Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/8=160
M:6/8
K:Amin
['e2 A AAA', 'd2 B']  
X:1
L:1/8
Q:1/8=160
M:6/8
K:Amin
 e2 A AAA | e2 d B3 | e2 A AAA | G2 A B3 | e2 A AAA | e2 d B3 | d2 B g2 B | A3 A3 :| e2 d e^fg | 
 a2 ^f gfe | d2 B g2 B | d2 B d3 | e2 d e^fg | a2 ^f gfe | d2 B g2 B | A3 A3 :|  