Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
M:6/8
K:Amin
['G2 A', 'A2 d e2 ^f gfg eag fed']  
X:1
L:1/8
M:6/8
K:Amin
 (A/G/) | EAA G2 A | Bed Bcd | edB G2 A | B2{cB} A GED | DED G2 A | Bed Bcd | ede gdB | 
{c} BA^G A2 :: d | e2 ^f gfg | eag fed | e2 f gfg | e^f^g a2 a | b^gb a^fa | gfe de^f | gfe fdB | 
{c} BA^G A2 :|  