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
['f3 dfd AdA F2 F GFG Ecd', 'A,CE A,CE', 'd2 d']  
X:1
L:1/8
M:6/8
K:D
 f3 dfd | AdA F2 F | GFG Ecd | edc d2 A | f3 dfd | AdA F2 F | GFG Ecd |1 ecA d3 :|2 ecA dcB |: 
 ABA FED | F/G/AF FED | A,CE A,CE | A,CE cBA | FEF AFD | GFE D/E/FD | CEC A,CE | GEC D3 :: 
 F2 A d2 d | ede fdB | ged d2 d | Bcd ecA | AFA d2 d | ede fdB | gec Ace | gec d3 :|  