In response to the demise of the tonal system of composing music, musicians in the early twentieth century looked for new approaches to composing that would restore a sense of coherence to music. One such approach was devised by Arnold Schoenberg, who formulated what is now known as the serial composition system, or "twelve-tone" method.

As a natural consequence of the increasing chromaticism of the time, the previous system of "functional tonality" which gave music much of its sense of order began to lose its effectiveness. A diatonic set of seven pitches which defined a key became so diluted by chromaticism that tonality lost its meaning. A mathematical system for achieving a sense of order was needed; complete equality of all twelve chromatic pitches and the emancipation of dissonance were also important objectives of the new system.

Next Up: Pitch Classes

Project Manager:   V.S. Manoranjan, Chair, Math
Content: Charles Argersinger, Music
Programming:   CJ Kentler, Math

Washington State University
Department of Music
Department of Mathematics
Pullman, Wa. 99164