MODESTO, Calif. — Blues Traveler is the rarest of musical acts — a jam band with a major chart hit.

Phish never has charted, nor has moe., Widespread Panic or Umphrey’s McGee. The Grateful Dead’s long, strange trip had worn on for 20 years old before a heavy MTV rotation made “Touch of Grey” its lone top 10 hit.

But if the 1995 hit “Run-Around” is the lone song of the band’s vast repertoire that strikes a familiar chord, do yourself a favor and stream a Blues Traveler live performance — not so much to be able to identify the songs but to prepare for a head-on rock show with a decidedly jammy feel.

John Popper’s distinctive voice, along with his Jimi-inspired harmonica played in staccato twin-lead with guitarist Chad Kinchla, comprises the signature sound of Blues Traveler. And you never know when the band will see fit to take a three-minute track out to 10 minutes, or improvise seamless segues between a series of songs that will leave the crowd breathless for a half-hour.

Blues Traveler is in the middle of a management change, which has left Popper unavailable for interviews, but he told Joanne Schenker of Glide Magazine in 2011 that when “Run-Around” and the follow-up “Hook” — both off the album “Four” — hit the charts hard in 1994, the band’s live audience grew exponentially and changed dramatically almost overnight.

“It was a very surreal year,” Popper said. “There were our normal fans, who were a bunch of hippies, and then 50 million 12-year-olds who hate every other song we play except “Hook” and “Runaround.”

“And when you play those two hits, it’s like a Beatles concert. Meanwhile, all our regular fans are Dead dancing to all our other songs and then they have to stand there disgusted while we play those hits. It was very hard to keep the two factions from killing each other.”

No actual fan faction violence ever really occurred.

And such peace befits a band that traces its roots to the idyllic New Jersey town of Princeton. It’s home to a great Ivy League university and apparently — at least in the 1970s — as a breeding ground for jam band leaders.

Phish frontman Trey Anastasio attended preppy Princeton Day School just a couple years before Popper and Spin Doctors founder Chris Barron were classmates at Princeton High.

After it was discovered at an early age that Popper had an ear for harmonizing, he grew up trying various instruments. He didn’t have the patience for practice or teachers, but developed an affinity for playing harmonica.

While he was trying out as a trumpeter in the Princeton High jazz band, it came time for Popper to show off his chops with a solo during the band’s reading of Thomas Dolby’s “Blinded Me With Science.” Instead, Popper put down his instrument and reached into his trumpet case for one of his ever-present harmonicas, holding it up to make sure he had the blessing of the director.

“Luckily it was the right key and the teacher said, ‘Go for it,’” Popper said in Glide Magazine. The next day I’m in the first-string band and the principal is checking me out and everybody knew my name. It was really weird. All of a sudden I was like the quarterback on the football team.”

Blues Traveler was born as a Princeton garage band, and after graduation the members moved into an apartment in Brooklyn under the guise of going to college at the New School. In fact, they took advantage of the rehearsal space the New School provided, but dropped out as soon as paying gigs covered the rent.

The band was discovered by an A&M Records scout and toured the East Coast as a pet project of Bill Graham Presents. Many of those early shows put the young musicians on a bill as the opener for the Allman Brothers Band.

“That was like going to school,” Popper told Glide. “Bill Graham started managing us pretty early and he had us opening for them right away. And I know what he was thinking. He was like, ‘You guys have to look at the possibilities of what you can be.’ And for us, it was way eye-opening to see how they (the Allmans) put on a show every night and how BIG it could get. We got to play with them a lot.”

Blues Traveler has released 11 studio and three live albums, but as is the case with all jam bands the proof is in the frequent improvisational moments within the live performance. And that’s where the band is blessed.

The strength of “Run-Around” and the six-time platinum sales of “Four” have allowed the band to continue to chart its own path, to play music the way it wishes.

Loud, energetic and always fresh.

“(When we started) we were thinking more about an organic kind of fame,” Popper said. “More like The Grateful Dead. And I have to say, even though it sounds like a cliché, that the success on ‘Four’ certainly helped us, but we just really wanted to be good musicians. It proved to be the one thing that paid our bills more than anything else.

“The success of ‘Four’ guaranteed us work, which is really what it’s about because I love playing in front of an audience.”