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:Ador
['e2 dB', 'BAAG A3 B EGBG']  
X:1
L:1/8
M:4/4
K:Ador
 e2 dB eAAB | e2 dB AGBd | e2 dB eAAB | (3efg dB BA A2 | eAdB eAAB | e2 dB AGBd | e2 dB eAAB | 
 egdB BAAG || A3 B EGBG | AGAB deed | A2 AB EGBd | (3efg dB BAAG | A3 B EGBG | ADAB deed | 
 A2 AB EGBd | egdB BA A2 ||  