I just googled for way too long .. trying to tie this piece into a movie theme, because it sounds SO familiar I assumed it must be a movie or TV theme. Couldn’t find anything. Perhaps someone took the main theme and ‘popularised’ it?
Schumann’s Marchenbilder op. 113 no. IV
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Marchenbilder (Fairy Tales), Op. 113 IV. Langsam, mit melancholischem Ausdruck