OVER SEVERAL YEARS and four albums, the Bad Plus has been throwing down the gauntlet, serving up a very distinctive brand of bad-to-the-bone music.

While the band answers (sometimes) to the calling of jazz trio (and record for the Heads Up jazz label), keyboardist Ethan Iverson, bassist Reid Anderson and drummer David King work out with dark, ruminating, improvisational takes on rock and pop classics - tunes from the catalogs of heavys like Rush, Led Zeppelin and Nirvana, and dream weavers like Burt Bacharach and Tears for Fears.

Now, on their new album "For All I Care" and with the tour bringing them to Chris' Jazz Cafe tonight and tomorrow, these Bad boys are taking the music to the next level - for the first time adding a kindred vocal spirit, Wendy Lewis.

Moreover, they're underscoring the hold that modernist classical music has on them. On the new set, the musicians slide in atmosphere-drenched works by Ligeti, Babbitt and Stravinsky alongside the likes of Pink Floyd's "Comfortably Numb," Yes' "Long Distance Runaround," Nirvana's "Lithium" and Flaming Lips' "Feeling Yourself Disintegrate."

I caught up with keyboardist Iverson riding in the tour van the other day to find out how it's all going - and if they really do care.

Q: So what are we to call this music of yours? To whom does it appeal? And are your role models those popular jazz guys from the 1960s and '70s like Ramsey Lewis and Herbie Mann, who crossed over to the pop charts by covering tracks by the Beatles and Dobie Gray?

Iverson: Someone called us "avant garde populists," which is as close as we're going to get. Our audience, frankly, depends on where we're playing. This week, we're playing the 9:30 Club in Washington, D.C. It's a rock club, so we'll face mostly rockers there, with a pretty young average age.

Then the next two nights we'll be with you at Chris', so the crowd there might identify more with jazz and be a bit older. But these days almost everyone in America is into rock, to a degree. It's what we all know, it's our folklore, so working with this music, finding the best in it, comes totally naturally to us, as guys in our upper 30s.

As to the origin of re-interpreting popular music, that really goes back to people like Chopin, Liszt and Mozart, who wrote variations on the popular opera themes of the day.

Q: What motivated you guys to add a vocalist? Was there any thinking that it could help get you sales and play on radio stations?

Iverson: I don't know how to answer that question. I try to not pay much attention to the charts, to what's getting played. It was really this simple: after four studio albums, it was time for a collaboration.

In a certain way, it might be more obvious to work with a sax or guitar player, but Wendy and Dave go way back. And it came together so easily. We talked about it, did a rehearsal, and she just fit. Ultimately, the human voice is the greatest instrument.

The audience really connects with her. She's such a pro, such a passionate singer. And after being three guys riding around in a van for six or seven years, it's nice to have her new energy offstage as well as on.

Q: Have you had any feedback, positive or negative, from artists whose work you've covered? And weren't you asking for trouble covering the Bee Gees' "How Deep Is Your Love" on the new set?

Iverson: The bassist for Black Sabbath, Geezer Butler, came to one of our gigs in Los Angeles and told us afterwards that he loved our version of "Iron Man." That was really cool. There's a rumor that Wilco likes our version of "Radio Cure" [on the new album]. As to the Bee Gees, I've always loved that song. It never had a negative association. I think it's a minor masterpiece, and I like our version, too.

Q: Really, that's what's going on with the title of your album "For All I Care," isn't it? While the expression could be taken as a negative, you mean it as a positive, right?

Iverson: It's a song quote from [Nirvana's] "Lithium," but it means we care about all this music - it all comes naturally to us. And we think there are a lot of people today who just love music without putting a tag on it. We can't be concerned about how people will respond, though. Our philosophy is just keep your head down and play.

Q: The new album was mixed by Tchad Blake, who's got quite a heritage in rock 'n'roll, working with Peter Gabriel, Pearl Jam, Elvis Costello . . . . What was his input, and which version do you like better sonically, the CD or the vinyl?

Iverson: Tchad's a genius. If you listen to a bunch of his records, you can identify that he has a very specific, very strong sonic identity. I think he did a great job for us. The sound is very focused and punchy. If you've got a really great record player, I think the vinyl version sounds better. *

Chris' Jazz Cafe, 1421 Sansom St., 8 & 10 tonight and tomorrow, $25, 215-568-3132, www.chrisjazzcafe.com.