Three years shy of ninety, Cecil Taylor is heralded as both an iconoclast and a generator of beauty. Each role impacts his art, to be sure, but there’s a sizable contingent of longtime fans who are betting on the latter persona to emerge when the Whitney launches its “Open Plan: Cecil Taylor” exhibit. A sense of the sublime has developed in the pianist’s idiosyncratic approach during the past six decades; this exhibition is a telling overview that offers admirers film portraits, revealing personal items, and, of course, performances. Taylor himself plays with drummer Tony Oxley and dancer Min Tanaka in a kickoff performance on Thursday, April 14. Shows by former Taylor associates including Tristan Honsinger (Friday, April 15), Andrew Cyrille, Enrico Rava & William Parker (Saturday, April 16), and Jemeel Moondoc (next Friday, April 22) are also scheduled. Taylor’s world has long been one of jazz’s most intriguing, and this chance to see how his art connects its innumerable dots is a must-see.