Music is an art of contrasts. It’s in the contrasts of tension and release, consonance and dissonance, loud and quiet, fast and slow, harsh and soft, and so on, that sound becomes music. These contrasts don’t just exist on the music’s surface as it unfolds; they are created across the sections and movements that make up large-scale pieces, and, with careful programming, expand over an entire concert. That is precisely what happened in the second of Sir Simon Rattle and the Berlin Philharmoniker’s concerts of this year’s London Residency, the genius of which lay not only in its exploitation of the contrasts in the work of just one composer – Jean Sibelius – but in the complete commitment of both conductor and orchestra to embody and communicate those contrasts to a transfixed Barbican audience.

The concert programmers were helped out on this score by the composer, whose Third and Fourth Symphonies could not be more different. The former is a surprisingly light, jovial affair, whereas the latter is one of the most devastating, annihilative pieces of music ever written: at least, it felt that way in this performance, which amplified the symphony’s sense of crushing futility with painfully sensitive subtlety.

Separating the symphonies, violinist Leonidas Kavakos joined forces with Rattle and the Berlin Phil for the Violin Concerto. Kavakos’ presence on stage was a joy: with unaffected disregard for convention, the shoulder-length-haired, unshaven, slightly scruffy soloist gave little hugs to the front desk violinists; turned his back to the audience when not playing to enjoy the full sight and sound of the orchestra; and even joined in with the firsts during the odd tutti section. Although the concerto’s silvery, elusive first movement was a touch disappointing – the orchestra were a little stodgy, not giving the violin the space it needs to breathe – the second movement was staggeringly beautiful. The third’s relative emotional deficiency is compensated with fireworks, and, although Kavakos’ upper register lacked the booming intensity of the lower throughout, there were sparks aplenty in his playing.

Most of the images we have of Sibelius show a formidable, stone-faced, ultra-serious introvert, the sort of intense face which might reflect the depths of depression and disillusionment with the world represented in the Fourth Symphony. This is why the start of the Third Symphony, with its jolly opening for cellos and basses, is somewhat startling; it seems at odds with the image we have of its creator. The opening passages are brimming with life: a brightly evocative, almost Highlandish melody sweeps out, ocean-like, over the orchestra, sounding so fresh I could almost feel the spray on my face, smell the salty air. The winds, so often used by Sibelius to overlay the texture with short, cellular shards of melodic material, were wonderfully vibrant; the strings produced an amazing quality of controlled energy in the mid register which dominates the movement; the horns, revelling in their epic Lord-of-the-Rings motif (clearly and cleverly borrowed by Howard Shore for its triumphant expansiveness), resounded gloriously. Elements of the hesitancy which characterises the second movement occur here, too – especially in the repeated intervallic motif drawn from the violins’ opening melody – but in general it is with a confident sense of happy adventuring that this first movement moves towards its final, warm plagal cadence. Nothing could be more different from the hopeless snuffing out of the Fourth Symphony’s heavy-hearted opening movement, which – though the horns finally do break through the suffocatingly dark murk to herald a momentarily redemptive brass chorale – succumbs all too easily to the desolation prefigured by its harsh opening dischord. A deeply moving, introspective cello solo and a truly riveting passage for high strings heightened the sense of tragedy, of the humanity that seems to be at stake within the music.

The Third symphony’s second movement is less positive than its precedent, veering uncertainly, at the pluck of the underlying strings, between the flute’s cold loneliness and the clarinet’s lyrical nostalgia. The ensemble playing here was magnificent, both in passages of radiance and heart-stopping pianissimo; throughout the symphonies, Rattle generated a truly astonishing balance and togetherness from his players. The melodic fragmentation that creates this movement’s defining sense of hesitancy returns at the start of the final movement, but infused with a greater sense of confidence. Urgent ostinati and harsh stopped horns provide the piece’s first slightly aggressive edge, before the violas force a measured melody across the violins’ more scatty bows, introducing a chorale that sweeps everything along in its wake. The momentum generated here is entirely lacking in the Fourth Symphony’s second movement – which never manages to get itself going and remains in a despondent slump – and is rarely achieved in its final movement, despite the intriguing introduction of the xylophone, scything ironically through the texture with forced, major-scale sonorities. The contrast is almost unbearable.