Cuban music tends to involve a direct discussion: between voice and drums, between voice and chorus, between horn sections. Jazz tends to spread a discussion around, or build a hive of many discussions at once.
The explicit merger of the two traditions at Rose Theater on Thursday night both amplified and streamlined the discussion. The conversation made for an ambitious season-opening collaboration for Jazz at Lincoln Center between the pianist Chucho Valdés, the percussionist and singer Pedrito Martinez, the trumpeter and composer Wynton Marsalis and the Jazz at Lincoln Center Orchestra. The best parts of the sprawling suite were about calling the deities of the Santeria religion with six drumming hands and one clarion voice, and also about sound and resonance.
The two traditions are so interconnected in a general sense, through social and aesthetic history, that no part of either needs to be off the table for a project like this. The idea of big-band swing arrangements mixed with Afro-Cuban rhythm is about 70 years old, and Mr. Marsalis has dealt with that in many Jazz at Lincoln Center concerts. But there’s also a tradition of the religious chanting-and-drumming music of Santeria in a jazz-related context.
It might have started with Mr. Valdés’s father, Bebo, who in the early 1950s introduced the sacred double-headed batá drums into a jazz-influenced dance band at the Tropicana club in Havana, where he was musical director. Chucho did something similar, starting in 1972, including batá drums with jazz trio on his landmark record “Jazz Batá.”
More recently, the percussionist Román Díaz and the pianist David Virelles have been moving this tradition into avant-garde waters. Mr. Díaz, a teacher and elder among rumberos and Afro-Cuban drummers in New York, was there on Thursday, in the middle of a percussion trio with Clemente Medina on the left, and Mr. Martinez on the right. Wherever the music went, through the dynamics and virtuosity of Mr. Valdés or the jazz orchestra players, they were its cool-tempered power center.
The suite, called “Ochas,” after La Regla de Ocha, another name for Santeria, fell into eight parts dedicated to different orishas, or saints, in the Yoruba religion. Each part — for the trickster Elegua, the blacksmith Ogún, the elder Obatalá, and so on — started with an opening invocation and established its own distinct sound world, through Mr. Marsalis’s arrangements for standard jazz-band instrumentation; many of them rose to some sort of dramatic peak of drumming, chanting and improvising. As it stands, the suite is probably too long: 2 hours 45 minutes, with two intermissions. But it didn’t flag.
Universalizing jazz is Mr. Marsalis’s mission. And some of his writing in the first and second halves — an elegant, whirling language perhaps drawing on Ellington and Basie and Moacir Santos but pushed to original results — was a recognizable and nameable flag planting: Here stands jazz, and here stands Mr. Marsalis’s compositional style.
When that style retreated a bit, and the arrangements simplified, narrowing down into six-eight grooves and call-and-response riffs, modes and vamps built on perfect fourths — at times not far from middle-period Coltrane — the music grew into something greater.
Mr. Valdés boosted the energy for a few of those passages, making the piano talk with great, hard, ringing chords and single notes like rapid-fire arrow shots. The force and charisma in his technique never really get old. (Despite top billing on the program, he wasn’t onstage for very long; the orchestra’s regular pianist, Dan Nimmer, took over for most of the concert, playing with far more neutral affect.)
The program notes could have been a book. This is a world of contexts: those of the three principal musicians, as well as the meanings of various rhythms, Lucumí chants and movements in Santeria. But when Mr. Martinez opened his mouth to sing — in the invocations for each part of the suite, and in the musical discussions that followed with chorus singers and the orchestra — no context was needed to understand the power of his voice slicing through a mass of sound, his phrasing intricately weaving through the rhythmic accents.