Here is a nice introduction to improvising romantic-sounding music and songs on the piano. The first half of the video is more pertinent to beginning pianists. Practice moving through the C, Fm and G chords while improvising notes with the right hand. This chord progression is at the "heart" of many romantic ballads and songs.
Here are representations of the C, Fm and G chords that he uses in the video.
C
Fm
G
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