By the late 1870s, Brahms had grown very confident of his ability to manage the major genres of instrumental music, and whereas works like his First Symphony and the first two string quartets are the products of many years of drafting and revising, he tackled his String Quartet No. 3 in B flat major, Op. 67—his last string quartet—in just a single year: 1876. It is often lamented that Brahms left posterity just three string quartets; but they make for a perfectly complementary trio. Each is in a position nearly equidistant from the other two around the dramatic wheel. There are the headlong plunges into raw physical drama and even gritty (for Brahms) pathos in the C minor Quartet (Op. 51 No. 1), and then the gentler, more lyric but still minor-mode strains of the A minor Quartet (Op. 51, No. 2). To round the threesome out, Brahms composed a bright and sunny work in B flat major that happens also to be one of the most flawlessly-crafted items in the repertoire. Brahms dedicated the String Quartet No. 3 to his friend Professor Th. W. Engelmann, and it was premiered in Berlin in October of the same year he composed it.

The first of the quartet's four movements is a Vivace in 6/8 time. Brahms seems to be having great fun throwing accents and sforzandos into the "wrong" parts of the measure throughout the spiccato first theme. The second theme is similarly fun-loving—it moves into 2/4 time leaps around on a little dactylic rhythm (long/short-short) and sounds, at least until the legato second strain of the theme arrives, uncannily like a famous children's folk song. An Andante in F major serves as the slow movement; it has in the middle of it two measures of 5/4 time—an unusual thing for Brahms. An Agitato (Allegretto non troppo) fills the scherzo position and is written in true da capo form. The glory of Op. 67, many feel, is the extraordinary final theme and variations movement (Poco Allegretto), at the end of which the theme of the first movement makes an encore appearance.

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