Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
M:4/4
K:G
['D2 [G,B,]2 .[CE]2', 'BcdB ABcA']  
X:1
L:1/8
M:4/4
K:G
 BAGE D2 [G,B,]2 | .[CE]2 .[CE]2 .[B,D]2 .[G,B,]2 | [DB]AGE D2 [G,B,]2 | .[CE]2 .[CF]2 [B,G]4 :: 
 BcdB ABcA | BcdB AFED | BcdB ABcA | [CG]2 [CF]2 [B,G]2 z2 :|  