Greene played during the 1960s on New York's free jazz scene, gigging with musicians including Alan Silva and Marion Brown, among others.

[2] He joined Bill Dixon's and Cecil Taylor's Jazz Composers Guild in 1964, and also performed with Rashied Ali, Albert Ayler, Gato Barbieri, Byard Lancaster, Sam Rivers, Patty Waters, and others.

Klez-Edge has a recording Ancestors, Mindreles, NaGila Monsters (2008) on John Zorn's Tzadik label.

Greene's performance and recorded groups based in New York from this time include a duet with bassist Mark Dresser; a quartet with trumpeter Roy Campbell Jr., Lou Grassi and Adam Lane; a trio with Ed and George Schuller on bass and drums (recorded on the CIMP label); and a quintet with the Schuller brothers, Russ Nolan on saxes and flute and Paul Smoker on trumpet.

His autobiography written over 20 years, Memoirs of a Musical Pesty-Mystic, was published in 2001 (Cadence Jazz Books).