Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:6/8
K:D
['A3 AFA', 'def a3 baf', 'd2 f fef', 'Add fdd']  
X:1
L:1/8
M:6/8
K:D
|: A3 AFA | B3 BdB | A3 AFA | fge fdB | A3 AFA | B3 BAB | def afe | fdB BAB :: def a3 | baf afe | 
 def afe | fdB BdB | def a3 | baf a2 f | g3 f3 | edB BAB :: d2 f fef | fef fef | d2 f fef | 
 edB BAB | d2 f fef | fef def | g2 e f2 d | edB BdB :: Add fdd | edd fdB | Add fdd | edB BAB | 
 Add fdd | edB def | g2 e f2 d | edB BdB :|  