Atlanta’s Hank & Cupcakes are only a two-piece, but theirs is a sound that’s bigger, sonically richer and more viscerally galvanizing than that of any 12-piece funk ensemble or multiple-strat-toting metal outfit you could think to name. Married couple and Israeli ex-pats Sagit “Cupcakes” Shir and Ariel “Hank” Scherbacovsky call it “indietronic,” but there’s really no way words can do justice to their irrepressible and insistently hook-y brand of electronic indie-pop hybridized with deliriously danceable rock ‘n’ roll.

“We had just come out of being in another band, and we were experiencing a period of creative emptiness, where we just weren’t sure what our next move should be,” says Shir, explaining the band’s genesis during a recent phone interview. “Ultimately, Hank & Cupcakes was born out of that boredom and uncertainty. The two of us just started rehearsing together, with no commitments other than to enjoy being 100 percent creative, just a bass and drums.

“We began exploring very deeply, and we found a way to make up for all the musicians that were ‘missing’ from our lineup. We don’t do things in the traditional way a bassist or a drummer would do things. There’s a lot of creativity and being unconventional involved in the way we approached our instruments.”

Shir gives a good deal of the credit for crafting H&C’s rafter-shaking, multi-dimensional racket to hubby Scherbacovsky, and his ingenious four-string manipulations. “He has this incredibly complex rig, like a mad scientist kind of thing,” she says. “He splits every signal into four lines, with different effects. It makes his bass sound like a full band.”

To be sure, the story of Hank and Cupcakes’ crazy travelogue of a career, and of the consequent evolution of their one-of-a-kind, genre-redefining sound is hella fascinating all by itself.

It all began when Tel Aviv natives Scherbacovsky and Shir met while playing in a band as members of the Israeli army back in 1999. They clicked both musically and personally, and played in a couple other projects together before marrying and moving to Havana to study jazz and indigenous Cuban music.

Their Cuban sojourn was cut short by the country’s uneasy political climate, and thus the couple bounced back to Israel and undertook the aforementioned creative transformation before officially founding Hank & Cupcakes and moving to Brooklyn, NY in 2008.

Stateside, it wasn’t long before H&C’s emergent pop savvy and colorful, cathartic live sets built a buzz, turning the band into a minor New York legend. They started touring outside the state, traveling all over the U.S., playing CMJ and various other stops on  the up-and-comers festival circuit before trekking abroad to Europe and the Middle East.

A publishing deal ensued, and then, on the eve of releasing their debut record, Hank & Cupcakes signed a recording contract from major label BMG.

But the idyll of having a major label record deal proved to be short-lived. “It was a situation where we had an album ready to come out, and all of a sudden, the label started questioning things,” Shir says. “Then they demanded we bring in co-songwriters. And then they said the budget was gone. We were used to being involved in all aspects of our band, from business to music to promotion, but they didn’t want us being our own leaders. They wanted to keep us out of the loop.”

Shir says the band managed to find a loophole in their contract, then secured their release in 2013 — miraculously enough, with rights to the songs they had written still intact. Liberated, they went on to release their debut “Naked” independently in 2013.

Two more albums — including 2014’s “Cash for Gold” and last year’s “Cheap Thrill” — and a move to Atlanta later, and the buzz the band started building before the BMG derailment is mounting yet again. H & C learned to create their own videos, and have since released a slew of video singles, several of them in conjunction with famed fashion photographer Javier Ortega.

The duo have also logged literally hundreds of dates on the road; they’re currently gearing up for a four-month touring run, the end of which will see them head back to the studio to record songs for a fourth Hank & Cupcakes release in 2018.

“I think most of our growth has come thanks to playing all of those shows these last few years,” Shir says. “We’ve become much more elaborate in what we do, and it’s also helped our sound to grow much bigger. Our performance level has gone way up.

“Next up, we’re going to get back into a very intense writing and recording mode. Then we’ll see what the next album is going to be like.”

Hank & Cupcakes will play Preservation Pub Sunday, May 27 at 10 p.m.