Cat and the Moon members (L-R) Elias Alexander, Eamon Sefton, Charles Berthoud, Ricky Mier and Kathleen Parks met while studying at the Berklee College of Music.The band’s name is taken from the title of a William Butler Yeats poem. Its co-founder is a protégé of renowned Sligo-style fiddler Brian Conway, one member has taught at the Boston Harbor Scottish Fiddle Camp, and another is a dynamic, peripatetic bagpiper. And over the past few years, the band has become a fixture at Greater Boston Irish/Celtic venues and events like The Burren, the Irish Culture Centre of New England’s annual festival, and BCMFest.

Don’t pigeonhole local quintet Cat and the Moon into the “Celtic” category, though. It’s just not that simple.

For one thing, there’s an unmistakable bluegrass strain running through their music, evident in the rolling cadence of five-string banjo and backing-on-the-offbeat by guitar. But wait a minute – now they’re playing a jazz/funk mash-up, in the Bela Fleck/”Newgrass” style, an electric bass line walking along the melody, and percussion accentuating the rhythm. And then they shift gears again, and tear through a bona-fide traditional Irish reel. Hey, did they just play Bach?

You have to be pretty darn good musicians to pull this sort of thing off, and the members of Cat and the Moon – Kathleen Parks (fiddle), Ricky Mier (banjo), Charles Berthoud (electric bass), Eamon Sefton (guitar), Elias Alexander (percussion, bagpipes) – certainly fit that description: They were all good enough to get into the Berklee College of Music, which is where they met and developed their sound over the past few years. They’ve preserved the fruits of this formative period on their recently released debut CD.

Trite as the phrase may be, “expect the unexpected” can aptly describe the Cat and the Moon oeuvre, such as stray riffs you’ve heard before but perhaps can’t immediately place – yes, that’s Bach’s “Presto Sonata in G Minor” Mier and Parks briefly reference during “The Taste.” Appropriately enough, “Cat and the Moon” could serve as a signature track for the band: Parks opens with some aggressive rhythmic chopping before she and Mier glide into the melody, with its twisty-turny accents and time signature shifts. Just as you realize you’ve heard the theme from “Inspector Gadget,” Mier and Berthoud go into a pas-de-deux that ends with snatches of “The Sailor’s Hornpipe” and “Pop Goes the Weasel,” and then Parks embarks on a percussive step-dance break, trading off beats with Alexander before the band has one more go at the main theme.

The band’s treatment of the traditional Irish reels “Fermoy Lasses/Cup of Tea” unfolds slowly and quietly, Parks working in increasingly complex variations and improvisations over Sefton’s steady chordings, until Mier raises the starter’s pistol and they’re off and running on “Cup of Tea,” at least for a little while – Parks and Mier take improvisational solos, and the tune begins to recalibrate in bluegrass mode, then at the end seems almost, but not quite, back in its Irish setting.

That track and “Home Again,” which uses a brisk jig rhythm as its foundation, showcase Mier’s ability to tease out triplets as if he were playing a tenor banjo – the kind you use with a plectrum – as opposed to the fingers-operated five-string brand. Parks, meanwhile, uses her fiddle not only for melody but also for creating mood and texture, such as during one of Berthoud’s patented bass solos on “Moonrise.” Alexander brings out the bagpipes for a set of tunes he co-wrote, “Sunset Run/Enemy Feminine Anemone,” the latter of which is a driving, head-for-the-hills jig that recalls the work of Scotland’s “acid-croft” bands like Shooglenifty.

“I think it’s a good picture of where we are, where we’ve come from,” says Mier. “The music – Celtic, bluegrass, funk, blues, disco, whatever – is the culmination of all our experiences, and it’s the conversation we have with one another.”

All the members of Cat and the Moon are skillful musicians, and each gets a chance to shine, but it is co-founders Parks and Mier who are unquestionably the band’s focal point – visually as well as musically. In performance, they’ll frequently engage one another as they trade off licks, sometimes striking rock-star poses, other times effecting deadpan glances, all the while spinning out a litany of riffs, harmonies, and duets. Theirs is a fascinating pairing, from opposite sides of the country – Mier is from San Francisco, Parks from north of New York City – and from quite different musical paths.

Parks’s family provided her considerable inspiration: Her father is a professional trumpet player in a polka band who also plays jazz, and her mother is a dancer in Irish as well as Polish tradition. With a grandmother from Galway, it’s no wonder Parks took up Irish stepdance at a young age, and – after starting out on classical violin at age 5 – Irish fiddle at age 9, when she began studying with Conway.

When she was 13, Parks heard pioneering fiddler Eileen Ivers, and was taken by her fusion of Irish and world music, as well as jazz and other genres. “It was so beautiful and powerful, and I thought ‘That’s what I want to do!’ So I got close to my dad and learned more about what he played, like swing and funk – he introduced me to Earth, Wind and Fire – and that helped in getting used to playing improvisations.”

Mier, who is unfailingly gregarious and effusive – he’s been known to start a conversation by showing off coin tricks – describes his childhood musical activity as “making stuff up. My parents listened to disco, and I grew up downloading; sometimes I’d hear something and say, ‘It would be cool to play this in a band.’” Mier started on guitar in middle school, “but it had too many strings, so I got a bass instead.” He had enough natural ability to take advanced music classes on both instruments in high school, and besides learning classics such as “Stairway to Heaven” and “Blackbird,” he got very good at fingerpicking.

“Then someone showed me a banjo,” he recalls, “and I dragged Mom to the store to show her the song I learned. A few weeks later, she surprised me with a banjo that I never put down.”

If Eileen Ivers was Parks’s big revelation, Bela Fleck – with his technical proficiency and inventive progressive bluegrass style – was Mier’s. As he became more and more familiar with the banjo, Mier put together a band with some fellow students to play bluegrass, although “there wasn’t a violin or fiddle player in the entire school.”

Then Mier met Boston-area banjo player Gabe Hirshfeld on social media, who told him about Berklee. “I checked it out and fell in love,” he says.

Jam sessions are as regular an occurrence at Berklee as, say, breathing. So naturally enough, Mier and Parks crossed paths at one such get-together. As Mier recalls it, although they both knew an Irish tune – “The Swallowtail Jig” – they didn’t have any bluegrass tunes in common.

“So we just instantly made stuff up,” he says. “She was amazing. I showed her a few of the tunes I’d come up with, and she got it just like that.”

“Most all of what we did at first was funk,” adds Parks, the only member of the band still in Berklee. “Being in a place like Berklee, you’re at a crossroads. There are so many ways to go, if you allow yourself to be open to the possibilities of something new. This was totally different than what I was used to with Irish sessions, and I really loved it.”

Even as they began building their own repertoire, Parks and Mier found other kindred spirits at Berklee like Sefton, a Boston-area native whose formative experiences included playing with Celtic fiddle band Chasing Redbird and attending the annual Boston Harbor Scottish Fiddle School (he’s now on the faculty). One of Sefton’s pals at Berklee was Alexander, an Oregonian who plays a music store’s worth of instruments including Scottish bagpipes, is also a top-notch percussionist, and a certifiable live wire. And then there was Berthoud, who came all the way from London – “Charles is astoundingly good,” says Mier. “He can do things on the bass that are just unbelievable, and he’s open to a lot of different styles and vibes. He fit right in.”

There are certain challenges to forming a band at Berklee. Perhaps the biggest is that most every Berklee student seems to be part of a half-dozen other bands or collaborations. That’s certainly true for Cat and the Moon: Mier and Parks play with bluegrass unit Twisted Pine, for instance, and Parks, Sefton, and Alexander are members of Irish-Scottish group Fresh Haggis; Alexander also is front man for Afro-Celt/funk ensemble Soulsha. It took a lot of work and focus, Parks and Mier say, for Cat and the Moon to mesh their talents and ideas and come up with something cohesive enough that would endure beyond a jam session.

“One thing that helped a lot was that we had a residency at The Burren for a couple of months,” says Mier. “When you have a regular gig where you have to play for three hours at a time, you get better, and you develop a chemistry.”

Adds Parks, “Playing at The Burren definitely improved not only our collective musical abilities, but also our entertainment skills. It’s one thing to sit around playing music with each other, but when you have an audience you have to keep them in mind, too, and do what you can so they enjoy themselves.”

Last year, the band felt ready to hit the recording studio, another crucial milestone in its development.

“We were road-tested by then, but we knew we had to really fine-tune our arrangements and make sure we were all together,” says Mier. “I gave everyone a big pep-talk: ‘This needs to be the definitive recording of Cat and the Moon.’ I didn’t mean in terms of playing absolutely perfect, with no mistakes. I wanted us to think about how we wanted to sound: What is it that defines us as a band?

“We really came together on this, and I think the result is totally us.”

But the band isn’t content to stay that particular “us,” say Parks and Mier. They’re looking to embark on a new direction, which involves Parks’ abilities as a singer and songwriter.

“Kathleen’s written some great songs,” says Mier. “It will really add a whole new dimension to our sound, and give us more ideas to work with.”

Where Cat and the Moon is concerned, anything seems possible – which is what Yeats suggested at the end of the poem that is the band’s namesake: “Maybe the moon may learn/tired of that courtly fashion/a new dance turn.”

For more about Cat and the Moon, see catandthemoon.com.