Avishai Cohen & Abraham Rodriguez Jr.
‘Iroko’ (naïve Records)
At the Blue Note through April 29

There are all kinds of Latin Jazz bands, just as there are many varieties of North American jazz groups. One major difference is that most so-called modern jazz has long since relinquished its connection to social dancing: The Modern Jazz Quartet never played anybody’s prom.

Yet virtually every variety of Afro Cuban jazz is eminently danceable — except perhaps at the Blue Note. There, the payoff is that nearly every seat is amazingly close to the bandstand, but the price is that the tables are so tightly packed together that at least three patrons have to stand up everytime someone needs to go upstairs to the “gift shop.” 

This made it all the more tantalizing, frustrating, and ultimately rewarding that the Israeli-born bassist and bandleader Avishai Cohen has brought his new ensemble, Banda Iroko, to the Blue Note. Everyone in the room was immediately shaking, moving, and “chair dancing” as best we could to that irresistible clave beat.

Banda Iroko, who played their first show at Paris last month and are now making their American debut, was born out of Mr. Cohen’s desire to work with the veteran conguero and singer Abraham Rodriguez Jr. Together, they assembled a unique ensemble of five additional players, including two more percussionists, Jose Angel and the trap drummer Horacio “El Negro” Hernandez, the latter known equally for his precise rhythms as for his extravagant outfits; two horns, alto saxophonist Yosvany Terry and trumpeter Diego Urcola; and vocalist Virginia Alves. 

The band, whose first album, “Iroko,” is being released next week, is a very specific kind of Afro-Cuban ensemble. The entirety of the music is driven by vocals and percussion, i.e., rhythm. All members of the group sing, except the two horns when they’re actually playing. 

There’s no piano or guitar — the most customary melodic and harmonic instruments of all jazz. The major melodic responsibility therefore is given to the vocalists. The two horns play countermelodies, counterpoint, and improvised solos, but the tune itself is carried by the singers. 

Even though there are three percussionists, the entire enterprise is driven by Mr. Cohen, who’s powerful bassistry introduces and lays down the groove for most numbers, and then energetically propels the works forward.

For their first set of a six-night run at the Blue Note, they started with “The Healer,” which also opens the album. From there, they played a mix of originals, Cuban songs, and tunes that will be familiar to New York listeners. Virtually everyone in the group was featured at some point, including Mr. Terry, who doubles on an African-derived percussion implement, the shekere, which is essentially a net of beads woven around a gourd. 

Mr. Cohen introduced Mr. Rodriguez with the phrase, “He’s got a world of songs that he sings.” They made the point with “Exodus,” a theme composed by the Austrian-born Ernest Gold for a movie about the founding of Israel. “Exodus” not only was a crossover hit for the African-American jazz saxophonist Eddie Harris, but it also inspired the 1977 Bob Marley song of the same title. Hearing it reinterpreted by an Afro-Cuban jazz group seemed to bring it full circle, internationally and conceptually.

The group also crossed musical boundaries with a driving rearrangement of a Sicilian-influenced melody by a French classical composer, “Sicilienne,” by Gabriel Faure. On the lighter side, Mr. Rodriquez led the ensemble in playing and singing a 1959 pop hit, “Venus.” At first we weren’t quite sure what we were hearing, as Mr. Rodriquez chanted the opening riff and led into the central lyrics. The words are the same, but the group has reshaped the melody and upgraded the rhythm, and on the whole, transformed “Venus” into a grown-up woman from the object of teeny-bopper obsession. 

Where they made “Venus” into something more adult, they also took “It’s a Man’s World” and softened its edges; where James Brown’s original is rather harsh and rough around the edges, so Mr. Rodriquez and the group made the song into something more tender and romantic.  

The album concludes with “Fly Me to the Moon,” though, alas, they didn’t get to it at the first set. Bart Howard’s song has made a truly pan-stylistic journey from a cabaret waltz (3/4) to a big band Sinatra swinger (4/4) to Cuban clave (6/8). Yet it’s indicative of how what Mr. Cohen described as Mr. Rodriquez’s “world of song” that said world now extends to the moon as well.