Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
Q:1/4=104
M:2/4
K:E
['B GEEG B2 BB GEEG', 'z F GEGB cBec BG F2', 'z F GABB A2 AA GABB', 'z F GEGB cBec BG F2 E2']  
X:1
L:1/8
Q:1/4=104
M:2/4
K:E
 B | GEEG | B2 BB | GEEG | F2 z || F | GEGB | cBec | BG F2 | E2 z || F | GABB | A2 AA | GABB | 
 F2 z || F | GEGB | cBec | BG F2 | E2 z |]  