Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:3/8=90
M:6/8
K:C
['G E>DC c>BA G>FE F>EF D>EF E>DC', 'G2 B/c/ d>cB f>ed c>BA ^G^FE ABc']  
X:1
L:1/8
Q:3/8=90
M:6/8
K:C
 G | E>DC c>BA | G>FE F>EF | D>EF E>DC | G3- G2 F | EGc A2 G | ^FAd BAG | ^FGA DG^F | G3- G2 || 
 B/c/ | d>cB f>ed | c>BA ^G^FE | ABc EA^G | A3- A2 A/B/ | cGE ADF | EDC G2 F | EGc A2 d | 
 BAG c2 d | edc GcB | c3- c2 |]  