Compose melodious music utilizing the prescribed letter representation and integrating the given thematic element.
X:1
L:1/8
Q:1/4=177
M:6/8
K:D
['G2 E AGE EDD', 'GFG ABA ^cAG Add d2 e fed']  
X:1
L:1/8
Q:1/4=177
M:6/8
K:D
{G} F2 D{A} G2 E | AGE EDD |{FG} F2 D{GA} G2 E | AGE EDD |{FG} F2 D{GA} G2 E | AGE EDD | D=cA GFE | 
 FDD EDD :: ABA AGF | GAG GFG | ABA ^cAG | Add d2 e | fed cAG | F<AF G>FE | dcA GFE | FDD EDD :|  