On rare occasions, one sees a concert so excellent that it becomes genuinely hard to come up with the words to describe it. The Máirtín O’Connor Trio’s show at Newtown Meeting House, hosted on April 10 by The Shamrock Traditional Irish Music Society, was one of those concerts.

Everything was perfect. The band members were energized and the house was filled with an appreciative audience. One cannot imagine a better start for the trio’s nine-day East Coast tour.

The trio is comprised of Máirtín O’Connor on two-row button accordion, Cathal Hayden on fiddle and tenor banjo, and Seamie O’Dowd on guitar and vocals. Each is a master of his instrument and a veteran of numerous other well-known Irish traditional ensembles.

Many excellent bands could be described in much the same fashion. But what makes this trio unique is their deep musical connection. They have a tight rapport that reminds me of the great duos of traditional music, such as the fiddler Martin Hayes and the guitarist Dennis Cahill. To see that almost telepathic connection in a larger group is a rare treat.

The concert last Friday evening began with a pair of jigs, “The Boys of Coonamore” and “The Tongs By the Fire,” flowing into a pair of reels, “Ed Reavy’s” (also known as “The Hunter’s House”) and “The Rose in the Garden.” Mr O’Dowd started the set off with a series of delicate, chiming notes on the guitar, mostly played on open strings, which created an unusual and effective harmonic accompaniment for Mr Hayden’s fiddle and Mr O’Connor’s accordion. On the second tune of the set, his backing switched to a driving strumming pattern.

“It’s great to be here,” Mr O’Connor said. “At this stage in our lives, it’s great to be anywhere, but it’s especially great to be here in this beautiful building. Fair play to you in Newtown for preserving it.”

The next tune was an unusual hornpipe with swing influences, titled “Catwalk.” Mr O’Connor wrote the piece after an unusual tour in Italy, he said, which included a gig playing at a fashion show “in which the models elegantly marched up and down while listening to jigs and reels. It was a great moment for us, and a great challenge for them.”

Mr O’Dowd’s native County Sligo is well known for its many legendary instrumental musicians, but “there weren’t a lot of songs about Sligo until a man from California named Thom Moore showed up there in the Seventies,” he shared.

Mr Moore’s “Believe Me, Sligo” is a modern classic which has been sung by many artists. Mr O’Dowd’s own take, with finger-picked guitar and thoughtful touches of accordion and fiddle, can stand with any of them.

The band followed that song with a set of polkas composed by Mr O’Connor: “Pat’s Polka,” named for his late uncle, a harmonica player; “Begley’s Frolicks,” written for the Kerry musician Séamus Begley; “Dance of Life,” and “Jamaican Jam.”

The Inagh Valley is a beautiful place in the western Irish region of Connemara, which inspired Mr O’Connor to write a lovely, gentle, meditative tune by that name. The Trio followed “The Inagh Valley” with a unique jig, also written by Mr O’Connor, called “Rocking the Boat,” which is dedicated to the Irish filmmaker Bob Quinn, best known for his documentary Atlantean, which looked at possible connections between ancient Ireland and North Africa.

“As I Roved Out” is an old song from the Ulster Scots tradition, written from the perspective of a man who meets with his old sweetheart, who reproaches him for having broken his promise to her and wedding “the lassie who has the land.” He acknowledges that he made a terrible mistake, saying “when I turn to embrace my darling, instead of gold sure ‘tis brass I find.” The song was popularized in the Seventies by the great singer and bouzouki-player Andy Irvine, who recorded it with the band Planxty. Like many others, Mr O’Dowd learned “As I Roved Out” from Mr Irvine, but his own version, opening with simple droning accompaniment by Mr O’Connor on the accordion, was stunning, evocative and chilling, perhaps the best take on the song I’ve ever heard.

“The Drogheda Jig,” an unusual 13-part tune, was collected in the 1800s by Canon James Goodman, a Church of Ireland clergyman who himself was a skilled player of the uilleann pipes, the Irish bellows-driven bagpipes. “For this tune, I always feel like a piper trapped in an accordion-player’s body,” Mr O’Connor said.

Mr Hayden has won All-Ireland Championships on both fiddle and banjo, and his solo banjo work on a set of jigs including “The Donegal Lass,” written by Brian Finnegan of the band Flook, demonstrated a deft sense of phrasing and a supple musicality.

The concert “officially” ended with a classic set of reels associated with the great Galway accordionist Joe Cooley: “The Humours of Tulla,” “Last Night’s Fun,” “Cooley’s Reel,” and “The Wise Maid.”

But no audience could allow a concert like this one to end without demanding to hear more music. The Máirtín O’Connor Trio chose a very different classic for their encore: George Frederick Handel’s The Arrival of the Queen of Sheba, which Mr O’Connor recorded with De Danann in the Eighties. Their lively, unusual take on the Baroque sinfonia was a perfect finale to a brilliant evening.