Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/8=180
M:6/8
K:D
['d2 A F2 D', 'c2 d ecA d2 e f3']  
X:1
L:1/8
Q:1/8=180
M:6/8
K:D
|: d2 A F2 D | GFG ABc | d2 A F2 D | EGF E3 | d2 A F2 D | GFG A3 | BGB e2 d | cBc d3 :: c2 d ecA | 
 d2 e f3 | e2 f ^gfe | aba gfe | c2 d ecA | d2 e f3 | B2 G A2 d | cBc d3 :|  