Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:4/4
K:Edor
['BE (3E^DE']  
X:1
L:1/8
M:4/4
K:Edor
 BE (3E^DE B,EGB | AD (3D^CD A,DFA | BE (3E^DE BABd | egfe dBAd | BE (3E^DE B,EGB | 
 AD (3D^CD A,DFA | BE (3E^DE BABd | egfe dB A2 ||  