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:Gmin
['DGG G2', 'dgg g2 a b/a/g/a/b/g/', 'G2 =B/d/ gd=B G>Bd/B/ G>=Bd/B/ c_BA fcG']  
X:1
L:1/8
Q:1/8=180
M:6/8
K:Gmin
|: G/F/ | DGG G2 A | B/A/G/A/B/G/ A/G/F/G/A/F/ | G/F/D/C/D/E/ F2 G | ABG FDC | DGG G2 B | 
 A/G/F/G/A/B/ cAc | d/e/fd cAd | G3 G2 :: B/c/ | dgg g2 a | b/a/g/a/b/g/ afd | cff f2 g | 
 a/g/f/g/a/f/ gfd | dgg g2 a | b/a/g/a/b/g/ a/g/f/g/a/f/ | gfd cAd | G3 G2 :: =B/d/ | 
 gd=B G>Bd/B/ | G>=Bd/B/ c_BA | fcG F>Ac/A/ | F/G/AB cBA | B/A/G/A/B/G/ c/B/A/B/c/A/ | dg^f gab | 
 gfd cAd | G3 G2 :|  