If New Orleans-based rock band MuteMath used to get maximum mileage out of synth-powered dance beats and chilled-out atmospherics, they veer into new sonic territory with their latest effort. Led by charismatic singer/keyboardist Paul Meany, the band recently independently produced a new 13-song collection titled Odd Soul (due for national release on Oct. 4). It rocks with more grit and blues than anything they’ve ever released.

“This is the first record we’ve self-produced,” says Meany. “We had a pretty clear idea of how we wanted this record to sound, and we knew how to get there. We’ve recorded enough and learned enough about our band to feel confident about it. We locked down in my house in New Orleans and went for it.”

Meany and his bandmates — Roy Mitchell-Cardenas (bass/guitar) and Darren King (drums) — were eager to dig deeper into their musical roots. They avoided the distraction of label and financial affairs and concentrated on playing and writing.

“We were trying to amplify it all more than before,” says Meany. “There are some elements of what we came up from in New Orleans. The songs ‘Odd Soul’ and ‘Blood Pressure’ have a touch of soul. They’re all cut from the same tree. These are songs we are honest about — and we unearthed a lot of themes that we’ve wanted to talk about for a long time.”

Some touched on spirituality and religion — topics Meany has dealt with since his days in the 1990s and early 2000s as a member of Earthsuit, a New Orleans-based contemporary Christian rock group.

“Much of it is about our experience growing up and what I’d call eccentric Christianity,” Meany says of the new songs. “Darren and I were in the throes of all that during the late 1980s and ’90s. We’ve gathered a lot of stories and anecdotes over the years. It’s the central theme of this Odd Soul of ours.”

While they prepared for sessions last year, MuteMath found themselves dealing with a major adjustment in the lineup, too. In April, the band announced that longtime guitarist Greg Hill was no longer with the band. Hill had actually given notice last fall.

“Greg left the band last year, right as we started recording this new record,” says Meany. “We were certainly in a head-space where we all needed a change. Things could keep going the way they were. I think [2009 album] Armistice took a toll on us. Greg was ready to go. I think changing up the scenery was good as we went into a new record.”

MuteMath carried on with studio work as a trio, with Mitchell-Cardenas handling much of the guitar duties. They wanted to resolve it and focus on creating a vibrant new set of songs.

“It wasn’t a vast change for us, after all, but it certainly was an x-factor,” admits Meany. “The guitar became a new instrument for the three of us in a lot of ways. We didn’t have the opportunity to pick up a guitar and express our ideas like this before, so it was a new method. Roy played most of the guitar, but we all participated.”

MuteMath enlisted Todd Gummerman as the new guitarist for the band, just in time for a quick summer tour of Japan. Gummerman’s technique and performance style fit nicely into the band’s sound and stage show.

“We prefer to perform as a four-piece,” says Meany. “Todd’s such a great musician, so it’s worked out great. I’d like to think that this is an important new chapter for us.”

Compared to previous works, the new songs on Odd Soul are less hectic and synth-based. The instruments seem hot and saturated. Meany’s singing is a bit more gutsy than before.

On the band’s much-lauded previous album, Armistice, electronic effects and ambient guitars played a large role in the sound. The upbeat tune “Spotlight” scored big with fans. Critics compared the music to Radiohead, Muse, and New Order.

Old Soul bypasses some of the familiar dance-rock and pop elements. There’s newfound energy to the music. Maybe it’s a collective step into a new maturity.

“I think this record is probably our most high-spirited album we’ve ever done,” says Meany. “It’s very dynamic and energetic. We certainly didn’t talk ourselves out of much in the studio, which was a big change. We played around a lot more. I think the music benefited from that.

“We had to create something that was moving us now,” Meany adds. “Messing with riffs and turning things up worked well. We wanted to cut to the chase and play the music we’re most moved to play. Anything that popped up and came close to sounding depressing got nixed. We just weren’t interested in that. I don’t feel we’re very good at being dark, so we didn’t waste any time being dark. We wanted to make something that was glaringly bright.”