Wynton Marsalis has played enough classical music that he could easily refute Duke Ellington’s 1931 boast that “it don’t mean a thing if it ain’t got that swing.” When it comes to specifically American sounds, however, the occasionally pugnacious trumpeter isn’t about to pick a fight with jazz royalty. Swing, he says, is the bedrock of most of the music that matters from this continent, and from its southern neighbour as well.

“All of the musics in the Americas, the dance musics, derived from one African rhythm, the clave,” he explains, on the line from a tour bus threading through the mountains of northern California. “Swing is a derivation of that rhythm—and each of the countries in the Americas has a version of that rhythm.”

Unprompted, Marsalis begins to sing an African beat, then demonstrates its American and Cuban cousins. Next, he scat-sings a Charlie Parker melody, demonstrating how swing gave birth to bop. It’s pretty cool—the Straight is essentially getting a private lesson on the fundamentals of jazz, as well as a précis of the Harvard lecture series Marsalis began this April.

Don’t despair, though: if you’re not in a position to take a call from Wynton or enroll in the Ivy League, you can still brush up on your jazz history when the trumpet virtuoso’s 15-piece Jazz at Lincoln Center Orchestra plays a Vancouver International Jazz Festival show this week.

“We have about 150 songs out here—music from all periods of jazz, from the 1920s to contemporary pieces,” he says. “We’re demonstrating the continuum of the music, and that all periods of it are enjoyable. Audiences love the mix, because we’ll play a really contemporary piece, maybe something [saxophonist and JLCO member] Sherman Irby wrote a month ago, and after that we’ll play ”˜Snake Rag’ that King Oliver and Louis Armstrong recorded in 1923.

“I find that people always enjoy hearing music that’s not segregated into time periods,” he continues. “And of course it’s very difficult to play music from all these periods well, so the musicians we have are fantastic.”

They’re also able to venture beyond genre boundaries, it seems. In recent months, Marsalis and other members of the JLCO have shared the stage with artists as diverse as French accordionist Richard Galliano, British guitarist Eric Clapton, and flamenco-inspired Spanish pianist Chano Domí­nguez. One collaboration that hasn’t been much of a stretch, though, has been Marsalis’s superficially unlikely hookup with country icon Willie Nelson.

“When we play with Willie, it’s just like eating barbecue from Texas,” says the trumpeter. “I’m from Louisiana, so it’s the same food—although we showed them what to do with catfish. They just use it as bait.”

Wynton Marsalis and the Jazz at Lincoln Center Orchestra play the Orpheum Theatre on Sunday (June 26).