THERE is a new photograph of The Pixies, in which they're flanked by a baying wolf. You wonder whether the creature is fearful, or fiercely protective, of the band. Perhaps it represents their spirit animal: a symbol of feral cravings and instincts. Or maybe it is howling at them, as one might the moon – its cries not unlike those of Black Francis, their wild vocal thaumaturge.

Then again, it might just be a throwaway prop. “I'm afraid that's all it is,” says Pixies founder member and drummer David Lovering, with an apologetic laugh. “We did those photos in Brooklyn prop house, and they kept wanting to put these things in beside us. Usually we object to having stuff like that, but this time we thought we'd just do it, for the hell of it.”

Whatever the reason, real or imagined, the wolf is not the first beast to rove across the ravaged alt-rock of the Boston band, whose malevolent pop and surrealist punk has influenced David Bowie, Radiohead and Nirvana. Since they formed in 1986, they've been variously plagued by Caribou (on their 1987 debut EP, Come On Pilgrim), Snakes (2014's Indie Cindy), and praying mantids (their new album Head Carrier) – not to mention a Monkey Gone to Heaven (1989's seminal Doolittle) – over a tumultuous career that has weathered fractures, splits, reported brawls, reunions and the loss of a well-loved linchpin.

For 28 years (break-up notwithstanding), the indie alchemists' line-up comprised guitarist and vocalist Black Francis (aka Frank Black, born Charles Thompson), guitarist Joey Santiago, bassist and vocalist Kim Deal, and drummer David Lovering (who turned down an offer to join Foo Fighters after The Pixies split). New bassist and vocalist Paz Lenchantin joined in 2014, following the sudden departure of Deal, who also made huge alt-rock waves with The Breeders.

Deal was nigh-on synonymous with The Pixies – her bass and vocal swagger at the heart of many of their best-loved songs – and if fans of the band felt lost when she left, then they were not alone. “We were lost as well,” says Lovering, who recalls her announcing she was leaving after a seemingly amicable band dinner. “It was a very hard time. I remember that. But there was no real reason why, or why not, and we all wish her really well.” True to this sentiment, there's a shimmering girl-group ballad on Head Carrier, All I Think About Now, which the band have called a tribute to Deal.

That said, The Pixies are laughing in their lupine promo shot, and the new album sounds like they're having a ball. Despite it being their first without Deal, Head Carrier feels like a celebratory affair, as it revels in religious esoterica (Plaster of Paris), Mesopotamian deities (Baal's Back), and raucous Neil Young invocations (the title track). The drummer nods. “It was a great experience all over,” he says. “We had so much time to work out songs. We had six weeks of rehearsing as a band, and that was a luxury we haven't had for a long time. Each Pixies album back in the day got quicker and quicker to make, so we were kind of re-living what it was like as a baby band in Boston. That was a joy.

“And working with Paz has been a whole new experience,” he says of The Pixies' rewired (and ever-cardinal) rhythm section. “Having worked with Kim for so long, I didn't know anything different. And I'm not saying that's a bad thing – that was a wonderful thing, I thought. But having Paz? Well, that's a new animal. And she's such a good bass player, she's making me play better, because I don't want to get embarrassed,” he laughs.

The band have enjoyed a long and illustrious alliance with producer Gil Norton, who helmed their mid-period triple-header of Doolittle (1989), Bossanova (1990) and Trompe Le Monde (1991), and with whom they re-joined forces on Indie Cindy. For Head Carrier, however, they wanted to be less defined (or confined) by the band's history and mythology, and more fired-up by the band itself. In its new incarnation, that required a radical approach – or, as they put it, “a punch in the face.” They hired a new producer, Tom Dalgety (Killing Joke, Royal Blood, Simple Minds).

"I think this has all really just been about change for us,” Lovering says. “It was all around. It was there while we were having fun in the studio, and with a new bassist, and it was there with Tom producing. His name and credentials were perfect when we looked him up. And also, he was able to say, 'I don't like that song – throw it away,'” Lovering laughs. “That's pretty tough. I don't think The Pixies had ever heard that before.”

The self-proclaimed “dysfunctional band” (Lovering's words) first assembled in early 1986, after college friends Santiago and Thompson advertised for a bassist who was driven by a musical love of folk revivalists Peter, Paul and Mary and hardcore punk trailblazers Husker Du. They only received one reply – from Deal – who brought Lovering on board.

"I had worked with Kim's husband, and he knew I was a drummer, so that was how it originally came about,” Lovering recalls. “I hadn't played drums in a long time when they asked me – I was going to school by then – so I was surprised that I even went along. It's interesting looking back on it, now I'm really thinking about it, because I don't remember that much about going to meet them.

“I remember they had an old square Linn drum [machine] though, and Charles had this acoustic guitar, and he was just playing stuff, early songs,” he continues. “And I was trying to play along, with my fingers, on the Linn drum. But that's about it. Although, when I asked Joe about it later, he was like – 'man, you were so stoned that day'. And I don't rule that out. So I can't tell you that much more about the day we formed. But we left on good terms, as far as I recall.”

And lo, that was the birth of The Pixies. Their initial tenure stretched from 1986 to 1993, they were split from then until 2004, and when they got back together, “through a series of phonecalls that were started by a joke Joey made on the radio”, they re-entered the studio, fired straight into Monkey Gone To Heaven, and never looked back.

It's one thing to reform and play old favourites, but another thing to reboot your canon with a new album, as The Pixies did with Indie Cindy, their first new LP since Trompe Le Monde. When did the subject of new material first come up? "Well, when we reunited in 2004, and up until 2011, we played reunion shows, we played our old catalogue, we toured Doolittle, and after that, we realised we'd been back on the road for over seven years,” Lovering offers. “Which was surreal, because that was longer than we'd initially been a band, before the split. So that was surprising, and that was also the impetus of what came next. We thought, 'we can do this, we know what we like to do as a band, we're still viable, let's write new songs'. And here we are now, with Head Carrier, another new album...”

But Lovering hadn't counted on that. He never believed there was a chance The Pixies would get back together. Which is why, when they split, he became a professional magician. He called himself The Scientific Phenomenalist, and toured with Grant-Lee Phillips, The Breeders and Camper Van Beethoven. “If you'd told me I was going to be a magician when I was younger, I'd have rolled on the floor laughing,” he says. “But I went to a magic convention years ago, and I saw magic that I'd never seen, like really cool close-up magic, and I was fascinated. I just didn't know how they did it. After that, I took classes, I read books, I joined clubs. I woke up many times in bed with packs of cards all strewn around me. I love magic. It has a sense of wonder. It suggests that somehow, the impossible is possible.

“I could have picked a better career choice though,” Lovering quips. I'm not so sure. Whether in magic, or in music, he has long summoned invisible forces, subverted reality, defied nigh-on impossible things.

Head Carrier is out on September 30. The Pixies play Glasgow Barrowland on December 2.