Arnold Schoenberg's Piano Concerto, Op. 42, was the composer's first work since the Violin Concerto, Op. 36 to employ his "method of composing with 12 tones that are related only to one another." Four of his previous works—Kol nidre, Op. 39, the Second Chamber Symphony, Op. 38, the Variations on a Recitative for Organ, Op. 40, and Ode to Napoleon Buonaparte, Op. 41 (all completed between 1938 and 1942)—retain serial principles in a relaxed form or dispense with them completely. For the first time in four years, Schoenberg would base a work on a single, ordered, 12-note series. This series appears in the opening theme of the concerto, both in the linear right hand of the piano part and in combination with the left hand (some pitch repetition does occur).

Although it is written in one movement, the concerto falls into four sections, marked Andante, Molto allegro, Adagio, and Giocoso. The division is symphonic in nature, and the rondo-like aspects of the finale reinforce this impression. The richness of the piano part is evocative of Brahms' music, as is the distribution of material between the solo and orchestra parts. Schoenberg partitions his row into two hexachords (six-note groups), each of which he tends to subdivide into trichords (three-note groups). Unlike the row Schoenberg designed for his Ode to Napoleon Buonaparte, Op. 41, various combinations of pitches do not result in traditional triads. However, Schoenberg's permutations of the row are sometimes very free, even from the beginning of the piece, resulting in occasional quasi-tonal passages. This freedom in the use of the row enables Schoenberg to write the thick, fourth-based chords at the end of the Molto allegro and the Adagio. At such moments the work seems to be moving away from the 12-tone idiom. The clear triple meter of the first section is eerily reminiscent of the Viennese waltz in both the melody and accompaniment. Entering hesitantly at first, the orchestra gradually becomes an equal participant in the proceedings. In the Molto allegro, Schoenberg employs a device he had used in his Op. 11 piano pieces—a chord in harmonics created by silently depressing four keys, then causing the strings to vibrate by striking the same notes in a lower register. The orchestra alone opens the tense, tragic Adagio, thereafter alternating with the piano's solo passages. Separation between the two forces is created in this section, in which a potential climax is averted by a moment of silence and a genuine cadenza for the piano. Oddly, the very beginning of the Giocoso returns to an F sharp far more often than would be possible in a strictly worked out 12-tone composition, reflecting Schoenberg's relaxed approach to his own method in this piece. A recurrent rhythmic motive permeates the entire section, which, in its contrasting moments and sweeping gestures, sounds at times as if it were composed in the late nineteenth century.

Sketches for the concerto suggest Schoenberg put down his first ideas on June 27, 1942; his date at the end of the finished score is December 10, 1942. The premiere of the Piano Concerto was given at the NBC Studios in New York with Eduard Steuermann at the piano and Leopold Stokowski conducting. Steuermann had also participated in the first performances of Ode to Napoleon Buonaparte, Op. 41, and Pierrot lunaire, Op. 21.

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