Kōjō No Tsuki : 荒城の月 ("The Moon over the Ruined Castle") from Thelonious Monk's interpretation on his "Straight, No Chaser" LP, simply called "Japanese Folk Song" on the track listing.
Kōjō No Tsuki (C-) - Rentarō Taki
Sakura Sakura : さくら さくら ("Cherry Blossoms, Cherry Blossoms") another oldie-but-goodie I thought was suitable for a Monk-style arrangement. The chord progression is my own recipe.
Sakura Sakura (F-) - Traditional