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:G
['GBG AGA', 'dBd BdB']  
X:1
L:1/8
M:6/8
K:G
 vDEF GBG | AGA ABG | DEF GBG | AEE GEE | DEG GBG | AGA B2 g | gfe dcB | AGE GED :: vBdd dBd | 
 BdB dBG | Bdd dBd | AGE GED | Bdd dBd | BdB def | gfe dcB | AGE GED :|  