Commissioned by the City of Birmingham Symphony Orchestra, Tippett's Piano Concerto was declared "unplayable" by the pianist chosen for the 1956 premiere, Julius Katchen. At the last moment, Louis Kremer substituted for Katchen.

Tippett's predilection for musical structures of the eighteenth and nineteenth centuries is clear in the format of the Piano Concerto. The piece is in three movements, the first a fast, sonata-form structure, the second slow and lyric, and a rondo finale. However, the harmonic basis for much of the piece—chords built of fourths—is clearly modern. These chords are not treated as dissonant sonorities requiring resolution; they are the consonant, primary harmonies of the piece and form the harmonic background to support the fluent, lyrical, profusely decorated language Tippett developed while composing The Midsummer Marriage. his choice of the concerto genre reflects his belief that innovation should grow from within a tradition. To the traditional juxtaposition of soloist and orchestra in the first movement Tippett adds an additional ensemble, drawn from the orchestra, of solo viola, celesta, and muted horns.

In the first movement, Allegro non troppo, we hear passages of sudden contrast that have precedents in The Midsummer Marriage. For instance, in the transition to the second theme an energetic line of sextuplets begins a canonic process that becomes the accompaniment for a lyrical melody of sustained notes and arpeggios in the solo viola. The sextuplets disappear, horns accompany, and the celesta enters quietly with the rhythm of the viola melody. Without warning, winds and brass loudly state fragments of irregular length from the sextuplet passage between rests, bringing the forward motion to a halt. Curiously, the viola passage shows up at random places in this otherwise traditionally organized sonata-form movement. Numerous piano passages in the movement are reminiscent, if not imitative, of Bartók.

Through much of the second movement, Molto lento, the high strings are silent. Meanwhile, the rest of the orchestra performs canonic passages as the pianist spins out arpeggio figures. Near the end of the movement, the violins and violas enter with a passionate outburst, only to be rebutted by the piano. Tippett's attempt to create the broad, soaring lines he used effectively in The Midsummer Marriage falls short; the percussive nature of the piano almost precludes this.

Tippett's finale is a rondo form in which the orchestra takes the main theme and the piano provides contrasting episodes. Between the episodes, the orchestra states only one of the three themes of the ritornello, which returns in full at the end. The third episode is a duet for piano and celesta, bringing together the two keyboard instruments, which until now have had unrelated roles.

A few aspects of the Piano Concerto have their origin in Tippett's The Midsummer Marriage. For instance, the opening idea of the concerto derives from the Act III continuation of Sosostris' aria. Also, the "temple" music of the opera finds its way into the celesta passages in the first and last movements.

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