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:A
['E A>GA c>BA [fdA]3']  
X:1
L:1/8
M:6/8
K:A
|: E |"A" A>GA c>BA | [ecA]3"D" [fdA]3 |"A" e>cA A>Bc |"D" F3- F2 E |"A" A>GA c>BA | 
 [ecA]3"D" [fdA]3 |"A" e>cA"E7" BAG |"A" A3- A2 :: c/d/ |"A" e2 e"E" efg |"D" a2 f a2 f | 
"A" e>cA A>Bc |"D" F3- F2 E |"A" A>GA c>BA | [ecA]3"D" [fdA]3 |"A" e>cA"E7" BAG |"A" A3- A2 :|  