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Here is AllMusic's description of Mozart's Flute Concerto No.2 In D Major, K.314:
For nearly two hundred years, scholars believed Mozart's Flute Concerto No. 2 in D major, K. 314 (K. 285d) was originally composed for the flute in Mannheim in early 1778. In 1952, musicologist Bernhard Paumgartner demonstrated conclusively that Mozart reworked the Oboe Concerto in C major, K. 271k, into a concerto for flute. Mozart composed the Oboe Concerto for Giuseppe Ferlendis, oboist in the orchestra of the Archbishop of Salzburg, sometime between the beginning of Ferlendis' service at the Salzburg court (April 1, 1777) and Mozart's departure for Mannheim (September 22, 1777). Mozart's father probably sent the manuscript of the Oboe Concerto to Mozart, when he apparently used the work in an attempt to get himself out of an embarrassing situation. According to Mozart, Ferdinand Dejean, a surgeon with the Dutch East India Co. whom Mozart had met in Mannheim, commissioned three flute concertos from the composer. Only one exists from this period, K. 313/285c. Most likely, Mozart revised the Salzburg Oboe Concerto to present to Dejean as a new flute concerto. Mozart never finished the third piece and the composer's fee was not fully paid. (Dejean also commissioned three flute quartets, only two of which Mozart finished.) Continue Reading...The above was conducted by James Galway at Lincoln Center in New York in 1983. At least one source says this is at the most popular Mozart concerto.