Just in time for the Cheltenham Jazz Festival, the good weather has arrived. The sun always seems to shine on this festival – which is just as well, as it takes place in an array of marquees, big and small, in the delightful Montpellier Gardens, alongside exotic food stalls and beer tents. The festival deserves the weather’s blessing, as it hasn’t forgotten that jazz can be fun.

Jason Moran, American virtuoso pianist and composer, hasn’t forgotten either. He is one of several big-name American musicians at the festival, alongside Randy Newman and Bill Frisell, and on Saturday afternoon he played a set with his long-standing trio of bassist Tarus Mateen and drummer Nasheet Waits.

Thanks to the vagaries of Bank Holiday trains I missed the first numbers of the set, but it took only a few minutes to be engrossed by the trio’s sheer exuberant inventiveness. Fun might not be the first word this trio’s music brings to mind, as it often rises to a knotted, atonal intensity. But this state is no sooner reached than the trio undercut their own high-seriousness with something unexpected – as in the first number I heard, where an intimidating blizzard of multiple rhythms on drums morphed slyly into a funky back-beat, via a Latin slouch and an up-tempo swing.

Jason Moran

It was an entertaining display of Moran’s amazing stylistic flexibility and harmonic subtlety. But more than that, it showed a real lyrical gift. He likes to fashion arching open-ended phrases which come round again and again, as if they hold a secret which Moran would like to fathom. At the end, just as things were getting really intense, Moran launched into a vamping stride number that evoked his hero Fats Waller.

Later in the day came another band able to inhabit any jazz style you could name with perfect ease and rousing wit. Kansas Smitty’s House Band has become one of the hottest properties in British jazz, and this uproariously inventive set showed why.

Sometimes, as in Jelly Roll Morton’s Courthouse Bump, or Ellington’s Jump for Joy (in which the band were joined by vocalist Clare Teal on terrifically sassy form) they caught an old style to perfection. But more interesting and no less joyous were the self-composed numbers like Short Stack, which pitched a stabbing, film-noir phrase against a good old-fashioned swing bass. Once again, jazz’s past was made to seem thrillingly alive.

The Cheltenham Jazz Festival continues until May 7. Tickets: 01242 850 270