The court of young Prince Leopold at Cöthen was the penultimate step on Bach's professional ascent from organist at Arnstadt, in 1703, to Kantor at Leipzig, from 1723 to the end of his life. He had been Konzertmeister at Weimar (1708-1717) before his appointment as Kapellmeister at Cöthen, where he remained for six years. He wrote much instrumental (rather than liturgical) music in this secular position, although most of it has been lost. Among the survivors were the Brandenburg Concertos and three other concertos for one or more solo violins with string and continuo accompaniment: the A minor and E major concertos for his concertmaster at Cöthen, Joseph Spiess, and the D minor Concerto for Two Violins.

Formally, he cast all but Brandenburg No. 3 in three movements—quick, slow, quick—modeled on the Italian Baroque concertos of Vivaldi. Bach's genius was the ability to individualize as well as transcend the style of that older and admired contemporary who was indirectly his mentor. In the Violin Concerto No. 1 in A minor, BWV 1041, as in the other two violin concertos, the central movement is an aria without words—lyrical, expressively warm, ever gentle, yet inescapably melancholic in case of the A minor, perhaps the most inherently somber key in the tonal lexicon. On either side, an implicit although unmarked Allegro leads off in 2/4 time, with ritornello structure. As usual in Bach's concertos, the soloist's relationship with the full-ensemble passages hangs in a fascinating balance between competition and cooperation. A jig concludes in 3/8 time, marked Allegro assai and foreshadowing the rondos that Haydn and Mozart developed after Bach's death.

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