'I Love a Piano," wrote Irving Berlin, and who could blame him? Without that wondrous instrument—and other technological marvels that populate the musical world today—our cultural landscape would be much bleaker. But modernity exacts a price: It loosens our connections to the simple, natural conditions in which musical expression first arose.

There are societies still rooted to those origins. In Africa, as writer Kofi Agawu has noted, whole symphonies emerge from the commonplace rhythms of life—the sounds of chopping, grinding and pounding food, for example, or the fetching of water. Through these daily communal efforts, villages collectively sing music into existence.

Mr. Terry, artistic director of the event, began his career as a percussionist. "In 1978-79 I was playing drums," he recalled, "often with tap dancers—a generation that has mostly passed on now. And I realized I could displace everything I was doing on the drums to my body. So I began to map it out, to create a system. Two great dancers—Charles 'Honi' Coles and Charles 'Cookie' Cook—took me aside and said, 'You know, what you are doing is very similar to what is known in vaudeville as hambone.' But it moved differently, and had different rhythms."

It marked his opening to a wider world of music-making without instruments. "Once I started creating pieces," he said, "it became obvious that I had to find other body musicians." And so he created Crosspulse (crosspulse.com), which has been discovering and presenting such artists—as well as offering workshops to the public—ever since.

Observing Mr. Terry and his colleagues in action is like visiting an anatomical carnival where hands, fingers, feet, bellies, rumps and mouths engage in an endless musical ballet. But the concept is not new. Similar presentations have been an American tradition since the 19th century, when dancers and folk musicians often stunned audiences with virtuosic rhythmic displays.

Charles Dickens saw one of the most famous practitioners, a man known as Juba, during an 1842 visit to New York, and described him this way: "Single shuffle, double shuffle, cut and cross-out, snapping his fingers, rolling his eyes, turning in his knees, presenting the backs of his legs in front… Dancing with two left legs, two right legs, two wooden legs, two wire legs, two spring legs—all sorts of legs and no legs."

Naturally, even within the genre, performance styles vary, depending on cultural origins—something that should be apparent on Thursday, when the featured artists will cover a broad geographic swath. One might expect flamboyance from the Brazilians, for instance, and raw intimacy from the Inuit throat singers, who, Mr. Terry says, stand so close they practically sing into each other's mouths. "The individual culture really does shine through," he said.

Cultural dynamics also affect audience reactions. "I've presented this music as a soloist and with groups all over the world, including Europe, Indonesia, Japan, China, Brazil and Costa Rica," Mr. Terry said. "There's a certain rhythm to audiences, and you can feel the differences. The first time I performed in Indonesia, there was some humor in the piece, and the reaction was so explosive it scared me."

According to Bill Bragin, director of Lincoln Center Out of Doors, that diversity of perspectives embodies the very purpose of the series. "This is our 40th anniversary season," he explained. "It started as a community street-theater festival. We present music of all types—from jazz, roots music, punk and Latin to marching bands—along with other arts, like dance. All the concerts are free. We look at New York as an international city and we want to reflect that, while delivering a consistent level of excellence."

Indeed, the International Body Music Festival is just one of the events this summer to showcase what Mr. Bragin calls "cultural hybridity." "In Keith's work," he said, "cultural specificity is important, but at the same time there is throughout the program a sense of commonality. He's drawing from many rich traditions, while creating an evening that everyone can enjoy."