There’s a song on John Oates’ new album, “Reunion,” about a renowned musical duo that stayed together for decades even as their relationship became strained. But the name of the song is not “Daryl Hall & John Oates.”

Instead, it’s called “Sonny Terry & Brownie McGhee.” Written by Oates and Joe Henry, it’s inspired by the great folk-blues duo Oates was a fan of growing up in North Wales, when his tastes were shaped by visits to the Philadelphia Folk Festival and the Uptown Theater on North Broad Street.

Now, Oates is headlining this year’s Folk Fest at the Old Pool Farm on Aug. 17, as the annual gathering returns after a hiatus last year, marking the first time it was not held in any form since 1962.

Oates made headlines last November when his rift with Hall — with whom he founded the Philadelphia pop-soul group that scored hits like “Sara Smile,” “You Make My Dreams,” “Rich Girl,” and many more — went public amid a rancorous legal battle. That partnership is over and done with, said Oates, speaking via Zoom from his home in Woody Creek, Colorado.

Hall & Oates is “absolutely” finished, said the singer and guitarist who cowrote many of the band’s best-loved songs and sang lead on “She’s Gone” and “How Does It Feel To Be Back.”

“Fifty years is a long time to be together with anybody,” he said.

He’s actually understating the length of the union: the duo first met as Temple University students at the Adelphi Ballroom in West Philadelphia in 1967. Two years later, they formed their own group and released a first album, “Whole Oats,” in 1972.

“A house that’s divided isn’t strong enough to stand,” Oates sings on the gently captivating “Sonny Terry & Brownie McGhee.” “Nothing gets decided by drawing lines in the sand.”

Was it written with tension between Hall and Oates in mind? It was, Oates says. But not consciously.

Terry, a harmonica player who died in 1986, and McGhee, a guitarist who died 10 years later, “grew to dislike each other,” Oates says. “They had a bad relationship. But then one of them lost his eyesight and the other lost his ability to walk. And they literally needed each other to get on stage.

“I wanted to write a story about lending a helping hand and make it a metaphor for kindness. And then I realized that deep down psychologically, I had been processing this situation between Daryl and myself. I was exorcising things that had been going on in my life.”

Oates is glad that it happened accidentally. Had he addressed the split in more specific terms, “it would either have fallen flat or sounded bitter and vindictive,” he said.

And he’s neither of those things, “not about Daryl Hall or my relationship with him or not working with him. In fact, I’m very happy about it because I think I’ve freed myself and, in a sense, I’ve freed Daryl to be whoever we can be in the later stages of our creative life. It’s a gift in a way.”

Hall & Oates’ last album of original music was “Do It For Love” in 2003. But they continued touring. I asked Hall how they avoided hating each other after so many years.

“Ever talk to a couple that’s been together for 40 years?” he answered. “They go beyond hate. No, the truth is in any successful relationship, you have to have a certain freedom to be the person you are.”

The duo was inducted into the Rock & Roll Hall of Fame in 2014, and their HoagieNation festival launched in 2017. But it failed to return in 2022 and Hall and Oates played their final show in Laughlin, Nev., in October 2022.

Recent tours “were never uncomfortable,” Oates said. “We always got along very well on the surface.” But he was frustrated “because I had to wear two different hats” and “couldn’t commit to either thing 100%. At a certain point, I said, ‘I have to do something else.’”

He gets that Hall & Oates fans are disappointed.

“People are always heartbroken when a long-term relationship falls apart. I understand people have a fondness for the memories they associate with the music they love and grew up with. I do, too. And I can’t deny the powerful emotions that I’ve been feeling, dealing with departing from a 50-year relationship. A friendship. It’s a big deal.”

But he’s also enjoying his freedom.

“I’m having so much fun. I just sat in with Lyle Lovett. A few weeks before that, I sat in at the Ryman with Del McCoury’s bluegrass band. Incredible opportunities are coming my way now and I have the flexibility to actually do them.”

“Reunion’s” title track was inspired by Oates’ father, Al, who turned 101 last month but has had recent health struggles. “We were worried he was headed to a reunion with my mom.” Ann Oates died in 2017.

But Al Oates pulled through, “and I started thinking about the word reunion, and reuniting with my former self, the musician I used to be.”