In adapting a concerto for some other instrument, Bach would typically give the solo part to the harpsichordist’s right hand, leaving the range and key of the original solo part intact, and add a left-hand part.
The result is that the range (and the key) of the right-hand almost always resembles the way Bach wrote for a particular instrument in his other works. To an experienced eye the identity of original instrument – usually violin, oboe, or oboe d’amore – is fairly obvious.
Even among musicologists, who are a pretty contentious lot, there is widespread agreement about the original form of most of Bach’s concerti. The two solo parts of the C-minor Concerto exactly fit the range of the violin and the oboe. The arpeggiated figurations of the violin part are absent in the oboe part, since such passagework is not idiomatic for oboe.
In the slow movement, the two instruments trade pieces of the same long-lined melody while the accompanying strings are relegated to an almost unnoticed background. The result is a timeless tenderness not so different in effect from the slow movement of Mozart’s Third Violin Concerto.
And here is Bach’s concerto for violin and Oboe: