Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/8=180
M:4/4
K:Amin
['A3 B AE E2 A2 Bd edBA', 'ea a2']  
X:1
L:1/8
Q:1/8=180
M:4/4
K:Amin
 A3 B AE E2 | A2 Bd edBA | G3 A GEDE | G2 BG dGBG | A3 B AE E2 | A2 Bd edBA | G2 Bd efge | 
 dBGA BA A2 :| ea a2 ea a2 | eaab aged | eg g2 eg g2 | egga gedg | ea a2 ea a2 | eaab aged | 
 cBcd efge | dBGA BA A2 :|  