Michael Andrews is not a rock star. He has 20 albums to his credit as a pop songsmith, film and TV composer, guitar and piano player, and record producer, and he and Gary Jules even charted a No. 1 U.K. hit with their cover of Tears for Fears’ “Mad World” from the Donnie Darko soundtrack. Andrews also scored Miranda July’s acclaimed Me and You and Everyone We Know and has just started working on Jake Kasdan’s upcoming feature, The TV Set. And he certainly counts a rock star or two among his friends. But fame just doesn’t seem to be on his agenda — if he even has an agenda at all. And apparently he doesn’t, despite his busy schedule.

“I’m a terrible planner, that’s the funny part,” says the musician, talking about his upcoming Tuesday-night residency at Tangier in Los Feliz. “The fact that it actually comes together is really insane.”

Since September 2005, on and off, Andrews has been hosting what he jokingly calls “Open Mike Andrews” at Tangier, during which he plays songs from his forthcoming album, Hand on String, with a band (regular players include Gus Seyffert, Joey Waronker, Amir Aghmai and Joe Kennedy), and also accompanies the guest musicians who’ve joined him that night, collaborating on their songs and throwing in the odd cover just for good measure: Cyndi Lauper, anyone?

Scott Sterling, who produces events under the Fold banner, first suggested the Open Mike Andrews concept. It wasn’t until about a month into the residency, however, that Andrews admitted to Sterling, “You know, this is a lot of work.” And Sterling said, “I know. When I suggested it, I meant that you play and then they play. I didn’t expect you to play with every single person.”

Still, the format stuck, and the shows became an opportunity for audiences to share in musical processes that normally take place out of the public eye. “I like the immediacy of it; I like improvising,” says Andrews, noting that there’s never more than one rehearsal. “I think it’s important for people to see the process of collaboration and mistakes being made.”

This loose approach draws local talent like Eleni Mandell; Becky Stark and Steve Gregoropoulos from Lavender Diamond; Gary Jules; and Inara George, whose band Andrews belongs to. Van Dyke Parks came one night and promptly disappeared after performing one song, true to his mystique. Pulp’s lead singer, Jarvis Cocker, made a last-minute appearance during Fashion Week in October, and although Andrews didn’t know the song “The Cunts Are Still Ruling the World,” he gave it a go.

There may or may not be surprise guests at Tangier on January 3 when Andrews’ residency starts up again (“I wish I knew what it was gonna be,” the bad planner admitted just a couple of weeks before the show in December), but he is looking forward to building momentum for the release of his solo record at the end of that month. Packaged with a full-size book of gorgeous watercolor illustrations by Geoff McFetridge, Hand on String is a melodic, melancholy collection reminiscent of artists like Nick Drake and Smog.

“I always say, here come the party tunes,” he chuckles, adding, “I think hopefully it’s understandable that I can do a personal record and it doesn’t mean that I can’t have fun.”

The recent packed houses and widening circle of players would seem to indicate that the kids can handle what Andrews reluctantly calls an “adult” record. But he doesn’t want to even guess about his place in the Los Angeles music scene.

“I guess I try not to look at myself in the context of anything, because then you end up always feeling more or less than that,” he says. “Basically, it’s just one night in L.A.”

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