Wynton Marsalis and the Lincoln Centre Jazz Orchestra have performed in Edinburgh a couple of times, but this closing night concert will be the Glasgow debut for the celebrated New York-based big band.

They take their name from their base of operations, the Frederick P. Rose Hall in Columbus Circle, an adjunct of the Lincoln Center built specifically for the jazz orchestra in 2004. As Marsalis regularly points out, it is the first formal concert hall in the world tailored for the acoustic demands of jazz rather than classical music.

Marsalis is arguably the best-known name in contemporary jazz, and has long been associated with what his detractors see as a conservative, overly tradition-rooted approach to jazz that is at odds with the experimental dimensions that historically fuelled the music’s march through the 20th century.

It is a claim he refutes vigorously, pointing in the case of the LCJO to a roster of music that runs from Louis Armstrong and Duke Ellington to John Coltrane’s A Love Supreme and the music of Ornette Coleman as proof of breadth, and insists that their mission is not defined by preserving old music in stasis on the bedrock of swing and blues.

‘We play a lot of different music and a lot of new music, and when we do play something from the jazz repertory, we play our own solos and come up with our own thing. And yet for some reason, although we are doing all this new music all the time, we are perceived as a repertory orchestra.’

While the trumpeter acknowledges that they are very proud of the tradition of jazz to which they happily belong (and they run a strong education programme in schools), he is equally adamant that it is not a yoke around their necks.

‘The fact is I love jazz, I love to swing, I love jazz musicians, and I believe that jazz has to be portrayed and celebrated for what it is. This music helps our children to understand who they are.’

Old Fruitmarket, Glasgow, Sun 27 Jun