Soundgarden has not yet revealed what its plans are in the wake of frontman Chris Cornell's suicide Wednesday (May 17) night in Detroit. But prior to the tragic loss, guitarist Kim Thayil told Billboard that projects -- both new and archival -- were in the works.

Among those is another set of new material to follow-up 2012's King Animal, which has been in motion, at its own pace, for awhile. "It's been a couple years of intermittent songwriting sessions," Thayil said shortly before the start of Soundgarden's spring tour. The group has to work around Cornell's solo shows and drummer Matt Cameron's commitments to Pearl Jam, of course, but Thayil said that, "We look for opportunities where all four of us are available and then we get together and we show each other what we've been working on, what we've been writing on our own and see if there's anything that can be contributed from that sharing process. And then we like to jam and see if any ideas come out collaboratively that we can work on."

Thayil revealed that "there's some songs that have been demoed. I think Matt's demoed some things completely, stuff he's recorded on his computer. Chris has demoed a few things. He's written lyrics for ideas that I've written and that Ben and Matt have written. There's some things that have been documented in rehearsal. There's some things that are at the demo stage. There's some that are still in the developmental stage -- ideas that we've jammed on that we're working on arrangements for.

"Every different stage within the process of songwriting is being addressed at this point."

Meanwhile, Soundgarden was also considering its next archival projects after expanded and remastered editions of Badmotorfinger last fall and Ultramega OK earlier this year. Thayil says there are definitely more treasures in the Soundgarden vaults that merit being heard. "There are a number of recordings sessions that were never released for various reasons," Thayil said. "There are some we recorded with a previous drummer and they weren't really up to our satisfaction. There's stuff we haven't released that we recorded with (producer) Jack Endino that were intended for Sub Pop release that didn't happen. The Screaming Life EP was supposed to be a full-length album but Sub Pop wanted to do an EP, so there's material that was recorded for that. We've been able to address many of the aspects from our catalog, both released and unreleased, and I think we will continue to do so."

There's also the question of a Soundgarden induction into the Rock and Roll Hall of Fame. The group has been nominated in the past, and Thayil said that after watching Cameron get in this year with Pearl Jam, Soundgarden merits inclusion as well. "Y'know, it's not my call," Thayil says. "Pearl Jam's a no-brainer, and Nirvana. But, yeah, I think Soundgarden, Alice In Chains, to another degree Mudhoney and Screaming Trees, we've all had great success that certainly surpasses that of a number of artists that are in the Rock and Roll Hall of Fame. But we're subject to the judgment of other folks, ultimately. I think there would be something cool about it, but it ultimately doesn't reflect what we've achieved critically or commercially with our body of work."