Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:4/4
K:Dmin
['defd e2 dA cAAc', 'E2 ED']  
X:1
L:1/8
M:4/4
K:Dmin
|: defd e2 dA | cAAc dcAd | fefd gfed | cAAF DFAc | defd e2 dA | cAAc dcAF | ABAG FDFD |1 
 E2 EC D2 dc :|2 E2 ED E2 ED |: EFED CDFD | E3 E FE C2 | FAce gfed | cA A2 a3 a | agfe d2 dA | 
 cAAc dcAF | ABAG FDFD |1 E2 ED E2 ED :|2 E2 EC D2 dc ||  