Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
Q:1/4=120
M:4/4
K:Gmix
['B G<GBG AFFA G<GBG AGBG D>GBG AFFA', 'G3 B G<G f_B AFFA G<Ggd g>agd']  
X:1
L:1/8
Q:1/4=120
M:4/4
K:Gmix
 B | G<GBG AFFA | G<GBG AGBG | D>GBG AFFA | GcBA G3 :: B | G<G f_B AFFA | G<Ggd g>agd | 
 f>gfA AFFA | GcBA G3 :|  