In 1961, cellist Gregor Piatigorsky suggested to Rózsa that he write a double concerto for him and violinist Jascha Heifetz. Rózsa readily agreed, as Heifetz had already been making a strong case for the composer's violin concerto. He worked on the concerto during summer breaks between film assignments, showing the soloists the drafts in progress. Heifetz and Piatigorsky squabbled over who was getting the longer solos and more brilliant passages, so Rózsa carefully allotted equal solos, virtuosity, and lyricism to each player. He completed the second movement, a theme and variations, first; this the soloists premiered in 1963, with a reduced orchestra.

The entire Sinfonia Concertante is built upon original themes in Hungarian folk style. The first movement, Allegro non troppo, begins with sweeping, vital music for the soloists and an orchestra with a well-stocked percussion section. Very soon, however, this subsides into more intimate material for the soloists, rather like Rózsa's scoring for film scenes in which the hero or lovers privately vow to prevail over adversity. These two musical ideas are thoroughly developed, often with heavy interjections from the orchestra. The movement ends in a brilliant flash, but on a rather expectant, unresolved chord.

The second movement, as mentioned, was premiered separately, with an orchestra of Mozartian proportions, as Theme, Variations, and Finale, Op. 13a. The variations begin with an original theme of strikingly Hungarian musical character, which receives several imaginative treatments alternating between dance-like (in a generally fierce mood) and martial. Most memorable is one with fiery whirling strings over stamping, irregularly accented brass. The finale gathers everything that came before and sums it up with utmost logic and drama.

The third movement, Allegro con brio, begins with a fiery orchestral introduction, music that is almost warlike (perhaps a comment on Heifetz's and Piatigorsky's bickering over equal time). The soloists enter with a skittering Hungarian-style dance tune, although the cellist quickly introduces a broader, more lyrical idea. The orchestra surges back in, pushing the soloists ahead in a forceful treatment of the movement's basic melodic ideas. The Sinfonia Concertante ends, as one would expect, with a brilliant flourish for the soloists and orchestra.

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