Ron Carter Big Band (Friday through Sunday) Last year Mr. Carter, the eminent jazz bassist, released “Ron Carter’s Great Big Band” (Sunnyside) — somehow his first big-band album as a leader, featuring crisp arrangements by Bob Freedman. For this run he calls on veteran section players and some extremely sharp rhythm-section partners: Russell Malone on guitar, Donald Vega on piano and Kenny Washington on drums. At 7:30 and 9:30 p.m., Jazz Standard, 116 East 27th Street, Manhattan, (212) 576-2232, jazzstandard.net; $30. (Chinen)