Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/8=140
M:2/4
K:G
['g2 gf/g/ ag ge dB BA', 'ED B,D ED']  
X:1
L:1/8
Q:1/8=140
M:2/4
K:G
 d | g2 gf/g/ | ag ge | dB BA | GA Bd | g2 gf/g/ | ag ge | dB BA | G2 G :| D | G>A BA | GE ED | 
 B,D ED | B,D ED | G>A BA | GE ED | B,D ED | G2 G :|  