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Does Josef Matthias Hauer's 1919 twelve-tone method predate and diminish Arnold Schoenberg's credited invention of the technique?

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Austrian composer Josef Matthias Hauer published his own "law of the twelve tones" in 1919, four years before Arnold Schoenberg developed the better-known version of twelve-tone technique in 1923, yet standard accounts, including this atlas's own entity, credit Schoenberg as the technique's developer without addressing Hauer's prior claim or how independently the two systems were conceived.

What would resolve this A documented comparison of Hauer's 1919 method and Schoenberg's 1923 method, including whether Schoenberg knew of Hauer's work while developing his own, would clarify how the current attribution to Schoenberg alone should be qualified.
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Wikimedia FoundationTwelve-Tone Technique, Wikipedia History section
Quote, Twelve-Tone Technique, Wikipedia History section
The technique was first devised by Austrian composer Josef Matthias Hauer, who published his "law of the twelve tones" in 1919. In 1923, Arnold Schoenberg developed his own, better-known version of 12-tone technique, which became associated with the "Second Viennese School" composers.
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