Compose melodious music utilizing the prescribed letter representation and integrating the given thematic element.
X:1
L:1/4
Q:1/4=170
M:4/4
K:Amin
['E G F E', '']  
X:1
L:1/4
Q:1/4=170
M:4/4
K:Amin
"C" g/^f/ g/a/"G" g/f/ e/d/ |"C" c d e2 |"C" g/^f/ g/a/"G" g/f/ e/d/ |"Am" c"E" B"Am" A2 :: 
"C" c e"G" d3/2 B/ |"Am" c e"G" g2 |"C" c e"G" d3/2 B/ |"Am" c"E" B"Am" A2 |"C" e e"G" d d | 
"C" c B G2 | e e"G" B B |"Am" A"E" ^G/F/"Am" E2 ::"C" E G"G" G F |"Am" E A"G" G F |"C" E G"G" G F | 
"Am" F"E" F"Am" F2 :|  