[2] He wrote it for the cellist Robert Hausmann, a frequent chamber music collaborator,[3] and his old but estranged friend, the violinist Joseph Joachim.

The concerto makes use of the musical motif A–E–F, a permutation of F–A–E, which stood for a personal motto of Joachim, Frei aber einsam ("free but lonely").

[7] Richard Specht also thought critically of the concerto, describing it as "one of Brahms' most inapproachable and joyless compositions".

[citation needed] Later critics have warmed to it: Donald Tovey wrote of the concerto as having "vast and sweeping humour".

[10] Cohn notes several progressions that divide the octave equally into three parts, and which can be analyzed using the triadic transformations proposed by Hugo Riemann.