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:G
['d2 d', 'gfe dBG GAG E3- E2 D G2']  
X:1
L:1/8
M:6/8
K:G
 G2 G BGB | d2 d efg | dBG GAG | E3 E2 D | G2 G BGB | d2 d efg | dBG ABA |1 G3- G2 D :|2 G4 Bc || 
 d2 d dBd | e2 f gfe | dBG GAG | E3- E2 D | G2 G BGB | d2 d efg | dBG ABA | G4 Bc :|  