For an experimental-minded band with an ear for hooks, there’s a fine line to walk between pushing new sounds forward and maintaining a larger audience’s attention. That’s the dichotomy at work in the music of Yeasayer, the Brooklyn band that released its third record “Fragrant World” late last month.

The follow-up to their breakthrough indie hit “Odd Blood” picks up where that eclectic mix of far-flung rhythms, synths and off-kilter dance beats left off, on songs like “Longevity,” a churning layer cake of sound that squiggles and glitches, but coalesces into a romantic, multi-tracked harmonized groove.

“That’s the challenge, right? Trying to make some interesting sounds, but have them work in a three-and-a-half to four-minute context,” says vocalist Chris Keating. “Trying to walk that line between experimenting and still have interesting melodies that are accessible, it’s part of the fun.”

Theirs is a process of stuffing as many tracks into one song as possible, says Keating.

“We’ll build up songs until they’re sky-high and start to strip away for a lot of it.”

He says it’s a technique he’s long admired in Prince.

“We pile on ideas, then strip away a lot of the middle and lower layers, and leave this floating melody,” says Keating. “He was an expert at that kind of craft.”

The result makes for a richer listening experience.

“I’m into putting on headphones and hearing interesting sounds, having an album swirl around you,” says Keating.

A lot of their songs are three different tracks chopped together. Keating wishes he could release full versions of every piece of song on the album.

“You can’t put out songs every week for a year, which I would like to do,” he says.

A bigger artist — for example, he says, Kanye West — could “drop a song on his website, once every week, but when he puts out the album someone really evaluates that piece of work as an artistic statement as opposed to a collection of songs.”

You could spend a lot of time doing the same for “Fragrant World.”

Just don’t call it ‘world music’

The band, somehow saddled with the “indie world music” moniker, says that was an inside joke that’s gotten out of hand.

“It’s clearly inaccurate,” Keating says. “I think some of that is subtle, not intentional, racism. Because we have a guy in the band who happens to have dark skin and an Indian background, people talk about ‘that world-music band.'”