Without leaving Port City Music Hall, the audience Thursday night got to take a world tour.

Banda Magda established wide musical roots and tied them all together through fine musicianship and the dynamic personality of the group’s founder.

Magda Giannikou sings in several languages (French, Spanish, Portuguese, Greek), and it’s probably safe to say that most in the crowd didn’t know precisely what she was singing at any given moment, though a few Greek- and Spanish-speaking folks made efforts to let her know they did.

But the Greece-born, Boston-educated frontwoman kept most in the crowd fully engaged through the power of her voice, expressive stage presence and the wide range of influences she brought to her work on the accordion.

She did introduce, in English, the origins and themes of most of her songs, including the fantastic tale that is at the heart of the group’s latest album. “Le Tigre Malin” recounts a parable of fear and courage as three antelopes encounter the titular menace. After a fierce, or wild, as she called it, instrumental introduction that combined rock guitar with intense polyrhythms from the quintet’s two percussionists, the singer moved to the edge of the stage to enlist the help of audience members as she related the story, her animated features providing additional drama.

With band members hailing from Argentina, Japan and the United States, many musical flavors came and went during the 90-minute performance. Elements of pop, rock and jazz held things loosely together, but all of the musical components blended seamlessly in the singular vision of Giannikou.

The leader often wordlessly vocalized as she dug deep into her accordion keyboard, engaging with guitarist Ignacio Hernandez to share a particularly salient harmony or percussionist Keita Ogawa to ground the musical moment.

Ogawa was a bit of a show in himself, offering a humorous interlude where he worked out a rhythm on a set of squeaky-toy pigs. Later he evolved a strong solo, beginning on a wooden cajon box before employing a number of exotic instruments. Augmented by a second percussionist and electric bass, it was easy to ride the rhythms to wherever the music was going.

A couple of quieter songs added variety and made it clear that Giannikou also has a way with reflective pieces based on romantic themes about places and people.

“Muchacha” established a plaintive tone and “Thiamandi” later felt like one that came from the singer’s heart to cap off this highly entertaining concert co-presented by the State Theatre and Portland Ovations.

Giannikou announced that she and the band were off to Japan the next morning for a tour. Many in the crowd expressed a hope that the worldly Banda Magda would come back around this way soon.

Steve Feeney is a freelance writer who lives in Portland.