Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
Q:1/4=60
M:6/8
K:Gmin
['GAG FGA', 'A2 A BAB cBc dBG ^F>=ED GAG']  
X:1
L:1/8
Q:1/4=60
M:6/8
K:Gmin
"^(Editorial suggestion)" GAG FGA | BAG A2 D | GAG FGA | BAG A2 |: A | BAB cBc | dBG ^F>=ED | 
 GAG =FGA |"^1" BAB G2 :|"^2" BAB G3 |]  