In Durham, two of the world’s most enterprising and important new-music ensembles convene for a rare double-bill. The JACK Quartet, now at the end of a two-year Duke Performances residency, has set new international standards for audacity, imagination, and excellence. Likewise, over the course of a decade, New York sextet yMusic have restlessly explored the nexus between contemporary classical music and indie rock, collaborating with the likes of Bon Iver and Ben Folds while premiering works from Caroline Shaw and St. Vincent’s Annie Clark. Duke Performances’ ensemble-in-residence two years before JACK Quartet came to Durham, yMusic is “at the forefront of a rapidly changing performance culture,” as The New York Times declared. The JACK begin the concert with a trio of recent pieces from living composers who are emerging, legendary, or somewhere in between. The Quartet opens with a new work from Tyshawn Sorey, the prolific jazz improviser and hybrid-minded composer. John Zorn’s Nachträglichkeit, based on the abstract mystical work of Swedish artist Hilma Af Klint, follows, with yMusic flutist Alex Sopp. The JACK concludes with Zosha Di Castri’s First String Quartet, repeatedly surging between between silence and storms. After the intermission, yMusic plays the southeastern premiere of a substantial new Duke Performances/Carnegie Hall commission from one of the hottest American composers working today, Andrew Norman. Lauded by The Boston Globe for his “staggering imagination,” and the Los Angeles Times for his “daring juxtapositions and dazzling colors,” Norman is one of classical music’s most striking new stars.