Like their two predecessors, Brahms’s third and fourth symphonies appeared within only a year or so of each other: No 3 in 1883, and No 4 in 1884 (movements 1, 2) and 1885 (movements 3, 4). And though this is within only a decade of the premiere of the first symphony, they represent an entirely new stage of maturity, obviously written to more precise compositional goals: in the case of No 4, the application of formal variation principles throughout a symphony; in No 3, the symphonic application of a motto theme with the distinctiveness of a Leitmotiv. 
Although no lengthy history comparable with that of the First Symphony is known for No 4, it seems reasonably clear that the concept of the finale pre-dated the rest of the work, and that the preceding three movements were written to complement it and lead to it. The important Berlin choral conductor Siegfried Ochs recalls in his autobiography a meeting at which he was present with the composer and the great orchestral conductor Hans von Bu?low (who had become Brahms’s supporter by the 1880s having turned away from Wagner), at which Brahms had proposed a symphonic movement on the ground bass melody of the last section of Bach’s Cantata 150 ‘Nach dir, Herr, verlanget mich’.