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The University High School Band
The History and Theory of Music

Serialism

Serialism

One of the most significant developments in music theory during the Twentieth Century was the "Second Viennese School," spearheaded by German composer Arnold Schönberg. He developed a technique called serialism, which kept music devoid of tonality by using all twelve tones of the chromatic scale equally.

This unnatural equality was produced using a tone matrix.

A tone matrix is a 12 x 12 grid. Each row or column of the grid is called a series, hence the name of the system. There are four steps to filling out the matrix.

One begins a tone matrix by randomly (or not) lining up all twelve tones of the chromatic scale and putting them on the top line of a grid. This is called the prime series, or P0.
Then, down the left column, the tone row is written using the same intervals, but upside-down. This is called the inverse series, or I0.
Next, the tone row is transposed, so that the intervals remain the same, onto the second line. Since this is a transposition of the prime series, it is notated by a "P" and the number of semitones in the transposition: in this case, P6.
This process continues to fill out the entire matrix.

When composing in a serialist manner, a composer must use a full series before he or she is allowed to repeat a note. There are forty-eight possible series: