For over 40 years, the Kronos Quartet has been reimagining what a string quartet can be and fostering new music from diverse composers, more than 850 works and arrangements so far. So what is the quartet up to these days? Commissioning more pieces, naturally.

This time the project is also an educational initiative called “50 for the Future: The Kronos Learning Repertoire.” Carnegie Hall, a partner in the venture, has appointed Kronos to this season’s Richard and Barbara Debs Creative Chair, and the ensemble played a sold-out concert at Carnegie’s Zankel Hall on Saturday.

Over five seasons, starting with this one, Kronos is commissioning 50 composers (25 men and 25 women) to write pieces exploring contemporary approaches to the string quartet, aimed at student players and emerging professional ensembles. (Four of the nine pieces on Saturday’s program were part of this initiative.) In speaking to the audience, the group’s founding violinist, David Harrington, explained that after giving the premieres of the pieces, Kronos will create digital materials, including scores and parts, which will be available free online starting later this month.

This bracing, eclectic program opened with a “50 for the Future” work: Aleksandra Vrebalov’s “My Desert, My Rose,” which the composer describes as a series of patterns that are subject to the players’ in-the-moment choices as to length, meter, tempo and dynamics. The intricate, industrious patterns — involving plaintive lines, obsessive ostinatos, string scratchings and more — exuded adventure and intensity.

Kronos also played “Ancient Echo” from “Four Chinese Paintings” by Wu Man, the Chi