Esperanza Spalding @ Barbican, London

Effortless. That’s the word that best describes the tall, slender girl with the improbably large afro who stands with her arms wrapped around a double bass in the centre of the Barbican’s stage. A seemingly virtuoso bassist and singer, Esperanza Spalding is in the middle of a spellbinding performance that is passionate but also somehow detached – she makes it look so easy it’s like she’s just practising.

She can be forgiven for seeming otherworldly. In her mid-twenties and on her third solo album, Spalding has just become the first jazz musician to win the Grammy for best new artist. She is being feted around the world as a rising jazz star who also has popular appeal, like Norah Jones only more authentic. She sounds a bit like the singer Cleo Laine, but with a smooth self confidence that belies her years.

And of course, she can play the bass as well as sing, an unusual talent for a female musician. With the double bass you really have to grip hold of it, master it. The instrument’s size means you must be firm but also, especially when extending long fingers down the neck to the high notes, tender. With her long arms and wide smile Spalding has both qualities: tall enough to control the instrument but with the tender touch of a mother running fingers through her children’s hair.

She can sing too, and oh what a voice. Shifting between lyrical and wordless expression, even to whistling so perfect it sounds like it’s coming from a hidden instrument, Spalding’s voice is a revelation. She has the confidence to sing solo, letting the band fall silent while her voice pirouettes light and carefree among the higher registers of her sizable range.

A jazz artist with a classical background, she sings in Spanish and Portugese as well as English and has an affinity with Latin American music. Her mother is part-Hispanic and she worked with legendary Brazilian musician Milton Nascimento on one of the album tracks.

She is joined tonight by drums, piano and strings, as well as backing vocalist Leala Cyr, who appears from the sidelines to duet in masterful fashion. It feels ad hoc, but then Spalding picks up her bass and the two are suddenly spotlighted together, and from somewhere soft Brazilian percussion gives the piece a compelling rhythm. It takes the audience a minute to realise that Spalding is producing scat sounds with her throat – her performance is so smooth that no one noticed it wasn’t the drummer.

Spalding’s intention with her latest album, Chamber Music Society, was to create music for the home: immediate and close-up, like what chamber music was in earlier years. Throughout the show she does her best to cut through the formality of the Barbican’s surroundings. Barefoot, she seems as relaxed as if she was singing lullabies in her bedroom. Her performance is so compelling that we forget the cavernous size of the Barbican’s downstairs hall with its rows of polite and silent concert goers.

But though the idea is that Chamber Music Society is close-knit and homely, in fact this explanation is disingenuous. The music, even the lyrics, are expansive. “Are we a million tiny grains of sand in one mighty hand?” she sings at one point. Behind her on a wall is projected a huge block of colour changing from red to blue to black. The amphitheatre is packed: the music is colossal. And yet it is also small – at the end of the show Spalding sits in an armchair beside a table lamp; she’s back at home.

For an encore Spalding returns to the stage with her pianist, Leo Genovese, to perform an intimate number. The lyrics are haunting: “They say if you die in a dream, you die in real life. Well I just died in your eyes.”