Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:6/8
K:G
['G2 B', 'G2 Bcd cde f2 d g3 gec']  
X:1
L:1/8
M:6/8
K:G
 G2 B G2 B | g2 e def | e2 d cBc | BGD G2 :: Bcd cde | f2 d g3 | gec dBG | FAD G3 :|  