Every duo needs a straight man, and in the Swell Season, that’s Marketa Irglova. No, she’s not a man, nor is the Swell Season merely a duo. But to audiences who swooned for the 2006 hit indie romance “Once,” the face and voice of the Czech-born Irglova are inseparable from those of Glen Hansard, her musical partner and co-star in the film. Hansard, much older, is the more effusive of the pair, introducing songs in a twitchy Irish brogue and strumming his guitar so hard you can see splinters fly off of it.

Irglova is a calmer, more studied performer. At the 9:30 Club on Monday night, on her first tour as a solo artist, the 23-year-old Oscar-winner reaffirmed the beauty of her singing while demonstrating that the new songs she’s written on her own don’t have the transcendent power of those she and Hansard write together.

Chairs had been placed on the club’s usually standing-room-only floor and the stage pushed forward, presumably to make the space feel cozier on an evening that appeared to fall well short of selling out. The 95-minute gig’s first half sagged under a surfeit of tunes from “Anar,” Irglova’s recent solo debut — first-person, mid-tempo piano ballads, one barely distinguishable from the next if not for her occasional, diffuse preambles, such as the one she gave to “Only in Your Head.”

Things picked up when she introduced the most prominent member of her three-piece band, Iranian singer and percussionist Aida Shahghasemi, who played a large, hand-held drum called a daf. After what was surely the most epic drum solo in delicate, interior, piano-based-indie-folk history, the two women sang songs in their native tongues. Irglova traded her keyboard for a guitar to close the set with “I Have Loved You Wrong.”

Her encore included “This Right Here,” a song slated for her next album, and “Falling Slowly,” the Oscar-winning love theme, during which Shahghasemi’s voice took the place of Hansard’s. It was the only performance of the night when he wasn’t missed.

Klimek is a freelance writer.