Jazz is something that people all around the world love, and it is now commonplace to see it listed as one of America's most vital contributions to world culture. Yet it remains impossible to define. Try it sometime with a group of jazz fans, and you'll see what I mean. This elusive quality reflects what makes jazz the international musical language it has become. It has a protean nature that has been picked up on, extended, and elaborated by musicians the world over, and not just as something to imitate, but as an idiom to be adapted to the needs of whatever group takes it on.

Caribbean influences were a vital element in the music of 19th-century New Orleans, where jazz evolved.

If you think jazz is hard to define, try to get a handle on Latin jazz sometime. Some feel it's a relatively recent phenomenon while others see it as a primary element of the music from the beginning. Caribbean influences were a vital element in the music of 19th-century New Orleans, which is where jazz evolved out of. Cuban orchestras, Mexican clarinetists, Haitian dance styles, and every combination of Pan-Caribbean musics played a large role in the mixture that eventually came to fruition in the overwhelming genius of the first wave of Crescent City jazz greats.

Danzas became a genre of classical piano pieces, and eventually was transformed into a vocal form, the habanera (from the Spanish Habana, for Havana). Indeed, America's first blues hit, W.C. Handy's 1914 "St. Louis Blues," had a habanera strain that created a scintillating juxtaposition with the song's main blues chorus. You can hear what Jelly Roll Morton, jazz's first great composer, used to call the "Spanish tinge," throughout his work and that of many of jazz's other early giants.

During the 1920s and 30s, various dance styles with Spanish and Caribbean roots, such as the rhumba and the conga, became extraordinarily popular in America and around the world. But the music that the jazz bands played for them never went beyond the idiomatic surface of what they truly represented. In the meantime, American jazz was being heard in Cuba, Puerto Rico, and other Caribbean cultures and creating a new generation of musicians who strove for a new blend of their own native rhythmic formulas with the extended harmonic and melodic spheres of jazz.

Juilliard Jazz Ensembles Paul Hall Monday, Dec. 9, 8 p.m. Free, no tickets required.

The Puerto Rican valve trombonist Juan Tizol was a mainstay of the Duke Ellington Orchestra from 1929-1944, and contributed many wonderful songs to the band's repertoire, including "Caravan," "Moonlight Fiesta," and "Perdido." But Tizol was the exception rather than the rule among the swing bands. While a handful of players like the flute virtuoso Alberto Socarrás and the tuba player Ralph Escudero had played with the very best jazz musicians, it took the arrival of Cuban-born Mario Bauza in New York to set the stage for the creation of what eventually became known as Afro-Cuban jazz.

Bauza was a multi-instrumentalist-arranger-composer who hungered to hear jazz interpreted by a first-rate Afro-Cuban band, instead of the other way around. In 1940, he formed a band along with his brother-in-law Frank Grillo (who went by the name of Machito), which they called Machito and the Afro-Cubans. Their use of jazz-influenced harmonies and concepts wedded to a solid Caribbean beat was tremendously exciting and influential. Among the musicians who worked in the band were Tito Puente and the arranger/composer Arturo "Chico" O'Farrill. They would go on to distinguished careers, each creating their own musical worlds by blending to various degrees the influences of jazz and Afro-Cuban music.

Among the musicians Bauza encountered during his years with the big bands in the 1930s was a young trumpeter from South Carolina by way of Philadelphia. John Birks "Dizzy" Gillespie was entranced by Bauza's mastery of Latin-American idioms, and began to integrate their rhythmic patterns into his own compositions as early as the mid-40s. And shortly after forming his own big band in 1945, Gillespie hired an authentic Cuban conguero named Chano Pozo, and together they galvanized the entire jazz world. Though Pozo died tragically in 1948 in a barroom brawl, his example of rhythmic genius and thrilling showmanship energized the nascent Latin jazz scene into a vital genre, with unlimited potential.

Soon thereafter, Charlie Parker recorded with Machito's band, and a whole slew of first-rate bands led by Puente and Perez Prado became in-demand at ballrooms that could no longer book jazz bands, the great majority of which were no longer interested in playing for dancing. To some, this divorce from the music's terpsichorean roots has led to jazz's diminishing popularity in terms of general demographics. Latin jazz has stayed firmly rooted in its functional origins and continues to flourish.

The Juilliard Jazz Ensembles are playing some of the very best of the Latin jazz tradition, peppered with new works, at their concert on December 9. Come and see how hard it is to stay put in your seat when they turn the heat on!

Loren Schoenberg, who teaches jazz history, has been on the faculty since 2001.