Serialism

Brief History and Overview of The Serialization of Music

Alex Stackhouse

Serialism, when referred to in music is a compositional technique in which all or some aspects of the music are determined using numerical patterns.  This process is referred to as “serialization”.  The process developed post-WWII from the 12-tone chromatic music of Arnold Schoenberg and the second Viennese school, especially his students Anton Webern and Alban Berg.  These three composers represent a cross-section of serialism as a whole, from the works of Weberm, who adhered vehemently to the tenets of serialism, to that of Alban Berg, who regarded the rules more loosely, incorporating elements of romanticism into his serial work.  Schoenberg’s serial compositions represent a sort of happy medium between the polarized views of Webern and Berg.

Serialism began with the serialization of pitch in modernist music, and grew outwardly.  The pitch patterns are based on numerical patterns which determine tone rows.  The basic tone row consists of the numbers 0-11, each number representing a different pitch, with 1 being C and 11 being B.  This basic tone row beginning on C is known as P0, or Prime row 0, because it begins on C, which is represented by the number 0, and the row is a prime row.  A prime row is a row that shares the same intervallic relationships between pitches as the original tone row.  In the basic row each pitch is used only once.  Although repetition of pitches is allowed in succession, once the composer leaves a pitch it may not be used again until each other pitch in the tone row is used in order of the row.

The basic tone row may undergo several transformations to provide variations on pitch order throughout a composition.  The most basic transformation is the transposition.  In a transposed tone row the intervallic relationship between the pitches remains the same, but the row is “moved” so that it begins on a different pitch.  For instance, if the first 2 pitches in the basic tone row (P0) were C and D, and the row was transposed up a half step, the first two pitches of the transposed row (P1) would be C#/Db and D#/Eb.

The next transformation the tone row may undergo is called a retrograde transformation.  In this transformation a prime tone row is played backwards.  In a prime tone row beginning on C, the retrograde transformation would be called R0, because the transformed row is a retrograde row whose prime row begins on C.

The third transformation is called the inversion.  In an inverted tone row, the intervallic relationships between pitches in the prime row are reversed, or “inverted”.  For example, if the interval between the first two pitches of P0 was a minor third (such as C-Eb), in the inverted row, known as I0, the interval between the first two pitches would be a major sixth (C-A).

The final and most complex transformation is the retrograde-inversion, abbreviated as RI.  In this transformation the prime row is played backwards and inverted.  The row is reversed as in a retrograde transformation, and the intervallic relationships between pitches is inverted as in an inverted tone row.

It is possible to see every possible derivation of a basic tone row in a matrix that is generated by the composer to use as a reference for quickly employing the various transformations of the basic tone row.  When reading the matrix left-to-right you are reading a prime tone row, or a transposition of the basic row.  Right-to-left is the retrograde transformation of each of these prime rows.  Reading the matrix top-to-bottom gives inverted tone rows, and reading bottom-to-top gives you rows that have undergone transposition and retrograde inversion.  For modern composers there are several effective matrix generators located on various music theory sites that will generate a complete, printable matrix when fed a basic tone row.

As more and more composers began experimenting with serialized pitch, some composers seeking to further serialize their compositions began to experiment with the serialization of other aspects of music, such as instrumentation, dynamics, and tempo using the same numerical rows from the matrices used to generate pitch.  The serialization of many or all aspects of a composition became known as “total serialism”.

Serialism has been highly influential on experimental composers in the 20^th century.  From Arnold Schoenberg to Igor Stravinsky to John Cage to Pierre Boulez, many of the most popular and successful modernist composers have experimented with the technique, some even devoting their careers to serial compositions.  Although widespread use of serialism has diminished, it remains a huge milestone in the history of music and art.