Occasionally in years past, the Coachella Valley Music and Arts Festival brought in legends of the classic rock era and stature to supplement the indie/youth orientation of the bill, including Paul McCartney, Roger Waters, Leonard Cohen, and Steely Dan. Promoter Goldenvoice has lately seemed less interested in that cross-generational crossover — leaving it up to the younger artists themselves to make it happen, by offering cameos from their biggest influences.

Friday, it was the teen brothers Lemon Twigs bringing on Todd Rundgren for a climactic collaboration on his 1972 “Couldn’t I Just Tell You,” a song on anyone’s list of the half-dozen quintessential power pop singles. “It was such a dream come true for us,” says Brian D’Addario of getting the wizard/true star to step in on the “Something/Anything?” classic.

Sunday, Thundercat brought the 1970s lightning with a three-song appearance by Michael McDonald, a drop-in that’s somewhat less surprising, since the Doobie Brother appeared on Thundercat’s “Show You the Way,” though probably no one at Coachella was expecting a bonus performance of “What a Fool Believes” in anyone’s set.

“Todd said he’d never been” to Coachella, D’Addario recounts. “He said, ‘I hear that’s the one that people die at.’” D’Addario is reluctant to give away any secrets about how the Twigs got Rundgren to join them in the desert. “I don’t want other people stealing our idea,” he jokes. But the brothers met him after Rundgren’s New York City Winery show in March, and their managers subsequently reached out to each other about making a joint appearance happen.

Rundgren was impressed by what he saw before he got on stage — especially compared to other acts he caught before leaving the festival. “After watching the Twigs and seeing what they do, a lot of the other bands seemed kind of like shucking,” Rundgren says. “Like, the Twigs should have been on the big stage, and put one of these shucking bands on the smaller stage.”

In at least one sense, Rundgren was more impressed by Coachella than he expected to be. “I expected it to be funkier than it was. It’s actually a fairly well organized — one might even say anally organized — event,” he says. “I was interested to see what people wanted to listen to, and some of it seemed obvious to me, like the big crowd for Radiohead, while there were some bands that I had never heard of that were drawing fairly substantial audiences, if only out of curiosity. But overall, the event impressed me as something like a hookup … less about the music and more about girls being as scantily clad as they possibly can, and men getting really drunk and hitting on them. Music seemed an aspect of it, but it didn’t seem to be the principle reason why people were there.”

But he has nothing but laudatory words for his hosts, saying the Twigs “have a natural performance sense, [as opposed to] what tends to happen nowadays, where bands go to extremes in terms of either mopey-ness or artifice on stage. But both these guys have been performers for a considerable portion of their lives, and when they get to the stage, it just seems really natural what they do, as if they’ve been doing it for 10 years — and I know that isn’t quite possible, because the youngest of them is only 18 years old. Listening to them on record is one thing, but when you see them live and how effective they are and how musical they are, it’s another experience, and I was really impressed. There’s a variety of influences that a lot of contemporary artists have I more or less ignored. It seems like they’re willing to put in the effort to come up with very elaborate arrangements that have lots of tempo and time-signature changes and interesting sort of suspended chords — stuff that you don’t hear from a lot of other artists anymore. The symphonic approach that you might attribute to a band like Queen, that’s too much work for a band nowadays,” he says, chuckling.

For the Lemon Twigs, Rundgren is dad-rock, which in their case is a very commendable thing, remembering that their father “always told us about his Utopia [album, “Deface the Music”] where they dressed up as the Beatles, because my dad really liked that,” says the elder of the teen D’Arrios. We were generally aware of him, and then we got really into him when we made the record, because our producer, Jonathan Rado, is really, really into Todd.” What they came to love is his “coupling that love of songs with experimentation — he just has the ability to do both — and then the way he’s continued to do his own thing. I think that’s something we also want to continue to do, and not feel like we have to appeal to what other people’s expectations of us are. He obviously wants to fully explore every facet of everything that he can do in music. Even a lot of our other favorites don’t do that.”

McDonald believes that musical appreciation tends to skip a generation, which is why he can go over so well with a Coachella audience while a star closer to the median between his age — 65 — and the average fest-goer might not.

“Each generation tries to disassociate itself with the last generation,” McDonald says. “And then about three decades later, people kind of start to maybe appreciate what you might have done a while back that you don’t even realize you did. So it’s been fun to get out and play with bands like this,” says the singer, who’s also performed at other recent festivals with Solange and members of Vulfpeck and Snarky Puppy. “We were around long enough ago that we aren’t from just 10 years ago, so, you know, people aren’t holding up crosses at us,” he laughs.

McDonald was on stage with Thundercat in the Mojave tent for three numbers — their collaboration “Show You the Way,” plus the former’s “What a Fool Believes” and the latter’s “Them Changes.” “Watching Steve [Bruner] play bass, he’s almost like a culmination of Stanley Clarke and Marcus Miller, in putting something together that is influenced by so many of the people that came before him,” McDonald says. “I always kind of think of stuntmen. Back in the old days the big trick was falling off your horse, and now these guys are falling off 15-story buildings. It’s amazing what some of these young musicians accomplish, to me, Steve is one of those.”

McDonald drove down from Santa Barbara with his daughter, who provided tips on who to see, like Sampha. “The whole weekend for me was a lot of going to school on what I was seeing and hearing, and I’m really impressed by the artistry of people we saw like Father John Misty. There’s a whole other thing in that they’re fearless in the fact that they’ll get into their niche and develop this thing that they do without any regard for what’s commercial or what isn’t commercial or what record companies or managers would or wouldn’t tell them to do. It’s impressive to me that these guys do what they do best with no fear and develop it to a fine art.”

McDonald was left with some questions, though. “Father John Misty’s band was great, and it was a large orchestra, so of course I’m thinking from the standpoint, too, of a practical touring musician, like: How does he afford all those people?”