From a small and cluttered stage in Armstrong Park on a recent Sunday, percussionist Bill Summers announced in a slightly bemused tone, "This is the biggest black audience we've ever had." Actually, for a Los Hombres Calientes gig, the crowd was pretty small — maybe a couple of hundred attendees of the Louisiana Black Heritage Festival — but the nine — piece band courted it with a spirited set of Afro — Latin jazz anyway.

Somehow the sight of Summers shaking a shekere (an African gourd rattle) through tunes with titles such as "El Negro" and "Foforo Fo Firi" doesn't seem very New Orleans. Armstrong Park is of course named after Louis, and it's that "traditional" sound that draws many tourists here (and keeps many musicians employed).But Summers would be the first to tell you — and co-Hombre Irvin Mayfield the second — that it's wrong-headed to think of a mostly black band with a Latin name as any kind of ground-breaking experiment. Their point is to mine the sounds of New Orleans, Africa, and the Caribbean for long-standing connections — to turn jazz's tradition vs. innovation debate back in on itself, reaching so deep into tradition that the results sound innovative.

Less than four years after what seemed likely to be one-shot lark at a local club, Los Hombres Calientes have come a startlingly long way. (Even the name, Spanish for The Hot Men, was basically a joke, riffing off a lineup of New Orleans rappers known as the Hot Boys.) Recently, the band snared a Grammy nomination for its third record, New Congo Square, in the Latin jazz category.

A few days after the Armstrong Park show, after a workshop session at Dillard University (where Mayfield is an artist in residence), the co-leaders explain that much of what makes the band appear unusual is, in their view, the core of the enterprise: their trans-generational partnership, the outsider label they record for, even their relationship with New Orleans.

Mayfield, 24, was born and raised here and at age 9 started playing trumpet in one of the brass bands that still prowl certain neighborhoods. "In New Orleans you can really only play two things, the trumpet or the drums. And the trumpet's the leader of the band." He later pursued a more "modern" sound and seemed headed down the path other celebrated local trumpet players have taken — out of the city. Wynton Marsalis, Terrance Blanchard, and Nicholas Payton all built successful careers by signing with major labels. While New Orleans's music community can be insular and boosterish, it's also small enough that everybody knows everybody. Mayfield's mother, for example, had known pianist Ellis Marsalis "forever." Which is how Mayfield ended up finding a place to stay in New York at the home of Ellis's son, Wynton.

Percussionist Summers, 53, was born in Detroit but came from a New Orleans family. He studied ethnomusicology at the University of California, Berkeley and landed in the original fusion-funk Headhunters lineup with Herbie Hancock. "I graduated when I got that gig with Herbie Hancock," he says. After a successful spell in Los Angeles, working with everyone from Miles Davis to Stevie Wonder to Quincy Jones, he came to New Orleans a decade ago with the dream of founding a multi — disciplinary arts institute on land he had inherited. And for less tangible reasons, too: "The vibe and the culture is killin'. It's kickin'. This place is like mecca to me."

Inevitably, their paths crossed. Mayfield and drummer Jason Marsalis, Wynton's youngest brother, were getting interested in Cuban sounds — making some "danceable" music. If Summers is laid-back and graceful, Mayfield is indefatigable and brash; when he bumped into Summers, the man he says he considers a giant, he simply blurted out that he wanted to start a band with him. In short order, Summers, Mayfield, and Marsalis were the center of Los Hombres Calientes, whose debut performance immediately kicked up a buzz. Marsalis left after the second album, replaced on "New Congo Square" by seasoned Cuban drummer Horacio "El Negro" Hernandez and New Orleans's Ricky Sebastian.

Later, Mayfield met Mark Samuels, a refugee from the oil business who was running a one-artist label called Basin Street Records. Four months after their first gig, the band had the top-selling CD at the New Orleans Jazz & Heritage Festival. That disc, recorded in a few days at Summers's house, was named the contemporary jazz album of the year by Billboard.

"I mean come on," Summers says. "That's a surprise. The greatest surprise is that I left Los Angeles, where people go to try to win a Grammy, to try to make records, I came back to New Orleans and we've had this success. That's a story that musicians need to hear. You don't have to go to Los Angeles, and deal with the plastic people and the music industry, to make it happen." Basin Street has proved inventive and ambitious, and for New Congo Square the label even put up the money for recording sessions in Cuba, the Dominican Republic, and Jamaica; the result is an exhaustive (and at 78 minutes, occasionally exhausting) tour of Caribbean sounds, with New Orleans as the northernmost point. Each tune suggests a place, and all point to common roots.

Mayfield, now settled back into New Orleans, seems to take the success as a given. ("We've changed a lot of things in New Orleans," he declares.) But there's a fervor to his belief in the band's achievements and potential that's charming to behold. "This is a Caribbean city! People don't realize that!" The next disc, he says, will delve into Haitian culture. "Doing our records is like a treasure hunt. Not only can you shake your ass to it, but you learn a hell of a lesson."

At Armstrong Park, Summers offered up a more direct lesson to the crowd. That very land, as it happens, was once the site of the famous Congo Square, or Congo Plains, where on a Sunday in, say, 1740, up to 600 Africans (slaves given the day to themselves) would gather, singing songs in a slew of languages and, Summers clarifies, "getting down." You can, in other words, draw the line from those days in Congo Square right to New Congo Square. Toward the end of the set, Summers encouraged the Black Heritage Festival crowd to watch for the group's club shows around town: "We need you, brothers and sisters." This wasn't a commercial plea; it was another bid at making a connection. Remember, he added, when you see the band's flyers, that "Los Hombres Calientes is a bunch of los negroes."

This story appeared in the March 24, 2002 edition of The Boston Globe.