Perfectionists like Fred Hersch are generally their own harshest critics, but even he can’t deny that something very special happened at the Windham Civic Center Concert Hall on this August night in 2014. Not only is Thelonious Monk’s “In Walked Bud” imbued with the deft syncopated touches needed to pull off Monk’s music successfully, it is also full of contrapuntal daring, radical reharmonizations, and rhythmic inventions that take the familiar piece to some wholly new territory. His original “Whirl,” dedicated to the iconic 20th-century ballerina Suzanne Farrell, is both kinetic and graceful while his reimagining of Juan Tizol’s “Caravan” sounds alternately informed by Scott Joplin, Ran Blake, and Cecil Taylor. His gentle interpretation of Jerome Kern’s “The Song Is You,” normally played at a blazing uptempo as a chops showcase by jazzbos, is slowed to a luxurious ballad pace and rendered as a kind of gorgeous jazz lullaby. Perhaps most precious and transcendent of all is his sublime take on Joni Mitchell’s “Both Sides Now.” That Hersch, a notorious stickler for every aspect of sound on his recordings, was pleased with this live performance is saying a lot. Of his ten solo albums, this may be his best.