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Josef Matthias Hauer (19 March 1883 – 22 September 1959) was an Austrian composer and music theorist. He is most famous for developing, independent of and years before Arnold Schönberg, a method for composing with all 12 notes of the chromatic scale.

Hauer was born in Wiener Neustadt and died in Vienna. He had an early musical training which included zither, cello, choral conducting, and organ, but evidently did not include theory and composition, for he claimed that he was self-taught.

In 1918 he published his first work on music theory (a tone-color theory based on Goethe's), and in August 1919 devised his method for composing with twelve tones. Hauer's compositional techniques of composition are extraordinarily various and range from building-block techniques to methods using a chord series that is generated out of the twelve-tone row (["Melos"). In fact, his compositional techniques change almost from each piece to the next.

The so-called 44 "tropes" and their compositional usage ("trope-technique") are essential to Hauer's twelve-tone techniques. In contrast to a twelve-tone row that contains a fixed succession of twelve tones, a trope consists of two complementary hexachords in which there's no fixed tone sequence. The tropes are used for structural and intervallic views on the twelve-tone system. Every trope offers certain symmetries that can be used by the composer.

Hauer wrote prolifically, both music and prose describing his methods, until 1938, when his music was added by the Nazis to the "degenerate art" (Entartete Kunst) exhibit. Wisely keeping a low profile, he stayed in Austria through the war, publishing nothing; but even after the war he published little more, although he probably wrote several hundreds of pieces which remained in manuscript.

From the 1920s Hauer has been a model for literature several times, e.g. in Otto Stoessl's Die Sonnenmelodie, Franz Werfel's Verdi (Matthias Fischboeck). It has been found out that - besides Arnold Schönberg and Theodor W. Adorno - Hauer was also a model for Adrian Leverkühn in Thomas Mann's novel Doktor Faustus. Late in life Hauer spoke about Mann, as well as Theodor W. Adorno, with great bitterness, for he felt that both men had misunderstood him. Adorno had written about Hauer, but only disparagingly. Because of his later achievements and developments it has also been assumed by many scholars that Hauer is also a model for the "Joculator Basiliensis" in Hermann Hesse's Glass-bead Game.

All of Hauer's copious compositions after 1940 are named Zwölftonspiel or Zwölftonmusik (Twelve-tone game, or twelve-tone music.)

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