Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
M:6/8
K:Gmix
['(A/B/) cBA B>cB AGE', 'g^fe age dBG G2']  
X:1
L:1/8
M:6/8
K:Gmix
 (A/B/) | cBA B>cB | AGE G>AB | cBA Bed | BAA A2 (A/B/) | cBA B>cB | AGE GAB | cde ded | cAA A2 :: 
 (e/^f/) | g^fe age | dBG G2 (e/^f/) | g^fe agf | e^f^g a2 (e/f/) | g^fe age | dBG G2 (A/B/) | 
 cBA Bed | cAA G2 :|  