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:A
['efec B4']  
X:1
L:1/16
M:2/4
K:A
 efec B4 | efec B4 | e2cBe2cB | ABcB A4 | e2FAB2BA | FEFA E4 | c2cABcBA B4 | E2FAB2BA | FEFA E4 |]  