Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:9/8
K:G
['c BAG EGG DGG BAG', 'E2 c Bdd ded dBG cee efe']  
X:1
L:1/8
M:9/8
K:G
 c | BAG EGG DGG | BAG EFG A2 c | BAG EGG DGG | BAG EFD E2 :: c | Bdd ded dBG | cee efe e2 f | 
 gfe dcB AGA | BAG EFD E2 :|  