Prom 36, Royal Albert Hall, LondonProm 35, Royal Albert Hall, LondonProm 32, Royal Albert Hall, London

Rhythm gives birth to melody at a landmark Prom to honour the superstar of misnamed minimalism

The Royal Albert Hall is accustomed to showcasing veteran performers – the Liza Minnellis, the Engelbert Humperdincks – but the cheer that went up late on Thursday night was for the father of minimalism, Steve Reich, 75 this year and showing no signs of quitting his baseball cap yet.

And as the minutes ticked towards midnight, and a few Cinderellas scurried away, the cloth of gold that is Music for 18 Musicians unfolded, the major item in Prom 36. For 18 musicians, read 19, for Reich sat in at one of the four pianos, which, with the many instruments for six percussionists, two violins, two clarinets/bass clarinets (Ensmble Modern) and the four female voices of Synergy Vocals, wove the remarkable textures of the 1974-6 piece, receiving its first Proms performance. Rhythm is everything here, melody born out of it rather than drawn over it; rhythm is both warp and weft, ever altering, imperceptibly. If Reich ever goes into textiles, I'll buy the lot.

He opened the concert with Rainer Römer in Clapping Music, scored for two pairs of hands. This five-minute musical Rubik's Cube is a delight – the two performers clap the same rhythmic pattern together, then one skips ahead, 12 times, until the pair reunite. Do try this at home – it's ridiculously hard. Mats Bergström was the guitarist in Electric Counterpoint, a kaleidoscope for the ears.

Earlier in the evening, Ukrainian conductor Kirill Karabits celebrated that day's news of his extended tenure with the Bournemouth Symphony Orchestra with a ripsnorting Rachmaninov Symphony No 2 in Prom 35. Karabits's gift for the endless, questing phrase, mirrored by the orchestra's facility, makes this the perfect match. Ailish Tynan was the soprano soloist in the wordless, gymnastic Concerto for Coloratura Soprano by Glière, a witty whoop of glee.

Why did Mahler write no opera? From his earliest compositions, he was drawn to the alchemy of voice and orchestra, to the simultaneous expressions of ideas that opera can encompass. But there is no Mahler Ring cycle, no Pelléas and Mélisande. Maybe Mahler's operas are simply called song cycles or symphonies.

At 18, he began Das Klagende Lied, which contains so many of the musical elements that were to become his hallmark – the falling plangent phrases, the alarm calls of the woodwind and brass, the angular laments. Two brothers compete for the hand of an enigmatic queen. When one finds the flower she desires, the other kills him for the bloom and for the bride it will bring. A minstrel, alighting unwittingly upon the bleached bone of the dead brother, carves it into a flute which, played at the wedding feast, tells its own terrible story as celebrations and castle alike crumble.

The voices and narration of the tale at Prom 32 were shared between the BBC Singers (chorus master Stephen Jackson) on scintillating form – with soloists including mezzo-soprano Anna Larsson, stepping in for an indisposed Ekaterina Gubanova – and six outstanding boys from the Westminster Cathedral choir, two singing solos superbly, unfazed by the cavernous reaches of the Royal Albert Hall. Every voice had us wide-eyed with horror, as Edward Gardner, an accomplished musical storyteller in his role as music director at English National Opera, and the outstanding BBC Symphony Orchestra propelled the thriller to its end. Enthralling.

In the first half, Gardner, the BBCSO and Christian Tetzlaff had already had us on the edge of our seats for a Brahms Violin Concerto that will be my benchmark interpretation from now on. The soloist's scorching opening statement, the airy sweetness of his calming serenades, and the heel-stomping dances of the final movement were all breathtaking. Tetzlaff, playing as if his life depended on it, transported his audience from the Hungarian gypsy camp to the salons of Vienna. It was the trip of lifetime.

BBC Proms (0845 401 5040), to 10 Sep

Next Week:

Anna Picard hears Viktoria Mullova's double whammy at the Proms

Classical Choice

The radical, inventive opera season Tête à Tête ends at the Riverside Studios, Hammersmith, west London (020 8237 1111), with whole works and work in progress (to 21 Aug). At the Proms, Valery Gergiev conducts the Orchestra of the Mariinsky Theatre in Tchaikovsky's Swan Lake, rarely played in its entirety outside the theatre (Mon).