Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/4
M:2/2
K:D
['', '^G G', 'd d']  
X:1
L:1/4
M:2/2
K:D
 E2 |: F2 (F A) | d2- d A | B (d g d) | [Fd]2- [Fd] A | (B A) G B | (A G) F A |1 ^G G (A B) | 
 A2 (=G E) :|2 ^G G (=G E) | F2 |] f e | d2 d2 | d g (a g) | f2 d2- | d d d d | c2 G2- | 
 G c (d c) | d2 A2- | A2 f e | d2 d2 | d g (a g) | f2 d2- | d d d d | c2 G2- | G (B A G) | F4- | 
 F2 |]  