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
['D |]: DFA', 'e fdB BAF ABA', 'DED D2']  
X:1
L:1/8
M:6/8
K:D
 D |]: DFA d2 e | fdB BAF | ABA AFD | EFE E2 D | DFA d2 e | fdB BAF | ABA dAF |1 DED D2 D :|2 
 DED D2 d |: dfa afd | gbg faf | dfa afd | cee e2 f | dfa afd | gbg faf | BdB AFA |1 DED D2 d :|2 
 DED D2 D |]  