Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/4
K:D
['', 'f2 ed', 'de f2 dF G2 FE', 'FA d2 f2 e4']  
X:1
L:1/8
M:2/4
K:D
 FE |:"D" D2 FG | A2 de | f2 ed |"G" d2 cB |"D" A2 BG |1 F2 AF |"A7" E4- | EG FE :|2"A7" FG- GE | 
"D" D4- | D z |] ABc |]"D" d3 e | f2 ed |"A7" e>f ec | A2 Bc |"D" d3 e | f2 ed |"A7" e3 c | 
 [AA]G FE |"D" D2 FG | A2 de | f2 dF |"G" G2 FE |"D" D2 FA | d2 f2 |"A7" e4 |"D" d2 |]  