Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:3/4
K:G
['DAcB G2']  
X:1
L:1/8
M:3/4
K:G
 D2 GFGA | BABcdB | c2 ecec | ecgf d2 | g2 dedc | BABcdB | c4 AF | DAcB G2 | A2 cB G2 | DAcB G2 | 
 AAcB G2 | DAcB G2 |]  