It was, he recalls, composed in "Boulder, Colorado, on a nylon-string guitar and had a kind of ranchero beat." Throw in a crimson Wild West sunset and a mariachi trumpet and you have the essence of Calexico in a nutshell.
Formed by multi-instrumentalist Burns and drummer John Convertino in 1996, Calexico take their name from a small town on the US-Mexico border. It's no red herring. With its twanging instrumentals, crisp horns, sighing pedal steel and rattlesnake drums, their music is redolent of dry heat, vast blue skies and a highly cinematic brand of desert drama.
Although Burns and Convertino first met in California, where for a short spell they were both in Howe Gelb's venerable Giant Sand, it was only after moving to Tucson, Arizona, that the pair conceived Calexico. With roots in indie-rock and alt.country, over seven albums the band's sound has evolved into a kind of widescreen frontier music, created on the cusp of cultures and genres. Much of it taps into the romantic notion of the American West, albeit with something unsettling and rather turbulent in its undertow. Burns admits to "a love for those landscapes and themes, but there's a lot of tension and turmoil beneath the surface of things. I think everyone can relate to that".
In many ways Calexico are a truly modern American band, reflecting the growing influence of the Hispanic population and addressing the country's continuing schisms over race, immigration and cultural identity. They frequently sing in Spanish, and in both their music and their words they tend to champion the kind of places that have traditionally been marginalised (or worse) by the Caucasian rump of North America: Mexico, the Dominican Republic and, increasingly, Cuba: on Tucson-Habana, their 2010 collaboration with Spanish singer Amparo Sanchez, they even recorded at Havana's legendary EGREM studios. A key thread in their music is our complex relationship with roots and place. "Why do we leave, and why can't we leave? I keep coming back to those questions," says Burns. "Everyone is moving, and I wanted to capture some of that in these songs. Your head and heart is always searching for connections, a meeting place, some kind of avenue for the future. In America, people sometimes look at us funny when we sing in Spanish – like, I want to jump on this train, but there is a hesitation."
Their latest album, Algiers, was recorded in another of the world's great musical and cultural trysting posts. The record is named not after the Algerian capital, but the less renowned district of New Orleans where the pair spent several weeks recording the album. The results are quintessentially Calexico, yet the music tingles with the city's distinctive atmosphere of mystery, superstition and voodoo vibes. "We've always loved New Orleans," says Burns. "There's so much history, so many ghosts, even vampires. It carries a lot of weight. We recorded in a studio in this unassuming area, in a beautiful, old, wooden former Baptist church with a great sense of musical and spiritual history. We were tapping into the vibe of the studio, the district, and the city, which is a portal between North and South America, the old world and the new world. It rejuvenated us."
This week the band make their first visit to Scotland for five years. On stage, Calexico are a blur of sound and colour. Fleshed out to a seven-piece, they play a dizzying array of instruments, with some members juggling accordion and trumpet on the same song. "There is a lot of theatre to it, with so many multi-instrumentalists in the band," says Burns. "It's always interesting to see who is standing in front of the trumpet section. It's usually the ladies, checking out the facial hair ..."
According to Burns, "as you get older you don't just come to play music, you want to connect to a place". Having followed a trail from his own surname to the work of Robert Burns, he points out that, among the Mediterranean, South American, Caribbean and Western influences seeping into Calexico's songs there are trace elements of Celtic music. "The songs we write are inspired by so many different genres and traditions," he says. "A while ago I was really getting into Scottish and Irish folk, those chords and those time signatures, and there's a lot of that in our music. The last song on this record, The Vanishing Mind, is definitely inspired by Scottish folk song. I love that mix in the songwriting process. You never know where it is going to lead, and I like that."
Algiers has been out less than six months, and Burns concedes that the song he started writing back in Boulder is one of only a couple of new compositions. Still, he hopes to get back to the studio "sooner rather than later, and keep up the momentum of the tour. I'd like the next record to be a little more raw, a little more worn. I'd love to go back to New Orleans but it would be great to see this as start of a series of travelling and recording. Cuba would be fantastic, but I'd love to go further." It's the least we can expect from a band whose music recognises few borders.
Algiers is out now on ANTI. Calexico play O2 ABC, Glasgow, on Friday.