Like London buses, you wait ages for a bit of Rachmaninov, and then you suddenly get three pieces all at once. In a nifty piece of programming for this year's Proms, Rachmaninov's last three compositions were played over three consecutive nights, but the delights of this particular concert were as much in the first half as in the second.

To stimulate the senses, we had the world première of Emily Howard's Torus, a concerto for orchestra written for the Royal Liverpool Philharmonic Orchestra and Vasily Petrenko, with whom she has had a long and fruitful association. Howard's fascination with how ideas from the world of science and mathematics can inspire musical creation has continued in her latest work. A torus is basically a ring doughnut shape. Howard visualised the image of "a sphere with its heart ripped out" during its composition, with the result that the void becomes as important as the substance. For this reason, contrasts are important in this work: calmness and nervousness; consonance and dissonance; fast and slow.

Torus uses an extraordinary array of musical techniques to create startling effects and meditative passages, with sudden bursts of fleeting and violent activity over quieter, slowly shifting harmonies. One of the striking features involved a cataclysmic outburst leading into a disturbing passage involving microtones and sinister glissandi increasing in tensile strength before fragmenting again. There were scintillatingly grotesque climaxes and ethereal, enigmatic passages before the music just disappeared in mid-air. The RLPO under Petrenko performed brilliantly, weaving the myriad textures and soundbursts with virtuosity and purpose to give the piece the respect it deserves. This was an accomplished and absorbing new work by a composer who is keen for us to hear the overall shape of the piece rather than become distracted by surface detail. This is a philosophy I like.

Shostakovich wrote his Cello Concerto no. 1 in E flat major in 1959 for Mstislav Rostropovich following an impulse stimulated by his admiration for Prokofiev's Symphony-Concerto, particularly the way it had been written in adversity, a sentiment also shared by Shostakovich. In a change to the advertised billing, the young Russian cellist Alexey Stadler stood in as a last-minute replacement for Truls Mørk, who was unable to perform due to illness. Stadler revealed an unassuming but steely determination as he played with attack and rhythmic clarity in the sardonic march-like Allegretto, and with intensity and eloquence in the meditative second movement with a light, rather than rich, tone. The cadenza was well-controlled, and the Finale with its driving rhythms and folk tunes saw Stadler powering through relentlessly with sharp acidity and crisp, metrical precision. It did feel a little deliberate and methodical in places, but it was an impressive and convincing performance nonetheless.

Petrenko's instinctive shaping of Shostakovich's music was inspired and the RLPO was excellent in support, with wailing winds and blaring horn against incisive strings in the outer movements and a wonderfully delicate and pensive tone in the second movement. There were one or two minor balance issues between orchestra and soloist, but otherwise there was perfect symbiosis. Full marks to this young cellist for stepping up to the plate so admirably, and he treated the audience to an encore with the Sarabande from Bach's Cello Suite no. 2 in D minor.

Rachmaninov's penultimate work, the Symphony no. 3 in A minor, has some similarities with his Symphonic Dances, with a strong element of nostalgia for his native Russia after settling in the USA. This feeling became more pronounced over time as Rachmaninov struggled with constant thoughts of the torture inflicted by Soviets on the Russian people. This three-movement symphony has a plentiful supply of tunes evoking memories of Russia and is brightly orchestrated with a rich variety of tone colours but with greater focus and economy of musical articulation than in his previous works.

Petrenko and the RLPO captured the full melancholy of Rachmaninov's longing with bittersweet optimism and bright tone colours flitting across the orchestra. The sweeping orchestral flourishes were overwhelming and triumphant, with luxurious strings, lucid and plaintive winds and warm brass throughout. Petrenko drew out of the orchestra an added measure of agitation and flamboyance in the first movement with an emotional yearning in the second movement as Rachmaninov makes his impassioned plea for the Russia he could not return to. The lively Finale had plenty of drive as Petrenko conveyed the full sense of false optimism and resignation before building up through irregular and jarred rhythms into the extraordinarily frantic ending.

As an encore, Petrenko plumped for Tahiti Trot, Shostakovich's frivolous orchestration of Tea for Two, written in just 45 minutes in order to win a bet.