The Leipzig Gewandhaus Orchestra may not have quite the Straussian credentials of its Saxon rival in Dresden, the Staatskapelle, but few ensembles can more justifiably be regarded as a true custodian of German musical culture. Strauss himself regularly conducted the Leipzig orchestra in his own music in the early 20th century and, a few generations back, Mozart did the same. Both composers are the focus of the Leipzigers’ latest residency at the Barbican Centre, following on from the success of their Brahms cycle two years ago and this time centring on Strauss’s tone poems and Mozart’s concertos. It was launched, family concert apart, with a rip-roaring coupling of Strauss’s Don Juan and Ein Heldenleben, separated by the more tempered sound-world of Mozart’s last piano concerto.

And what a launch: the upward sweep of the orchestra’s strings and thrusting virility of the ensuing main theme of Don Juan felt like the unleashing of an unstoppable force of nature. Under the direction of Riccardo Chailly, in his last couple of seasons as music director before he is succeeded by Andris Nelsons in 2017, the orchestra demonstrated a remarkable unanimity of spirit and action. Often very small transitions of dynamic were made evenly across the stage with the subtlety of a collective rubato. Chailly never let the tension wane, yet he drew plenty of contrast between the moods of the different themes, from the main one depicting the Don’s surging libido (the Leipzig woodwind in pulsating overdrive in their accompaniment) to the sweetness of that portraying his latest conquest – or is it really Juan’s own self-regard?

Ein Heldenleben, too, opens with an upward surge as the hero (Strauss himself this time) propels himself into the world, sonorously conjured up here by the Leipzigers’ lower strings and horns. Again, pacing was exemplary, placing and balancing of textures exquisite – the depth of tone colour and sense of arrival in the final E flat major chord were exceptional. Frank-Michael Erben’s violin solos, Strauss’s portrayal of his wife (‘[she’s] a bit rough,’ the composer once said, ‘but she’s what I need’), were full of character, and the sweetness of his tone and phrasing, as his very first entry seeps in from the music’s previous pomposity (presumably Strauss himself), was beguiling.

With all this heady passion, egoism (from the composer, it should be said) and energy on display, Mozart’s Piano Concerto No.27 in B flat major, K595 proved just the balm. And it was sheer luxury to have one of days today’s supreme Mozartians at the keyboard in the Portuguese pianist Maria João Pires. Her combination of repose with crystalline pianism was perfect for conveying Mozart’s melodic charm and rhythmic joyousness in this concerto. But just as rewarding was the accompaniment from Chailly’s orchestra, pared down to chamber-orchestra dimensions and, for many of Pires’s solo passages, just to the front desks of the strings. The result was a supremely well-attuned partnership, ranging from chamber-like intimacy to the noblest of tuttis and with the limpidness of Pires’s playing at its heart.