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
['G>AB B>AG ABc cBA ABG FED GAB', 'D3 de=f fed cde cBA Bcd efg']  
X:1
L:1/8
M:6/8
K:G
 G>AB B>AG | ABc cBA | ABG FED | GAB BAG | B^cd efg | fed ed^c | d3 D3 :: de=f fed | cde cBA | 
 Bcd efg | BAG AFD | GAB cde | def gdB | ecA dBG | DEF G3 :|  