MINNEAPOLIS — Four years or so after Soundgarden split up, lead vocalist and rhythm guitarist Chris Cornell had what he now calls “an epiphany.”

“One of our songs — I think it was ‘Pretty Noose’ — came on the radio while I was driving around, and frankly it just crushed the newer songs before it and after it and had more of a timelessness to it,” one of rock’s mightiest squealers remembered.

“I realized Soundgarden had become a ‘classic’ kind of band, the kind that wasn’t going to go away.”

So why, then, did it take so long for Soundgarden to finally return? Cornell explained that and a lot more in an interview during rehearsals two weeks ago, a week before the quartet hit the road on a tour that lands Saturday at the Orpheum Theatre in Minneapolis.

The more metallic counterpart to Nirvana and Pearl Jam in the Seattle grunge scene that exploded in 1991 — with Cornell’s window-shattering voice and Kim Thayil’s thundering guitar work setting it apart — Soundgarden pretty well retired at its commercial peak in 1997, following the release of the “Superunknown” and “Down on the Upside” albums. Those records scored heavy radio play that persists today with the singles “Spoonman,” “Black Hole Sun” and (its last and arguably best hit) “Blow Up the Outside World.” The radio hits led to the Lollapalooza mega-tour of 1996 with Metallica and arena headlining dates.

With success, predictably, came internal problems. Cornell said the main reason Soundgarden split was that it had simply gotten too big — not in terms of records and concert tickets sold, but the number of people involved.

“We broke down communicatively, because we had all these other people peripherally involved in the band. Decisions were made that we didn’t all agree on, or even know about. That created tension.”

On the other hand, Cornell justifiably bragged, “I actually think we went out on a creative high. There was a certain amount of relief when we did stop playing together that we didn’t mess things up creatively. We never sucked.”

Most Soundgarden fans would not say the same about Cornell’s erratic solo career, which reached its odd peak in 2009 with the poppy Timbaland-produced album “Scream.” Fans were more receptive to his stint in the supergroup Audioslave (2002-2007) with the three instrumentalists from Rage Against the Machine, but it paled in comparison to their old bands.

As for the other dudes in Soundgarden, drummer Matt Cameron joined Pearl Jam in 1998 and hasn’t looked back (he’ll juggle both bands this year) while Thayil and bassist Ben Shepherd were surprisingly inactive. Cornell said they all remained friends but rarely talked business.

Strangely, it was business matters that finally brought them back together in 2010.

“Usually, there’ll be a record label to handle promotion of the back catalog and B-sides, and someone overlooking stuff like T-shirts and a fan club,” he said. “We didn’t have anyone doing that for us. We didn’t even have a functioning website.”

All of which was a good thing, he said: “That led to the four of us finally getting together and sitting down in the same room, and it really was as simple as that. Until we were all together, we couldn’t really feel each other out on the idea (of reuniting).”

They proceeded to feel things out in 2010, issuing “Telephantasm: A Retrospective” and playing a short tour around Lollapalooza. That led to last year’s concert album “Live on I-5,” which fulfilled their old contract with A&M Records and set up what Cornell called “the perfect scenario” to make a new record and become more of a full-time band.

Some observers wondered if Cornell was hesitant to reform Soundgarden for fear of having to hit all those high notes he wailed back in his 20s.

“Clearly, I’m not going to be able to sing this way forever,” he said. “I think people get too hung up on singers and their range, sort of like they’d expect Michael Jordan to get out on a basketball court and play like he once did. It’s physically impossible.”

That rare bit of humility didn’t last long, though: “I’ll probably never retire. I’ll just adapt and do what I have to do to keep the music interesting.”