Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/2=90
M:4/4
K:G
['dc BGBd', 'G2 df a2 a2 afdf b2 g2']  
X:1
L:1/8
Q:1/2=90
M:4/4
K:G
 dc | BGBd eceg | fdfa g2 dc | BGBd gdcB | cdBc A2 dc | BGBd eceg | fdfa gfga | bgfg ec AF | 
 G2 G2 G2 :: df | a2 a2 afdf | b2 g2 g2 ga | bagf edcB | cdBc A2 dc | BGBd eceg | fdfa gfga | 
 bgfg ec AF | G2 G2 G2 :|  