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As Tom Petty and the Heartbreakers wrap up a 40th anniversary tour with three shows at the Hollywood Bowl this week, only the truly OCD among us may notice or care that this year actually marks the 41st anniversary of the group’s self-titled 1976 debut album. The good news about the dodgy math is that it might put us a year closer to 45th and 50th anniversary tours than we thought we were. Should the Bowl just get them on the books now?

Maybe that’s premature, if you take Petty at his word when he told Rolling Stone late last year that he was “thinking this may be the last trip around the country … I’d be lying if I didn’t say I was thinking this might be the last big one.” His own band members scoffed at that, though, and it helps that, from all appearances at Friday’s show, he and the Heartbreakers still like each other, even after five months on the road — something that can’t be said of very many rock groups celebrating their fourth anniversary. This tour has the feel of a victory lap, certainly, but not remotely a valedictory lap.

The focus this go-round has been on 40 (or 41) years of greatest hits, more so than on the group’s 2013-14 tours, which made a bit more room for deep tracks and covers. Even with that as an m.o., a two-hour set still involves leaving a few signature classics out, though fans likely didn’t notice the absence of “Breakdown” or “Don’t Do Me Like That” ’til they compared notes in the Uber on the way home, if at all. Petty is not being particularly spontaneous with the set lists on this tour — the lineup of songs Friday was exactly as it was for their June show in Pasadena at the Arroyo Seco Festival, minus one — but you’d be hard pressed to argue with the acuity of this one, which is bookended by barnburners from that ’77 debut.

In between came tracks that have felt like much bigger hits over time than they were in their initial moment; 1994’s “You Wreck Me,” which never even made the Hot 100, now commands the penultimate encore slot just ahead of “American Girl,” with a sense of inevitability and zero complaints. That was one of five songs performed from the “Wildflowers” album, perhaps a remnant of the original plan to put out a boxed set of outtakes from that period this year and support it with a more intimate tour. Any tour that counts even unofficially or in miniature as a “Wildflowers” support tour is a good one, and if Petty did make good on his intention to commemorate that still-underrated ‘90s album — say, next year, nudge nudge — he’d be greeted with a lot of happy hearts.

The only significant change-up for the 2017 tour has been the addition of two female backup singers, England’s Webb Sisters, who get to do a few more choreographed moves than they did back when they were supporting Leonard Cohen. Though ever-present, their support was mostly more textural, if not almost subliminal. But they did manage to finally make “Don’t Come Around Here No More” (one of the few Petty songs ever to spotlight female vocals on record) adhere more to the original. They also got louder and clearer on “Runnin’ Down a Dream,” an only slightly startling addition to a perennial previously untouched by female larynxes.

But the show was obviously about reconvening with old friends — among them, drummer Steve Ferrone and utility player Scott Thurston, whom Petty can still kid about being the new guys, even though they’ve been around for more than half the group’s tenure now. With apologies to the E Street Band and any other instrumental stalwarts in popular music, the contest for MVP in all of rock and roll continues to come down to a tight race between members of one group — guitarist Mike Campbell and keyboardist Benmont Tench.

The Heartbreakers' Mike Campbell and Tom Petty at the Hollywood Bowl, September 22, 2017

The players’ primary showcase Friday night was a more-than-10-minute version of “It’s Good to Be King,” the jam-band portion of the evening, which had Petty and Campbell trading guitar solos … although not doing so much trading that it wasn’t still clear Petty considers his wingman the king. Tench was afforded fewer organ and piano solos, yet you could make the case that he’s the one member of the group who is essentially soloing all night, though you have to listen a little closer to catch on to the fact that Tench is constantly playing solos beneath the solos, not to mention adding improvisational flourishes even to Petty’s meat-and-potatoes verses and choruses. You don’t have to have played together for 40 years — or more, counting Mudcrutch — to lock in this seamlessly, but it helps.

As for the man himself? Petty remains the perfect combination of an everyman who is One of Us and a rock superstar definitely not One of Us … his slow-drawling, almost stoner-like asides creating the most relaxed possible atmosphere for the audience, even as those shades hide the sharp eyes of one of rock’s most historically astute craftsmen. Rather than take the posture of a towering figure, he spends a lot of the night hunched over his guitar, as if he means to creep up on us. He’s won us over without ever seeming like he’s trying to, which maybe is one factor in why America isn’t any more tired of him and his Cheshire grin in 2017 than we were in a pre-MTV era.

The Bowl run and overall tour wrap up Monday night, where the show will be opened, as on the previous two, by another great, Lucinda Williams. Her legend hasn’t completely crossed over to the mainstream; on the way into the Bowl, a woman could be overheard hoping that she would do her biggest hit, “I Hope You Dance” (ahem). But even Petty fans who mistook her for some other LW got a good hour’s worth of Williams’ essence … and “Essence,” one of the best rock songs ever written about love-as-intoxication, done up at the Bowl in an arrangement that made it sound like a lost Neil Young classic.

Lucinda Williams opening for Tom Petty at the Hollywood Bowl, September 22, 2017

Williams is ostensibly promoting her release next Friday of “Sweet Old World,” a 25-year-old album that she’s completely re-recorded for its 25th anniversary. But she didn’t play much off that, surely figuring that its acoustic nature would not be the way to win over an only half-familiar Petty crowd, so the Bowl got the loud Lucinda. That included as a rousing climax “Honey Bee” (not to be confused with the Petty song of the same name), the raciest song ever written about apiarists. She also revived “Changed the Locks,” thanking Petty for recording it back in ’96. That still marks the only time Petty has ever covered someone else’s song on a studio album, an honor that made Williams a natural to help round out a history-honoring tour.