Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/2
K:Amin
['', 'A3 A, A,3', 'cG G2 EGce', 'cG G2 EGce']  
X:1
L:1/8
M:2/2
K:Amin
 A,B, |: C2 A,C EA,CE | AEED E2 AB | c2 Ac eAce | aeed e2 ab | c'bag fedc | BddB d3 f | 
 e3 f edcB |1 A3 A, A,3 B, :|2 A3 A, A,3 a |: a2 fa bf f2 | fe^de ae e2 | e^def e=ddB | cdcB A3 a | 
 a2 fa bf f2 | fe^de ae e2 | e^def e=dcB |1 A3 A, A,3 a :|2 A2 AB A3 B |: cG G2 EGce | cG G2 EGce | 
 dB B2 GBdB | cc'ba gfed | cG G2 EGce | cG G2 EGce | dB B2 GBdB |1 cBcd c2 AB :|2 cBcd c2 ||  