The composition consists of three movements in the fast-slow-fast pattern typical of classical instrumental concertos:
Clara Schumann reacted unfavourably to the concerto, considering the work "not brilliant for the instruments". Richard Specht also thought critically of the concerto, describing it as "one of Brahms' most inapproachable and joyless compositions". By contrast, Donald Francis Tovey wrote of the concerto as having "vast and sweeping humour".
Richard Cohn has included the first movement of this concerto in his detailed discussion of various composers' use of triadic progressions. Cohn has also analysed such progressions mathematically.
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