Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/2
K:G
['E G2 A', 'E G2 A']  
X:1
L:1/8
M:2/2
K:G
 GFGA Bdef | gfga gedB | e [Aa]3 abag | (3efg ab aged | efga bgag | fage dcBG | BGAG FGDG |1 
 E G2 A G2 DF :|2 E G2 A [DG]4 |: (3DEF GA BGAB | GBeB dBAG | E [EA]3 ABAG | (3EFG AB AGEG | 
 G,B,DF GABd | gbge dBAG | BGAG FGDG |1 E G2 A [DG]4 :|2 E G2 A [DG]2 DF ||  