Bright Sheng's new violin concerto was written for Gil Shaham, who gave the premiere in Detroit late last year. It is called Let Fly, and the title could be an instruction – early on, there's an airiness to the solo part and a sense of movement in the orchestra that speaks of the Chinese-born Sheng's skill in colouring western musical styles with genuine borrowings from the east: in this case, it's the veering notes of "flying song", a kind of yodelling from mountainous southern China.

Yodelling sounds better on the violin than on the voice, and Sheng's first movement is lyrical and expansive – but the western side of his style is here a kind of prairie-gazing melancholy, close to stock Americana. In its final, orchestra-wide appearance the melody nearly becomes bland. It is saved, just about, by the needling trumpets nagging at it.

The second movement, all glacial harmonies and ethereal sonorities, is one to contemplate the stars by; in the middle, the violin has a whole tune made only out of natural harmonics – glassy high notes created by touching rather than pressing on the strings. A passage of violin improvisation leads into the finale, which resembles nothing more than a wonky hoedown. The airy music of the start finally returns, so that the two can combine briefly at the close; but shouldn't this return feel like something that's been fought for? Here and elsewhere, the transition between styles seems too easy. Still, Shaham played it eloquently, and was clearly loving every minute.

As for the BBC Symphony Orchestra – they seemed to be enjoying playing for Sakari Oramo, still in his first season as chief conductor. He maintained a taut hold on their snappy reading of Dukas's Sorceror's Apprentice, and was in full command of a driven, colourful performance of the Concerto for Orchestra by Bartók – another composer who went to the US, bringing the music of his home with him.

• This concert is available to hear on BBC iPlayer until 16 May