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
['GED GAB GBA G2 G']  
X:1
L:1/8
M:6/8
K:G
 BA | GED GAB | GBA G2 G | G2 A Bcd | efg fed | e2 B d2 A | Bcd efg | fed g2 B | dBA GED | 
 GAB GBA | G2 G G2 A | Bcd efg | fed g2 B | dBA GED | GAB GBA | G2 G G3 :|  