Pianist Burton Greene first garnered attention in the early ’60s, plying expressionistic free jazz. In recent years, the pianist has turned his attention to klezmer-based improv—sometimes playful, sometimes achingly somber. On May 19 at the Firehouse Space, Greene gigs with the able rhythm team of bassist Adam Lane and drummer Lou Grassi. On May 22 at Spectrum, he plays a solo set, featuring new works including "Variations on the Hungarian Folk Songs of Bela Bartok." A screening of Moldavian Blues, a new short documentary on Greene's life and work, precedes each night's performance.