Mozart conceived three piano-concerti K.413, 414 and 415 in 1782, one year after he had settled in Vienna as a more or less freelance musician. By then he had already composed four concertos for piano and orchestra, one for three (or two) pianos and orchestra, and another one for two pianos and orchestra. It was also the period in which he was working on his opera Die Entführung aus dem Serail, K.384 and on the first String Quartet No. 14, K.387 of the six dedicated to Haydn in 1785.
From onset, his idea was to get these works (K.413, 414 and 415) published; he obviously expected a positive response from the public, not only on the financial level but also as a composer and piano virtuoso. In order to enhance the attraction for his publication, he decided to write these concertos in such a way that they could be performed not only with full orchestra (i.e. strings and winds) but also with a reduced accompaniment of only string quartet. Clearly, Mozart did not consider this strategic starting point as an artistic limitation, but rather as a challenge: in fact, already the score without the wind parts should leave nothing to be desired. This resulted in very careful and beautiful string writing, matching the solo part in the most effective and intimate way. The wind parts were then conceived to accentuate and “colour” certain passages in the accompaniment with even more depth.