Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/8=180
M:6/8
K:G
['d cAG GFG cAG', 'cAd cAG', 'gag gdc', 'gdd fdd', 'B2 G A2 G', 'BGB AFA DED FED Add fed', 'DED AFA DED Add fed cAG']  
X:1
L:1/8
Q:1/8=180
M:6/8
K:G
|: d | cAG GFG | cAG G2 d | cAG GFG | cAG F2 d | cAG GFG | cAG A2 G | FGA fed | cAG G2 :: d | 
 dAd cAd | cAG G2 d | cAd cAd | cAG F2 d | cAd cAd | cAG A2 G | FGA fed | cAG G2 :: (3d/e/f3/2 | 
 gag gdc | BGG G2 d/e/ | =fgf fcB | A=FF F2 d | gag gdc | CGG G2 d | =fgf fed | cAG G2 :: 
 (3d/e/f/ | gdd fdd | gdd fdd | gdd fdd | cAG (3G/e/f/ | gdd fdd | gdd fddf/ | g/ag f2 d | 
 cAG G2 :: D | Gdd Gdd | cAG G2 A | B2 G A2 G | cAG F2 A | B2 G A2 G | B2 G A2 G | FGA fed | 
 cAG G2 :: G/A/ | BGB AFA | DED FED | Add fed | cAG FGA | BGB AFA | DED FED | Add fed | cAG G2 :: 
 G/A/ | BAB DED | AFA DED | Add fed | cAG FGA | BGB DED | AFA DED | Add fed | cAG G2 :|  