Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/4
M:4/4
K:G
['A G']  
X:1
L:1/4
M:4/4
K:G
 _B z/ B/ A G | A G/F/ G z | d3/2 _e/ d c | d/c/ c _B z | B/c/ d3/2 c/ B | d G/A/ G _E | 
 =F _B B c | _B A G z |]  