Jazz in New Orleans was nursed on Latin music. Pictured is clarinetist Lorenzo Tio (senior) who performed and taught both aspiring and some of the eventually legendary jazz reed musicians. His father came from Veracruz and played saxophone in Tampico (Mexico) and his brother Luis as well as his son Lorenzo Tio (junior) performed jazz.
African call-response music in New Orleans got blended with European patterns of beats. Cuban music introduced 2 musical measures performed as if one measure which somewhat disassociated melody and rhythm if simply played as a 3-2 or 2-3 rhythm (called "clave"). Providing for an easier listening experience in the 1800s it evolved into what is generally called "habanera" (Havana, Cuba); 1803's "San Pascual Bailon" was one such song of popular line dance ("contra-danza") in Cuba.
The Cuban morphing of the "clave" style into 6-8 and 2-4 time made their music more suitable for dancing than just call-response. Blacks then syncopated the "contradanza" dancing rhythm which infused more swing into it and created what is sometimes called "contradanza habanera." Blacks also retained the traditional strong 1st part call and weaker 2nd part answer musical pattern. Incidentally, the 1800s USA vaudeville black "cake walk" would come to include "habanero" rhythms.
Sheet music, like 1836's "La Pimienta", was vital to the spread of "habanera" music and late 1800s "La Paloma" (by Sebastian Yradies) took Mexico's music public by storm. In the 1870s it would be simply called "danzas" in Mexico. Louisiana's piano genius and super-star composer L.M. Gottschalk was in and out of Cuba such that he introduced some "habanera" features in his own1850s to 1860s works. Mexican music was re-invigorated in 1890 when "Tu" (by Eduardo Sanchez de Fuentes) introduced the so-called "hammock rhythm" to the "habanera" genre.
New Orleans hosted the 1884-1885 "World's Industrial and Cotton Centennial" exposition. Not only did the Mexican National Conservatory tour the USA in 1884 introducing "habaneros" in it's repertoire, but so did the Mexican Calvary 8th Regiment band sometimes playing "danzas". Leading to the mass issuance in 1888 of 8 "danza" sheet music arrangements by the publisher Junius Hart. By the way it is a presumptuous fallacy that there were no black New Orleans music readers.
Several Mexican musicians stayed in New Orleans after the 1885 exposition closure. For example the early "Dixieland Jazz Band" member Alcide "Yellow" Nunez, whose parents were Mexican and Cuban, had an uncle from the Mexican regimental band who remained in NewOrleans. Another family member Perlops Nunez had one of the original black New Orleans bands. "Chink" Martin (played with early white jazz band of "Papa" Laine) was another whose ancestry was Mexican and Spanish having been taught guitar by similarly heritaged Francisco Quinones. Martin recalled that New Orleans' Royal Street between Dumaine and Esplanade was once a majority Mexican and Spanish neighborhood. The 1895 and 1898 Spanish-American fighting brought black American troops in further contact with Cuban culture.
As New Orleans pianist "Jelly Roll" Morton explained: "… if you can't manage to put tinges of Spanish in your tunes you will never be able to get the seasoning, I call it, for jazz." He was a composer and re-arranged the popular "habanero" of earlier decades "La Paloma" describing it thusly : "… you leave that left hand just the same. The difference comes in the right hand - in the syncopation ... changes the color from red to blue."