The Notwist produce some of the most interesting sounds in Germany these days. In February, the rock band’s new album Neon Golden finally crossed the Atlantic for its American debut, a year after its critically acclaimed premier in Europe.

“This is the first time we tried [to put together] everything we wanted to do—the electronica, the string arrangements,” the curly-haired Acher, who speaks with a vague European accent, says of the album. “Something that has always been important to the Notwist is the song,” which they say they assemble like “a puzzle.”

The Notwist are known for their unique compositions, which apply a down-to-earth pop sensibility to immaculately textured compositions. The band’s subtle sense of timing and diverse instrumentation—at times evoking strings and accordions—rivals indie groups like Grandaddy in sophistication.

But when they formed in 1989, they were actually a hardcore punk band, reflecting the German scene that surrounded them. It wasn’t until their second album Shrink that they gradually took on more diverse influences, which ranged from jazz to experimental electronica from the likes of Autechre and Oval.

Last Sunday, on their first American tour in five years, the band set off T.T. the Bear’s Place in Central Square with favorites from Neon Golden, including songs like “Pilot and This Room” and the mellow and airy “Pick Up the Phone.” Acher’s plaintive voice onstage sounds much like it does on record, hovering softly over washes of keyboard and guitar played to fluid but complex rhythms. What is surprising about the live show is the band’s newfound energy, which ultimately elevates the Notwist above the realm of sentimental ambient pop.

With drummer Martin Messerschmidt, bassist Micha Acher and Martin Gretschmann on the keyboard, the band maintains the energy of its punk days without losing any of its textural sophistication. At the show’s most climactic moments, the band steadily layered powerful buildups of sound one on top of another.

Neon Golden was a long time coming, as the band’s members have been preoccupied with side projects. Gretschmann also produces left-field electro under the name Console. And Markus Acher plays for Lali Puna, another well known experimental German band.

“For us it’s really important to get new ideas and play with other musicians,” Acher says. “We want [the sound] to be always interesting…to have new elements.”

The serious and pensive man cracks a smile when he recalls growing up in Germany with a father who was extremely fond of “Dixieland music.”

“My father played a lot with Dixieland bands…he was very ambitious,” Acher says. “His dream was always to have a Dixie band with his two sons.”

The Acher brothers grew up listening to Southern bands and American punk rock. Then they began playing in local venues as a small college band, eventually achieving their current prominence.

Acher has a lot to offer for aspiring young musicians.

“I would tell them…not to follow leaders,” he says. “Most of what teachers tell you is not important. The important thing is to find your own voice, not how well you can play or how many chords [you know]. It’s better to concentrate on a few things and make something original.”

“It’s important to be open-minded [and] to listen to all kinds of music,” he says.