If Kim Thayil had it his way, Soundgarden might not be celebrating the 20th anniversary of their biggest and best-selling album, Superunknown.

"Record companies like these nice, solid numbers, the multiples of fives and 10s," the guitarist said by phone from a festival in Krakow, Poland. "If it were up to me, I'd have waited a couple of years and done Superunknown 22 — or a great prime number, like 23." He wishes they'd released a 23rd-anniversary edition of 1991's Badmotorfinger, "if for no other reason than to mock — in loving fashion, of course — our peers who put out 20th and 25th and 30th anniversaries of albums. It's easy to sell, but we are a little bit more obnoxious and smartassy, so a nice prime number that's not a multiple of anything but itself would be perfect for us."

It'd certainly fit Superunknown, a lumbering, shape-shifting behemoth fueled by bizarrely tuned guitars and jagged time signatures that ultimately sold some 9 million copies. Still, for Soundgarden, 20 years is a good time to look back on the glory days of grunge.

Superunknown was released on March 8, 1994 — the same day as another alt-rock all-timer, Nine Inch Nails' The Downward Spiral. The groups were even supposed to tour together that fall before vocal issues sidelined Soundgarden singer Chris Cornell. Now, 20 years later, they're back on the road for a co-headlining tour that hits at Tampa's MidFlorida Credit Union Amphitheatre on Monday.

In those two decades, Soundgarden spent 12 years broken up before reuniting in 2010 and releasing a new album, 2012's King Animal. They've also delved into their sizeable history and legacy, releasing compilations featuring troves of demos and live recordings, including this year's sprawling five-disc reissue of Superunknown, which features demos, B-sides, live takes and much more.

There's a difference between creating new music, like King Animal, and curating one's back catalog, but the analytical, detail-obsessed Thayil, 53, finds a measure of artistic satisfaction in both.

"Re-releasing something with new mixes and new mastering, it isn't the initial thing that pops into our heads as artists, but it is something we will supervise as artists," he said. "Because if we don't, the record company will put out what they think is great, and it may clash with what we envision."

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Here's another nice, round number: It's been 30 years since Thayil and singer Chris Cornell co-founded Soundgarden, the first Seattle grunge band to sign a major label contract.

That bit of trivia is usually overshadowed by the immediate success of their Emerald City friends Nirvana and Pearl Jam, who blitzed the mainstream rock landscape long before Soundgarden released Superunknown.

Thayil wasn't surprised by this. "People still embrace Nirvana as this successful punk rock band, but they are basically a pop band with some punky overtones on the guitars and in the vocals," he said. "It surprised people that they would become that big, but it shouldn't have, because in context, Nevermind's a really poppy and slick record. It's really well produced."

Soundgarden, on the other hand, challenged listeners at every turn. They identified as a punk band before they turned metal, and even after a couple of releases on A&M (1989's Louder Than Love and Badmotorfinger), their sonically and structurally ambitious music defied easy categorization — singles from Superunknown were nominated for Grammys in the fields of rock, hard rock and metal. Can anyone name two weirder hits from the grunge era than the silverware-clattering Spoonman or the apocalyptic Black Hole Sun?

"We didn't design ourselves to be that hugely successful or commercially successful," said Thayil. "Maybe we have short attention spans, and that's why we write songs in weird time signatures, to keep ourselves interested."

The stylistic diversity of Superunknown is due in part to the democratic nature of the band. All four members contributed significant chunks of music — not just the Beatles-obsessed songsmith Cornell and heady metalhead Thayil, but also bassist Ben Shepherd and drummer Matt Cameron. (Cameron, who is also in Pearl Jam, is sitting out this Soundgarden tour; filling in is veteran session drummer Matt Chamberlain.)

When Soundgarden reunited in 2010, "we initially got together for partnership and business purposes — to attend to our catalog, merchandising and fan club," Thayil said. After that, they started jamming and discussed playing a show. Cameron brought some new songs he'd been working on. "The next thing you know, we were incredibly enthused to make a record," Thayil said. "We took tentative steps, put our foot in the water, it gradually got deeper, and before you knew it, we were swimming across the channel."

Almost immediately, Soundgarden began excavating their archives, releasing a greatest-hits album, 2010's Telephantasm; then Live on I-5, a live recording of a 1996 concert; then 2012's box set Soundgarden: The Classic Album Selection.

Owning their legacy is important to Soundgarden, who in 2013 became eligible for the Rock and Roll Hall of Fame. Many of their peers (Nirvana, Alice In Chains, Stone Temple Pilots) have dissolved or died off, and ultimately, it's not clear what influence grunge acts like Soundgarden have had on today's modern rock artists.

Thayil, for his part, sees it mostly in niche, experimental metal bands like Boris, Sleep, Sun O))) and the Dillinger Escape Plan, who are opening this tour with Nine Inch Nails. "You have a lot of darker, moody, bleak subject matter, and that doesn't play well at a party or social events, but it works well with musicians," he said.

Twenty years after Superunknown, though, conventional pop songs still aren't part of Soundgarden's mission statement.

"Writing accessible, catchy pop songs is probably not beyond our abilities," Thayil said. "It's hard to write one that people are going to love, but it's easy to write with those kind of formulas. But we've never been that way."