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The first performance of the final version of the Quartet is said to have been given by the Budapest Quartet in Washington DC in January 1943. We have not traced a performance there and then by that group, nor for any month and year in Washington for which that might be a mistake. The Washington Post of May 23 and 25, 1943 announced a performance by the Budapest Quartet that included the Barber Quartet in Washington on May 28.
No quartet performers are listed for this premiere.
Washington Post, pre-concert announcement on April 1, 1951
Possibly in San Francisco