The late Allen Toussaint was a musical giant—a songwriter, producer, arranger, pianist and singer without equal. He brought the sound of New Orleans to the world with records like Benny Spellman’s “Fortune Teller” and Ernie K-Doe’s “Mother-in-Law,” adding a second-Line syncopation to the foundation of rock-and-roll. His piano playing is at the heart of his final album, American Tunes, and, as usual, he’s full of unexpected twists and surprising flourishes. Toussaint adds a gentle swing to Fats Waller’s “Viper’s Drag,” with a hint of reggae in his left hand as he drops quotes from “St. Louis Blues” and Grieg’s “Hall of the Mountain King” into his arrangement. He slows down the Professor Longhair standard “Big Chief,” sprinkling it with sparkling arpeggios that suggest Bach on a Bourbon Street bender. Drummer Jay Bellerose and bassist David Piltch contribute a Latin pulse to Bill Evans’“Waltz for Debby.” Toussaint takes it at a measured tempo, his right hand trills ornamenting the melody. Rhiannon Giddens contributes vocals to Duke Ellington’s bluesy “Rocks in My Bed” and “Come Sunday.” On the latter, Toussaint supports her powerful, sanctified vocal with subtle bass notes from his left hand. The album closes with Paul Simon’s “American Tune,” featuring Toussaint’s sole vocal performance. His weary tones are supported by his own piano and Bill Frisell’s pensive guitar. He brings an aching melancholy to the lyric, and when he sings, “I’m trying to get some rest,” it’s hard to avoid thinking of the long sleep he was so close to.