As was also the case with his contemporaries, Mozart composed relatively little music in minor keys. When he did so it was almost always with specific purpose, and in forms that we would today consider "serious" -- the string quartet, the symphony and concerto. How then are we to account for a serenade (Mozart's own rubric for K. 388, unlike the Wind Serenade in E flat, K. 375, which he left untitled) in the minor mode composed for wind instruments? After all, the serenade was traditionally a work for light, relaxed entertainment on ceremonial or civic occasions. Those composed for wind band, or Harmoniemusik, in particular were associated with outdoor entertainment -- pieces to be casually overheard rather than listened to intently. Yet there is every evidence that after he settled in Vienna in 1781, Mozart took the genre seriously; all three wind serenades he composed during 1781 and 1782 are major works that far transcend the normal modest ambitions of such works.
The composer himself told his father Leopold in a letter that he had taken particular care over the E flat Serenade, although this may be because he was hoping to impress the Emperor Joseph II, who in the spring of 1782 had formed his own Harmoniemusik consisting of eight, rather than the usual six, performers. We know a fair amount about the genesis of that work and its revision from sextet to octet; virtually nothing, however, is known about Mozart's motivation to compose of the C minor Serenade other than the fact that it dates from much the same period as K. 375, July 1782 -- the date on Mozart's own autograph manuscript. Was it perhaps also designed in the hope of making an impression on the new Emperor (Joseph had been on the throne only two years)?
Whatever the reason, this radical work -- with its stormy, explosive opening Allegro, and "learned" canonic Minuet, and its contrapuntal complexity -- was totally out of keeping with then-current expectations for the genre, and one can only guess at the composer's reasons. Mozart never mentioned the work in his correspondence, and no documentary evidence relating to it has yet emerged. Like the revised version of K. 375, it is scored for the octet forces of Joseph's Harmoniemusik -- pairs of oboes, clarinets, horns and bassoons.
That Mozart himself was obviously aware of the serenade's unusual and atypical character (and perhaps quality) may be gauged by the fact that several years later, probably in 1788, he arranged it for a very different genre, transforming it into the String Quintet in C minor, K. 406 (K. 516b).