The Italian composer Antonio Vivaldi had his set of concertos titled L'estro Armonico, Opus 3 (Harmonic Inspiration) published in 1711. This was a set of 12 concertos for one, two or four violins and was a very influential set of compositions. Bach was introduced to the music of Vivaldi with these concertos while he was in the employ of the Duke of Weimar's court for the second time from 1708 to 1717. Bach went on to transcribe and arranged 8 of Vivaldi's concertos for differing ensembles. The concerto in A Minor for two violins, violins, cello and continuo was arranged by Bach as a concerto for solo organ.
From his childhood, Bach learned from other composers by copying out or arranging their music. it was a time when many works were copied out by hand by composers and performers as the publishing of music was an expensive endeavor and as a result the printed copies were expensive to purchaseVivaldi's work was assimilated by Bach in the same way, and Vivaldi made a lasting impression on his music.
Vivaldi's original concerto's figured bass continuo part was fleshed out by Bach, with the two solo parts and accompaniment spread out over the manuals of the organ. It is interesting to compare the original with Bach's transcription, as it gives some idea of Bach's skill and knowledge of what the organ was capable of. Bach was a literal 'one man band' when he played the instrument. Bach maintained the Italian style of the originals as well as most of the notes contained in the two solo violin parts. The violin and organ are two vastly differnet instruments, so the literal transrciption of most of the solo parts causes some real difficulties for the organist, but as Bach made these transcriptions for his own use, that was probably of no concern. The concerto is in three movements:
I. Allegro - The concerto begins with two chords and a downward run. Vivaldi's concertos are full of fast scales up and down the fingerboard of the violin and Bach includes them in this concerto. The first movement is rapid and is in the home key of A minor.
II. Andante - In Vivaldi's original, the first four bars of the second movement are played by all the instruments, after which they are repeated throughout the movement as a continuous accompaniment to the solo violins that play different melodies. Bach maintains the ostinato in one manual as the soloist parts play in the other. The pedals are silent in this movement, and it is in the key of D minor. The soloists remain silent as the four bars of the beginning play to end the movement.
III. Allegro - The music returns to a brisk tempo and the key of A minor. After the initial statement is repeated, Bach changes the chords played by one of the solo violins to running sixteenth notes while keeping the original eighth notes of the original, one of the few actual alterations to the notes of the original. This adds brilliance to the music, perhaps Bach was flexing his organ playing muscles. He must have liked the effect for he repeats the changes later in the movement.
There was probably more than one reason for Bach's transcription. Perhaps his royal employer wished to hear the music of Vivaldi, perhaps Bach wanted to show his employer what he could do on the instrument. Whatever the extenuating reasons, Bach took the opportunity and made it a learning experience.