-tone technique (also known as dodecaphony). The matrix systematically presents all possible permutations of a chosen tone row, including its inversions, retrogrades, and retrograde inversions. For example, if a composer begins with the tone row C-C#-D-Eb-E-F-F#-G-Ab-A-Bb-B, the corresponding matrix will display all its transformations, offering a structured source for melodic and harmonic material.
The significance of this aid lies in its ability to streamline the compositional process by organizing the complete set of row forms derived from the prime row. This facilitates efficient access to pitch relationships and ensures adherence to the principles of serialism. Historically, the twelve-tone technique, developed by Arnold Schoenberg, aimed to create atonal music by giving equal importance to all twelve tones of the chromatic scale, thereby avoiding tonal centers. The matrix allows composers to readily explore the intervallic and melodic possibilities inherent within their chosen tone row, ensuring consistency and structural coherence in atonal compositions.
