Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
M:2/4
K:A
['BA GE E2', 'dB c>B ce d2 cB c>A cA']  
X:1
L:1/8
M:2/4
K:A
|: AA BA | GE E2 | AA Bc | d2 cB | A2 BA | GE E2 | c/d/e dB |1 A2 A2 :|2 A2 AB |: c>A cA | d>c dB | 
 c>B ce | d2 cB | c>A cA | d>c dB | c/d/e dB |1 A2 AB :|2 A2 A2 ||  