Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/8=120
M:6/8
K:G
['', 'E EDE G2 A BeB dBd edB', 'fdB ABA ABd egf e2 f g2']  
X:1
L:1/8
Q:1/8=120
M:6/8
K:G
 E |: EDE G2 A | BeB dBd | edB GAB |1 ABA AGE :|2 AGF G2 B || d2 d def | gfe fdB | ABA ABd | 
 egf e2 f | g2 e fed | edB gfg | edB AGA | BGG G2 E |]  