12-tone Technique
One of the most innovative developments in twentieth century music has been the technique for systematically ordering musical events, generally referred to as serialism. The first significant voice for this new approach to composition was the German composer Arnold Schönberg.

As this concept relates to pitch, Schönberg's principle orders all twelve pitches within an octave in such a way that no single pitch has dominance over another.  This is contrary to tonal music in which there exists a hierarchy of pitch significance.  Schönberg's 12-tone system was generally referred to as the atonal method of composition because of its lack of tonal center.

The ordering of pitches had very specific and strict procedures.  They are as follows:
1.  The row, or series, must contain all twelve pitch-classes of the chromatic scale in a specific and predetermined order with no repetitions of any one pitch-class.
2.  The permissible row forms include a row's original (prime) form, inversion, retrograde, and retrograde-inversion as well as the twelve transpositions of each. The total number of row forms (permutations) is forty-eight and can be represented concisely in a chart called a matrix.

3.  Strict atonal treatment of the row requires that:
     - no notes be doubled at the octave,
     - tonal melodic or harmonic elements (intervals) are to be avoided, and
     - no note should be sustained to the point where it becomes a focal pitch.
4.  In order to maintain uniformity of musical material one must make exclusive use of one row per composition.
The matrix is a concise representation of all 48 possible row permutations in a 12x12 grid. The four possible row forms are given by the four directions in which one can read the row notes off of the matrix for a given row.  (See the example below.)
Click here to download a blank matrix form.