You probably know more trumpeters than you think: Herb Alpert, Louis Armstrong, Chet Baker, Don Cherry, Miles Davis - and we're only up to D in the alphabet. Arturo Sandoval might not feature on your list, but he's one of the most celebrated players still blowing strong.

At New York's famous Blue Note Jazz Club, the Cuban musician is returning to the stage where he recorded last year's live album, his first in a 30-year career. The cosy venue has, ahem, trumpeted the talents of many a legend, including Tony Bennett, BB King, Ray Charles and Sandoval's personal mentor, Dizzy Gillespie, and every seat in the house tonight has the backside of an expectant jazz fan firmly rooted to it.

Sandoval's six-piece band and their various instruments are tightly packed on to the small stage with the precision of a Jenga tower. With no fanfare, percussionist Tomas Cruz sets the scene by rhythmically bashing his palms against a trio of conga drums with such speed and focus he must surely have gone home with his hands blistered and wrapped in bandages. Saxophonist Ed Calle leads the melody, while drummer Alexis Rice, pianist Javier Concepcion and Armando Gola on the bass give more understated performances. Meanwhile, Sandoval, his back modestly to the audience, coolly strikes subtle chords on a keyboard. You wouldn't guess he was the star of the show. Until, that is, he picks up the instrument that has won him four Grammy Awards.

It's not every musical form that can keep an audience in its grip with a set solely of ten-minute-plus songs, but it takes deaf ears to tire of an artist blowing his own trumpet as expertly as Sandoval. Cheeks red and puffed like an airbag, the 56-year-old turns to the audience and begins a long, breathless stream of notes that would induce a coronary in weaker-lunged performers.

Now, jazz is hardly a verse-chorus-verse genre. Tonight, there is no repetition and the melodies are elaborate; no one is likely to be humming any tunes when they leave. It's easy to overlook how carefully structured each piece is, with significant chunks appearing improvised, albeit flawlessly so. Notably, one song breaks midway and Sandoval launches into an extensive and showy scat. His bandmates take a breather as he curls his tongue round a series of spot-on impressions, sounding uncannily like a trumpet, bass, double bass and didgeridoo - and looking not unlike someone who should be sectioned. He throws his fingers around the air as if he is actually holding the instruments. It's mesmerising stuff.

You assume Sandoval is making up the nonsense boo-be-de-bopping as he goes along, but after about five minutes of extraordinary vocal acrobatics, the band suddenly jump back in - in sync. They provide highly skilled support. Cruz juggles a compendium of drums, bells and woodblocks and things to be shaken, rattled and, indeed, rolled; Calle proves as proficient brushing his fingers over the piercing electric clarinet as he is tossing the saxophone about like an elephant's trunk.

The audience clearly loves the set. During each song, one fan, sat at a table inches from Sandoval's feet, closes his eyes and lolls his head around with the melody. He applauds with the excitement of a 15-year-old girl at a Justin Timberlake concert. He's not alone.

Sandoval jokes that his birth in Cuba was a mistake (he became a US citizen in 1998). He muses that the jazz movement has lost its way and he intends to bring it back to North America. He could probably see it home single-handedly.