Twelve Tone Technique

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Twelve-tone technique is a method of composition that utilizes variations of tone rows manipulated by mathematical calculations to create a piece of music. The tone row is simply a string of twelve notes, organized however the composer wishes. Strict twelve-tone technique, as it was first devised, requires the composer to use all twelve notes of the chromatic scale, without repetition of any note. The notes are numbered by using the corresponding number of half-steps from the reference tone (the first note in the tone row). These numbers are called the pitch classes. Strict technique allows the composer to make only a few changes to this main tone row. The composer is allowed to invert the row, write it in retrograde (backwards), or put it through an interesting mathematical equation, similar to an algebraic matrix. The basic matrix is organized in this way: the names and numbers of the notes of the first tone row are written in the first row of the 12 by 12 matrix. The composer then takes the numbers in the first row, subtracts each number from twelve, and writes the resulting pitch classes and their corresponding note names in the first column. He continues in this manner until the matrix is filled.

Let us say that the first three notes (and their pitch classes) in the composer's tone row are E (0), A (5), and D sharp (11), with E being the reference tone. The first tone is already written, so the composer goes on to the second tone, A. He subtracts five from twelve, the result of which is seven. The corresponding tone is B, so B (7) is written in the second row of the first column. He continues in this way with the next ten tones. These notes determine the starting tones of the new tone rows. The composer then adds the pitch class of the first note in the second row to each of the pitch classes in the original tone row, subtracting twelve if the sum is equal to or greater than twelve. Going back to our example, the composer would add seven (the pitch class of B) to five (the pitch class of A), which equals twelve, and subtract that from twelve, leaving zero. This corresponds to the reference tone, E. The composer would write E (0) in the second row of the second column and continue on to the next tone, D sharp. The composer would go on in this way until he has completed the matrix. If he has done his mathematics correctly, the tones in the diagonal from the top left to the bottom right should be only the reference tone. The new tone rows the composer discovers in the matrix are then organized in any fashion, and the composer is left with what is generally an atonal melody. At times, distinct tonality will be noticed.

Twelve-tone technique was invented by the Austrian-American composer Arnold Schönberg in the early 1900’s. Schönberg began his career in composing conservatively enough; one of his first compositions, in 1899, was Verklärte Nacht (Transfigured Night) for string orchestra. Schönberg began a new type of composition technique in the early 1900’s. He later described why he desired a new technique when he wrote, “Composition…is above all the art of inventing a musical idea and the fitting way to present it.”(1) Schönberg’s search for ‘the fitting way to present’ his musical ideas led him to create twelve-tone technique during World War I, and he began writing music using the technique in 1922.

Schönberg's first piece for orchestra using twelve-tone technique was his Variations for Orchestra, Op. 31, written in 1926. Schönberg and the few composers he taught, such as Alban Berg and Anton Webern, were at this time the only composers using the twelve-tone technique, and critics and audiences alike were hostile to this new music. But composers had begun to tire of the well-used Romantic styles, and deciding that tonality was an exhausted realm of composition, they slowly ventured into atonality and twelve-tone technique. Most composers did not like to use strict twelve-tone technique - even Schönberg broke many of his own rules. Composers tried starting a new tone row in the music before finishing the first one, and multiplying the matrices for more tone rows. They also changed the technique to control such variables as rhythm and dynamics. Soon, twelve-tone technique evolved into a new composition method called serial music. People are of differing opinions regarding the musicality of twelve-tone music. For some, twelve-tone music and other atonal pieces are peerless in music history, while many others are irked when they cannot detect any obvious melody. The latter complain that true music is not written merely from mathematical formulas. But Schönberg was aiming at beauty, not mathematical noise. Speaking on twelve-tone music, he said, "Form in the arts, and especially in music, aims primarily at comprehensibility. The relaxation which a satisfied listener experiences when he can follow an idea, its development, and the reasons for such development is closely related…to a feeling of beauty."(2) Schönberg believed that the beauty of the mathematics only enhanced twelve-tone music. Nevertheless, the question of the true beauty of twelve-tone technique will probably always remain a controversial subject.


Arnold Schoenberg Center. <> (accessed October 15, 2004). Brand, Juliane. Constructive Dissonance: Arnold Schoenberg and the Transformations of Twentieth-century Culture. Berkeley University of California Press, 1997. Frisch, Walter. The Early Works of Arnold Schoenberg, 1893-1908. Berkeley University of California Press, 1997. Oglethorpe University. <> (accessed October 15, 2004).

(1)Schoenberg, "Zur Frage des modernen Kompositionsunterrichtes," Deutsche Tonkünstler-Zeitung (5 November 1929); translated as "On the Question of Modern Composition Teaching" (1929), in Style and Idea, pg. 373-376, esp. pg. 374. (2)Schoenberg, "Composition with Twelve Tones (1)," pg. 251