Karlheinz Stockhausen composed Klavierstücke in cycles: pieces I–IV in 1952; V–VIII in 1954–1955; XI in 1956; and IX–X in 1961. He dedicated pieces V–VIII to Tudor. These recordings are not dated, but they most likely represent Tudor's first recordings of the set.

Stockhausen had never encountered a virtuoso like Tudor. The performances in these excerpts display his astonishing control of dynamic range, and of percussive and delicate textures. During the period from 1954 to 1965, when Tudor was concertizing widely in Europe and the United States, he corresponded regularly with Stockhausen about aspects of performance and the interpretation of notations in his piano works. In this excerpt from a 1955 letter, Stockhausen explains that in Klavierstück VI he intended the pianist to play five or six different speeds that change in relation to a "principal tempo change," just as he intended a "principal duration" to dominate the piece. Tudor performs the version of Klavierstück VI published by Universal Edition in 1954–1955.