His dear friend, colleague and master violinist Joseph Joachim had been a friend since they first met when Brahms was nineteen years old. There is bound to be friction between two such remarkably talented artists, but the major riff between them had nothing to do with music. Joachim, evidently a very jealous and suspicious husband, had accused his wife of infidelity. Brahms wrote the wife a consoling letter telling her he believed she was innocent of the charges, and years later when Joachim sued for divorce Brahms' letter was read in court and helped the court to decide in her favor. It was the first Joachim had heard about the letter, and he became furious. He didn't speak to Brahms or associate with him for years, but continued playing and promoting Brahms' music.
I. Allegro - The orchestra opens the work with a powerful but short statement. The cello enters with more introductory material until the orchestra winds silence the cello's passion with the first theme of the movement. Both of the soloists play their version of the theme, after which the orchestra returns with more thematic material. Brahms, a composer that was accused of being over-academic, changes thematic material each time it is repeated, a process Schoenberg called developing variation. Brahms was an academic in the sense that he revered and used the older forms of music, but he made changes within the form to suit the purpose of expressing himself. The soloists play thematic material and the variations with and against each other while being accompanied by an orchestra that also does the same with the soloists.
II. Andante - Two measures of introduction lead to the statement of the main theme by soloists and strings:
III. Vivace non troppo - Brahms had a fondness for dance music, especially Gypsy dance music. The main theme of this rondo/sonata hybrid is rhythmically strong, vibrant and is heard immediately in turn by first the cello and then violin. There's much going on throughout the movement, with some of the thematic material turning reflective in nature, a characteristic found in most of Brahms late works.
The Double Concerto was Brahms final work for orchestra. The last years of his life were devoted to chamber music, music for voice and music for piano. Brahms and Joachim remained on cordial terms for the rest of Brahms life, but they no longer had the same kind of friendship as before the riff.