More musicology

[Matthew H. Fields <fields...>]

Hey, as long as there's a musicologist reading here, I have a pet
question, too.

A couple years ago, I was commissioned to write a piece for a
trombone quartet.  Starting with the notion that trombones can do
a pretty good shofar immitation, I soon found myself using shofar
blasts to mark the sections of a sonata-formed double fugue on the
following two melodies:

1) This one is known to me as either "L'shana Tova" or the chorale
tune for singing "Mi Khamokha" on high holidays:

2/2, 2 flats:
F .F|G   F   |D   E   |F   . G |F x F .F|G   F   |G   A   |

     B       |F   x F |B       |D       |C B A G |F   B   |

     G       |A       |B       |~   . ||

2) And this one is known to me as the refrain for "Khad Gadya":

4/4, 1 flat:
FG|A A B B |CDCBA F |A B CFDB|A G F ||

Does anybody out there know any sources for these two tunes?  My
instinct is that they're both of German origin, but I really don't
know.