Hm.

Brought the sheet music with At My Window down to my Bach-loving friend. As predicted, she bit her lip and said "Mmm, difficult enough key", but then started picking it out thoughtfully. Then she stopped, and said "No, this can't be all of it, there's only four bars." I thought (being ignorant of music) that perhaps this meant that the songs at the bottom of the sheet were just a taster, but she shook her head and pointed to the next one, saying "Look, there are 14 bars in this one."

So that's me stymied, unless anyone can come up with anything further.

I'm going to bring her down Jerusalem now and see what she can make of it.