Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/4
M:2/2
K:G
['D G f G A _B2 =f2']  
X:1
L:1/4
M:2/2
K:G
 D | G f G A | _B2 =f2 | =B2 c2 | d2 z d | _e d d c/c/ | d2 _B d | c _B A G | A2 D2 | G3/2 G/ F2 | 
 G2 z |]  