Playing by Ear and Jane Austen Music

  Playing by ear has no official term that I am aware of for when someone re-composes music based on hearing something, be it a simple melody, a vocal piece with accompaniment, or a complex jazz improvisation. 

When I "pulled this by ear," it was a special point in my aural training because for the first time I really "re-composed," so to speak, a full and rich rendition of a very excellent piece of music.  Before most of my aural renditions had been just completing an assignment.  When my teacher heard this, he said I had turned a page in my skill.  Those are special moments for a teacher. It just took the right piece to inspire me, no necessity or particular knowledge of what is achievable as far as aural renditions.  Sometime I'll get myself recording on my digital piano and put my rendition on here.
Later, I received the score of this piece in the book "Jane Austen's World."  The rendition there added a few touches to mine, but actually I had re-composed a much fuller rendition of the film soundtrack than the book offered.  One advantage of playing by ear! 
If you can hum it, you can play it by ear.