Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/4
Q:1/8=200
M:3/4
K:Amin
['', 'A e2 A d2 A c B', 'a g2 d e A2 e2 f/e/']  
X:1
L:1/4
Q:1/8=200
M:3/4
K:Amin
 A |: e2 A | d2 A | c B A | G E3/2 D/ | E2 E/D/ | E G3/2 D/ | E G E/G/ |1 A2 A :|2 A3 || e2 d/e/ | 
 a2 a | g2 d | e A2 | e2 f/e/ | d2 B | c2 d | B/A/ G2 | e2 A | d2 A | c B A | G E3/2 D/ | E2 E/D/ | 
 E G3/2 D/ | E G E/G/ |1 A3 :|2 A2 A ||  