Classical Music: Saxton, Haydn Mendelssohn Barbican Centre, London

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Ever since the 18th century, the string quartet has proved the ultimate test for composers. The reason lies not just in the challenge of composing well for two violins, viola and cello playing alone. Context is equally crucial. Produce a dud overture, and a programme also featuring a featherweight ballet might save your reputation. But write a string quartet, even a good one, and works by a classical master are sure to be your revealing concert companions.

Robert Saxton, born 1953, and one of Britain's most assured instrumental composers, kept company with Haydn and Mendelssohn on Wednesday night at the Barbican - positioned, as it were, between emblems of the composer as late-flowering genius and youthful bloom. In his earlier days, Saxton himself was something of a prodigy; as a boy, he wrote to Benjamin Britten on the subject of composition, and received an encouraging answer. Yet even Britten's own distinction as an infant phenomenon pales in contrast with that of Mendelssohn, who wrote his Octet for strings at the tender age of 16.

This celebrated work formed the single item in the second half of the concert, the Chilingirian Quartet teaming up with their special guests, the Endellion Quartet, for a reading that projected both the sheer joy of chamber music and the happy spirit of this score. Earlier, the Chilingirians had given the first of Haydn's Op 76 Quartets, unceasingly inventive, with more than its fair share of Haydnesque surprises and a baroque-like quality of rhythmic momentum.

In fact, the defining feature of both these pieces, not least in these performances, was their sense of velocity. And as if responding to the challenge, speed was no less essential to Saxton's Barbican Centre commission, Songs, Dances and Ellipses, here receiving its world premiere. Four fast movements, grouped in pairs of outer sections, flanked a weighty central part that redefined the exuberance of its surroundings in terms of quiet introspection.

Throughout, Saxton's fine command of quartet idiom was well displayed - whether in the gentle lines of the opening bars, the forceful tremolandi of the episodes of dance, or the resonant octaves of the conclusion. Yet no less exciting was the unfolding form, conceived of in terms of a vast harmonic cycle, and revealed in stages, like the skull beneath the skin, by strategic cello phrases and long-held notes among the inner voices.

If all this reminded you of the primal architecture of planetary motion, you'd no doubt be pleasing the composer; mathematics, astronomy and the interaction of human and celestial spheres were his inspiration. Beethoven was famously inspired by the "starry heavens" but was hopeless at maths. Saxton completes the equation, with a starry vision, and a vision of number working in fruitful harmony as well.