The concept of eras in music is merely a device used by scholars and teachers to subdivide the vast history of the subject into more digestible chunks, so it is well to remember that elements of one era overlap quite often into differing eras. If the 50 - year period between 1720 - 1770 can be considered the Rococo era, there was considerable overlap within the Baroque era at the beginning of it and within the Classical era at the end of it. Composers can be difficult to pigeonhole into any one era as many times works were written with specific occasions, performers and patrons in mind, which would determine the style. Even within a single composition there could be sections representing more than one style.
The development of the solo concerto in the early 18th century by Vivaldi can be thought of as one example of the reaction against the learned contrapuntal composing style of the Baroque. The 12 concertos printed as L'estro Armonico in 1711 were widely distributed and studied by many composers, including J.S. Bach who made many transcriptions of them. Not all of the concertos are for solo violin. Some are for two, three or four violins and may be technically considered concertos grosso, but it is the style in which they were composed and the ritornello form that they used that were so influential.
With the contributions by J.S. Bach to the solo concerto literature in the style of Vivaldi, he can be considered at least an occasional composer of works in the Rococo style. As the elder Bach was the only teacher that his son C.P.E. Bach ever had, it is natural that the son was taught not only the learned style of counterpoint, but other styles as well. C.P.E. Bach can be considered a Rococo composer, but he also expanded beyond that and was one of the primary composers in the development of the Classical style later perfected by Haydn and Mozart.
C.P.E. Bach composed works in most genres of his time, and the number of concertos is considerable, with some 52 works. All of his concertos are originally written for keyboard, but he did make alternate versions of a few of these for other instruments such as flute, oboe, and cello.
He arranged two concertos for solo oboe in 1765, with the first one being in B-flat major which amounts to an enjoyable equivalent of 18th century easy listening music, while the second concerto in E-flat major shows more of Bach's quirky style. They were likely written for a prominent soloist whose name is not known, but who was probably a traveling virtuoso or member of the local orchestra in Berlin. The concerto is written for oboe, strings, continuo and is in three movements:
I. Allegro - The orchestra begins the work with a stubborn two note motive played in the violins over a shifting accompaniment in the other strings. The theme expands and goes off in a different direction until it returns to the opening two note motive. A rather awkward sounding chord progression (completely intentional, Bach usually has some harmonic surprises in his better compositions) leads to the entrance of the oboe. The oboe takes up the two note motive and develops the music that was introduced in the opening by the orchestra. The orchestra tosses out music in its own episodes and as an accompaniment to the soloist in Bach's version of ritornello form. A cadenza is played by the soloist, after which previous material is repeated by the orchestra in an early form of a sonata recapitulation. A short coda by the orchestra ends the movement.
II. Adagio ma non troppo - The middle movement is in C minor. The orchestra plays the melancholy theme which is taken up by the soloist and varied while the orchestra accompanies and comments. The oboe plays a short cadenza after which the orchestra repeats the melancholy theme without the oboe. The music moves to a cadence to an E-flat major chord and the last movement is played without a break.
III. Allegro ma non troppo - The final movement has a three to the bar theme played by the orchestra. AS in the previous movements, the oboe takes up the theme, expands and varies it between the orchestra's restatement of it. After the oboe develops the theme, it repeats it almost as it was first played. The orchestra then makes its final comments and closes the work.