Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
Q:1/8=180
M:4/4
K:G
['BG G2 BGBd g2', 'bg g2 agef gfge dega']  
X:1
L:1/8
Q:1/8=180
M:4/4
K:G
 A3 c BG G2 | BGBd g2 fg | eA A2 BGBd | egdB AcBG | A^GAc BG G2 | BGBd g2 ga | bgag egfa | 
 gedc BG G2 :| bg g2 agef | gfge dega | bgdg bgdg | eaag a2 ga | bg g2 agef | gfge dega | 
 bgaf egfa | gedc BG G2 :|  