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For a month now, the world's greatest rock- and-roll band has been holed up in this private school in Toronto--putting itself back together again for yet another tour--and it's made itself right at home in typical fashion. In the room Mick Jagger has appropriated, white curtains are pulled wide open for maximum sunlight, fluffy white rugs cover the floor and a humidifier blasts 24/7 to protect his 62-year-old voice from the arctic AC. In fact, he's shivering: like the other Stones, he has zero body fat. (He works out daily with a dance instructor--"not exactly a choreographer; he just helps me plot out my stage moves.") He's wearing loose white cotton pants, a pink, pin-striped dress shirt, black and red Adidas. He points to a full-length gray and white fur coat. "I was wearing that because it's so cold in here," he says, "but I thought I'd better take it off before you came in, or it could look a little... well, too much."

Keith Richards, meanwhile, has converted a classroom into a candlelit den, with blackout curtains, dozens of blood-red roses and a skull he uses for a candy dish. Cigarette smoke hangs in the air. "It's comfy, innit?" he says, gesturing around with a clawlike hand. Richards, 61, wears a tattered scarf around his head, and random charms--an eagle head, a cross, a Chinese coin--hanging from his matted quasi dreads. He says he has no idea what-all is in his hair: his kids and his friends like to decorate him while he's passed out. Richards has no trainer, no regimen, and plots out exactly nothing. "Mick has to get up in the morning with a plan," Richards says. "Who he's going to call, what he's going to eat, where he's going to go. Me, I wake up, praise the Lord, then make sure all the phones are turned off. If we were a mum-and-pop operation, then he'd be Mum."

This mum-and-pop operation called the Rolling Stones has been in business now for 43 years. Just three of the original five--Jagger, Richards and drummer Charlie Watts--are still running the shop; guitarist Brian Jones died in 1969 and bassist Bill Wyman retired in 1993. They haven't had a No. 1 album since "Tattoo You" in 1981. But while most of their peers have either died, dropped into obscurity or taken to limping periodically through sad "reunion" tours, the Stones remain one of the world's top concert attractions. Want a ticket for this year's tour, which kicks off in Boston on Aug. 21? Hurry, it's almost sold out. The question is, when they step onstage, do they still feel it? The answer is, why else would they bother? "I could see why some people may think we're phoning it in after all this time," says Richards. "But playing the music we do, and playing it with these guys, 'Jumpin' Jack Flash' can be a new song to me every night. I mean, we don't need to do it to feed our families. We don't need to do it to prove anything. And nobody wants to be the first one to get off a moving bus. You end up in the dust--'Uh, excuse me, where's my suitcase?' "

In recent years, the Stones' tours have gotten more praise than the new albums they write and record before hitting the road. Their last album, the double-CD "Forty Licks," was mostly repackaged material. "There's no harm in doing that occasionally," says Jagger, "but we didn't want to do it again so soon. You become like an oldies band." The Stones' latest, "A Bigger Bang," which comes out in early September, is a welcome throwback to their scrappy beginnings. This time all the songs are new--a raw, "Little Red Rooster"-style blues number, a couple of Richards's endearingly bedraggled ballads and the usual raunchy, swaggering club anthems. Jagger is clearly proud of it. "We put new stuff out because we still can," he says. "We have lots of it--it's not like we're just eking it out. Rock fans tend to be conservative. 'Ah, I much prefer "Brown Sugar".' Yeah, well, but listen to this, c--t."

Producer Don Was, says Jagger, "is always worried the songs won't sound like the Rolling Stones. I don't care if it sounds like them--us. It would be an achievement if it didn't." But "A Bigger Bang" is classic Stones all the way. It's their longest record in 33 years and is sequenced to sound like two sides of an old vinyl album. "The record company felt it was too long," says Jagger. "But I said, 'What's the favorite Rolling Stones album of all time?' 'Well, "Exile on Main Street".' 'There, you see? "Exile." And how long is that?' 'It's over an hour.' 'And the problem is?' 'Uh, nothing'."

Jagger and Richards say they worked together more closely on "A Bigger Bang" than they have in years, partly because Watts, the only other original Stone, was battling throat cancer. "We were sitting across the table looking at each other," says Richards, "like, 'You. Me. That's all there is.' It was all built on two acoustic guitars, and in such a sparse and stripped-down way that if you tried to elaborate on it later you'd lose the whole essence of it." The Stones' new music sounds more spontaneous than most of their recent efforts, and Jagger sounds angrier than he has in years. Since the band's last studio album, Jagger has ended his 23-year relationship with wife Jerry Hall, and was taken to court over an illegitimate child he fathered with a Brazilian model, which may explain such lyrics as "Oh no! Not you again, f---ing up my life/It was bad the first time around/Better take my own advice." But the most searing moment, on a song called "Sweet Neo Con," isn't personal but political. "You call yourself a Christian, I call you a hypocrite/You call yourself a patriot, well I think you're full of s--t." "It is direct," Jagger says with a laugh. "Keith said [he breaks into a dead-on Keith imitation], 'It's not really metaphorical.' I think he's a bit worried because he lives in the U.S." Jagger smiles. "But I don't."

The tension between Jagger and Richards--primarily, but not exclusively, creative--has always been at the heart of the Stones. Jagger the arty, natty cosmopolitan, Richards the scruffy blues purist and regular guy; Jagger dancing and prancing, Richards standing there with a cigarette dangling. Over the years, they've quarreled and reconciled, recorded solo albums and reunited, and neither has really thrived without the other. "Many times we wanted to kill each other," Richards says now, "or at least cause some serious damage. But it's always about details, never about fundamentals. An album cover--'You can't do that!' It's quite silly, really. I've known the man since he was 4... and I was 3-1/2 [he gives a broad wink]. Our kids have all grown up around each other--the Jaggers and the Richardses. All of that has made us patriarchs." They can both remember when they were teenage amateurs, opening for the real patriarchs: Bo Diddley and Little Richard. "The only blue I knew was the school blazer I'd just shed," says Richards, in a well-rehearsed line. For all Jagger's strutting arrogance and Richards's world-weary decadence, they've hung on to a touch of that innocence. Each keeps the other honest: Richards is there to remind Jagger that he's a musician; Jagger is there to remind Richards that he's a star.

As usual, the Stones' new tour will feature grandiose spectacle that's at odds with their rock-club roots and their musical minimalism. It will have two stages, at least a truckload of props--including some mysterious papier-mache screaming heads that now sit on a table outside Jagger's dressing room--and seats for a few lucky fans that are built right into the stage set. And as usual, the type-A Jagger is all over everything. "What about concert T shirts?" he asks rhetorically, running his hands through his hair until it stands up like a fright wig. "The set? The stages? The videos, onstage and off? There's too much to do, and not enough hours in the day. And then there's the rehearsal. [He puts on a fake cruise-director smile.] 'Is everyone all right, then? Are we all happy?' Nannying."

And--as usual--Richards is sitting back and taking the long view. "It's that fascination with music that is still the core of the band," he says. "Charlie sits around and talks about this fantastic Coltrane solo. Thank God, it's the one thing that hasn't left us. You can get disillusioned with the state of the world, but the music's still OK." He takes another drag of his cigarette. "Maybe we're just a product of our time," he muses. "Would our band translate if we were just starting out now? I'd say we'd probably be able to make a living, but I'd keep the day job." For Jagger, this is the day job--at least until he gets onstage. "Sometimes you might feel 'Here we go again.' Feel a little cynical about it," he says. "But you get out there and it takes over." And here they go again.