Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
Q:1/4=120
M:9/8
K:G
['edc BAG']  
X:1
L:1/8
Q:1/4=120
M:9/8
K:G
"^Allegro" d | gdB gdB cBA | GGG GGG G2 A | Bcd edc BAG | AAA AAA A2 D | GAB GAB cBA | Bcd Bcdedc | 
 def gfe dcB | ABc edc BAG | FGA GAB ABc | Bcd cde def | gdc BAG TA3 | G6 |]  