Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/4
M:3/2
K:G
['d G', 'a/g/ f']  
X:1
L:1/4
M:3/2
K:G
 G/A/B/c/ d G d G | F A2 c B A | G/A/B/c/ d G d D | D G2 B A G :| g a/g/ f g/f/ e a/g/ | 
 f d2 f e d | c d/c/ B c/B/ A d/c/ | B (G G) B A G :|  