Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/16
M:2/4
K:Edor
['BcdB AGFE D2EF', 'E4 B2>c2 d2e2 d2B2 A2>A2 (B2e2) (e2f2)']  
X:1
L:1/16
M:2/4
K:Edor
 E2BB BcdB | AGFE D2EF | G2FE BAGF | E4 E2 z2 | E2B2 BcdB | AGFE D2EF | G2E2 BAGF | E2>E2 E4 :: 
 B2>c2 d2e2 | d2B2 A2>A2 | (B2e2) (e2f2) | (e2d2) B2>c2 | dcde d2B2 | AGFE D2EF | G2E2 BAGF | 
 E2>F2 E4 :|  