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:Amix
['ABcd egfg edBd', 'aAAA aAbA aAAA agef']  
X:1
L:1/8
M:4/4
K:Amix
|: ed |"A" c2 B2 ABcd | egfg edBd |"G" gBBB gBaB | gBBB gfed |"A" cdBc ABcd | egfg edBd | 
"G" gfgd"D" efed |"E" c2 B2"A" A2 :| | eg |"A" aAAA aAbA | aAAA agef |"G" gBBB gBaB | gBBB gfeg | 
"A" aAAA aAbA | aAAA agef |"G" gfgd"D" efed |"E" cdBc"A" A2 | eg |"A" aAAA aAbA | aAAA agef | 
"G" gBBB gBaB | gBBB gfeg |"A" aAAA"G" gAAA |"D" fAAA"A" e2 ef |"G" gfgd"D" efed |"E" cdBc"A" A2 ||  