Künzel was a student at the Thomasschule in Leipzig, Germany, and Schüler der Leipziger Thomasschule and was a member of the Thomanerchor in 1973.
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He was a student at the Thomasschule zu Leipzig and University of Leipzig, then organist of the city's Paulinerkirche from 1716 (whose music director he became in 1723) then its Nikolaikirche from 1721.