From their first meeting in May 1853, Brahms and internationally famous violinist Joseph Joachim (1831-1907) became the best of friends. For several years the two collaborated on the study of composition, orchestration and counterpoint, and Joachim's string quartet played through some of Brahms' chamber music. Brahms wrote many of his counterpoint exercises at the organ, creating Baroque-style compositions often based on hymn melodies.

While in Düsseldorf in 1856, visiting Clara Schumann, Brahms composed the numerous works for the organ, of which only four survive and only two were published during his lifetime: the Fugue in A flat minor and the Prelude and Fugue on "O Traurigkeit," published in 1864 and 1882, respectively. The other two are Preludes and Fugues in A minor (dedicated to Clara Schumann) and G minor, printed together in 1927 as part of Johannes Brahms Sämtliche Werke, by Breitkopf & Härtel in Leipzig.

At the top of Brahms' manuscript of the Prelude and Fugue for organ in A minor is the inscription, "Präludium und Fuge für die Orgel. Meiner lieben Clara zum 7. Mai 1856" (Prelude and Fugue for the organ. To my dear Clara for 7 May 1856). On May 7, 1856, Brahms celebrated his thirty-third birthday. At the end of the manuscript Brahms asks Clara if she finds the piece too "pedantic."

After the initial statement of its leaping, detached melody, the Prelude's second voice enters, imitatively, in the bass. Brahms pursues a four-voice texture throught most of the piece, at the midpoint of which he refers, in the pedal part, to the subject of the ensuing fugue.

The fugue begins in A minor and 4/4 meter; its answer, entering in the fourth measure a perfect fourth below the subject, is real (every interval of the subject is preserved in the transposition down a fourth). Two more entries of the subject complete the exposition of this four-voice study in Baroque counterpoint. In the episodes between the following subject entries, hardly a measure passes without a fragment of the subject, either transposed, inverted or both. References to the opening of the Prelude appear in the pedal part shortly before Brahms increases the intensity and pushes through a lengthy diminished chord to a close on A major.

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