Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/4=120
M:2/2
K:C
['Bc d3 G', 'G3 E']  
X:1
L:1/8
Q:1/4=120
M:2/2
K:C
 D3 C c3 c | d2 cB A2 G2 | AB c2 AB c2 |1 A4 c4 :|2 A4 c2 Bc |] d3 G G2 Bc | d3 G G2 Bc | 
 d3 G G3 E | G4 c4 | BA BA G3 E | A3 A c4 | BA BA G3 E | D3 C c4 |]  