Compose melodious music utilizing the prescribed letter representation and integrating the given thematic element.
X:1
L:1/8
M:2/4
K:Amix
['', 'e2 cA', 'eaaf gfed']  
X:1
L:1/8
M:2/4
K:Amix
 cd |: e2 cA eAcA | Aeec defa | e2 cA eA c2 | BABc defa | e2 cA eAcA | Aeec defa | e2 cA eA c2 | 
 BABc defd || eaaf gfed | eaaf g2 fd | eaaf gfed | cABc defd | eaaf gfed | eaaf g2 fg | afge faed | 
 BGGd BGBd :|  