Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
M:3/8
K:Gmix
['f4 e2', 'gdBc d2']  
X:1
L:1/8
M:3/8
K:Gmix
 f4 e2 | d3 Ade | fe(df)ed | f2 e2 d2 | f4 e2 | d4 c2 | B3 ABc | d2 B2 G2 :: gdBc d2 | gdBc d2 | 
 g3 fga | b2 a2 g2 | gdBc d2 | gdBc d2 | g3 fga | g6 :|  