Fig. 2.9 Margrave of Brandenburg,
There are six concertos in the Brandenburg collection, and Bach composed this music over a period of several years. At the time Bach compiled these concertos into the set known as the Brandenburg Concertos, he was the court music director for Prince Leopold of Cöthen. The court orchestra at Cöthen was reknowned for its large size and fine players, and it is likely that Bach wrote this music for Cöthen orchestra performances (some music scholars suggest that some of the concertos were written even earlier, while Bach worked for the Duke of Weimar).
When Bach traveled to Berlin to make final arrangements for a new harpsichord he was acquiring for Prince Leopold, he was asked to play for the Margrave Christian Ludwig of Brandenburg. The Margrave was apparently so pleased with Bach's performance, that he requested music for his library. In response, Bach dedicated his Brandenburg Concertos to the Margrave of Brandenburg, and in 1721, sent a dedicatory letter to the Margrave along with a manuscript copy of the music.  The following excerpt from Bach's dedicatory letter illustrates the effusive praise and somewhat obsequious language musicians often used to curry favor with potential patrons:
I had a few years ago the pleasure of playing before Your Royal Highness, at your Highness's command, and whereas I noted on that occasion that the modest talent for music that Heaven has bestowed upon me found favor in Your eyes, and whereas in departing your Royal Highness deigned to honor me with the charge to send Your Highness some compositions of mine, therefore I have, in accordance with Your Highness's most gracious charge, taken the liberty of fulfilling my most humble duty to Your Royal Highness with the present concertos, which I have scored for several instruments. 
TECHNIQUE TIPS: This musical arrangement is taken from the first movement of Bach's Brandenburg Concerto No. 5. It is in the musical form of a concerto grosso. A concerto grosso is an instrumental concerto for a small group of soloists called the concertino, which play in contrast to the main body of instrumentalists or orchestra called the ripieno or tutti. Bach scored Concerto No. 5 for three solo instruments: flute, violin and harpsichord (this concerto was designed to feature the new harpsichord Bach brought back from Berlin). These solo instruments (the concertino), play their part in contrast with the orchestra (or tutti). This arrangement features the melody in the violin part for both the concertino and tutti sections, otherwise, there would be frequent rests. This movement is marked allegro, a lively and brisk tempo. As you play the rapid sixteenth notes, use short bows in the upper third of your bow.