Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
M:2/2
K:Ador
['', 'GBdf g2', "abag eaab c'bag"]  
X:1
L:1/8
M:2/2
K:Ador
 gf |: eA(3AAA egfg | eA(3AAA e2 dB |1 G2 BG DGBG | GBdf g2 fg :|2 GBdf g2 ga | bagb a2 || ag | 
 eaag abag | eaab c'bag | eggf gage | dega bgag | eaag abag | eaab c'bag | edef gage | dBGB A2 ||  