When Australian electronic pop band Cut Copy plays The Joy Theater Friday night, it will be days after the band was in Brazil on the eve of the World Cup.

“Where we were staying, the Dutch team was staying next door at the hotel,” said the band’s bass player, Ben Browning. “They were on the beach doing press things, and there were fans everywhere.”

He admits that the members aren’t big soccer fans, but Australia is in the World Cup, “so we’re looking forward to watching a few matches.”

The band is on tour after the 2013 release of “Free Your Mind,” a trippy departure for the band from its well-constructed pop songs and a tribute to the dance music that inspired it.

Cut Copy released its debut album in 2001, which was a quiet period for electronic dance music. The band wasn’t even the biggest news out of Australia at the time.

Cut Copy often shared bills with The Avalanches, whose “Since I Left You” received international acclaim for its rich, dense web of samples collaged together into a dream-like sound over hip-hop beats. But The Avalanches have long promised a second album that has yet to appear, while Cut Copy has grown as a band, writing catchy, well-constructed songs framed by whatever electronic or acoustic sounds best supported singer Dan Whitford’s vocal melodies.

On 2011’s “Zonoscope,” there are songs that sound like they could be the product of any band that liked The Beatles. They were once the electronic outlaws, but now they’re the more conventional electronic offering and DJs are the upstarts.

“Free Your Mind” is a salute to a specific phase in modern dance music’s development. It reflects Whitford’s affection for acid house, the early 1990s dance music that was huge in England and big in Australia.

“Acid house and original house started in Chicago and Detroit and New York, but it really took off in Europe and the U.K.,” Browning said.

American audiences have rarely kept track of British dance music’s numerous permutations, so acid house largely passed unnoticed here. Browning points to the success of bands Daft Punk and Disclosure as evidence of renewed interest in the sound.

“It’s probably bigger now than it’s ever been in the U.S.,” he said. “I’m sure a lot of our fans are pretty savvy about the sources of our music.”

The music that inspired “Free Your Mind” wasn’t the music that inspired Browning, though.

A rave culture developed in Australia, but he was 12 or 13 and more interested in his dad’s Neil Young records than the latest dance tracks.

The bands he played in before Cut Copy were more conventional and involved fewer mechanical elements.

“It was certainly a learning curve for me finding a way to add groove to a very rigid sound.”

Since dance music can often be trance-inducing, he has to be careful not to lose track of where he is in the song, but he considers those hypnotic moments a good thing.

“That indicates that we’re building some tension for a release at some point,” Browning said. “It’s all part of the drama.”