In 1721, J.S. Bach dedicated six orchestral pieces to Margrave Christian Ludwig of Brandenburg, ostensibly in response to a commission, but more likely as a sugarcoated job application. These pieces display a variety of styles, influences, and musical preoccupations and were probably not conceived of as a set. However, all of them share in Bach's great talent for absorbing new styles (among them the Italian concerto grosso) and then expanding and improving upon them. At any rate, the Margrave never thanked Bach, paid him a fee, staged a performance of the works, or offered him a position. Such was life, even for Bach.

The Concerto No. 3 in G major may have been written while Bach was at Weimar, given that it (along with Nos. 1 and 6) is reminiscent of the Italian concerto, a genre with which Bach was fascinated at the time. The motoric rhythm, clear melodic outline, and motivic construction owe a lot to the comparable works of Vivaldi, but the clarified harmony and more interesting counterpoint are unmistakably Bach's. The work's two main sections, both in G major (one alla breve, the other in 12/8 time), are separated by a brief Adagio which may be realized as a short violin cadenza. The concerto is written for three violins, three violas, and three cellos, with bass and continuo. The relationship between the instruments is subjective to the listener; as the positioning of the parts fluctuates, it may appear that there are no soloists, that the players are all soloists, or that the violins, violas, and cellos occupy their own solo groups. The Italian concerto grosso's distinction between concertino (a small group of soloists) and ripieno (the full ensemble) becomes in Bach's hands, and especially distinctively in the Brandenburg Concerto No. 3, a kaleidoscopic range of colors and shades.

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