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:Ador
['G EAA ABc BAG', 'eaa aga']  
X:1
L:1/8
M:6/8
K:Ador
 G | EAA ABc | BAG c2 A | BGE EDE | GED D2 G | EAA ABc | BAG ABd | ede gdB | ABA A2 :: d | 
 eaa aga | bab c'2 a | bge ede | ged d2 g | eaa aga | bag a2 g | ede gdB | ABA A2 :|  