Sons of Apollo, featuring bassist Billy Sheehan, at House of Blues Cleveland May 15

Over the past three decades, Billy Sheehan has enjoyed pockets of platinum success in David Lee Roth’s solo band and as a founding member of Mr. Big.

Today, he’s again hoping to find a mainstream audience with new project Sons of Apollo, which includes vocalist Jeff Scott Soto (Journey, Yngwie Malmsteen’s Rising Force), drummer Mike Portnoy (Dream Theater), keyboardist Derek Sherinian (Dream Theater) and guitarist Ron “Bumblefoot” Thal (Guns N’ Roses).

“This is a chance to play with some guys I haven’t worked with before that are good friends,” said Sheehan, calling from Anaheim, California. “It was an interesting twist, a variation on a theme, and it’s been extremely successful. Who would have thunk it?”

That twist and variation marks a digression for Sheehan, who is a respected rock bassist. The Sons of Apollo’s recently released first album, “Psychotic Symphony” — which debuted at No. 1 on Billboard’s Heatseeker Albums chart, as well as No. 10 on the Rock chart —is decidedly a prog-rock affair.

The new project boasts a sound bonding those of Dream Theater, Van Halen, Deep Purple and Led Zeppelin.

“This band is a lot heavier, and it’s a lot of low-tuning, so it changed my style quite a bit because I’m holding these big, giant super-deep low notes as opposed to playing any linear stuff or things that are more complicated and up high on the bass,” Sheehan said.

“It’s a different style and experience. There’s new, challenging, exciting improvisational magic happening live on stage. It’s exciting. It’s fun.”

Fans attending the Sons of Apollo’s show May 15 at House of Blues Cleveland can expect to hear plenty of new tunes, including the heavy “Lost in Oblivion” and the intricate “Labyrinth,” as well as a few covers, such as Van Halen’s “And the Cradle Will Rock…” and Dream Theater’s “Just Let Me Breathe” and “Lines in the Sand.”

Sheehan is admittedly conflicted regarding the latter band.

“It’s difficult to not have this misinterpreted all of the time, so I’ll say it as carefully as possible: I was never a Dream Theater fan,” Sheehan said. “I was never into the band. Why? There are only 24 hours in the day, and you can only be into so much stuff. Plus, when I got into prog music, it’s when it first began with King Crimson and Genesis.

“That style and that type of progressive music I love. The modern stuff doesn’t excite me as much. Does it mean it’s bad? No. It just doesn’t do it for me.”

Sheehan told a story about how initially he didn’t care for Rush. However, in the early ’90s, Mr. Big twice toured with the Rock & Roll Hall of Fame act. During that time, he admittedly opened his mind to the trio and became quite a fan.

It sounds like he’s hoping Dream Theater fans, who can be quite vocal and territorial about their favorite prog-rock act, will at the very least show the same latitude and acceptance of Mr. Big.

“I know Dream Theater fans are particularly not Billy Sheehan fans, in the least possible way, ever,” Sheehan said. “The vitriol and hatred I’ve seen spewed at me for being alive is disturbing.

“It blows my mind. Mr. Big is a rock band. We’ve made some adventurous moves into material that is more complex. I’m extremely proud of that band. I wish people would relax a little bit in the wars between bands. Love what you love. If you don’t like it then spend your time and effort praising what you do like instead of trying to violate humanity with some of your comments and criticisms. It’s disturbing.”

Sons of Apollo

When: 7 p.m. May 15.

Where: House of Blues Cleveland, 308 Euclid Ave.

Tickers: $25 to $30.

Info: ticketmaster.com.