Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
Q:1/8=160
M:6/8
K:G
['GAG GAB ABA ABd edB gdB', 'BGG dGG']  
X:1
L:1/8
Q:1/8=160
M:6/8
K:G
 D | GAG GAB | ABA ABd | edB gdB | AGA BGD | GAG GAB | ABA ABd | edB gdB | AGG G2 :| A | BGG dGG | 
 efg dBG | BGG dGG | edB AGA | BGG dGG | efg dBG | gfg aga | bgg g2 :|  