Ancient Love Song - travels back in time and interacts with/falls in love with woman who becomes integral to history of the kingdom/becomes Empress. Also affects how things happen.
Splash, Splash, Love - travels back in time and interacts with/falls in love with famous king in Korean history. Also affects how things happen.

Both are short (Splash, Splash Love is shorter), both travel back through a medium - rain puddle/precious stone medallion, both are sweet and poignant.