FAIRFIELD — As a boy growing up in a small town in County Clare, Ireland, Damien Connolly was exposed to traditional Irish music at an early age.

But he was not immediately drawn to the sound.

“My musical influence is basically my dad. He’d have friends over and play and he’d play it on the radio. It was really annoying to me when I was growing up,” Damien said.

An accomplished musician, his father, Martin, even competed in the Fleadh Cheoil, a national Irish music competition, winning the title of All-Ireland button accordion player in 1978.

“At about 11 or 12, he brought me to an accordion class he was teaching. I honestly went just to make him happy. But then I just loved it and I started taking classes and then, after about a year, I started to teach myself from recordings,” Damian said from the basement of his Fairfield home on a recent Tuesday, seated between his wife, Sally, and 12-year-old son, Colman.

The trio comprise a family band. Sally — who grew up in Easton with a family that played “old-timey and bluegrass music” — is a singer and plays a flute that, unlike the metallic classical instrument, is made of African blackwood or rosewood and is better suited to the traditional Irish style. Colman is a pianist who began playing around the age of 6.

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For more information on the Connollys, visit irishmusicfairfieldct.weebly.com

Around them on the walls are hung an acoustic guitar, a mandolin and a fiddle, on which Damien is also an accomplished player. A harp — which the Connollys’ 9-year-old daughter Clara will soon take up — sits on the floor in a case beside Sally. Colman sits on a stool and plays the wooden piano in the corner of the room. And on Damien’s lap is the button accordion — the instrument with which he has primarily built his musical reputation.

As a teenager, Damien — now a theology teacher at Lauralton Hall and an instructor at Sacred Heart University — would listen to tape recordings of button accordion performances on repeat to improve his skills, stopping the tape and rewinding over parts he hoped to master. He quickly began making strides and demonstrating prowess on the accordion, soon outpacing his older brother. As a teenager, Damien’s education on the instrument would continue in Ireland’s remote pubs, where he would travel with his father to see legendary traditional Irish musicians, like button accordion virtuoso Joe Burke, play shows and jam with local musicians.

“It would just be in random pubs all over the rural areas. Nobody would really know about this person except for those people who had been hard core into Irish music,” Damien remembered. “For those who were traditionalists, those would’ve been like going to see Michael Jackson. You’d swear you were in the presence of God Almighty.”

Ultimately, Damien developed into one of Ireland’s elite players of the button accordion — a fixture of traditional Irish music.

The button accordion, as opposed to the piano accordion, features a series of buttons instead of keys played with the right hand on the melody-side keyboard. Another set of fewer buttons sits on the bass-side, played with the left hand. Enclosed in the wooden casing on which the buttons sit is a series of reeds, which Damien likened to harmonicas. Between the wooden casings are the bellows, which are compressed or expanded to manipulate the sound.

“Depending on the kind of accordion you have there might be one harmonica, two harmonicas, three or four. The kind I have has three,” Damien explained. “Basically, for whatever note I play there are three going. One is usually the exact note, one is usually a little bit flat and one is usually a little bit sharp, just to give it a rounded tone.”

While the piano accordion is played occasionally in traditional Irish music, the button accordion is favored.

“The first kind of accordion introduced to Ireland was the button accordion — and that was back in the 1800s. You had the Industrial Revolution and things were mass produced and they eventually made their way to Ireland,” Damien explained.

Sally became interested in Irish music while an undergraduate at Brown University, where she studied behavioral neuroscience but continued to play music. After she graduated, she applied for a grant to study Irish music in Ireland. In 1999, the couple met at Fleadh Cheoil, the same annual all-Ireland music festival where Damien’s father once played.

Damien followed in his father footsteps, twice winning the top prize at Fleadh Cheoil, and Colman is doing similarly, winning bronze in his age division in 2016.

“It’s like the Olympics of Irish music. It’s been like that for about 50-plus years,” said Damien.

In 2003, Damien and Sally moved to Fairfield to raise a family. Damien has continued to play gigs regularly throughout Connecticut and perform at workshops and festivals around the country. He plays several times a month at the Playwright Pub in Hamden and has performed at the Irish Heritage Center in Milford.

On Nov. 26, the Connollys will perform at the Gaelic American Club in Fairfield.

But Damien is anxious to play more, especially with his family. He hopes to add his youngest son, Tristan, 7, who plays the whistle, to the group and to turn people on locally to the music of his childhood.

“People want to hear ballads, stuff they can drink to, stuff they can sing to,” Damien said.

But the more old school, more traditional stuff, Damien believes, is also more refined and more distinct.

“The possibilities have just started to emerge,” Damien said. “It’s just trying to make the vision work.”

justin.papp@scni.com; @justinjpapp1