Happy summer! It’s been a historic couple of weeks in Hollywood — what with Paul McCartney gigs, White Stripes in-stores and Prince residencies. (See my Prince concert notes below.) But summer’s just begun, and the next two weeks offer some worthwhile rock doings.

ROBOTS INVADE L.A.: Daft Punk make pop music in the guise of electronica, and it’s an absolutely delightful celebration of music itself — from the Beach Boys to Parliament to glam rock and beyond. Ten years after they recorded their live album (Daft Punk: Alive 1997), the robots return to L.A. to launch a limited tour of the U.S. I am excited as shit to see them, and feel horribly lucky. (I missed their much-ballyhooed set at last year’s Coachella.)

Daft Punk play the L.A. Sports Arena on Sat., July 21.

? BEATLES INVADE THE EGYPTIAN: If you’re a Beatles fan, a documentary-film buff, or just a regular guy like me, you are gently urged to check out a beyond-rare screening of the film What’s Happening! The Beatles in the U.S.A. (1964), opening the Mods & Rockers film fest this weekend at the Egyptian. This intensely intimate documentary was shot with hand-held cameras by the legendary Maysles brothers — who had crazy access to the Fabs during their first U.S. trip. Largely filmed in hotel rooms, train compartments and even inside the Beatles’ limos, this is the documentary that inspired A Hard Day’s Night. And it makes an excellent companion to that film, providing real-life glimpses of the boys’ first serious reckoning with their own monstrous stardom. And, my God, they smoked a lot! The quiet moments are also revealing: They seem dazed and tired at times, perhaps already creatively restless — in one shot, John sits in a chair, fiddling with a whistle, almost absent-mindedly playing what sounds like “Strawberry Fields Forever.”

A re-edited version of this film was released in 1994 (The Beatles: The First U.S. Visit), but this pristine original cut is bizarrely unavailable anywhere, and has never been released on DVD. (Don’t even try to Netflix it, yo.) Note: The rest of the festival is also fab, seriously, and includes the much-whispered-about, rarely seen ’06 doc Who Is Harry Nilsson (And Why Is Everybody Talkin’ About Him?) (Saturday, July 14); The Beach Boys Live in London (Sunday, July 15); and Led Zeppelin Live at the Royal Albert Hall (Wednesday, July 18).

What’s Happening! The Beatles in the U.S.A. shows Friday, July 13, at the Egyptian Theatre with the Maysles’ Gimme Shelter. For tickets, go to www.modsandrockers.com.

? PRINCE INVADES HOLLYWOOD: As a Prince fan, I’m deeply enjoying his rebirth as an aspiring pop star. Maybe he’s matured, maybe he needs the money, or maybe he just can’t stand life outside the spotlight — it doesn’t matter, really. The good news is, Prince seems to have outgrown his ?grudge against major labels and the world in general, and is eager once again to be a part of mainstream pop culture.

What’s a little less inspiring is the fact that he’s doing the whole corporate tie-in thing to promote his upcoming album and world tour: The “video” for “Guitar,” the first single off the forthcoming Planet Earth, is basically an ad for a certain cell-phone company.

Whatever. The song is no “Let’s Go Crazy,” but I’ll take it any day over anything off Come, The Rainbow Children, et al. And during his recent residency at the Roosevelt Hotel — I caught the show on Friday, June 29 — “Guitar” fit in nicely with a carefully chosen set list heavy on golden-era hits ’n’ B-sides.

One of the strangest things during the show, though, was watching Prince be forced to “warm up” the audience — who were chatting loudly in the back of the room for maybe the first half hour of the show (which began at 12:30 a.m. and lasted about 90 minutes). (This was not the case at his Las Vegas gig, which I reviewed in the spring.)

No doubt the audience was waiting for a hit: Prince and his band opened with a New Orleans–style “Down by the Riverside,” which morphed into a 20-minute gospel-blues vamp on “Satisfied,” off his last album, 3121. His new lyrics were hilarious — about his “cockeyed” woman (who asks for the pepper but looks at the salt!) — and proved that comic timing is yet another weapon Prince carries on his Total Entertainer tool belt. (And let’s not forget that unearthly falsetto, which he used to impressive ends in the opener.)

The set list was surprisingly similar to the Vegas show I caught, but this time I wasn’t as bothered by the brass section — specifically, the way its sonic harshness can bleach the darkness and mystery from Prince’s compositions. I still think “If I Was Your Girlfriend” suffers under the pomp and crash of the brass, but mostly the arrangements felt appropriate to the moment: This was meant to be a debauched house party more than a concert. It wasn’t meant to be the Total Journey a Prince fan always longs for, and experiences through his best albums.

He’s focusing on those best albums lately too, apparently leaning away from most of his late-’90s output (The Gold Experience, et al.). Even the newer songs he performed sounded vintage — like “Lolita,” off 3121, which sounds like it could easily be something he pulled from the vault. That’s good.

Funny thing, though: The songs bled into one another, and often echoed each other, as melodic and rhythmic motifs repeated — until we could hear a unified sonic landscape unfold around us. You could say we had entered Princeland; it certainly felt as if we were nestled in a knoll deep within his oeuvre, where you could hear how the loveliest regions of his catalog all connect. The bouncing “3121” became an update on “It’s Gonna Be a Beautiful Night” (from Sign o’ the Times), with a nod to “Hotel California,” while the whistles from “America” (off Around the World in a Day) were borrowed as a horn riff for “Musicology.” When his winning backup singers broke into a Wonder Twin–powered cover of Janet Jackson’s “What Have You Done for Me Lately,” we were all reminded of Prince’s shared Minneapolis DNA with Janet’s producers, Jimmy Jam and Terry Lewis.

As Prince and Co. dug deeper into the hit bag, the crowd loosened — “Kiss,” the “Bang a Gong”–inspired “Cream” (heavy cowbell!), “U Got the Look,” even a cover of Chaka Khan’s “Sweet Thing,” seduced and invited the crowd to sing along (which everyone did, loudly and without shame). As mentioned, his new song, “Guitar,” also blends well with those: It’s goofy yet poised in that way only Prince can pull off. Somewhat Bolanesque. Naturally, Prince closed with his abridged version of “Purple Rain” and, ever the showman, urged the audience to whoop along to that mournful “oo oo oo ooo . . .” refrain — which we did, again, even louder than before.

Despite midnight misanthropy and a bourgeois grudge against the wealthy, at that moment I couldn’t help but love my fellow man — even my fellow drunk, rich Hollywood creeps. For all their flaws, people can be awfully beautiful when they sing a kickass power ballad together.

And give “Purple Rain” credit: It’s more than just a crowd pleaser, more than just an oldie. Something about its inarticulate howl, and the triumphant, proud grief of its lyrics, expresses a pain that is uniquely private but utterly universal.

Prince declined to perform an encore, but he sat in during his band’s post-show jazz jam, held in an adjacent room (which began at 2:30 a.m. and went till about 4). This much smaller audience lounged on leather couches or stood around, while the band — featuring the husband-wife team of Josh and CC Dunham on bass and drums — riffed on “Straight, No Chaser.” I was wondering how Prince would adapt to a bebop situation; the answer was, he didn’t. After he appeared on the small stage and strapped on his guitar, bebop became rock pretty fast as the band seemed momentarily to tear into a variation on Nirvana’s “Smells Like Teen Spirit” — which was actually “Anotherloverholenyohead” (off the sublime Parade, an album sadly overshadowed by its monster hit, “Kiss”). Cutely enough, this version of the song employed the riff from “Rock Lobster” (or something very close to it). Prince’s solo on this one was what a dude would call “sick,” better than anything he’d done earlier in the night. I have never heard anyone produce a sound so thick and menacing — and yet elegant — from a guitar (including Mr. Jack White). Guitarwise, Prince is the closest I will ever get to Jimi Hendrix, but he’s much more sophisticated and versatile, even at his sludgiest. In short, this solo — as much a celebration of the act of the guitar solo as a solo in itself — was the single greatest guitar performance I’ve ever witnessed live.

Prince disappeared soon after “Anotherloverhole,” and the band played “Caravan” for the stalwarts, the very ?drunk and those who were sacked out ?on the couches. After the metal explosion we’d just witnessed, this served as a ?satisfying digestif. And then it was over. Walking out into the early morning, with a slightly brightening sky overhead, I felt a kind of music satisfaction I hadn’t felt in ages. The night was over, but the summer had just begun.

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