Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
M:4/4
K:E
['B3 A =G2']  
X:1
L:1/8
M:4/4
K:E
 B,2 | B3 A =G2 F2 | E3 F =G2 AA | B2 AB =c3 A | B4 z2 ee | =d3 =c A2 AA | B3 A =G2 FF | 
 E2 EF =G2 F2 | E4 z2 |]  