Geddy Lee is defining the essence of Rush.

"We're an unusual band, and our sound isn't palatable for every taste," says the singer and bassist.

"We're not the kind of band you can put on in the background while preparing dinner and drinking a glass of Chardonnay. We're a strange animal and I understand why we polarise people."

There is truth in the fact that Rush are unlikely to soundtrack many dinner parties. Yet the band's popularity goes deeper than many might think, to the extent that just shy of 40 years on from their first album, the Canadian trio will headline the SECC in Glasgow on Thursday night.

Prog-rock may have its critics but there is a durability to Rush that even the staunchest cynic should admire. There was finally recognition for the group's achievements earlier this year, when they were inducted into the Rock and Roll Hall of Fame after years of lobbying by their fans.

Lee himself always stated that he wasn't fussed, but confesses it was a different story at the event.

"All three of us were surprised at how emotional we did get on the night," he says.

"We walked into the room, and seeing the people in the room and those there to perform, we just felt this love. It definitely affects you, and as Neil [Peart, drummer] said in his opening remarks, we've said for years it wasn't a big deal, and now we see it actually is."

A softly-spoken interviewee, Lee is the antithesis of the rock star braggart and shies away from any melodramatic claims. He is, however, extremely upbeat about last year's Clockwork Angels album, the band's finest in some time. Being Rush, it is, of course, an epic concept record rooted in science fiction, to the extent that a tie-in book by the author Kevin J Anderson has been released alongside it.

The recording process itself, however, was a more stripped-back affair, with the band debuting two of the songs on a previous tour, rather than in the studio.

"The structure with our songs is always going to be complex and unusual. It's just how we think," chuckles Lee.

"That's our personality as a band, but we'd fallen into a trap where we overdubbed ourselves to death. When it's complex to begin with, I don't think it serves the songs as well to leave it so dense.

"What we learned by playing them live was that we didn't need the overdubs to make the songs big."

Some of those songs will undoubtedly sound vast at the SECC on Thursday, with the band joined by several string players for part of the lengthy set. Additional musicians is always something the group have avoided, and Lee admits the threesome are an "insular" bunch.

That is more a benefit than a hindrance, he feels.

"The fact we have stuck so closely together has made us good friends number one and made it feel like us versus them, which is a bonding thing – it's like a club no-one else belongs to. I think that has contributed to our longevity."

That longevity hasn't tempered Lee's enjoyment of hitting the road. He speaks warmly of the "raucousness, like a soccer crowd" of Scottish shows, and of seeing families now coming to Rush gigs.

"No-one expects to be around in rock 'n' roll after this amount of time, and to find that in some ways you mean more to more people now than ever before, then that's always kind of a shock, and a pleasant one.

"You walk out onstage and see fathers and sons and daughters coming to shows together, hell, just seeing female Rush fans now is always a pleasant surprise. It's been a strange, wonderful ride this career and we're just taking it all in."

Rush play the SECC on Thursday night.