Craft a musical piece that integrates the provided melodic theme and the corresponding alphabetical pattern.
X:1
L:1/8
M:4/4
K:C
['AB cAB^G A=GEF GABc dBGB cAB^G A=GED', 'AB cdef g2 eg']  
X:1
L:1/8
M:4/4
K:C
[M:4/4][K:G] f e ae ae (e.g .ce C E4)[Q:1/8=180]"^A dorian" AB | cAB^G A=GEF | GABc dBGB | 
 cAB^G A=GED | EAA^G A2 AB | cAB^G A=GEF | GABc dBGB | cAB^G A=GED | EAA^G A2 || AB | cdef g2 eg | 
 a2 ed cAAB | cdef gfgd | eaa^g a2 AB | cdef g2 eg | aged cAAB | cAB^G A=GED | EAA^G A4 |]  