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:Emin
['e2 EF GFGE', 'e2 B2 c2 BA G2']  
X:1
L:1/8
M:2/2
K:Emin
"^Moderato" e2 EF GFGE | gfge edcB | e2 EF GFGE | cBcA B4 | e2 EF GFGE | gfge edcB | b2 ag a2 gf | 
 g2 f2 e4 :: g2 fe e^dcB | g2 fe e^dcB | e2 B2 c2 BA | G2 FE"^tr" B4 | e2 EF GFGE | gfge edcB | 
 e2 B2 c2 BA | G2 F2 E4 :|  