Compose melodious music utilizing the prescribed letter representation and integrating the given thematic element.
X:1
L:1/8
M:4/4
K:Dmix
['FDAD FAAB', 'ed cAGE ED']  
X:1
L:1/8
M:4/4
K:Dmix
 | FDAD FAAB | cABG EFGE | FDAD FAAB | cAGE ED D2 :| FDFA d2 ed | cABG EFGE |1 FDFA d2 ed | 
 cAGE ED D2 :|2 FDFA df ed | cAGE ED D2 ||  