During his earlier years in Salzburg, Mozart composed eight wind divertimentos, works almost certainly designed for outdoor use, and primarily intended to fall pleasingly on the ear as little more than background music. Mozart being Mozart, many movements, of course, transcend such modest pretensions. Nevertheless, the three great wind serenades Mozart composed after settling in Vienna in 1781 elevate the form to unprecedented heights. While only one, the Serenade in C Minor, K.388, can be dated with any degree of certainty, it appears that all three were composed during the composer's first two years in Vienna. The first and most obvious difference between the Serenade in B flat and its Salzburg predecessors is the huge expansion in scale, both in terms of instrumentation and length. Instead of six (or eight) instruments, K.361 is originally scored for no less than thirteen - pairs of oboes, clarinets, basset horns (lower pitched members of the clarinet family), horns in F and B flat, and bassoons, with the bottom line strengthened by a string double bass.

The presence of a double bass suggests that the work was intended for indoor rather than outdoor performance; this notion is augmented by the first recorded performance, which took place at a benefit concert given on March 23, 1784 at the Burgtheater in Vienna. The concert was to benefit Mozart's friend Anton Stadler, a brilliant clarinetist and basset horn player for whom he later composed both the Clarinet Quintet in A major, K.581 and Concerto in A major, K.622. A member of the audience who heard the performance recorded the effect it made on him: "…glorious and sublime! It consisted of thirteen instruments…At each instrument sat a master - oh, what an effect it made - glorious and grand, excellent and sublime!"

This arrangement of the fourth movement is for standard string quartet, with an optional bass part for use with string orchestra.