Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:6/8
K:Dmin
['', 'D2 E F2 G ABA', 'GFG G<AF FEF DEF FEF F<GE EDE', 'd d^cd', 'GAG GEF']  
X:1
L:1/8
M:6/8
K:Dmin
 A,3 |: D2 E F2 G | ABA dzd | ABA GFE | FD/D/D D2 A, | D2 E F2 G | ABA dd/d/d | ABA GFE |1 
 DD/D/D D2 A, :|2 D3 DA/A/G | ^FGA AGA || A<BG GFG | EFG GFG | G<AF FEF | DEF FEF | F<GE EDE | 
 ^CDE F2 E | D3 DA/A/G || ^FGA B/A/GA | c<dB BAB | GAB BAB | B<cA AGA | FGA AGA | A<BG GFG | 
 EFG A2 G | F2 d d^cd | e2 B A/B/AG | A2 d d^cd | e2 B A/B/AG | A2 D ABA | GAG FGF | E^D=D ABA | 
 GAG F/G/FE | D2 d d^cd | e2 B A/B/AG | A2 d d^cd | fed A/B/AG | A2 D A2 A | GAG FGF | E^D=D ABA | 
 GAG F/G/FE | D3 DEF |: GAG GEF | GAG GEF | G2 B A2 ^G | AGF FEF | GAG GEF | GAG GEF | 
 G/G/GB AFE |1 DFA dEF :|2 D3 D2 A, ||  