Compose melodious music utilizing the prescribed letter representation and integrating the given thematic element.
X:1
L:1/8
Q:1/8=160
M:6/8
K:G
['B3 BAG F2 d d^cd', 'gfg b2']  
X:1
L:1/8
Q:1/8=160
M:6/8
K:G
 A | B3 BAG | F2 d d^cd | B2 g gfg | eag fed | B3 BAG | F2 d d^cd | ede fef | a3 g2 :| d | 
 gfg b2 d | gfg b2 g | fag fed | fag fed | gfg b2 d | gfg b2 g | fag fdf | a3 g2 :|  