Don’t try to pigeonhole the band RUNA, which performs for the Pastorius Park concert series Wednesday, June 24.

They’re not exactly Irish. They are not precisely Scottish. They’re somewhat Celtic … but only somewhat.

All of those genres influence their music, but to lead singer Shannon Lambert-Ryan, there’s another name that better defines what the band does – and what makes them stand out.

“We never really wanted to define ourselves into one specific genre because we all come from a variety of influences and musical and geographic backgrounds, and we love all different kinds of music,” she explains. “We just want to play really good music that we all enjoy really well. And so the catchphrase that we’ve come up with over the years is ‘Celtic roots,’ because we feel it encompasses all the different factions.”

A friend of the band, Brian O’Donovan of Clonakilty, West Cork, Ireland, defined RUNA’s distinctive approach further. He described traditional Celtic music as something akin to the roots and branches of a tree. It has evolved and grown. It’s the music of Ireland, Scotland, the United Kingdom, and the surrounding islands. And as the music traveled — as it certainly has — the branches of that tree spread out and sprouted in many places around the world. As the music migrated, it fused with different cultures, along with their dances and rhythms.

“Traditional music,” Lambert-Ryan says, “is simply music that’s being passed from one generation to the next, and on to the next, and everybody adds their own piece to it. And that’s something we’ve really embraced and loved jumping into for our entire career as musicians, but especially with this band.”

Here’s an example.

There’s an 19th century folk ballad called “The Lakes of Pontchartrain.” It’s about an Irish émigré who finds shelter with a compassionate Creole woman. He longs to return to — wait for it — the lakes of Pontchartrain.

The song is in 3/4 time — a waltz cadence. In the hands of RUNA, it becomes something very different.

“We’ve wanted to do that song since we started the band and kind of held off because we hadn’t quite figured out how we wanted to arrange it,” Lambert-Ryan said. “As we were putting it together, we said, ‘Why don’t we straighten it out a little bit and put it into 4/4 rhythm and give it more of a Cajun feel? You’ll hear a kind of two-step feeling to it as we play it. We wanted to give a nod to that because that’s where the story comes from.’”

For each tune, RUNA does whatever makes it sound best — not just to be different, but to advance the story. All of which makes a RUNA concert enjoyable not just for the audience, but for members of the band. (RUNA is usually a quintet, but for the Pastorius concert there are just four band members. In addition to Lambert-Ryan, the band will include her husband, guitarist Fionán de Barra, percussionist Cheryl Prashker and fiddler Tom Fitzgerald.)

This will be RUNA’s fourth or fifth appearance at Pastorius Park — Lambert-Ryan has lost count. In each case, the band tries to emulate the feeling of an old-fashioned traditional house party — something that might take place in someone’s cozy little living room. Small venue or festival crowd, fun is the goal. And again, not just for the benefit of the audience, but for the band as well. It’s like opening the fourth wall of the stage, Lambert-Ryan said.

“There’s an inclusion that happens,” she says. “We want the audience to feel like they’re not just observing something but participating. We love when that happens.”

In that sense, Pastorius Park is an ideal venue, she adds.

“Pastorius Park is part of the community, and you feel that sense of community,” she says. “You almost feel enveloped and wrapped up in it. It doesn’t feel like a performance so much as, everybody’s raring to go for the party and we just happen to step into that. And we feel really fortunate that we do truly have family and friends at that show, people we have grown with over the years. We always feel like we’re stepping into a family party when we go on stage there.”

The RUNA show is sponsored by Nolan Painting, and the concert series is sponsored by Temple Health Chestnut Hill Hospital. The performance begins at 7:30 p.m. Pastorius Park is located at 8177 Roanoke St.