On Brattle Street, a jazzy serenade from a bunch of Squares

How would he describe his musical chops at those open mics? “I wasn’t great, but people didn’t run from the room screaming.”

Leading the Squares, his occasional solos are short, punchy, and to-the-point, a style patterned after his heroes, the backing band of the late Ray Charles. And though a low-key presence onstage, he relishes his role as an emcee. On a recent Sunday he walked, mid-song, over to a toddler who was bobbing to the music and placed a sticky musical note on the happy child’s hand.

The band’s name was coined in similarly improvised fashion, says Trabilcy, who lives in Watertown. “Someone in the audience shouted, ‘What’s the name of the group?’ Being a spontaneous fellow, Squares in the Square popped in my head and I shouted it right back.”

How square are they? Most of the musicians aren’t young, true. But the material? “It’s old, too, but still hip,” says Trabilcy, who is on a mission to fight what he feels is an inward, alienating turn in most modern jazz. He loves seducing the non-jazz fan with music that is extraverted and fun.

The Squares simply couldn’t have happened without community help. The issue was electricity: Singers need mics and guitarists need amps.

“Denise Jillson of the Harvard Square Business Association told me there were electric outlets built right into Brattle Square, for the Christmas lights,” says Trabilcy. “And she managed to get Cambridge Electric to turn them on for us. But even before she could maneuver that, Bluestone Lane café allowed us once to plug into their wall sockets and run extension cords right out their front doors!”

There are no rehearsals. Additions to the repertoire are only played if “figured out in a minute,” Trabilcy says. It’s like a barroom open-mic jam session, but outdoors and without the booze.

As modest as Trabilcy is about his own skills, he is unabashedly proud of his band. The core members are bassist Lee Lundy, a Bahamian-American, and Sir Cecil, a drummer with Trinidadian roots and an ever-present rastacap who travels 100 miles from Northampton for each gig. Guitarists Mark Michaels and Dave Ehle, and saxophonist Karen Baseman, a lawyer, also receive praise from Trabilcy. The singers who sit in with the band vary widely in skill, but one of the best is young Elisabeth Waters, who possesses a light tone, elegant phrasing, and sure pitch.

Each weekend morning this spring Trabilcy’s band members texted him with the same question: “Will it be 55?”

“They act like I’m weather central,” he says. “But my rule is: If the temperature is predicted to rise to 55, with no rain, we’re on.”