Pyotr Ilyich Tchaikovsky's Piano Concerto No. 3 in E-flat major, Op. posth. 75, was originally begun as a symphony in E-flat. The composer ultimately abandoned this symphony, but, in 1893, started to rework it into a piano concerto, before abandoning all but the first movement, which he completed as a concert piece for piano and orchestra. It was published posthumously, in 1894, as a single-movement Allegro Brillante. The Symphony No. 6 Pathétique was the last of Tchaikovsky's compositions to be performed in his lifetime, but the Allegro Brillante, now known as the Piano Concerto No. 3, was his last completed composition.
Despite the composer's intentions stated prior to his death, there remains much argument as to what form this composition might have taken, had Tchaikovsky continued to work on the other movements. The matter revolves around two remaining movements from the unfinished symphony in E-flat. These had been left in sketch form by Tchaikovsky at the time of his death; but were later arranged, by former student and fellow-composer Sergei Taneyev, into a composition for piano and orchestra, entitled Andante and Finale. This was published in 1897 as Tchaikovsky's Op. posth. 79, even though it is actually Taneyev's personal arrangement of what is otherwise Tchaikovsky's unscored draft. Arguments concern whether it was worth Taneyev's efforts to resurrect this material—when Tchaikovsky had already expressed doubts as to its musical quality—and whether the Andante and Finale should be performed alongside Tchaikovsky's completed movement.
Most pianists performing the third concerto have only played the single-movement Op. 75. But there have been performances when this piece was played together with the Andante and Finale, forming a three-movement concerto, with this sometimes listed as Tchaikovsky's "Piano Concerto No. 3 in E-flat major, Op. 75/79."
In the 1950s, Russian musicologist and composer Semyon Bogatyrev used Tchaikovsky's sketches, including those used to create the single-movement Op. 75 and Andante and Finale, to form a conjectural reconstruction of Tchaikovsky's so-called "Symphony No. 7." The single-movement Op. 75 also serves as the musical basis for the ballet Allegro Brillante, conceived and choreographed in 1956 by George Balanchine for the New York City Ballet.