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
['G2 G', 'd d']  
X:1
L:1/8
M:6/8
K:G
 D | G2 G G2 G | GAB c2 c | B>B B B>A G | AE F G2 D | G>G G G2 G | G>A B c2 c | B>B B B>A G | 
 AE F G2 || d | d2 d d2 d | e2 d (d2 B) | B B B B2 B | B>c d e2 d | d d d (d c) B | c E F G2 z ||  