Klenau was among Arnold Schoenberg's advocates during the 1920s, and Schoenberg attended a concert of his music conducted by Klenau in 1923 in Freiburg.
Also according to Schoenberg, Klenau once defended his use of the twelve-tone technique as the basis of an opera (Klenau's output includes three twelve-tone-based operas in all, the first from 1932–33) as an example of National Socialist art, making an analogy of the row with the leader that everything else in the piece needed to follow. (This, and a political analogy made by Socialist composers, Schoenberg equally derided as "nonsense." He refers to Klenau as "the German composer, Paul von Klenau".)
^Schoenberg, Arnold. (1947.) Is it fair?, originally published in Music and Dance in California and the West, Hollywood, California, 1948. Reproduced in Style and Idea, pp. 249-50. (1975 edition.) New York: St. Martin's Press; Belmost Music Publishers. ISBN 0-520-05294-3.