Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/2
K:G
['Td4 d2 ef/g/']  
X:1
L:1/8
M:2/2
K:G
 D3 E/F/G/ TG4 | D3 E/F/G/ A2 d2 |{c} TB4 G/A/B/c/ d2- | Td2 d2 c TB3 | GABc d4 | cBcd Te4 | 
 de/f/ g2{g} Tf2 e2 | Td4 d2 ef/g/ | Td4 d2 ef/g/ | Td4{c} TB2 AB | c2 B2 cA F2 | G4 z4 :|  