There wasn't a whole lot of salsa 300 years ago in Leipzig, Germany, where J.S. Bach composed some of his greatest keyboard works. Yet after hearing the Cuban-American group Tiempo Libre play the fugue from Bach's Sonata in D Minor to the pulsating beat of a cha-cha, or turn the C Minor Prelude from The Well-Tempered Clavier into a fiery rumba, one might think otherwise.

Born in Cuba and based in Miami, three-time Grammy nominated Tiempo Libre (the name translates as "free time" or "time off") has been mixing up musical genres since its founding in 2001. Without a doubt, its most daring project has been its latest recording, "Bach to Havana," which spices up Bach's minuets, gigues and gavottes with Cuban rumba, danzón and guaguancó.

On Saturday at the Zoellner Arts Center, Tiempo Libre wil meld the seductive rhythms of Afro-Cuban music with the timeless compositions of Bach at the Bach Choir of Bethlehem's 2010 Gala. Also in the mix will be some Cuban classics such as "Guantanamera," "Lágrimas Negras" and "Son De La Loma."

But this won't be your grandfather's mambo, so bring your dancing shoes.

"I should tell you, this won't be a classical concert, it will be more like a Cuban dance party," says Jorge Gomez, 39, the group's leader and keyboardist, from his Miami home. "So even if it feels weird to dance to the music, you should do it — that's the reason we're coming here, to see people dance and enjoy the show." Gomez speaks in enthusiastic, percussive bursts, dotted with the same rhythms that pervade his music.

Actually, it shouldn't feel weird at all — the group's fiery conflation of Bach with traditional Cuban dance forms and Latin jazz and pop isn't a huge stretch. Cuba has a long tradition of embracing European classical music, and all seven members of Tiempo Libre were classically trained at La ENA, Havana's premiere Russian-style conservatory, where Bach's music is highly respected.

Gomez grew up with a healthy dose of Cuban music intertwined with the sound of his father, a respected classical pianist, practicing Bach in the family home.

Says Gomez, "Classical music was always a part of our life in Cuba. Here's basically our story: in the morning, classical training; at night, rumba and son, on every corner. One night I was listening to the music of Bach — who for me is the DNA of the music world — and said 'Hey, let's do this the Cuban way.' "

Gomez eventually escaped Cuba in pursuit of personal and musical freedom, first traveling to Guatemala in 1995, and eventually to Miami in 2000. It was there, in 2001, that he formed Tiempo Libre with other like-minded Cuban musicians who shared his passion for blending seemingly opposite musical styles.

"In the beginning, we played only jazz, then timba, then everything — jazz, timba, classical," Gomez says. "Bach in Havana," the group's third album, was released in May, 2009, and features guest artists Paquito D'Rivera on clarinet and sax, and Yosvany Terry on the African shekere, a percussion instrument made from a gourd.

Strictly speaking, Tiempo Libre plays timba, not salsa. The differences, explains Gomez, are many.

"If you mix the music of a social club with Chick Corea, you have timba — jazz and Cuban rhythms all mixed together. The instrumentation is also different. For example, in salsa you play with acoustic piano and acoustic bass. Timba you play with electric keyboards and electric bass — you're looking for a deeper sound. It's more energetic, with a more jazzy brass section. It's always different — we use a lot of improvisation," he says.

Call timba a souped-up variant of salsa, leaning more heavily towards funk, but still incorporating such elemental Afro-Cuban instruments as congas, timbales, guiro and maracas. Like their salsa-rooted predecessors, timba bands also boast a sonero — a lead singer skilled in improvised vocal gymnastics — and a back-up male coro, or chorus.

American pop music was a big influence on timba bands. Gomez recalls listening to Miami radio stations while he was growing up in Cuba. "Of course, we loved Michael Jackson, Cool and the Gang, Santana, but especially Earth, Wind, and Fire — they were a very big influence on us. They were one of the first timba groups in the United States, doing the same thing we are doing now," Gomez says. "Then I started listening to American jazz, and I still do every day of my life — like Chick Corea, Keith Jarrett, Spyro Gyra."

The remarkable thing about Tiempo Libre's Latinized Bach is how well it works — the group doesn't just set Bach's music to a Cuban dance form such as a son or guaguancó, but seems to uncover these rhythms within the music itself. The gavotte from Bach's French Suite No. 5 becomes a sparkling son — a dance style combining both Cuban and African elements. The Air on a G String morphs into a romantic Cuban bolero, while the Prelude in C Minor dances to the percussive rhythms of the clave, a pair of short wooden sticks that are an essential element of Afro-Cuban music. It's all aided by Gomez's cascading keyboard progressions and delicate phrasing.

"Bach in Havana" is not Tiempo Libre's only foray into classical crossover.

The group performs Gomez's duet "Para Ti" with Joshua Bell on the virtuoso violinist's latest album, "At Home With Friends," released in September, 2009. And in the fall of 2008, Tiempo Libre recorded the album "O'Reilly Street" with leading flutist Sir James Galway, which included an Afro-Cuban take on the jazz suites of Claude Bolling.

Even Gomez admits there are some risks to fusion. "Although Sony gave us permission to record the Bach album, they didn't know what to call it — is it tropical, classical or what?" he says. And he says he was also warned that Americans want to hear salsa, merengue and bachata, which are easier to dance to, than timba, which is not that well-known here.

"But I wanted to take the risk. Cuba is all about music. Cubans have to dance, to sing, to play anything. That's the way we grew up. For us, it's part of our life, to sing in the shower, to sing anywhere — it's the way we live," Gomez says. "I love to see other people's reaction to our music. It'll be the first time you'll see people listening to Bach while dancing to a conga."