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
['DGG BGG dBG GBd ege dBG', 'G2 A Bdd dBd egg g2 d']  
X:1
L:1/8
M:6/8
K:G
 E | DGG BGG | dBG GBd | ege dBG | AGA BGE | DGG BGG | dBG GBd | ege dBG | AGF G2 :| A | Bdd dBd | 
 egg g2 d | edB dBG | AGA BGE | DGG BGG | dBG GBd | ege dBG | AGF G2 :|  