The most prominent members of the Jazz Composers Collective would make a heck of a band: Ben Allison on bass, all-reeds player Ted Nash, pianist Frank Kimbrough, saxophonist Michael Blake, and trumpeter Ron Horton. Each of the four – and the collective’s other members as well – lead different groups with different goals. They tend to serve as sidemen in each other’s bands, and it’s fairly certain you’ll see one or more of them on stage at practically every set during this week’s Jazz Composers Collective Festival.

Like the venerable Chicago-based Association for the Advancement of Creative Musicians, the New York based Jazz Composer Collective is an organization of instrumentalist-composer-bandleaders who got together to better their lot professionally and support each other musically. Founded in 1992 by Mr. Allison, the collective now has a relationship with a prominent record label, Palmetto Records, that works with many of its members. It has also found a major club, the Jazz Standard, that features many of its member bands regularly.

A new album by Mr. Allison, Mr. Nash, or Mr. Kimbrough is always something to look forward to. I know I’m going to hear captivating melodies, surprising rhythms, intriguing structures, and brand-new instrumental combinations. I know the language will be primarily Modern jazz, but there will also be traditional song forms and a smattering – or even more – of free playing.

Though the emphasis is on composition, the major JCC groups are all comprised of killer improvisers. The organization has a historical imperative as well, having saved and restored the music of such neglected giants as Herbie Nichols and – this year – the brilliant, overlooked saxophonist Lucky Thompson.

This year’s festival began Tuesday with a duo of Mr. Kimbrough and vibraphonist Joe Locke with Ron Horton’s Septet. On Tuesday, both sets featured one of the collective’s largest and most ambitious ensembles, the nine-piece double quartet led by Ted Nash, principally playing tenor. In addition to a jazz rhythm section of Mr. Kimbrough, Mr. Allison, Erik Charlston (vibraphone), and Tim Horner (drums), there is a full-fledged classical string quartet, of Joyce Hammann and Paul Woodiel (violins), Ron Lawrence (viola), and Tomas Ulrich (cello).

Whereas Odeon – the band that Mr. Nash brought to Dizzy’s last month (he is also part of the Jazz at Lincoln Center Orchestra) – has a South American world music bent to it, his double quartet integrates two kinds of chamber music into a seamless sound. Traditionally, groups that combine jazz with a classical approach alternate one with the other, first a hot solo then a string ensemble. Throughout the set you heard jazz tenor and classical strings running parallel to each other. When violinist Joyce Hammann soloed, it was absolutely impossible to tell if she was improvising or playing a pre-written solo, since her part sounded so traditionally classical in texture.

The climax of the show was a new Double Quartet arrangement of the piece that has lately become Mr. Nash’s showcase, Debussy’s “Premiere Rhapsody.” He has also played this with Odeon, but the Double Quartet treatment is something else indeed – a sultry string arrangement of a jazzy torch tune that might have been heard on the soundtrack of an old film noir – when Mr. Nash switched from tenor to clarinet, it sounded like Miklos Rosza meeting Artie Shaw.

Until April 17 (116 E. 27th Street, between Lexington and Park Avenues, 212-576-2232).