Craft a musical piece that integrates the provided melodic theme and the corresponding alphabetical pattern.
X:1
L:1/8
M:2/2
K:Gmin
['BG^FG DG^FG', '(3(cBA) Ggg^f gag=f cAfA G2 G2 (3(gab)', '(3(cBA) (3(BAG) (3(cBA) (3(Bcd) (3(=e^fg) (3(=fed)']  
X:1
L:1/8
M:2/2
K:Gmin
 dc | BG^FG DG^FG | AF (3(FFF) AFcF | BG^FG DG^FG |1 cAfA Gc :|2 cAfA G2 G2 |] 
 !fermata!Ggg^f gag=f | dfcf ec (3(cBA) | Ggg^f gag=f | cAfA G2 G2 || (3(gab) (3(fga) gafg | 
 dfcf ec (3(cBA) | (3(BAG) (3(cBA) (3(Bcd) (3(=e^fg) | (3(=fed) (3(cBA) G2"_D.C." |]  