Brahms wrote this work during the summer of 1887, and conducted the premiere himself on October 18 in Cologne, with Joseph Joachim and Robert Hausmann as, respectively, the violin and cello soloists. Brahms had just turned 20 when he met Joseph Joachim (1831-1907), already a celebrated violinist at 22 and destined to be acclaimed also as a composer, conductor, and educator. It was Joachim who commended his new friend to Robert and Clara Schumann, thereby assuring his celebrity. For 30 years the two were fast friends despite the distance usually separating their power bases: Joachim's in Berlin, Brahms' in Vienna finally. "Jussuf," however, had a weakness -- obsessive jealousy of his wife Amalie, whom he accused of adultery in 1881 with his (and Brahms' and Dvorák's) publisher, Fritz Simrock. Brahms disbelieved, and said so in a consolatory letter to Frau Joachim. During divorce hearings she produced this letter in court, and the judge agreed publicly with its contents.
As a result, Joachim cut off communications with Brahms for six years, although he continued to play the composer's music. Finally, seeking to repair the damage, Brahms composed the "Double" Concerto as a peace offering; the effort was successful, although their camaraderie of former years was never fully restored. In addition to composing the "Thun" sonatas of 1886 for violin and cello, Brahms had been studying Baroque concerti grossi, so the sound of string instruments was in his ear. This concerto would be his last orchestral work.
From the Swiss vacation resort of Hofstetter on Lake Thun, he wrote to several persons about his "strange flight of fancy...for fiddle and cello." But first he sent a postcard to Joachim, received on July 19, 1887, by which time Brahms had completed the work and was copying solo parts. When Joachim responded enthusiastically by return mail, Brahms asked him to arrange a play-through with Robert Hausmann, who had introduced the Op. 99 Cello Sonata a few months prior; Brahms himself would accompany on the piano. This took place at Clara Schumann's home in Baden-Baden in September (her diary notes that "Brahms and Joachim have spoken to one another again after years of silence"). Although neither the Cologne premiere nor the first Vienna performance was a success, the concerto finally entered the repertory, even if it never enjoyed the success of his violin concerto or the two for piano.
The opening Allegro (A minor; 4/4) begins with the kernel of the main theme, then a cello "recitative," and finally the kernel of a more lyrical second theme. Next, the violin has a turn, though the cello intrudes after five bars, following which the orchestra finally gets to play a 44-bar exposition of themes already previewed. Soloists perform the traditional second exposition, but there is not, in the development or recapitulation, a lot of unison playing. Thoughout, the soloists are not stars with a supporting cast, but merely leading characters in a primarily orchestral drama. Unison passages appear in the A and A' sections of the sweetly autumnal, folk-flavored, song-form Andante in D major (3/4 time). The solo instruments dovetail or briefly overlap in an F major middle section, until a magical enharmonic transition leads back to unison playing.
The lighthearted but "not too lively" rondo (vivace non troppo) has repeating A sections with a staccato-marcato rhythm that wrong-headed playing can accelerate and by so doing adulterate. The B section is broader, with chords on the cello that the violin echoes. The C section, in F major, is similarly broad but longer, before the A material returns one more time, with a jaunty tilt of the cap and a kind of jig -- all the more entertaining in light of Brahms' short stature, bushy beard and, by then, Santa-like corpulence.