Bach’s keyboard music, sublime and seemingly inevitable in performance, has proven fertile ground for many jazz pianists. And given that Bach was one of classical music’s supreme improvisers, they understandably feel a kinship to him, too. Among them is Brad Mehldau, whose best work has often emerged out of the emotional directness of Radiohead or The Beatles. Arguably, however, it’s Bach that teases out his best work. Here, the American pianist and composer treats preludes, fugues, and other works (which he plays in their original form) as foundations for sophisticated, spirited, and often very beautiful originals. The feverish Prelude No. 6 in D Minor sparks from Mehldau a similarly febrile Toccata built on the Prelude’s relentless arpeggiations. And his playful Variations on the Goldberg Variations preserve the kernel of the originals while giving flight to some of his most imaginative and astonishing creations. For moments of genuine exquisiteness, Mehldau’s Intermezzo (track 10) and final Postlude both possess perfect balances of Bachian transparency and modern sentiment.