Mozart composed two piano quartets, a relatively rare genre during the Viennese Classical era. The E flat Quartet is the second, a work entered in the composer's thematic catalog on June 3, 1786. According to Mozart's earliest biographer Georg Nissen, he entered into an agreement with the Viennese publisher Hoffmeister for three piano quartets. Hoffmeister published the first, the Piano Quartet in G minor, K. 478, in either late 1785 or early 1786. A work of considerable complexity, K. 478 failed to appeal to the large amateur market at which such chamber music was generally directed. Poor sales resulted in Hoffmeister's abandoning the project, paying Mozart for the work he had published on condition that the second and third works not be composed. Why Mozart, who rarely composed without a purpose in mind, wrote a second work is not clear. Like the earlier work, it makes few concessions to the domestic amateur market, and the most likely explanation is that he composed it for use in his own concerts. It was probably the quartet played by Mozart in Prague early in 1787, the occasion on which the composer witnessed the triumphant success of Le nozze di Figaro in the Bohemian capital. Later that year, it was published in Vienna by Artaria as Op. 13, and the quartet also became one of Mozart's first works to be published in England when it appeared within a few months of its first appearance in Artaria's catalog. Like its companion, the E flat Quartet skillfully juxtaposes concerto-like writing for the piano with more integrated chamber textures. The overall mood of mellowness contrasts strongly with the dark drama of the G minor quartet. There are three movements, with a sonata-form Allegro followed by a Larghetto featuring a rapt dialogue between piano and strings. Exchange of material between piano and strings is also a feature of the high-spirited Allegretto that concludes the work. Both this work and the G minor quartet are among the peaks of Mozart's chamber music; they are works that far transcend the few models Mozart had available—works that in any case relied too much on a texture in which the strings merely accompanied the piano.

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