A Hawk and a Hacksaw perform on street corners, for fun and spare change, all around the globe. You'll find them plying this trade throughout Spain, Hungary, and Romania. Their vibrant music, heavy on strains of accordion and violin, reflects a variety of cultures, particularly folk traditions of Eastern Europe.

Just don't call them "Gypsies."

"We are not a Gypsy band," emphasizes founder Jeremy Barnes. "Gypsy music is music played by Gypsies, and the sound of Gypsy music depends on where they live." And Barnes and his partner, violinist Heather Trost, don't meet the basic criteria. "Neither of us is Roma."

Still, there are parallels. The tangled roots of the Gypsies begin in the Indian subcontinent, roughly a thousand years ago, then progress through ancient Persia, Armenia, and on to Western Europe. Since leaving home at age 18, Barnes has resided in France, England, Poland, Hungary, and throughout the U.S., including Denver, Chicago, New York, Athens, and Albuquerque.

For the last year and a half, the band have called Budapest home. They even shared co-billing with Hungarian quartet Hun Hangár Ensemble on their fourth album, released last year, which downplayed original compositions in favor of traditional Balkan melodies. "I had to take everything I had learned from working in a Western musical project and forget it," says Barnes.

Like the true Gypsies, Barnes's musical aesthetic has evolved as a consequence of his nomadic existence. Only, his early epiphanies were conducted in a tour van, not a caravan. "In 1996, I began playing with Neutral Milk Hotel," says Barnes, who contributed drums and organ to the seminal In the Aeroplane over the Sea. "On tour we used to listen to Bulgarian women's choirs. I had never heard anything like it."

A year later, he was living in Chicago's Ukrainian Village, south of Wicker Park. It was there, in a thrift store, that he discovered a used LP by Dumitru Farca¸s. "The cover was so nice. Dumitru is in a field with his instrument, cuddling a baby goat." The instrument turned out to be a tárogató, a reed instrument similar to the clarinet and saxophone, and the goat lover one of its leading virtuosos.

"I put the record on and was completely blown away," he says. "From then on, Romanian music became an obsession for me."

A decade later, the multi-instrumentalist would find himself making The Way the Wind Blows, the third AHAAH full-length, in a remote Moldovan village, assisted by Balkan brass ensemble Fanfare Ciocarlia. Critics praised the disc, anointing it "irreverent world music for punks," "first-class folk," and—here comes that word again—"bittersweet Gypsy-soul."

Such eclectic labeling is a dilemma shared by another close colleague of AHAAH, Zach Condon of Beirut. Both Barnes and Trost performed on Beirut's 2006 breakout Gulag Orkestar, and Condon returned the favor by playing trumpet on The Way the Wind Blows. Yet, Barnes dispels lazy comparisons between the two groups, as well as with other rock acts dipping into Eastern European musical traditions: DeVotchKa, Barbez, Gogol Bordello. "To my ear, DeVotchKa's folk elements seem to be more Western European, a mixture of Italian folk music with a heavy dose of Coldplay," he observes. "Beirut also seems more French to me."

He is equally articulate about why North American listeners seem increasingly fascinated by such acts of late. In Barnes's opinion, many fundamentals of Balkan and Eastern European music—"like playing songs in asymmetrical rhythms such as five, seven, and eleven, and using Turkish and Oriental ornaments in the melodies"—sound fresh and unconventional to Westerners weaned on pop music's square time signatures and major/minor tonality. And as a veteran percussionist, he says, "I love the absence of a traditional drum set."

Barnes has also, remarkably, made playing accordion seem cool. Or at least enjoyable. "Sometimes younger American people, even emo kids, see us and then come up and say things like, 'My grandpa used to play accordion and it was so nice to hear it again.'"

The instrument boasts less esoteric charms, too. It allows an individual to play melody, chords, and bass lines simultaneously. It also fits easily into an airplane overhead compartment, and, weighing around 15 pounds, is easy to carry. "When busking, it is always important to be able to run if needed," Barnes admits. Hey, you don't have to be a Gypsy to get hassled by the law.