School of the Flower, the 2005 full-length from San Francisco’s Six Organs of Admittance, was, as somewhat obscure indie rock goes, a popular breakthrough: In a few years time, Ben Chasny–the sole constant of Six Organs and the newest Comet on Fire–had gone from self-pressing a few dozen copies of his own debut and mailing them to friends to signing to one of the more revered independent outlets in America, Drag City.

The album followed suit, a concise, focused effort from Chasny, purposely mixing the diametric ends of his six-string career: gorgeous, finger-picked melodies influenced by Bert Jansch and distended electric excursions influenced by his stoner-psych saviors, meeting seamlessly on an elegant, understated trip. Of eight tracks, only one broke the six-minute mark, and those other seven seemed passable enough for college-age neophytes newly interested in “freak folk.” Was Bonnaroo the next Six Organs destination?

Hardly. The Sun Awakens, this year’s follow-up, finds Chasny unconsciously passing on the invitation to join Devendra Banhart’s march toward popular acceptability and TV-ready music videos, opting instead for the much more interesting avenue of non-linear progression. Again, only one track, the closing “River of Transfiguration,” breaks the six-minute mark, though the preceding six are among some of the most alluring and engaging melodies Chasny has written yet. But side one is only a placid Patty Waters-like invocation for the uninterrupted force of side two, a monstrous 24-minute drone for guitar, bass, voice and percussion, marking a sophisticated return to the raga-like movements that constitute Chasny’s early work. It’s well-constructed and thoughtful, a melody bubbling up through seraphim sheets of sound. It’s also one of the more avant things Drag City has released in a decade.

While most record labels would at least flinch over such obtuse anti-posturing from a keynote new artist, especially on the heels of their most accessible album, Drag City couldn’t be happier. “I was talking to the owner Dan Koretzky after I finished the record, and I was a little drunk,” says Chasny, laughing. “I said, ‘Hey, are you mad at me?’, and he said, ‘Why would I be mad at you?’ When I said I gave him a big ol’ drone song, he was like, ‘That’s what you’re supposed to do, man. You’re Six Organs.’”

Six Organs of Admittance plays Local 506 on Tuesday, July 11 with DeYarmond Edison. Hush Arbor and Sunburned Hand of the Man’s John Moloney join the band in its trio form. The $8 show starts at 9:30 p.m.