Singer-songwriter Dan Bejar, the lone constant in the shapeshifting Canadian collective Destroyer, has been surprised to find even longtime detractors tuning into the band’s latest album, “Kaputt” (Merge).

Even nine albums and 15 years into his role as the lone constant in the shape-shifting Canadian collective Destroyer, Dan Bejar can still be caught off guard. These days, the 38-year-old, who currently makes his home in Vancouver, is still reeling from the influx of attention the band has received since releasing “Kaputt” (Merge) earlier this year.

“People who actively despised Destroyer for 10 years are getting into this album,” said Bejar in a recent phone interview. “But I don’t pretend to understand the mechanics of music being disseminated or listened to or appreciated anymore. It’s all kind of a pleasant mystery.”

Similar things could be said of the band’s latest, a hazy album that arrives awash in dreamy guitar, mutant brass and Bejar’s distinctive vocals, which sound more relaxed than ever before. “I think the songs were written as voice memos, more or less,” said Bejar, who arrives in Madison with a seven-piece band in tow for a gig at the High Noon Saloon on Monday, April 11. “There are a lot of vocals where I just laid down a guide track right at the beginning of the recording stage … and in the end I just left them. It sounded so much more casual, which I thought was really good for the music.”

This casual vibe carried over into the recording process, which stretched out over a period of nearly 20 months. Despite the leisurely recording pace, many of the songs were actually written during a two-month creative outburst in the summer of 2008, pouring from Bejar in a way that he still doesn’t fully comprehend.

“(The lyrics) have a quality of hazy reminiscing and memories disappearing,” he said. “They arrived as little melodic lyrical snippets … and I just laid them down without trying to make sense of them. Honestly, I haven’t written much of anything since then, so I think something specific was going on in regards to this batch of songs.”

The first 14 months of recording were defined largely by inactivity. Twice a week, Bejar would retreat to the studio and casually attempt to translate the atmospheric, “billowy” sounds he heard in his head — sounds influenced by a Bryan (Ferry, Roxy Music singer and solo artist) and a Brian (Eno, solo artist and producer extraordinaire). Things took a slightly different turn once the other musicians arrived for the final six months of studio sessions.

“Once the lead players came in, their lines were so strong — whether it was lead guitar or trumpet or sax — that I couldn’t just use them for atmospheric effect,” he said. “It gave the record a more muscular feel.”

It also somehow turned Bejar into a de facto defender of the sax, a much-maligned instrument often associated with warm-glow 1980s cheese and soft-jazz cornballs that keep regular rotation on stereos in dentist office waiting rooms and elevators.

“I’ve always loved the saxophone and I didn’t know it represented something so unpalatable for most people,” he said. “I don’t think it instantly means Kenny G, but people either seem to view it as a novelty instrument that somehow works or a bad choice I made. There are definitely potholes for use of the instrument, but I don’t think we necessarily stepped in those.”

Bejar’s embrace of brass partially stems from a recent obsession with jazz — a fitting genre for a man who’s made a career of performing with a rotating cast of players.

“That’s always been a model for working that I’ve really liked as opposed to just getting together with four dudes in T-shirts or something,” he said. “Live, it’s also pushed us further from the ambient side of the record and more into hard jams. Our sax and trumpet players come from a improv background, so they have a tendency to go off.”