Compose melodious music utilizing the prescribed letter representation and integrating the given thematic element.
X:1
L:1/8
M:6/8
K:G
['G2 B', 'd BGB']  
X:1
L:1/8
M:6/8
K:G
 e | dcA G2 B | DDD G2 B | ABA cBA | BGE c2 e | dcA G2 B | DDD G2 B | ABA cBA |1 BGE c2 :|2 
 BGE E2 |: c | BGB d2 d | BGB d2 d | BGB d^cd | e=cA A2 c | BGB def | gfe dcB | AGA cBA |1 
 BGE E2 :|2 BGE c2 e ||  